Dark Matter Search by Single Phase Liquid Xe Detectors

Akihiro Minamino Department of Physics, School of Science, University of Tokyo

February 5, 2008

Abstract

There is substantial evidence that the galactic halo is composed of dark matter. The lightest supersymmetric particle, the neutralinos, is the leading candidate of dark matter. It is predicted that neutralinos can be directly detected through elastic scattering with nuclei in detectors. The XMASS Collaboration is developing liquid xenon detectors for the purpose of direct detection of dark matter. A single phase detector with 800 kg of liquid xenon is optimized for the direct detection of dark matter, and it is under construction at Kamioka Observatory. The expected sensitivity of this 800-kg liquid xenon detector for the neutralinos as dark matter is about two orders of magnitude higher than the present best limit in the world. A prototype detector was developed at Kamioka Observatory to check the performance of single phase liquid xenon detectors. With the detector, the physical properties of liquid xenon were measured, and the performance of energy and vertex reconstruction was conﬁrmed. We also search for the neutralinos with the detector though it was not optimized for a dark matter search. Although no dark matter signal was found, we obtained the upper limits, 1.70 10−5 pb for the spin-independent neutralino-proton cross section with neutralino× mass 62 GeV/c2, and 6.74 pb for the spin-dependent neutralino-proton cross section with neutralino mass 60 GeV/c2. These limits reach nearly the expected sensitivity of the detector within its restrictive conditions. From these measurements of the prototype detector, the feasibility of achieving the target sensitivity with the 800-kg liquid xenon detector was conﬁrmed. Acknowledgments

I would like to express my great appreciation to my adviser, Professor Yoichiro Suzuki for introducing me to XMASS experiment. I would also thank him for guiding and encouraging me throughout my graduate course. I would like to express my gratitude to Prof. M. Nakahata and Prof. S. Moriyama. They have guided me in many occasions. I learned many things related to physics and experiments from them. I never forget those who worked with me on the improvements of the prototype detector, A. Takeda and H. Ogawa. This thesis would never be completed without their help. I am grateful to those who worked for XMASS experiments, especially T. Namba, M. Yamashita, Y. Takeuchi, Y. Koshio, K. Ishihara, C. Mitsuda, Y. D. Kim, S. Suzuki, S. Nakamura, Y. Ashie, J. Hosaka, T. Sato, S. H. Moon, K. Ueshima and Y. Ebizuka. This thesis is greatly indebted to them. Thanks to J. Raaf and K. Kobayashi for their useful advices in writing this thesis. I would like to extend my gratitude to all the people who supported and encouraged me during my time in graduate school. I gratefully acknowledge the ﬁnancial support by the Japan Society for the Promotion of Science. Finally, I wish to express my deep gratitude to my family. Contents

1 Introduction 1 1.1 Dark Matter Problem ...... 1 1.1.1 Galaxy rotational curves and dark matter ...... 1 1.1.2 CMB, supernova and galaxy clusters ...... 3 1.1.3 Local halo density and Isothermal halo ...... 3 1.2 Dark Matter candidates ...... 7 1.2.1 Axion ...... 7 1.2.2 WIMPs ...... 7 1.3 LSP Neutralino - Best Motivated WIMP ...... 7 1.3.1 SUSY ...... 7 1.3.2 Neutralino ...... 8 1.4 Review of Neutralino Search Experiments ...... 10 1.4.1 Direct Search ...... 10 1.4.2 Indirect Search ...... 10 1.4.3 Search by Accelerator Experiments ...... 12

2 Dark matter direct detection experiments 14 2.1 NaI scintillator detectors ...... 15 2.2 Cryogenic detectors ...... 16 2.3 Liquid noble element detectors ...... 17 2.3.1 Single phase detector ...... 17 2.3.2 Dual phase detector ...... 17

3 Direct Detection of Neutralinos 22 3.1 R : Total Event Rate for v = 0 and v = ...... 22 0 E esc ∞ 3.2 Modiﬁed Spectral Function for vE = 0 and vesc = ...... 23 3.3 Cross Section at Zero Momentum T6 ransfer . . . 6 . ∞...... 25 3.3.1 Theoretical Framework ...... 25 3.3.2 Cross Section ...... 26 3.3.3 Spin-Independent (SI) Interactions ...... 27 3.3.4 Spin-Dependent (SD) Interactions ...... 28 3.4 F 2, Nuclear Form Factor Correction ...... 30 3.5 Detector response correction ...... 32 3.5.1 fQ, Quenching factor correction ...... 32 3.5.2 Combining results ...... 33

i 4 Properties of liquid xenon 38 4.1 Physical properties of liquid xenon ...... 38 4.2 Scintillation mechanism and properties ...... 38 4.3 LET dependence of scintillation yield ...... 39 4.4 Quenching factor of liquid xenon ...... 41

5 Single phase liquid xenon detector for Dark Matter search 43 5.1 Advantages of liquid xenon for dark matter search ...... 43 5.2 Features to be conﬁrmed ...... 44

6 Prototype detector 46 6.1 Detector setup ...... 46 6.1.1 Underground laboratory at Kamioka mine ...... 46 6.1.2 Low background PMTs ...... 47 6.1.3 Radiation shields ...... 47 6.1.4 Prototype detector ...... 48 6.1.5 Gas line ...... 49 6.1.6 Data Acquisition System ...... 50 6.2 Techniques for low background measurement ...... 51 6.2.1 Distillation of xenon ...... 51 6.2.2 Material selection and chemical etching of the reﬂector . . 52 6.2.3 Radon purge ...... 53

7 Performance of the prototype detector 58 7.1 Calibration ...... 58 7.2 Notations for analysis ...... 59 7.2.1 PMT number ...... 59 7.2.2 Source location ...... 59 7.2.3 Fiducial Volume (FV) ...... 59 7.2.4 Coordinate system of prototype detector ...... 59 7.2.5 ADC saturation cut ...... 60 7.2.6 Maximum PMT ratio cut ...... 60 7.3 Detector Simulation ...... 60 7.4 Gain and TDC oﬀset measurement ...... 61 7.5 Absorption length and light yield ...... 70 7.6 Vertex and energy reconstruction ...... 76 7.7 Photoelectron yield ...... 77 7.8 Vertex and energy resolution ...... 79 7.8.1 Energy resolution ...... 79 7.8.2 Reconstructed vertex ...... 79 7.9 Self-shielding power of liquid xenon ...... 87 7.10 Non-proportionality of scintillation yield ...... 87 7.10.1 131mXe uniformly inside the detector (Neutron activation) 88 7.10.2 137Cs from Hole A ...... 89 7.10.3 40K inside the radiation shield ...... 89 7.10.4 208Th inside the radiation shield ...... 89 7.10.5 Non-proportionality of scintillation yield and energy resolution ...... 97 7.11 Trigger and event selection eﬃciency for Dark Matter search . . 100 8 Dark Matter search by prototype detector 104 8.1 Measurements ...... 104 8.2 Stability of detector ...... 104 8.3 Trigger rate and event selection ...... 105 8.3.1 Noise cut ...... 105 8.3.2 Trigger rate ...... 105 8.3.3 Event selection ...... 109 8.4 Results ...... 115 8.4.1 Obtained spectrum ...... 115 8.4.2 Expected dark matter signal ...... 115 8.4.3 Systematic errors ...... 119 8.4.4 Constraint on Neutralino-Nucleus cross section σχ−N . . 122

9 Discussions 127 9.1 Background from outside the liquid xenon ...... 127 9.1.1 γ rays from PMTs, the lead shield and the ambient . . . . 127 9.1.2 Ambient neutrons ...... 139 9.2 Background from inside the liquid xenon ...... 144 9.2.1 Uranium series inside xenon ...... 144 9.2.2 Thorium series inside xenon ...... 154 9.2.3 Krypton inside xenon ...... 156 9.3 Background caused by the detector geometry ...... 158 9.4 Wave form analysis ...... 162 9.4.1 Deﬁnition of “mean hit timing” ...... 162 9.4.2 “mean hit timing” of the dark matter search run . . . . . 162 9.4.3 Tritium inside the liquid xenon ...... 172 9.5 Summary ...... 175

10 Future prospects 177 10.1 Single phase detector with 800 kg of liquid xenon ...... 177 10.1.1 Larger photo coverage and small dead angle from PMTs . 177 10.1.2 Thicker layer for self-shielding and larger ﬁducial volume 178 10.1.3 Further reduction of radioactive impurities in PMTs . . . 178 10.1.4 Radiation shield with water tank ...... 179 10.2 Expected sensitivity ...... 180

11 Conclusion 184 Chapter 1

Introduction

Recent results from Cosmic Microwave Background (CMB), Large Scale Struc- ture (LSS) and Type Ia supernovae observations have yielded a standard model of cosmology: a flat universe consisting of more than 70 % dark energy and about 23 % dark matter, and the remainder of ordinary (baryon) matter. An- swering the questions ”what is dark energy” and ”what is dark matter” become one of the most challenging tasks for physicists. This thesis and underlying experiment are intended as an exploration of the dark matter problem. Discovery of a dark matter particle will become both strong support of cosmological observations and predictions, and evidence for new physics beyond the standard model of particle physics. In this chapter, we first introduce the problem of missing mass in the universe and evidence from cosmological observations that suggest a large amount of matter in the universe is dark. We will then illustrate different theoretical explanations and models that may be used to explain the mysterious dark matter problem focusing on different particle candidates for dark matter. In the end, we will give a general review of neutralinos, the best motivated dark matter candidate in the framework of a supersymmetric model.

1.1 Dark Matter Problem 1.1.1 Galaxy rotational curves and dark matter The clearest evidence for the existence of dark matter is observed by the diﬀer- ence between the matter distribution implied by the luminosity and that implied by the rotation velocities, vc, of the spiral galaxies. The rotation velocity distribution of spiral galaxies expected from Kepler’s law is [v (r)]2 M(r) c = G (1.1) r r2 where r is the radial distance from the center of the galaxy, and M(r) is the total mass within the radius r. Since the orbital velocity can be measured by the Doppler shifts of the spectrum of the stars, the 21 cm line of HI gas (neutral hydrogen gas) and 2.6 mm line of COs, the mass distributions of the spiral galaxies are estimated from Eq. (1.1). On the other hand, the luminous matter

1 is found to be concentrated near the center of galaxies. If the total mass of the galaxy is concentrated near the luminous core of the galaxy, v must fall like r−1/2. The measured velocities, however, remain constant out to the distance as far as can be measured in almost all cases. This implies that M(r) r at large radius, and there exists a large amount of a non-luminous mass whic∝ h exceeds the luminous one. Fig. 1.1 shows the rotational curve for the spiral galaxy NGC6503 [1]. The luminous disk extends no further than about 5 kpc from the center of the galaxy. If the luminous matter was concentrated within this radius, the rotational curve would drop at larger radius. From the discrepancy between the observed rotational curve and the rotational curve expected from the luminous disk and gas, the existence of a dark halo is inferred. Based on this method, the typical mass density of the dark halo is estimated to be

Ω 0.1 (1.2) halo ≥ On the other hand, the mass density of the luminous part of the galaxy is estimated to be,

Ω 0.01 (1.3) luminous ≤ Thus the comparison between Eq. (1.2) and (1.3) indicates that the dark matter exists at the scale of a single galaxy.

Figure 1.1: Rotational curve for the spiral galaxy NGC6503. The points indicate the measured rotation velocities as a function of distance from the galactic center. The dashed and dotted curves are the contribution to the rotation velocity due to the observed disk and gas, respectively. The dash-dotted curve is the contribution from the dark halo. This ﬁgure is taken from Ref. [1]

2 1.1.2 CMB, supernova and galaxy clusters The dark matter was not created solely to explain the gravitational effects of galactic rotational curves. Actually it is an essential part of the big bang theory and is necessary to explain various cosmological aspects, such as the anisotropy of the cosmic microwave background (CMB) and structure formation in large scale. The CMB radiation is the radiant left over from the big bang when the universe was cooled. The radiation is highly uniform across the sky. While in 1992, NASA’s COBE satellite detected tiny fluctuations (also called anisotropy) of the CMB radiation. A similar probe, the Wilkinson Microwave Anisotropy Probe (WMAP), with much higher sensitivity than COBE reported more ac- curate results in 2003 [2]. The CMB anisotropy is associated with fluctuations of matter density in the early universe, thus can be used to study the initial conditions of cosmic structure formation. The WMAP results fit a cosmological 2 model with matter density of the universe at Ωmh = 0.14 0.02 and baryon 2 density at Ωbh = 0.024 0.001 with Hubble constant h = 0.72 0.05 [2]. Recent observations and measurements of the distance-redshift relation of Type Ia supernovae brought clear evidence of the acceleration of expansion of the universe. The acceleration of the universe expansion suggests an unknown type of energy, dark energy. A fit of the Type Ia supernovae observation data suggests a total energy density ΩΛ around 0.7 and mass density Ωm around 0.3 for a flat (Ωm + ΩΛ) cosmology [3] [4]. The gravitational instability and small fluctuations of the initial density field of the universe cause the formation of large-scale structure and the galaxy distribution in today’s universe. Thus measurement of the distribution of galaxy clustering at large scale can be used to determine the mass density of universe, and this is particularly investigated by the Sloan Digital Sky Survey (SDSS). Combined with the CMB anisotropy measurement by WMAP, SDSS results favor a low-density universe with Ωm 0.30 0.04 [5]. Combining the high-redshift superno∼ va surv ey, galaxy cluster observations and cosmic microwave background measurements, the normalized mass and energy densities Ωm and ΩΛ nicely converge in the cosmological parameter space, as shown in Fig. 1.2, which indicates an inflationary and flat cosmological model.

1.1.3 Local halo density and Isothermal halo Although the determination of a halo model is currently a very active topic of research in astrophysics, both local halo density, ρ0, and the WIMP velocity distribution represent a signiﬁcant systematic uncertainty. Therefore, the WIMP direct detection community uses the simplest reasonable model, the isothermal halo model. In determining ρ0 and v0, the galactic rotational curve is the most important observational quantity. The rotational curve of our Galaxy cannot be measured with the same precision as that of an external spiral galaxy, for instance NGC6503 in Fig. 1.1. It is, however, qualitatively the same because our Galaxy seems to be an ordinary spiral galaxy. The rotation velocity of our Galaxy increases linearly from zero at the center to roughly vc = 220 km/s in the solar neighborhood and remains roughly ﬂat all the way out to 25 kpc ∼

3 [8]. The observed rotational curve for our Galaxy is shown in Fig.1.3. In the isothermal halo, the shape of the rotational curve could be explained by assuming that the density distribution of the dark halo WIMPs is

ρ0 ρ(r) = 2 2 (1.4) 1 + r /r0

where ρ0 and r0 are ﬁtting parameters. Using the observed rotation velocity in the solar neighborhood, the local density of the halo dark matter is estimated to be

ρ 0.3 GeV c−2cm−3 (1.5) 0 ∼ with an uncertainty of a factor two or even more [9]. The following values are adopted by many dark matter search experiments.

−2 −3 ρ0 = 0.3 GeV c cm v v 220 km/s (1.6) 0 ∼ c ∼

4 Figure 1.2: Cosmological parameter space from high-redshift supernova survey [6], galaxy cluster observation [7] and cosmic microwave background measurement [2].

5 Figure 1.3: Rotational curve for our Galaxy [8]. The diﬀerent lines represent the contributions from the bulge (dotted), the disk (ﬁlled circles), the HI layer (crosses), the H2 layer (circles), and from the dark halo (dashed). The solid line represents the sum of the contributions.

6 1.2 Dark Matter candidates 1.2.1 Axion The axion was proposed as a natural new light pseudo-scalar boson to solve the CP conservation problem of strong interactions [10]. CP invariance of strong interactions is violated in the context of quantum chromodynamics (QCD) theory, which is not the case from an experimental point of view. Although particle physics has no preference for the axion mass, laboratory experiments and im- plications from astrophysical and cosmological eﬀects have excluded most of the mass range, leaving only two windows, 10−6 eV m 10−3 eV and ≤ a ≤ 2 eV ma 5 eV, for further exploration [11]. The recent experiment using the Sikivie≤ radio≤ frequency cavity technique to probe the axion mass range of 2.3 µeV ma 3.4 µeV resulted in no positive signal [12]. The recent results from the≤CERN≤Axion Solar Telescope imply an upper limit on the axion-photon 10 coupling, gaγ < 1.16 10 GeV at 95% C.L. for axion mass of ma 0.02 eV [13]. × ≤

1.2.2 WIMPs The widely discussed nonbaryonic dark-matter candidate is Weakly Interacting Massive Particles, WIMPs. “Weakly interacting” means that these particles interact only via the weak interaction (and gravity). Massive means suﬃciently massive to solve the structure-formation problem brought on by a baryons-only, or even a neutrinos and baryons, universe. This would require a WIMP mass of at least 1 keV. Incidentally, particle physics provides a good generic rationale for the existence of WIMPs. Supersymmetry (SUSY), a well-motivated and presently most-favored extension to the Standard Model of particle physics, implies WIMPs. The lightest new particle, the neutralino, predicted by SUSY would be an ideal WIMP. The details of these will be described in the next section.

1.3 LSP Neutralino - Best Motivated WIMP 1.3.1 SUSY The standard model (SM), which is a non-Abelian gauge theory based on the gauge groups SU(3)color SU(2)left U(1)hypercharge of strong, electromagnetic and weak interactions× acting on×the quark and lepton multiplets, is an extraordinarily successful theory, and describes all experimental results on the interactions between elementary particles with surprising accuracy. However, the SM has its natural drawbacks and unsolved problems. Among them are a large number of free parameters • the strong CP violation problem • not uniﬁed with gravity • ﬂavor mixing and the number of generations are arbitrary • the hierarchy problem •

7 SUSY presupposes that each elementary particle with spin j in the SM has a supersymmetric partner with spin j 1/2, as shown in Table 1.3.1. −

Normal particles SUSY partners Symbol Name Spin Symbol Name Spin 1 6 q = u, c, t up quarks 1/2 q˜u, . . . , q˜u up squarks 0 1 6 q = d, s, b down quarks 1/2 q˜d, . . . , q˜d down squarks 0 l = e, µ, τ leptons 1/2 ˜l1, . . . , ˜l6 sleptons 0 νe, νµ, ντ neutrinos 1/2 ν˜1, ν˜2, ν˜3 sneutrinos 0

g gluons 1 g˜ gluinos 1/2 W W bosons 1 χ˜1 , χ˜2 charginos 1/2 H charged Higgs 0

γ photon 1 Z0 Z boson 1 0 0 0 0 h H2 light scalar Higgs 0 χ˜1, . . . χ˜4 neutralinos 1/2 H0 H0 heavy scalar Higgs 0 1 A0 H0, P pseudoscalar Higgs 0 3 0 Table 1.1: Particle spectrum in the SUSY model[14]. Particle with spin j in the SM have supersymmetric partners with spin j 1/2 . | − |

From precise measurements of the coupling constants and the solution of the renormalization group equations for the evolution of the coupling constants, the possibility of unification within the SM is excluded. On the other hand, SUSY particles affect the slope of the running of the couplings, and unification of the coupling constants is obtained at 1016 GeV/c2 in the case of the SUSY breaking scale, M 1 TeV/c2 as shown in Fig. 1.4. In general, M must be in SUSY ∼ SUSY the range 100 GeV/c2 to about 10 TeV/c2 to provide this unification.

1.3.2 Neutralino In the minimum supersymmetric extension of the standard model (MSSM), the interactions of SUSY particles with ordinary particles are governed by “R- parity”. R-parity is given by

R = ( 1)3B+L+2S (1.7) − where B is the baryon number, L is the lepton number and S is the spin. The supersymmetric particles are assigned odd R-parities and the ordinary particles are assigned even R-parities. Conservation of R-parity has two consequences: the supersymmetric particles are created in pairs • the lightest supersymmetric particle (LSP) is stable. • The lightest neutralino (χ χ˜0), the lowest-mass linear combination of ≡ 1 photino (γ˜), zino (Z˜) and higgsinos (H˜1, H˜2), is the leading candidate for LSP

8 Figure 1.4: Three coupling constants in the Standard Model (SM) (a) and in the Minimal Supersymmetric Standard Model (MSSM) (b) [15]. Only in the latter case uniﬁcation is obtained. α1, α2 and α3 are the U(1) hypercharge, SU(2) electroweak and SU(3) strong couplings, respectively. and also for nonbaryonic cold dark matter. The photino and zino are expressed with the superpartners of gauge bosons (Gauginos), Bino (B˜) and Wino (W˜ ):

γ˜ = cos θW B˜ + sin θW W˜ 3 Z˜ = sin θ B˜ + cos θ W˜ (1.8) − W W 3 Thus, χ can be written as

χ = a1B˜ + a2W˜ 3 + a3H˜1 + a4H˜2 (1.9) The neutralino mass matrix is written as

M1 0 MZ cos β sin θW MZ cos β cos θW 0 M −M sin β sin θ M sin β cos θ 2 Z W Z W (1.10)  M cos β sin θ M sin β sin θ 0 − µ  − Z W Z W −  MZ cos β cos θW MZ sin β cos θW µ 0   − −    where M1 and M2 are the respective mass parameters of U(1) and SU(2) gaug- 2 ino, µ is the higgsino mass parameter, sin θW is the weak mixing angle, MZ is the Z boson mass, and tan β v2/v1, where v1 and v2 are the vacuum expectation values of the two Higgses.≡ If we assume the grand uniﬁcation, M = (5/3) M tan2 θ 0.5M is obtained, thus the neutralino mass matrix 1 2 W ∼ 2 is characterized by three parameters: µ, M2 and tan β. In general, three basic conﬁgurations exist:

9 Gaugino dominated : If M1, M2 µ, then the lightest neutralino is • primarily gaugino.

Higgsino dominated : If µ M1, M2, then the lightest neutralino is • primarily higgsino.

Mixed: If M1 µ, then the neutralino is a roughly equal mixture of • gaugino and higgsino.∼ It suffices to note that the bino, wino and higgsino have different interactions, so the composition affects both the annihilation cross section and thus the relic density as well as the cross section for neutralino-quark scattering.

1.4 Review of Neutralino Search Experiments

There have been three types of the neutralino search experiments: direct search experiments, indirect searches experiments and search by accelerator experiments. We will review these experiments in this section.

1.4.1 Direct Search As our Solar system moves in the galaxy, the earth encounters the dark matter halo with a relative speed. The WIMPs from the halo can elastically scatter oﬀ the target nucleus of a terrestrial detector, and transfer a small amount of energy (less than 100 keV) to the recoil nucleus. Successfully detecting this small amount of energy from the recoil nucleus will give strong support for direct detection of WIMPs. The main challenge of the direct detection of WIMPs is the discrimination of a WIMP recoil event from a background event. The gamma rays and neutrons will make background events with energies similar to that from WIMPs. Recently, the direct detection of dark matter experiments are among the most exciting and competitive experimental physics around the world. These experiments require a very low background environment, thus they are usually located in deep underground laboratories. This thesis represents one of this type of experiment. We will discuss the variety of designed detectors that currently search for WIMP dark matter in Chapter 2, and the expected WIMP event rate in Chapter 3.

1.4.2 Indirect Search Neutralinos can be trapped in the core of the Earth, the Sun, and the Galactic center and annihilate with each other. The annihilation process has many channels as listed in Table 1.2. The detection of its annihilation products, such as gamma rays, neutrinos, positrons and anti-protons, etc., from speciﬁc directions and locations will provide indirect information on the dark matter.

Antimatter WIMP self-annihilation will also produce particles such as positrons(e+), antiprotons(p¯), antideuterons(D¯), etc. The measured cosmic antiproton spectrum can provide information on the light neutralino and can be used to put stringent constraints on the supersymmetric conﬁgurations [16].

10 The searches for antiprotons or antideuterons have been performed by the Balloon-borne Experiment with Superconducting Spectrometer (BESS), and its recent results based on the cosmic-ray antiproton spectrum suggest an unknown source of antiprotons below 1 GeV [17]. For the cosmic antideuteron search, BESS found no candidates from their data during four balloon flights from 1997 to 2000, and derived an upper limit of 1.9 10−4(m2 s sr GeV/nucleon)−1 for the differential flux of cosmic-ray antideuterons,× at the 95 % confidence level, between 0.17 and 1.15GeV/nucleus at the top of the atmosphere [18]. The next generation antimatter detector GAPS (the General Antiparticle Spectrometer) identifies antimatter through the characteristic X-rays emitted by antimatter when it is captured in the target and forms exotic atoms. Its suf- ficient sensitivity to detecting antideuterons will enable it to probe the SUSY parameter space for a sensitive indirect dark matter search [19].

Gamma-Ray Lines γ rays may result from annihilations χχ γγ or χχ Zγ [14]. The rates of these processes are difficult to estimate b→ecause of uncertain→ ties in SUSY parameters and halo density profiles. However, the γ-ray intensity from neutralino annihilation in the galactic halo has a characteristic anglar dependence. The Energetic Telescope (EGRET) on the Compton Gamma-Ray Observa- tory has observed about 60 % higher integrated intensity for gamma rays above 1 GeV, than a model calculation of the emission based on dynamic balance and realistic interstellar matter and photon distributions from the galactic plane [20]. Elsaesser and Mannheim compared the extragalactic gamma-ray background from EGRET data with high-resolution simulations of cosmic structure +110 formation, and found a best fit value of neutralino mass around 515−75 GeV [21]. The next generation gamma-ray observatory GLAST (Gamma-Ray Large Area Space Telescope) is planned to launch in 2007. It will be able to detect gamma rays up to 300 GeV, with a sensitivity 2 10−9 photons cm−2 s−1 for gamma rays more than 100 MeV for a 2 year all-sky× survey, a factor of 30 better than EGRET [22].

Muon Neutrino Neutralinos scatter elastically oﬀ nuclei in the Earth, the Sun and the galactic center. If their velocities become less than the escape velocity in the process, they are gravitationally trapped in the core of them. The accumulated neutralinos can self-annihilate and produce various particles. Among the products, energetic muon neutrinos can escape from the core and be detectable in neutrino detectors placed on the surface of the Earth. The energetic neutrinos will un- dergo charged current interactions in the rock below the detector or within the detector materials. Therefore, neutralinos are indirectly detectable as upward- going muons. Since the energies of these muons will be typically 1/3 to 1/2 of the neutralino mass, they cannot be confused with ordinary neutrinos. Fluxes predicted for such muon neutrino events in SUSY models seem to fall for the most part between 10−6 and 10−2 events/m2/yr, as shown in Fig. 1.5. Several experiments are ongoing and have set limits on the ﬂux of upward- going muons from the Earth, the Sun and the galactic center. The tightest limits have been reported by the Super-Kamiokande Collaboration [23]. The new generation neutrino telescopes such as IceCube [24] and ANTARES [25] are under development.

11 annihilation channel ff¯ W +W − Z0Z0 W +H−, W −H+ Z0A0 χχ Z0H0, Z0h0 → A0A0, H0H0, h0h0, H0h0 A0H0, A0h0 H+H− gg, qq¯g Z0γ, γγ

Table 1.2: Neutralino-neutralino annihilation channels [14]. Where f and f¯ are the standard model, neutrinos, leptons and quarks, and A0 are axions.

1.4.3 Search by Accelerator Experiments The neutralino search is also performed by accelerator experiments [35]. Neu- tralinos could be produced in an e+e− collider through an s-channel virtual Z, or by t-channel scalar electron (selectron, e˜) exchange.

e+e− χ˜0χ˜0 or χ˜0χ˜0 (1.11) → 1 2 2 2 0 then the χ˜2 will decay into.

χ˜0 χ˜0Z∗ χ˜0ff˜ or χ˜0 χ˜0γ (1.12) 2 → 1 → 1 2 → 1 0 The signature is missing energy due to the undetected χ˜1 and one or two photons, two or four leptons, or one to four hadronic jets. Constrained Minimal Supersymmetric Standard Model (CMSSM) motivated by Grand Uniﬁed Theory (GUT) is often used for the analysis to simplify physics 0 interpretations. The absolute lower limit to Mχ˜1 mass for a certain parameter set is 40 GeV c−2 [35]. However, searches for a neutralino with mass lighter than 40 GeV c−2 are still needed because it is probable that GUTs may not work and in that case, neutralinos with masses of a few GeV c−2 can exist [36].

12 Figure 1.5: Predicted rates for indirect detection of neutralinos of mass mχ via observational rate of energetic muon neutrino events from annihilation in both the Earth and the Sun [14].

13 Chapter 2

Dark matter direct detection experiments

Neutralinos can be detected via elastic scattering with ordinary matter. Feyn- man diagrams of the spin-independent and spin-dependent neutralino-quark elastic scattering are shown in Fig. 2.1 and 2.2, respectively. Many experiments have been trying to reveal the existence of WIMPs by this approach. χ χ χ χ

q~ H, h

q q q q

Figure 2.1: Feynman diagram contributing to the spin-independent elastic scattering of neutralino from quarks.

The detectors for direct detection experiments should be equipped with the following three characteristics.

Low energy threshold Since the WIMP signal is expected to originate from elastic scattering, a feature- less, quasi exponentially decreasing energy spectrum will result. The relevant energy region will be typically below 100 keV. Therefore, the lower the energy threshold, the more of the signal can be detected.

14 χ χ χ χ

q~ Z

q q q q

Figure 2.2: Feynman diagram contributing to the spin-dependent elastic scattering of neutralino from quarks

Large target mass Since WIMP direct detection is a rare event search, one would need large target masses generally in order to gain suﬃcient statistics in a reasonable observation time of the experiment.

Low background The typical precautions of rare event searches (such as material selection and shielding) is essential to WIMP detectors in an underground laboratory. For nuclear recoil events, a generic background contribution originates from neutrons. On the other hand, the majority of background consists of electron recoils from photons (X-ray or γ-ray radiation) or electrons (β-ray radiation). Techniques to discriminate between these two types of energy deposition reduce the background signiﬁcantly.

2.1 NaI scintillator detectors

Dark matter searches using NaI scintillator detectors have been performed since the mid 1990s and some large scale experiments are still running. The nuclear recoil events can be distinguished from electron recoil events based on the scintillation light pulse shape discrimination (PSD), as shown in Fig. 2.3. The ﬁnal result from the UKDMC (UK Dark Matter Collaboration) from the NAIAD (NaI Advanced Detector) experiment has set the WIMP-nucleon cross section as shown in Fig. 2.5 and 2.6 [27]. The increasing amount of mass for the NaI detectors allowed the study of WIMP annual modulation with enough statistics. The DAMA Collaboration reported positive annual modulation signals (without PSD discrimination of nuclear and electron recoils) based on 100kg NaI(Tl) crystals with a total exposure of 108,000 kg day for a seven-year period run that ended in July 2002. They showed annual· modulated signals (see Fig. 2.4) with 6.3 σ CL and, claimed a detection of WIMP signal at a WIMP-nucleon cross section at σ 10−6 10−5 pb p ∼ −

15 Figure 2.3: Pulse shape discrimination (PSD) by using time constants for γ-ray (full line) and neutron (dashed line) event from NaI scintillation light for 13 - 16 keV energy span. Figure is taken from [26].

for a WIMP mass of 60 GeV c−2 [28]. The allowed region of DAMA is shown in Fig. 2.5. DAMA is currently the only experiment that claims positive WIMP detection. While many suggestions have been made to try to resolve the conﬂict of the DAMA results with other experiments with better sensitivity to WIMP searches, there is remaining doubt that the annual modulation signal from the DAMA experiment might be from some annual cycle remaining in the experiment itself, and not from a WIMP signal.

2.2 Cryogenic detectors

The application of cryogenic detectors operated at sub-Kelvin temperatures have good performance and sensitivity for WIMP searches. These experiments use the technology of detecting two signals from an event simultaneously - thermal phonons and ionization for the case of cryogenic Ge detectors. The EDELWEISS Collaboration used neutron transmutation doped (NTD) Ge heat sensors to read the thermal phonon signal from recoil event. The phonon signal has no quenching factor for nuclear recoil events. The ionization from nuclear recoils is reduced by the quenching factor, which allows the separation of these nuclear recoil events from electron recoil events. The ﬁnal result from EDELWEISS from three 320 g detectors over four months of stable operation with a total exposure of 62 kg d has set the WIMP-nucleon cross section as shown in Fig. 2.5 [30]. · The CDMS (Cryogenic Dark Matter Search) experiment uses cryogenic Ge

16 detector technology similar to EDELWEISS, and CDMS II has been running in Soudan Mine since 2003. The latest result from CDMS II with two towers, each consisting of six detectors, with a total exposure of 34 kg d for germanium and 12 kg d for silicon targets after cuts has set the WIMP-nucleon· cross section as shown· in Fig. 2.5 [31].

2.3 Liquid noble element detectors

The liquid noble elements are excellent scintillators, while at the same time ionization signals can be collected with an applied electric ﬁeld. The experiments using the pure scintillation light from liquid noble element detectors use one phase (liquid) as the working medium, we refer to them as “single phase detector”. Due to the diﬀerent ionizing density of nuclear and electron recoils in liquid noble elements, background discrimination can be realized by measuring simultaneously the ionization and scintillation signals from a liquid noble element detector. Usually ionization in this kind of detector is detected via their proportional scintillation in the gas phase, thus using both liquid and gas phase as working medium, we refer to this kind of detector as “dual-phase detector”.

2.3.1 Single phase detector The ZEPLIN I experiment published their ﬁrst result based on the PSD of liquid xenon scintillation light with a single phase detector operating in UK Boulby Mine and a total run of 293 kg d exposure. Instead of using PSD for bac· kground discrimination, a large scale liquid xenon detector such as XMASS single phase, would also be able to reject backgrounds based on a volume cut for events only in the center of the detector. This would allow a suﬃcient background rejection. The details about the XMASS single phase detector are discussed in Chapter 5.

2.3.2 Dual phase detector As discussed above, the scintillation and ionization signals are simultaneously detected by dual phase detectors. The direct scintillation light is detected by photon detectors, usually photo-multiplier tubes (PMTs) as S1. The number of primary ionization electrons from nuclear recoil events in these liquid noble elements, with typical energies at the 10 keVr level, is very small and can’t be detected efficiently with charge-sensitive devices. In these experiments, the primary electrons are drifted from the liquid to the gas phase with a drift field Ed in the liquid. Once they reach the gas phase, the signal will be amplified by means of proportional scintillation or electroluminescence by a strong field in the gas phase. The proportional scintillation is also detected by the PMTs as S2. The distinct ratio between the scintillation and ionization, S2/S1, for nuclear recoil events and electron recoil events provides unique background rejection for WIMP dark matter searches. The XENON experiment uses a dual phase xenon detector, and XENON10 has been running at the Gran Sasso National Laboratory since 2006. The latest result from XENON10, with 58.6 live-days of WIMP-search in a 5.4 kg liquid

17 xenon target, has set the world’s current lowest exclusion limit for the WIMP- nucleon cross section as shown in Fig. 2.5 [32].

18 Figure 2.4: DAMA annual modulation signal from a model independent ﬁt to a cosine function, showing the period of oscillation to be 1.00 0.01 year and oﬀset t at 140( 22) day. 0

19 (pb) -p χ SI

σ -4 10

-5 10

-6 10

-7 10

-8 10 2 3 10 10 10 -2 Mχ (GeVc )

Figure 2.5: Experimental results of spin-independent WIMP searches. The regions above the curves are excluded at 90 % conﬁdence level. DAMA’s allowed region is shown by the pink line[28]. The limits by EDELWEISS [30] and CDMS II [31] with cryogenic germanium detector are shown by the blue and light-blue lines. The world’s current lowest limit by XENON10 with a dual phase xenon detector is shown by the green line [32]. MSSM predictions are shown by the black line.

20 10 3 (pb) -p

χ 2

SD 10 σ

-1 10

-2 10

-3 10

-4 10 2 3 10 10 10 -2 Mχ (GeVc )

Figure 2.6: Experimental results of spin-dependent WIMP searches. The regions above the curves are excluded at 90 % conﬁdence level. The limits by UKDMC [27] and DAMA [29] with NaI(Tl) detectors are shown by the blue and green line. The limit by CRESST with a cryogenic Al2O3 detector is shown by the pink dotted line [33]. The limit by the Tokyo group with CaF2 scintillator is shown by the light-blue line [34]. MSSM predictions are shown by the black line.

21 Chapter 3

Direct Detection of Neutralinos

In this chapter, theoretical framework of the direct detection of neutralino is described [37].

3.1 R : Total Event Rate for v = 0 and v = 0 E esc ∞ The diﬀerential event rate per unit target mass (kg) is N dR = A σ v dn (3.1) A χ−N 26 −1 where NA is the Avogadro number per unit mass (6.02 10 kg ), A is the mass number of target nucleus, v is the dark matter velocit· y onto the target, n is the dark matter particle number density, and σχ−N is the neutralino-nucleus (χ N) cross section for zero momentum transfer. The cross section for non-zero − momentum transfer, σχ−N(non−zero), is expressed as 2 σχ−N(non−zero) = σχ−N F (ER) (3.2) which is discussed in Section 3.4. The total event rate, R, is then expressed as N N R = 0 σ v dn = 0 σ n v (3.3) A χ−N A χ−N 0 h i Z where n = ρD is the mean dark matter particle density given by the ratio of 0 Mχ the dark matter density, ρD, to the neutralino mass, Mχ, and v is the mean dark matter velocity. A Maxwell-Boltzmann dark matter velocith yi distribution is commonly assumed:

2 2 1 −|v+vE | /v0 f (v, vE ) = 3 e (3.4) 2 2 (πv0) where v is the dark matter velocity onto the target, vE is the Earth velocity relative to the dark halo, and v0 is the velocity dispersion. For vE = 0 and the local Galactic escape velocity, v = , v is expressed as esc ∞ h i 2 v = v . (3.5) h i √π 0

22 From Eq. (3.3) and Eq. (3.5), the total event rate for v = 0 and v = , E esc ∞ R0 is expressed as

N0 ρD 2 R0 = σχ−N v0. (3.6) A Mχ √π

−1 −1 R0 is conventionally expressed in units of kg day . Normalized to ρD = −2 −3 −1 0.3 GeV c cm and v0 = 220 km s , Eq. (3.6) becomes

361 σχ−N ρD v0 R0 = −2 −3 −1 (3.7) MχMN 1 pb 0.3 GeV c cm 220 km s −2 with Mχ , MN in units of GeV c . MN is the mass of target nucleus (MN = 0.932 A).

3.2 Modiﬁed Spectral Function for v = 0 and E 6 v = esc 6 ∞ The total event rate for vE = 0 and vesc = is expressed using Eq. (3.3) and Eq. (3.6) 6 6 ∞ √π v k 1 R = R h i = R 0 v f (v, v ) d3v (3.8) 0 2 v 0 k 2πv4 E 0 0 Z where k is the normalization constant

2π 1 vesc 2 k = dφ d (cos θ) f (v, vE ) v dv (3.9) Z0 Z−1 Z0 3/2 and k = π v2 is the value of k for v = . Eq. (3.8) is then, 0 0 esc ∞ 2 R(0, vesc ) k0 v 2 2 = 1 1 + esc e−vesc/v0 (3.10) R k − v2 0 1 0 R(vE, ) 1 1 vE 1 v0 vE 2 2 ∞ = π 2 + erf + e−vE /v0 (3.11) R 2 v 2 v v 0 0 E 0 2 2 R(vE, vesc) k0 R(vE, ) v 1 v 2 2 = ∞ esc + E + 1 e−vesc/v0 (3.12) R k R − v2 3 v2 0 1 0 0 0 x 2 where erf(x) = 2/√π 0 exp t dt and k1 is the value of k for vesc = written as − 6 ∞ R vesc 2 vesc 2 2 k = k erf e−vesc/v0 (3.13) 1 0 v − √π v 0 0 The recoil energy of the nucleus of mass MN caused by elastic scattering of the dark matter particle of mass Mχ with kinematic energy E is E = E r (1 cos θ) /2 (3.14) R − where θ is the scattering angle (in the center of mass) and

4MχMN r = 2 (3.15) (Mχ + MN )

23 With an assumption that the scattering is isotropic, and where ER is uniformly distributed over the range 0 E E r, then the differential event rate is ≤ R ≤ dR Emax 1 1 vmax v2 = dR(E) = 0 dR(v) (3.16) dE E r E r v2 R ZEmin 0 Zvmin 2 2 v0 where E0 = 1/2 Mχ v0 = v2 E, Emin = ER/r is the lowest energy of the incident particle which can produce a nuclear recoil of energy ER and vmin = 1 2 (2 Emin/Mχ) is the dark matter particle velocity corresponding to Emin. From Eq. (3.8), R k 1 vmax 1 dR = 0 0 f(v, v ) d3v (3.17) E r k 2πv2 v e 0 0 Zvmin then the differential spectral function is expressed using Eq. (3.16) dR R k 1 vmax 1 = 0 0 f(v, v ) d3v (3.18) dE E r k 2πv2 v E R 0 0 Zvmin For the simplest case of v = 0 and v = , Eq. (3.18) gives E esc ∞ dR(0, ) R ∞ = 0 e−ER/E0 r (3.19) dER E0 r Eq. (3.19) shows that the distribution of recoil nuclei is governed by the masses of the dark matter particle and target nuclei. With non-zero vE and finite vesc, Eq. (3.18) gives

dR (0, vesc) k0 R0 2 2 = e−ER/E0 r e−vesc/v0 dER k1 E0 r − k0 R0 dR(0, ) R0 2 2 = ∞ e−vesc/v0 (3.20) k E r dE − E r 1 0 R 0 dR (v , ) R √π v v + v v v E ∞ = 0 0 erf min E erf min − E (3.21) dE E r 4 v v − v R 0 E 0 0 R0 −c2 ER/E0 r c1 e (3.22) ∼ E0 r dR (vE, vesc) k0 dR(vE, ) R0 2 2 = ∞ e−vesc/v0 (3.23) dE k dE − E r R 1 R 0 −1 where c1 = 0.751 and c2 = 0.561 are parameters in Eq.(3.22) for vE = 244.0 km . The Earth velocity vE varies during the year as the Earth moves around the Sun. v 244 + 15 sin(2πy) km−1 (3.24) E ∼ where y is the elapsed time from March 2nd in year, is used in [37]. The Maxwellian velocity parameter, v0, and the escape velocity, vesc, are discussed by several authors [38] [39] , and v = (220 40) km s−1 (3.25) 0 v = (450 650) km s−1 (3.26) esc − are the commonly used values.

24 3.3 Cross Section at Zero Momentum Transfer

Neutralinos interact with quarks spin-independently (SI) and spin-dependently (SD). The cross section of each interaction can be calculated by assuming certain sets of parameters in the MSSM model [14] [40].

3.3.1 Theoretical Framework The theoretical framework we use in the context of the MSSM is reviewed in this section. The MSSM Lagrangian leads to the following low-energy effective La- grangian, , suitable for describing elastic neutralinoχ-quark interactions [40]. L = χγ¯ µγ5χq¯ γ α + α γ5 q + α χχ¯ q¯ q Leff i µ 1i 2i i 3i i i 5 5 5 5 +α4iχγ¯ χq¯iγ qi + α5iχχ¯ q¯iγ qi + α6iχγ¯ χq¯iqi (3.27) where qi denotes the quark and the subscript i labels up-type quarks (i = 1) and down-type quarks (i = 2). This Lagrangian is to be summed over the quark generations. Terms in Eq.(3.27) with coefficients α1i, α4i, α5i and α6i make contributions to the elastic scattering cross section that are velocity dependent, and may be neglected for dark matter with non-relativistic velocities. Terms in Eq. (3.27) with coefficients α2i and α3i contribute to the SD and SI interactions, respectively. α2i and α3i are written as follows.

1 2 2 1 2 2 α2i = Yi + Xi + Vi + Wi 4 M 2 M 2 | | | | 4 M 2 M 2 | | | | 1i − χ 2i − χ 2 h i 3 h i g 2 2 Ti 2 2 a3 a4 (3.28) −4MZ cos θW | | − | | 2 h i 1 ∗ 1 ∗ α3i = Re (Xi) (Yi) Re (Wi) (Vi) 2 M 2 M 2 − 2 M 2 M 2 1i − χ 2i − χ gM 1 1 qi Re (δ [ga g0a ]) D C + −4M B 1i 2 − 1 i i −M 2 M 2 W i H1 H2 D2 C2 +Re (δ [ga g0a ]) i + i (3.29) 2i 2 − 1 M 2 M 2 H2 H1 where Mqi is the quark mass. Eq.(3.28) and (3.29) are to be summed over q and i. M1i and M2i are the squark mass eigenvalues, Mχ is the neutralino mass, MZ 3 is the Z boson mass, MW is the W boson mass, Ti is the third component of the weak isospin, a1,2,3,4 are the neutralino composition parameters in Eq.(1.9),

MH2 < MH1 denotes two scalar Higgs mass, and θW is the weak mixing angle, 0 which is given by the ratio of the two weak coupling constants, tan θW = g /g.

∗ ∗ gMqi a5−i ∗ 0 Xi η11 η12eig a1 ≡ 2MW Bi −

∗ yi 0 3 ∗ gMqi a(5−i) Yi η11 g a1 + gTi a2 + η12 ≡ 2 2MW Bi ∗ gMqi a5−i ∗ 0 ∗ Wi η21 η22eig a1 ≡ 2MW Bi −

∗ gMqi a(5−i) ∗ yi 0 3 Vi η22 + η21 g a1 + gTi a2 (3.30) ≡ 2MW Bi 2 25 3 where yi denotes the hyper charge of the sfermion defined by ei = Ti + yi/2. η is the sfermion mass matrix and defined for each flavor qi by an angle θqi as η η cos θ sin θ 11 12 = qi qi (3.31) η η sin θ cos θ . 21 22 − qi qi Other parameters in Eq.(3.28) and (3.29) are δ = a , δ = a , δ = a , δ = a (3.32) 11 3 12 4 21 4 22 − 3 A = cos β, A = sin β, B = sin β, B = cos β 1 2 − 1 2 C = sin β, C = cos α, D = cos α, D = sin α (3.33) 1 2 1 2 − where α denotes the Higgs mixing angle, and tan β = v2/v1, where v1 and v2 are the vacuum expectation values of the two Higgses. α, β and Higgs mass, MH , are related by the following equations. 1 1 1 k 2 1 + k 2 sin α = − , cos α = (3.34) − 2 − 2 where c2 + r2 2r M 2 k = c − , c = cos 2β, r = H (3.35) c + r2 2rc M 2 − Z The cross section of the elastic neutralino(χ)-nucleon scattering is given by σ N N 2 (3.36) χ−N ∝ |h |Leff | i| q X where N is a wave function of the nucleus. | i 3.3.2 Cross Section The neutralino(χ)-nucleus cross section at zero momentum transfer is expressed as 2 2 σχ−N = 4 GF µχ−N CN (3.37) −5 −2 3 where GF = 1.66 10 GeV (¯hc) is the Fermi coupling constant, µχ−N is the × −2 −2 reduced mass of the neutralino (Mχ GeVc ) and the target nucleus(MN GeVc ),

MχMN µχ−N = (3.38) Mχ + MN

CN is a dimensionless number referred to as the enhancement factor that carries all the particle physics model information. CN is expressed by the sum of SI and SD terms. SI SD CN = CN + CN (3.39) SI SD In the following sections, CN and CN valuesare discussed for various nuclei. Since σχ−N can be expressed as 2 2 µχ−N CN µχ−N CN σχ−N = σχ−p 2 = σχ−n 2 (3.40) µp Cp µn Cn SI with the enhancement factor of proton Cp and neutron Cn. Here CN = CN + SD CN , and σχ−p and σχ−n are neutralino(χ)-proton and neutralino(χ)-neutron cross sections, respectively.

26 3.3.3 Spin-Independent (SI) Interactions The enhancement factor of the SI cross section is written as [40],

2 SI 1 (p) (n) CN = 2 zf + (A Z) f (3.41) π GF − h i where A is the mass number and Z is the atomic number. f (p) and f (n) are the neutralino(χ)-nucleon spin-independent couplings. They are written as the (p) (n) neutralino(χ)-quark spin-independent couplings, fTq and fTq , summed over the quarks that comprise the nucleon,

(p) f (p) α3q 2 (p) α3q = fTq + fT G (3.42) Mp Mq 27 Mq q=Xu,d,s q=Xc,b,t (n) f (n) α3q 2 (n) α3q = fTq + fT G (3.43) Mn Mq 27 Mq q=Xu,d,s q=Xc,b,t

where Mq is the quark mass, Mp and Mn are the proton and neutron masses, (p) (n) respectively. Parameters fTq and fTq are determined by the information of (p) quark mass ratio and chiral symmetry applied to baryons. The values of fTq (n) and fTq are as follows,

f (p) = 0.020 0.004, f (p) = 0.026 0.005, f (p) = 0.118 0.062 Tu Td Ts f (n) = 0.014 0.003, f (n) = 0.036 0.008, f (n) = 0.118 0.062(3.44) Tu Td Ts while

f (p) = 1 f (p) T G − Tq q=Xu,d,s f (n) = 1 f (n) (3.45) T G − Tq q=Xu,d,s In most case, f (p) f (n), therefore CSI A2 from Eq.(3.41), Tq ' Tq N ∝ SI SI CN CN 2 SI = SI = A (3.46) Cp Cn

is a practical estimation. Eq.(3.40) and Eq.(3.46) give

2 SI SI µχ−p 1 σχ−p = σχ−N 2 2 (3.47) µχ−N A

SI SI Eq.(3.47) can be used for the conversion of the obtained σχ−N into σχ−p. Eq.(3.47) indicates that materials with large A values are eﬀective for SI- interacting neutralino detection. Expected spectra in natural xenon for SI- interacting neutralinos are shown in Fig. 3.1.

27 -1 10

-2 10 counts/day/kg/keV -3 10

-4 10

-5 10

-6 10

0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.1: Expected recoil spectra in natural xenon for SI-interacting neutrali- −2 −2 −2 SI −6 nos (Mχ = 50 GeV c , 100 GeV c and 200 GeV c ) where σχ−p = 10 −2 −3 −1 pb is assumed. Here we take ρD = 0.3 GeV c cm , v0 = 220 km s , −1 −1 vE = 244 km s and vesc = 450 km s .

3.3.4 Spin-Dependent (SD) Interactions The enhancement factor of the SD cross section is written as [40],

8 2 J + 1 CSD = a S + a S (3.48) N π p p(N) n n(N) J where Sp(N) and Sn(N) are the expectation values of the proton and neutron spin in the nucleus N, a and a are the neutralino(χ)-nucleon spin dependent p n couplings, and J is the total spin of nucleus. ap and an are expressed as

α2q (p) ap = ∆q (3.49) √2GF q=Xu,d,s α2q (n) an = ∆q (3.50) √2GF q=Xu,d,s (p) (n) where the ∆q and ∆q are the quark spin contents of the nucleon, and are calculated as [40]

∆(p) = 0.78 0.02, ∆(p) = 0.48 0.02, ∆(p) = 0.15 0.02. (3.51) u d − s −

28 In the case of the neutron,

(n) (p) (n) (p) (n) (p) ∆u = ∆d , ∆d = ∆u , ∆s = ∆s (3.52) Eq. (3.48) is written as 8 CSD = λ2J(J + 1) (3.53) N π where 1 λ a S + a S (3.54) ≡ J p p(N) n n(N) λ is referred to as the Land´e factor. λ2 J(J + 1) values calculated on the basis of the odd group model for various nuclei are listed in Table 3.1. Eq. (3.40), (3.53) and Table 3.1 give

2 SD SD µχ−p 0.75 σχ−p = σχ−N 2 2 . (3.55) µχ−N λ J(J + 1)

SD SD Eq. (3.55) can be used for the conversion of the obtained σχ−N into σχ−p.

unpaired proton Isotpe J Abundance (%) λ2J(J + 1) 1H 1/2 100 0.750 7Li 3/2 92.5 0.244 19F 1/2 100 0.647 23Na 3/2 100 0.041 127I 5/2 100 0.007 133Cs 7/2 100 0.052

unpaired neutron Isotpe J Abundance (%) λ2J(J + 1) 3He 1/2 1.3 10−4 0.928 × 29Si 1/2 4.7 0.063 73Ge 9/2 7.8 0.065 129Xe 1/2 26.4 0.124 131Xe 3/2 21.2 0.055 183W 1/2 14.3 0.003

Table 3.1: Values of λ2J(J + 1) calculated on the basis of the odd group model for various nuclei [41].

Expected spectra in natural xenon for SD-interacting neutralinos are shown in Fig. 3.2. As a “model independent” analysis, the cases of pure proton coupling (an = 0) and pure neutron coupling (ap = 0) are also checked to interpret the experimental results in terms of spin-dependent interactions. λ2 J(J + 1) values calculated in the cases of pure proton coupling and pure neutron coupling for various nuclei are listed in Table 3.2 and Table 3.3.

29 -1 10

-2 10 counts/day/kg/keV -3 10

-4 10

-5 10

-6 10

0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.2: Expected recoil spectra in natural xenon for SD-interacting neutrali- −2 −2 −2 SD nos (Mχ = 50GeV c , 100 GeV c and 200 GeV c ) where σχ−p = 0.1 pb −2 −3 and the odd group model are assumed. Here we take ρD = 0.3 GeV c cm , −1 −1 −1 v0 = 220km s , vE = 244km s and vesc = 450 km s .

3.4 F 2, Nuclear Form Factor Correction

1/2 When the wavelength, h/q, with momentum transfer q = (2 MN ER) is no longer large compared to the nuclear radius, the effective cross section begins to fall with increasing q. Here h is the Planck constant. This effect is represented by a form factor, F , which is a function of the dimensionless quantity, q rn, where rn is an effective nuclear radius. The neutralino(χ)-nucleus cross section at zero momentum transfer, σχ−N , is corrected with this form factor as

2 σ (q rn) = σχ−N F (q rn) (3.56)

In the ﬁrst Born (plane wave) approximation, the nuclear form factor can be deﬁned as a Fourier transformation of ρ(r), the density distribution of ‘scattering centers’

F (q r ) = ρ(r) exp (iq r) dr (3.57) n · Z

30 unpaired proton Isotpe J Abundance (%) λ2J(J + 1) 19F 1/2 100 0.583 23Na 3/2 100 0.103 127I 5/2 100 0.133

unpaired neutron Isotpe J Abundance (%) λ2J(J + 1) 29Si 1/2 4.7 0.000012 73Ge 9/2 7.8 0.0011 129Xe 1/2 26.4 0.0024 131Xe 3/2 21.2 0.00014

Table 3.2: Values of λ2J(J + 1) calculated in the case of pure proton coupling for various nuclei [42].

unpaired proton Isotpe J Abundance (%) λ2J(J + 1) 19F 1/2 100 0.036 23Na 3/2 100 0.00067 127I 5/2 100 7.87

unpaired neutron Isotpe J Abundance (%) λ2J(J + 1) 29Si 1/2 4.7 0.051 73Ge 9/2 7.8 0.175 129Xe 1/2 26.4 0.385 131Xe 3/2 21.2 0.086

Table 3.3: Values of λ2J(J + 1) calculated in the case of pure neutron coupling for various nuclei [42].

For small momentum transfer (qrn < 2), a commonly used approximation is

2 2 (q rn) F (q rn) = exp (3.58) − 3 !

More precise studies have been done for spin-independent and spin-dependent interactions as follows. For spin-independent interactions, the form factor is written as[37],

j (q r ) 2 F 2 (q r ) = 3 1 n exp (q s)2 (3.59) n q r − n 2 1/3 where j1(x) = [sin(x) x cos(x)] /x , rn 1.14 A fm and s 0.9 fm represents the nuclear skin−thickness. ' ' Values of the form factor as a function of recoil energy for SI interactions

31 are shown in Fig. 3.3. Expected spectra in natural xenon for SI-interacting neutralinos with F 2, the nuclear form factor correction, are shown in Fig. 3.4. 2 F 1

-1 10

-2 10

-3 10

-4 10

-5 10 0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.3: Values of the form factor as a function of recoil energy for SI interactions.

For spin-dependent interactions, if the odd group model is assumed, the form factor is approximated by the Bessel function partially ﬁlled with a constant value [37],

j2 (q r ) (q r < 2.55, q r > 4.5) F 2 (q r ) = 0 n n n (3.60) n 0.047 (constant) (2.55 < q r < 4.5) n 1 3 where j0(x) = sin(x)/x and rn 1.0A fm. Values of the form factor as'a function of recoil energy for SD interactions are shown in Fig. 3.5. Expected spectra in natural xenon for SD-interacting neutralinos with the F 2, nuclear form factor correction, are shown in Fig. 3.6.

3.5 Detector response correction

3.5.1 fQ, Quenching factor correction For scintillation detectors calibrated with γ-ray sources, the apparent observed nuclear recoil energy is less than the true value; the ratio, the quenching factor,

32 -1 10

-2 10 counts/day/kg/keV -3 10

-4 10

-5 10

-6 10

0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.4: Expected recoil spectra in natural xenon for SI-interacting neu- −2 −2 −2 2 tralinos (Mχ = 50 GeV c , 100 GeV c and 200 GeV c ) with F , the SI −6 nuclear form factor correction, where σχ−p = 10 pb is assumed. Here −2 −3 −1 −1 we take ρD = 0.3 GeV c cm , v0 = 220 km s , vE = 244 km s and −1 vesc = 450 km s .

fQ, is determined by neutron scattering measurements. Experimenters prefer to work with γ-calibrated energies for easy identiﬁcation of background γ rays, so the recoil energy, ER, in the above spectra should be replaced by the visible energy Ev, using ER = Ev/fQ. While fQ for scintillation detectors might vary with ER, measurements so far show no evidence of signiﬁcant energy dependence. Neutron scattering measurements give fQ 0.2 for natural xenon [43] and 0.3, 0.08 respectively for Na and I in NaI(Tl)∼[44], over substantial energy ranges. The quenching factor, fQ, for various targets are listed in Table 3.4. In this thesis, we use fQ = 0.2 for natural xenon.

3.5.2 Combining results Expected spectra in natural xenon for SI-interacting neutralinos with F 2 and fQ corrections are shown in Fig. 3.7. Expected spectra in natural xenon for SD-interacting neutralinos with F 2 and fQ corrections are shown in Fig. 3.8.

33 2 F 1

-1 10

-2 10

-3 10

-4 10

-5 10 0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.5: Values of the form factor as a function of recoil energy for SD interactions.

Target Nucleus fQ Xe Xe 0.2 [43] NaI(Tl) Na 0.3 [44] I 0.08 [44] Ge Ge 0.25 [45]

Table 3.4: The quenching factor, fQ, for various targets

34 -1 10

-2 10 counts/day/kg/keV -3 10

-4 10

-5 10

-6 10

0 100 200 300 400 500 600 recoil enegy[keV]

Figure 3.6: Expected recoil spectra in natural xenon for SD-interacting neutrali- −2 −2 −2 2 nos (Mχ = 50GeV c , 100 GeV c and 200 GeV c ) with F , the nuclear form SD factor correction, where σχ−p = 0.1 pb and the odd group model are assumed. −2 −3 −1 −1 Here we take ρD = 0.3 GeV c cm , v0 = 220km s , vE = 244km s and −1 vesc = 450 km s .

35 1

-1 10

-2 counts/day/kg/keV 10

-3 10

-4 10

-5 10

-6 10 0 10 20 30 40 50 60 70 80 visible enegy[keV]

Figure 3.7: Expected visible energy spectra in natural xenon for SI-interacting −2 −2 −2 2 neutralinos (Mχ = 50 GeV c , 100 GeV c and 200 GeV c ) with F and SI −6 fQ corrections, where σχ−p = 10 pb is assumed. Here we take ρD = −2 −3 −1 −1 −1 0.3 GeV c cm , v0 = 220 km s , vE = 244 km s and vesc = 450 km s .

36 1

-1 10

-2 counts/day/kg/keV 10

-3 10

-4 10

-5 10

-6 10 0 10 20 30 40 50 60 70 80 visible enegy[keV]

Figure 3.8: Expected visible energy spectra in natural xenon for SD-interacting −2 −2 −2 2 neutralinos (Mχ = 50GeV c , 100 GeV c and 200 GeV c ) with F and SD fQ corrections, where σχ−p = 0.1 pb and the odd group model are assumed. −2 −3 −1 −1 Here we take ρD = 0.3 GeV c cm , v0 = 220km s , vE = 244km s and −1 vesc = 450 km s .

37 Chapter 4

Properties of liquid xenon

4.1 Physical properties of liquid xenon

The physical properties of liquid xenon are summarized in Table 4.1, and the isotopic composition of natural xenon is shown in Table 4.2.

4.2 Scintillation mechanism and properties

Due to interactions of charged particles in liquid xenon, the orbital electron may be lifted to a higher-level shell within the atom, excitation, or completely removed from the atom, ionization. The excitation states of electrons return to the ground state by emitting a photon, which gives scintillation light. The recombination of electron and ion pairs from ionization processes will also produce excitation states and further emit photons. The two processes can be illustrated as following [50]. Fast components

Xe∗ + Xe Xe∗ → 2 Xe∗ 2 Xe + hν (4.1) 2 → Slow components

Xe+ + Xe Xe+ → 2 Xe+ + e− Xe∗∗ + Xe 2 →

Property Value Condition Reference Atomic number 54 Mass number 131.29 [47] Boiling point 165.1 K 1 atm [47] Melting point 161.4 K 1 atm [47] Density 2.96 g/cm3 (liquid phase) 161.5 K [48] Radiation length 28.7 mm (liquid phase) [49]

Table 4.1: Physical properties of liquid xenon.

38 Isotope Abundance (%) Spin 124Xe 0.096 0 126Xe 0.090 0 128Xe 1.92 0 129Xe 26.44 1/2 130Xe 4.08 0 131Xe 21.18 1/2 132Xe 26.89 0 134Xe 10.44 0 136Xe 8.87 0

Table 4.2: Isotopic composition of natural xenon [58]. 129Xe and 131Xe have non-zero spin, so these nuclei can interact Spin-Dependently with neutralino.

Xe∗∗ Xe∗ + heat → Xe∗ + Xe Xe∗ → 2 Xe∗ 2 Xe + hν (4.2) 2 → The scintillation properties of liquid xenon are summarized in Table 4.3. The relation between the Rayleigh scattering length and the refractive index of liquid xenon is shown in Fig. 4.1.

4.3 LET dependence of scintillation yield

Scintillation yields (scintillation intensity per unit absorbed energy) in liquid xenon for ionizing particles are expressed as a function of the linear energy transfer (LET) for the particles [60]. The reduction in scintillation yield in the low LET region shown in Fig. 4.2 is explained as follows. According to the Onsager theory, when an electron produced by an ionizing particle is slowed down to thermal energy within the Onsager radius from the parent ion, the electron cannot escape from the influence of the parent ion, and the electron- ion pair recombines. Strictly speaking, the escape probability of the electron at the Onsager radius, where the Coulomb energy is equal to the thermal energy, is e−1. Conversely, an electron thermalized outside the Onsager radius should be free from the influence of the parent ion even if the external electric field may be nil. The electron thermalization range is estimated to be 4000-5000 nm for liquid xenon; they are beyond the Onsager radius (49 nm for liquid xenon). Therefore, it is reasonable to surmise that there exist a large number of electrons that will not recombine with the parent ion for an extended period of time (>ms) in the absence of an electric field. Such electrons will cause a reduction in scintillation in the low LET region. The Onsager theory falls short of thoroughly explaining the recombination process between electrons and ions in liquid xenon, due to the fact that the mean interval of electron-ion pairs produced by a minimum ionizing particle is approximately 100 nm, a value comparable to the Onsager radius itself in liquid xenon. In order to explore the subject matter further, a “volume recombination”, i.e., electron recombination with ions other than the parent ion, should be taken into consideration. Assuming such a volume

39 Property Value Condition Reference Peak emission wavelength 178 nm [51][52]

Spectral width (FWHM) 14 nm [51][52] ∼ Scint. Absorption length 100 cm [57] ≥ Rayleigh scattering length 60 cm n = 1.61 [58] ∼ xe Refractive index 1.61 0.1 (177 5) nm [59] Property Value Particle Reference Energy per scint. photon (23.7 2.4) eV electrons [53] 14.2 eV electrons [54] 12.5 eV, 12.7 eV electrons [54]

(19.6 2.0) eV α particles [53] (16.3 0.3) eV α particles [56] Decay time (Slow components) 45 ns electrons, γ rays [53]

Decay time (Fast components) 4.2 ns α particles [53] Decay time (Slow components) 22 ns α particles [53]

Table 4.3: Scintillation properties of liquid xenon.

Figure 4.1: Relation between the Rayleigh scattering length and the refractive index of liquid xenon [58].

40 Figure 4.2: Dependence of scintillation yield on LET in liquid xenon [60]. Solid circles represent yields for relativistic heavy particles whereas open circles represent those for electrons, alpha particles and ﬁssion fragments. Open squares represent γ-ray data. Solid curves are obtained from Eq. 4.3 by using seven values within the η0 range of 0.0-0.6. recombination, the scintillation intensity per unit absorbed energy, dL/dE, is given by the following equation,

dL/dE = [A(dE/dx)/(1 + B(dE/dx))] + η0 (4.3) where dL/dE is normalized to the scintillation yield at the flat top level, that is, in the limiting case of dE/dx , Eq. (4.3) becomes A/B + η = 1. A, B and → ∞ 0 η0 are adjustable parameters, and η0 is the scintillation yield at zero electric field in the limit of zero LET. In this thesis, the following value manifesting the best fit in Fig. 4.2 is used as η0 for liquid xenon.

η0 = 0. (4.4)

4.4 Quenching factor of liquid xenon

The scintillation efficiency of liquid xenon for nuclear recoils is different from that for electron recoils. The relative scintillation efficiency of nuclear recoils to electron recoils is called the quenching factor, fQ. The nuclear recoil energy, ER, is converted into visible energy, EV , with fQ as follows:

EV = fQ ER. (4.5) The quenching factor of liquid xenon was measured by some groups, and the results are listed in Table 4.4.

41 fQ 0.2 [43] 0.22 0.01 [61] 0.45 0.12 [62]

Table 4.4: Quenching factor of liquid xenon.

In this thesis, the smallest quenching factor in Table 4.4 , fQ = 0.2, is used for the following analysis to derive the constraint on the neutralino-nucleus cross section conservatively.

42 Chapter 5

Single phase liquid xenon detector for Dark Matter search

Experiments using pure scintillation light in liquid xenon detectors use one phase (liquid) as the working medium, we refer them as “single phase detectors.” We are developing a single phase liquid xenon detector for the purpose of the direct detection of WIMPs.

5.1 Advantages of liquid xenon for dark matter search

We select liquid xenon as a target of WIMPs because of its advantages. The advantages of liquid xenon are as follows,

1. Atomic number is large(Z = 54). Because of the large atomic number of xenon (Z = 54), γ rays are strongly attenuated in a short distance near the surface of the xenon volume, al- lowing us to make a low background environment at the center of the detector for a dark matter search. This self-shielding power of xenon for γ-ray backgrounds is the key idea of our liquid xenon detector. Fig. 5.1 shows attenuation coeﬃcients of γ rays in xenon. 2. Scintillation light yield is high ( 42, 000 photons/MeV). As mentioned in Chapter 3, the event rate∼ of dark matter rapidly increases by lowering the energy threshold. The light yield of liquid xenon is 42, 000 photons/MeV. It is similar to the high light yield inorganic scin∼tillator, NaI(Tl), so we can set a low energy threshold and achieve good sensitivity for the dark matter search. 3. Wavelength of scintillation light is relatively long. The peak wavelength of xenon scintillation light is 178 nm [51]. This is longer than other rare gas scintillators (Ar 128 nm), so the scintillation ∼

43 2

Total Attenuation

Photoelectric Absorption Attenuation Coefficients [cm / g]

Scattering Pair Production

Photon Energy [MeV]

Figure 5.1: Attenuation coeﬃcients of γ rays in xenon [46].

light of xenon can be directly detected by photomultipliers without using wavelength shifter. 4. Liquid and gas phase are available, which is good for purification. Xenon can be handled both in liquid and in gas phase, so it can be circu- lated and purified during operation. Fig. 5.2 shows the phase diagram of xenon. The purification of xenon will be described in Section 6.2.1.

5.2 Features to be conﬁrmed

The following features of liquid xenon must be checked in order to conﬁrm the feasibility of achieving the target sensitivity to the WIMP search with a large scale single phase detector: Self-shielding power of liquid xenon for γ-ray backgrounds. • Scintillation light yield. • Absorption length of liquid xenon. • These features of liquid xenon were measured with a single phase prototype detector, and the feasibility of achieving the target sensitivity of a single phase

44 2 10

liquid 10

solid gas 1 Pressure [atm. absolute]

−1 10

120 140 160 180 200 220 240 260 Temperature [K]

Figure 5.2: Phase diagram of xenon.

detector with 800 kg of liquid xenon was confirmed with these results as shown in Chapter 7. Radioactive impurities inside xenon must be reduced by distillation or other purification techniques, because backgrounds from these impurities cannot be removed by selecting an inner fiducial volume. Backgrounds from these radioactive impurities inside xenon were measured with the prototype detector, and purification systems of the 800-kg liquid xenon detector were designed as discussed in Section 9.2.

45 Chapter 6

Prototype detector

A prototype detector was developed to check the feasibility of a single phase detector for a dark matter search experiment as discussed in Chapter 7. This prototype was not optimized for a dark matter search because of its small photo coverage, large dead angle from PMTs and small self-shielding volume. In this chapter, the detector setup and low background techniques of the prototype detector are described.

6.1 Detector setup 6.1.1 Underground laboratory at Kamioka mine The laboratory for this dark matter search experiment is placed at Mozumi Mining and Smelting Co. located in Kamioka-cho Gifu, Japan. The laboratory is at a depth of 2700 m.w.e (meters water equivalent) and the muon flux is reduced by about five orders of magnitude compared to a surface laboratory. The neutron flux is also smaller than a surface laboratory by more than two orders of magnitude. However, the radon concentration in the mine air is rather high and since we have a seasonal change according to the direction of the wind in the mine tunnel, it must be shielded as discussed in Section 6.2.3. Typical environmental background sources at this Kamioka Observatory are shown in Table 6.1.

Surface Kamioka Observatory µ [cm−2 s−1][63] 1.1 10−2 10−7 × ∼ Thermal neutron [cm−2 s−1] 1.4 10−3 [64] 8.3 10−6 [65] Non-thermal neutron [cm−2 s−1] 1.2× 10−2[64] 1.2 × 10−5 [65] × × Rn [Bq/m3] (Summer) [66] 40 1200 Rn [Bq/m3] (Winter) [66] 40 40 γ(> 500keV ) [67] - 0.71 /cm2/s

Table 6.1: Typical environmental background sources at Kamioka Observatory

46 6.1.2 Low background PMTs We developed a low background PMT, R8778ASSY with Hamamatsu Photonics. Pictures and a technical drawing of the PMT are shown in Fig. 6.1 and Fig. 6.2.

Figure 6.1: Pictures of R8778ASSY.

Figure 6.2: Technical drawing of R8778ASSY.

The PMT has high quantum eﬃciency, 25 % for 178 nm photons. The quantum eﬃciency as a function of the wavelength∼ of the incident photon was measured by Hamamatsu Photonics and is shown in Fig. 6.3. Elements of the PMT were selected by HPGe detector measurements to reduce radioactive components [68]. Table 6.2 shows the content of radioactive impurity in it measured by the HPGe detector.

6.1.3 Radiation shields As the expected count rate caused by neutralinos is extremely low, radiation shields are inevitable for dark mater search experiments. We have adopted a

47 Quantum efficiency(%)

Wave length(nm)

Figure 6.3: Quantum eﬃciency of R8778ASSY as a function of the wavelength of incident photons.

U (mBq/PMT) Th (mBq/PMT) K (mBq/PMT) 60Co (mBq/PMT) R8778ASSY 18( 2) 6.9( 1.3) 140( 20) 5.5( 0.9)

Table 6.2: Radioactive impurity in R8778ASSY measured by HPGe detector. set of shields as listed in Table 6.3. The polyethylene shield and the boric acid shield act as a neutron moderator and absorber. The lead shield acts as the shield against the environmental γ rays. The EVOH sheet with radon free air purges radon gas from the inside of the shield. Details of the radon purge are described in Subsection 6.2.3. The OFHC copper shield acts as a shield against bremsstrahlung γ rays from the lead shield. The inner shield is made of OFHC copper and is set near the PMTs to shield γ rays from PMTs. Pictures of the radiation shields are shown in Fig. 6.4 and 6.5.

6.1.4 Prototype detector The prototype detector is a cubic vessel of liquid xenon made with OFHC copper, and the inner volume of it is 27000 cm3 with reﬂectors on the wall. Nine PMTs are attached on each face of the vessel, and scintillation photons are detected by a total of 54 PMTs through MgF2 windows. The absorption length of the MgF2 window for the scintillation light of liquid xenon is 14.63 cm. A

48 Outer shields material thickness purpose polyethylene 15 cm fast neutron moderator boric acid 5 cm thermal neutron capture lead 15 cm environmental γ rays EVOH sheet - Radon free air purge OFHC copper 5 cm γ rays from lead shield (bremsstrahlung)

Inner shields Inner OFHC copper shield 6.7 cm γ rays from PMTs

Table 6.3: Material of the radiation shields. Listed from the outside. schematic view and pictures of the prototype detector are shown in Fig. 6.6 and 6.7. Gaps between the 54 PMTs and the MgF2 windows were ﬁlled with a high refractive index material,“Krytox 16350” manufactured by DuPont, and we suc- ceeded in increasing the photoelectron yield of the prototype detector by reducing total reﬂections at vacuum.

6.1.5 Gas line The schematic diagram of the gas line is shown in Fig. 6.8. For safe operation, electromagnetic valves and rupture disks are installed in the gas line. If the pressure of xenon exceeds the threshold pressure, 0.18 MPaG (Gauge pressure), the pass for the reservoir tank is automatically opened by opening the electromagnetic valve. After that, xenon is safely collected in the reservoir tank without breaking the detector. The detector and the gas line were evacuated and baked for 2 weeks at a temperature about 373 K. The degas rate inside the detector and the gas line after baking was on the order of 10−5 Pa/second at room temperature. Xenon gas was passed through the SAES getter before ﬁlling the detector to remove impurities. The guaranteed performance of the SAES getter is listed in Table 6.4. The attenuation length of scintillation light in liquid xenon becomes shorter with these impurities, so these have to be removed. The radioactive impurity, Kr, cannot be removed with the SAES getter, so it was removed by a distillation tower before operation. As for the distillation tower, it will be discussed in Section 6.2.1.

Impurities H2O O2 CO CO2 N2 H2 CH4 Out gas <1 ppb <1 ppb <1 ppb <1 ppb <1 ppb <1 ppb <1 ppb

Table 6.4: Guaranteed performance of SAES getter.

A GM refrigerator was used to liquify the xenon. The temperature of the detector was kept at 173K by the refrigerator inside the vacuum chamber for insulation. The pressure inside the vacuum chamber changed from 10−1 to 10−3 Pa depending upon the temperature of the detector from room temperature to

49 Figure 6.4: Outer radiation shield.

173K. We could handle the xenon safely because xenon never becomes solid at 173 K as shown in Fig. 5.2. The rate of xenon introduction and collection was measured by a ﬂow meter attached in the gas line. The ﬂow rate is adjusted to 10 L/min (Introducing) and 15 L/min (Collecting).

6.1.6 Data Acquisition System The block diagram of the data acquisition system is shown in Fig. 6.9. The output signal from each PMT was divided into 4 outputs by a Lin- ear Fan-Out, and each output was fed into leading edge discriminator modules (VME standard), charge ADC modules (VME standard), 250 MHz FADC modules (VME standard) and 500 MHz FADC modules (VME standard). The output for the discriminator was amplified by a factor of 8. When the nominal gain of the 54 PMTs was 8.25 106, the threshold level of the discriminator was set to 0.25 p.e. Hit timing of×each PMT was recorded by TDC modules (TKO standard). The detector trigger required the coincidence of at least three hits within 95 ns. Trigger timing and veto timing were recorded by a TRG(TRiGger) module (VME standard). The live time of the measurement was calculated from the TRG information. The 250 MHz and 500MHz FADC modules have 2 and 12 input channels, respectively, so the outputs from the 54 PMTs are summed up with a Sum Amplifier before the FADC. Some of the outputs of the FADC were amplified by a factor of 8 to measure the pulse shape of the 1 p.e. signal. This data acquisition system was able to to measure the following delayed

50 Figure 6.5: Inner radiation shield

coincidence signal from radioactive impurities in xenon.

214Bi 214Po 210Pb (U-chain) → → 212Bi 212Po 208Pb (Th-chain) → → 85Kr 85Rb∗ 85Rb (Kr) → → The details of the analysis of the internal background measurements are discussed in Section 9.2.

6.2 Techniques for low background measurement 6.2.1 Distillation of xenon Commercial xenon includes krypton as an impurity. The β decay of 85Kr is one of the sources in the low energy region, hence it has to be removed from xenon for dark matter searches. A distillation system was developed for this purpose. A drawing of the distillation system is shown in Fig.6.10. The diﬀerence of the boiling points between xenon and krypton was used to remove the krypton (i.e., the distillation method). The boiling points of xenon and impurities are listed in Table 6.5. He, H2, N2 and O2 are removed with krypton during the distillation. CO2 and H2O are removed by the SAES Getter before the distillation. The 100 kg of xenon gas for the dark matter search was processed with 1.7 liters/minute before the operation. It took about 8 days to process all of the xenon gas. The krypton concentration in the processed xenon gas was measured by a gas chromatography and photoionization detector, and it was conﬁrmed

51 Figure 6.6: Schematic view of prototype detector. The cubic vessel of liquid xenon is made with OFHC copper, and the inner volume of it is 27000 cm3 with reﬂectors on the wall. Nine PMTs are attached on each face of the vessel, and scintillation photons are detected by a total of 54 PMTs through MgF2 windows. that the krypton concentration was reduced by about 3 orders of magnitude from Kr/Xe=3 ppb to 3.3 1.1 ppt. The detailed descriptionof the distillation is in [69].

6.2.2 Material selection and chemical etching of the re- ﬂector Substrates of the reﬂectors were made with 6N (>99.9999%) copper manufactured by MITSUBISHI MATERIAL Co. We etched surface of it with the following mixing solution. H SO (TAMAPURE-AA-10) : 6.9 % • 2 4 H O (TAMAPURE-AA-100) : 2.5 % • 2 2 H O (Ultra pure water of Super-Kamiokande) : 90.6 % • 2 TAMAPURE-AA-10 and 100 are manufactured by TAMA CHEMICALS Co., and each metallic impurity level is guaranteed to be 10 and 100 ppt or less. The

52 Figure 6.7: Pictures of the prototype detector. Reﬂectors are attached on the inner wall of the cubic vessel (left picture). Nine PMTs are attached on each face of the vessel, and scintillation photons are detected by a total of 54 PMTs (right picture).

He H2 N2 O2 Kr Xe CO2 H2O Boiling point (K) 4 33 77 90 120 165 194 273

Table 6.5: Boiling points of xenon and the impurities. etching was performed with PFA vat and PFA tweezers as shown in Fig 6.11. The depth of the etching was 10 - 20 µm. Pictures of the copper substrates before and after the etching are∼shown in Fig 6.12, and the luster of the copper is lost by the etching. After the etching, the substrates were washed twice with ultra pure water and dried with nitrogen gas to prevent oxidation, then they were wrapped with EVOH sheet in order not to be contaminated by radioactivity like 210Pb which is a daughter of 222Rn (222Rn cannot pass through EVOH sheet as discussed in Section 6.2.3). After the etching, 5N (> 99.999%) aluminum and 4N (> 99.99%) MgF2 were evaporated on the surface of the substrates as a mirror for the scintillation light of liquid xenon. Reﬂectance of this mirror was measured with the prototype detector as discussed in Section 7.5.

6.2.3 Radon purge The mine air contains 222Rn gas that is radioactive and could be a background source. The detector system was shielded by two layers of 222Rn shield. Outer and inner layers were the laboratory atmosphere and the atmosphere inside the radiation shield ﬁlled with the air from outside of the mine which was fed into a radon free air generator to remove still remaining 222Rn gas in it. The atmosphere inside the radiation shield was separated from the laboratory atmosphere with EVOH sheet which 222Rn gas cannot pass through. 222Rn concentration of the laboratory atmosphere and the atmosphere inside the radiation shield were monitored throughout the measurement, and these

53 3 9m VI-23 VI-7 collection tank VO-2 VI-16 VI-25 GM VI-22evac.

VI-24 refrigerator

VI-15 P4 VO-1

F2 VI-14 VI-21 evac. evac.

R-1 VI-8 VO-6 VI-1 VI-2 PO-2 VI-27 F1 VI-20 0.16-0.14MPa VO-4 VO-3 VI-26 VI-13 VI-17 PO-1 V1 RD-3 evac. 0.18- Xe bottle VI-6 0.20MPa Vacuum for insulation

VO-10 Ex Out SAES getter evac. VI-3 VI-5 P2 In VI-4 P3 evac. Detector VI-19 PO-3 30liter VI-18 VO-8 buffer tank VO-7 V2 PO-4 Emergency collection bottle Operation pressure: <0.1MPa Operation temperature: 173K VI-12 V2 Density @ 173K: 2.88g/cc

VI-11, VI-27 evac. VI-28 Normally closed Pneumatic valves VI-11VI-10 VI-9 VI-28 Check valve Vacuum for insulation >0.1Pa -> VI-11 open

Figure 6.8: Schematic diagram of Gas line of xenon.

were between 1 and 10 Bq/m3 and less than 0.2 Bq/m3, respectively.

54 FADC(500MHz, 12ch) Sum Amp Gate Generator Amp (x8) Input Stop Output Input

Delay Delay Cable ADC(64ch) (VME) (200ns delay) 54 PMTs Input PMT Gate

Attenuator PMT Sum Amp FADC(250MHz, 2ch) Input Output (VME) Hit timing of 54 PMTs Input Start Discriminator Amp (x8) I/O Registrer (VME) (NIM) (VME) Amp Gate Generator Coincidence Output Output Input Ch.2 TRG(VME) Data Ch.3 Input Pedestal Trig. tim. (Data) Ch.0 Ch.7 Clock Generator Output Trig. tim. Ch.1 (Pedestal) LED Trig. tim. Ch.3 (LED) Clock Generator Gate Generator Output Input Output Veto

Veto Veto for Data reading Veto Veto for AD Conv. (11µ s ) Veto for Data reading Veto for Gate Generator AD Conv. Gate Generator Output Input Veto for Stop Input Output (10µ s ) AD Conv. Latch Output Input I/O Registrer I/O Registrer (VME) Gate Generator (VME) Output Output Veto Input Input Data is BG mode Ch.4 Ch.1 ready Coincidence Ch.5 Level Adaptor For Output NIM TTL Mode select Ch.1 (COMPL) & Data ready signal TTL NIM Data reading (NORM) is finished Source mode

TDC (TKO) Gate Generator For TDC Gate Reset Output Veto Input

Gate Generator Gate 3 Latch Gate Generator Output Input Output Stop Input Output Input Veto for Gate 2 next trigger (1µs ) Gate Generator Input Input Output

Figure 6.9: Block diagram of Data Acquisition System

55 DV1 VO2 VO1 V1 V4 DV2 V11 V2 PI1

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Figure 6.10: Distillation system to remove krypton from xenon.

Figure 6.11: Pictures of chemical etching. Surface of copper substrate was etched with the mixing solution (6.9 % of H2SO4, 2.5 % of H2O2 and 90.6 % of H O). The depth of the etching is 10 - 20 µm. 2 ∼

56 Figure 6.12: Pictures of the copper substrate before (left) and after (right) the chemical etching. The luster of the copper is lost by etching.

57 Chapter 7

Performance of the prototype detector

7.1 Calibration

Calibration of the prototype detector was carried out by irradiation with γ rays and neutrons listed in Table 7.1 and 7.2. γ-ray calibration data was used to measure the absorption length and light yield of liquid xenon (described in Section 7.5), and to check the self-shielding power, vertex and energy resolution (described in Sections 7.8 and 7.9). Trigger and event selection eﬃciency for the dark matter search is discussed using neutron calibration data (described in Section 7.11).

source γ-ray energy [keV] 131mXe (Neutron activation) 164 137Cs 662 60Co 1173 1333 40K 1461 208Tl 2615

Table 7.1: γ-ray sources used for the calibration.

source particle per Am decay 241 −5 95 Am/Be 6 10 neutrons (4-8MeV) ×4 10−5 γ’s (4.43MeV) ×

Table 7.2: Neutron sources used for the calibration.

58 7.2 Notations for analysis 7.2.1 PMT number The PMT number for each of the 54 PMTs is deﬁned as shown in Fig. 7.1. This number is used for the following analysis.

Figure 7.1: PMT number of prototype detector.

7.2.2 Source location Hole A, B, C : Holes in the radiation shield for γ-ray collimation. The γ rays are collimated by the holes (Hole A, B, C) in the radiation shield as shown in Fig. 7.2.

Hole S : γ-ray collimator inside the radiation shield. The location of the γ-ray collimator inside the radiation shield (Hole S) is shown in Fig. 7.3.

7.2.3 Fiducial Volume (FV) In the analysis, we select an inner region of the single phase liquid xenon detector using the reconstructed vertex in order to achieve a low background environment. For the prototype detector, this inner region is selected as a cube (Full volume (89.0kg), 20cm FV (23.1kg), 15cm FV (9.73kg), 10cm FV (2.88kg)), as shown in Fig 7.4. Here “FV” means “ﬁducial volume.”

7.2.4 Coordinate system of prototype detector The center of the prototype detector is deﬁned as the origin of the coordinate system and the x, y, z axes are set as shown in Fig. 7.5. This coordinate system

59 is used for the following analysis.

7.2.5 ADC saturation cut When gain of each of the 54 PMTs is set to 8.25 106 as the nominal gain (see Fig. 7.7), each channel of the charge ADC saturates× at 200 p.e. Events with saturated channels are removed by the “ADC saturation∼cut.”

7.2.6 Maximum PMT ratio cut The “Maximum PMT ratio” is deﬁned as follows, “Maximum charge in the 54 PMTs” “Maximum PMT ratio” = (7.1) “Total charge of the 54 PMTs” Events near the PMTs have large “Maximum PMT ratio”, and these events are removed by the following “Maximum PMT ratio cut” before selecting the ﬁducial volume.

“Maximum PMT ratio” < 0.3 (7.2)

The cut value, 0.3, is decided in order to cut the following backgrounds from the dark matter search data, as discussed in Chapter 8:

115 β decays of In, which is a contaminant in the sealing parts of the MgF2 • window

Cherenkov photons generated at the MgF2 window of the detector and • quartz window of the PMT The “Maximum PMT ratio cut” is also applied to source calibration data before selecting the ﬁducial volume.

7.3 Detector Simulation

The particle produced in neutralino interactions are fed into a detector simulation code, in which tracks of particles, scintillation processes, propagation of scintillation photons and the response of PMTs are simulated. The detector simulator program has been developed based on the GEANT3 package [70]. Table 7.3 lists various processes which are considered in our simulation program. The GEANT4 package[71] is used for simulation of neutrons, because Geant3 is not optimized for low energy hadrons. Processes considered in GEANT4 are listed in Table 7.4. In connection with the propagation of charged particles, scintillation photons are generated according to LET dependence of the scintillation yield (see Eq. (4.3) and (4.4)). For the propagation of scintillation photons in liquid xenon, Rayleigh scattering and absorption are considered in our simulation code. At the boundary of the refractive indexes of liquid xenon and other transparent materials, scintillation photons are refracted or reflected according to the Fresnel equation. Light reflection and absorption in detector materials, such as surface of the PMTs and the mirror on inner wall of the detector, are also simulated. The attenuation coefficients of liquid xenon and reflectance at the mirror on

60 γ Compton Scattering Photoelectric eﬀect (e+, e−) pair production e Multiple scattering Ionization and δ-ray production Bremsstrahlung Annihilation of positrons Generation of scintillation photons

Table 7.3: List of the processes considered in GEANT3 simulator.

γ Compton Scattering Photoelectric eﬀect (e+, e−) pair production e Multiple scattering Ionization and δ-ray production Bremsstrahlung Annihilation of positrons Hadrons Decay in ﬂight Multiple scattering Ionization and δ-ray production Hadronic interactions

Table 7.4: List of processes considered in GEANT4 simulator.

the inner wall were tuned to reproduce γ-ray calibration data, as discussed in Section 7.5. For the simulation of the PMT response, the total number of p.e. detected in each PMT is derived by summing up individual p.e. with a weight of a single p.e. distribution. The geometry of the prototype detector deﬁned in GEANT3 is shown in Fig. 7.6.

7.4 Gain and TDC oﬀset measurement

The gain table of the 54 PMTs at room temperature was made with a gain calibration system[72] and HVs supplied to the PMTs were decided using this table. After that, the gains of the PMTs at an operating temperature of 173 K with this HVs were measured by LED light from optical ﬁbers attached in the detector as shown in Fig. 7.7. The hit occupancy of each PMT was adjusted to 1/100 by changing the intensity of the LED light (see Fig. 7.8). ∼ The timings of the 54 PMTs at the operating temperature (173K) were adjusted by measuring the relative TDC oﬀset with LED light data as shown in Fig. 7.9. The hit occupancy of each PMT was adjusted to 1/100, the same as in the gain measurement. The typical TDC timing distribution∼ of LED data is shown in Fig. 7.10 and the peak timings of each PMT were used as the relative

61 TDC oﬀset. These measured gains and TDC oﬀsets at the operating temperature (173K) are used for the following analysis.

62 Figure 7.2: Relative locations of the γ-ray collimators (Hole A, B, C) and the prototype detector.

63 Figure 7.3: Location of γ-ray collimator inside the radiation shield (Hole S).

Figure 7.4: Fiducial volume of prototype detector (Full volume, 20cm FV, 15cm FV, 10cm FV)

64 Figure 7.5: Coordinate system of prototype detector. The center of the prototype detector is (0, 0, 0).

Figure 7.6: Geometry of the prototype detector in GEANT3. Detailed geometry, such as holes in the radiation shield for the gas line and PMT cables, is deﬁned to reproduce the actual detector.

65 ) 6

10 14 ×

Gain( 12

0 0 10 20 30 40 50 PMT Number

Figure 7.7: Gains of the 54 PMTs at the operating temperature (173K).

66 10 6

10 5

10 4

10 3

10 2

1 -1 0 1 2 3 4 5 charge (p.e.)

Figure 7.8: Typical charge distribution of LED data for the gain calibration. Hit occupancy of each PMT is 1/100. ∼

67 50

10 Relative TDC offset (ns) 0

-10

-20

-30

-40

-50 0 10 20 30 40 50 PMT Number

Figure 7.9: TDC oﬀset of the 54 PMTs at the operating temperature (173K).

68 6000

5000

4000

3000

2000

1000

0 -20 0 20 40 60 Relative TDC timing without offset collection (ns)

Figure 7.10: Typical TDC timing distribution of LED data for TDC oﬀset adjustment. Timing distribution corresponds to the wave form of LED light.

69 7.5 Absorption length and light yield

Detector simulation is important for understanding the detector performance. Simulation parameters related to the scintillation photon tracking are listed in Table 7.5. Various reports on photon yield of liquid xenon exist as shown in Table 4.3. The absorption length of liquid xenon changes with water contamination in the liquid xenon. Reﬂectance at the mirror on the inner wall has never been measured. These simulation parameters (light yield, absorption length, reﬂectance of mirror) are measured with γ-ray calibration data as follows.

Parameter Value Comment Photon yield of liquid xenon 80.6( 4.0) photon/keV (at LET= ) Tuned ∞ Absorption length of liquid xenon 66( 10) cm Tuned Scattering length of liquid xenon 60 cm[58] Refractive index of liquid xenon 1.6 [59] Reﬂectance at mirror on inner wall 52(+4-6) % Tuned

Absorption length of MgF2 window 14.63 cm Refractive index of MgF2 window 1.44 Refractive index of Krytox 1.35 Quantum efficiency of PMT 33.6 % [72] Collection efficiency of PMT 90 % Reflection at PMT surface 20 %

Table 7.5: List of simulation parameters for scintillation photon (175nm).

PMT groups, “ring”s are defined as in Fig. 7.11. Charge distributions of the “ring”s of γ-ray calibration data, 137Cs (from Hole A, B, S) and 60Co (from Hole A, B), are used for the simulation parameter tuning. The χ2 method is used to find the best fit simulation parameters. χ2 is calculated as Eq. (7.3) and (7.4).

data ring 2 2 χ = χringj (7.3) i j X X

bin 2 2 [(Counts of bink(Data, ringj )) (Counts of bink(Sim., ringj ))] χringj = − (7.4) (Counts of bink(Data, ringj )) Xk Charge bins from -100 p.e. to 1000 p.e. of each “ring” are used for this χ2 calculation, and 1 bin corresponds to 10 p.e. First, the following simulation parameter sets are checked: Absorption length of liquid xenon : 40 - 80 cm (10 cm step) • Reﬂectance of the mirror : 40 - 80 % (10 % step) • Here, light yield is checked by multiplying the light yield factor for simulation data. χ2 distributions of these parameter sets are shown in Fig. 7.12, and

70 Figure 7.11: “ring” deﬁnition for simulation parameter tuning. The charge distribution of 8 PMTs on the top part of the detector are very sensitive to the liquid level of xenon because the MgF2 windows of these are not completely immersed in liquid xenon. So these 8 PMTs are excluded from the ”ring”. The PMT located at the point of γ-ray incidence is also excluded from the ”ring” as most of its charge is saturated.

the best fit parameters in these parameter sets are absorption length = 70 cm, reflectance of the mirror = 60 % and light yield = 79.8 photons/keV (at LET= ). Then,∞ following parameter sets near the previous best fit points are checked: Absorption length of liquid xenon : 50 - 80 cm (2 cm step) • Reflectance of the mirror : 40 - 60 % (2 % step) • The χ2 distributions of these parameter sets are shown in Fig. 7.13, and the best fit parameters in these parameter sets are absorption length = 66 cm, reflectance of the mirror = 52 % and light yield = 80.6 photons/keV (at LET = ). The light yield distribution of the minimum χ2 for each set of absorption length∞ and reflectance of the mirror is shown in Fig. 7.14. The charge distribution of the best fit parameters are shown in Fig. 7.15. From Fig. 7.13 and 7.14. Systematic errors are set as follows: Absorption length = 66( 10) cm • Reflectance of the mirror = 52(+4-6) % • Light yield = 80.6( 4.0) photons/keV (at LET = ). • ∞ These simulation parameters are used for the following analysis.

71 90

50 Absorption length of liquid xenon (cm)

3030 40 50 60 70 80 90 Reflectance at mirror on inner wall (%)

Figure 7.12: χ2 distribution of each simulation parameter set. The best fit parameter is absorption length = 70 cm, reflectance of the mirror = 60 % and light yield = 79.8 photons/keV. Around this best fit point, the χ2 distribution is checked more in detail, as in Fig. 7.13 and 7.14

72 80

60 Absorption length of liquid xenon (cm) 55

50 40 42.5 45 47.5 50 52.5 55 57.5 60 Reflectance at mirror on inner wall (%)

Figure 7.13: χ2 distribution of each simulation parameter set. The best ﬁt parameters are absorption length = 66 cm, reﬂectance of the mirror = 52 % and light yield = 80.6 photons/keV.

73 80

60 Absorption length of liquid xenon (cm) 55

50 40 42.5 45 47.5 50 52.5 55 57.5 60 Reflectance at mirror on inner wall (%)

Figure 7.14: Light yield distribution of minimum χ2 for each set of absorption length and reflectance of the mirror. Light yield is normalized to that of the best fit parameter, 80.6 photons/keV(at LET= ) with absorption length = 66 cm and reflectance of the mirror = 52 %. ∞

74 1000 1000 750 750 500 500

counts/bin 250 counts/bin 250 0 0 0 200 400 0 200 400 charge (p.e.) charge (p.e.) 1000 1000 750 750 500 500

counts/bin 250 counts/bin 250 0 0 0 200 400 0 200 400 charge (p.e.) charge (p.e.) 1000 750 500

counts/bin 250 0 0 200 400 charge (p.e.)

Figure 7.15: Charge distributions of γ-ray calibration (137Cs from Hole A). Real data is shown by black lines and simulation data with the best ﬁt parameters (absorption length = 66 cm, reﬂectance of the mirror = 52 %, light yield = 80.6 photon/keV (at LET = )) is shown by red lines. ∞

75 7.6 Vertex and energy reconstruction

Single phase liquid xenon detectors realize a low background environment at the center volume by using the self-shielding power of liquid xenon. Because of this reconstruction of the vertex and energy is essential for these detectors. The vertex and energy of each event in the prototype detector is reconstructed with the charge distribution of the 54 PMTs. Charge patterns of the PMTs are made with the detector simulation in a 30 cm cubic lattice with 0.3 cm step size (1030301 points). The charge patterns are deﬁned as

F = Fi(x, y, z) (7.5)

Here Fi(x, y, z) is the expected number of photoelectrons of PMT No. i for 1 photon which was generated at vertex (x, y, z). The vertex is reconstructed with the following likelihood of a Poisson distribution by comparing the detected charge distribution of the PMTs with Fi(x, y, z),

54 exp−µi µn log(L) = log i (7.6) n! i=1 X Here µi is

µ = F (x, y, z) “expected number of generated photons” (7.7) i i × where “expected number of generated photons” is calculated as

54 i=1 pe(i) “expected number of generated photons” = 54 (7.8) P i=1 Fi Here pe(i) is the charge detected with PMT No. i. P The vertex with maximum likelihood is selected as the reconstructed vertex, then the reconstructed energy is calculated as “expected number of generated photons” E [keV] = (7.9) Q.E. C.E. N P MT × P MT × photon

Here Q.E.P MT is the quantum eﬃciency of the PMT, C.E.P MT is the collection eﬃciency of the PMT and Nphoton is the number of generated photons per 1 keV with 662-keV γ ray (137Cs source run). The following values are used for the reconstruction:

Q.E.P MT = 0.336 (7.10)

C.E.P MT = 0.90 (7.11)

Nphoton = 57.1 photons/keV (7.12)

The detected charge distribution and expected charge distribution at the reconstructed vertex are shown in Fig. 7.16.

76 Figure 7.16: Detected charge distribution (black circle and number (p.e.)) and expected charge distribution at the reconstructed vertex (green circle and number (p.e.)).

7.7 Photoelectron yield

The photoelectron yield of the prototype detector is evaluated with γ-ray calibration data, 137Cs from Hole A. After the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV, the photoelectric absorption peak is ﬁtted with an asymmetric gaussian as shown in Fig. 7.17. Photoelectron yields of real data and the simulation for 662-keV γ rays are 1.935( 0.002) p.e./keV and 1.907( 0.003) p.e./keV.

77 137Cs from Hole A 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 total pe(p.e.) 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 total pe(p.e.)

Figure 7.17: Charge distribution of 137Cs from Hole A with the “ADC saturation cut”, “maximum PMT ratio cut” and 20cm FV. The photoelectric absorption peak (662 keV) is ﬁtted with an asymmetric gaussian (red line). Photoelectron yields of real data and the simulation for 662-keV γ rays are 1.935( 0.002) p.e./keV and 1.907( 0.003) p.e./keV, respectively.

78 7.8 Vertex and energy resolution 7.8.1 Energy resolution Energy resolution of the prototype detector was evaluated with γ-ray calibration data, 137Cs from Hole A. After the “ADC saturation cut” and “maximum PMT ratio cut,” the photoelectric absorption peak (662 keV) of each ﬁducial volume (Full volume, 20cm FV, 10cm FV) is ﬁt with an asymmetric gaussian as shown in Fig. 7.18. Energy resolution of the prototype detector for 662-keV γ rays is shown in Table 7.6.

137Cs from Hole A 10 4 10 3 10 2 arbitrary unit 10 1 0 200 400 600 800 1000 reconstructed energy (keV) 10 4 10 3 10 2 arbitrary unit 10 1 0 200 400 600 800 1000 reconstructed energy (keV)

Figure 7.18: Reconstructed energy spectrum of 137Cs from Hole A with “ADC saturation cut” and “maximum PMT ratio cut.” Photoelectric absorption peaks (662 keV) of each fiducial volume (Full volume, 20cm FV, 10cm FV) are fit with an asymmetric gaussian (pink line). The energy resolution of each fiducial volume is shown in Table 7.6.

7.8.2 Reconstructed vertex The reconstructed vertex of the prototype detector is evaluated with γ-ray calibration data, 60Co from Hole A and B. The reconstructed energy spectrum of each hole is shown in Fig. 7.19 and 7.20, and events near the photoelectric absorption peak (1000 < Ereconst. < 1400 keV) are used to check the reconstructed vertex. Peaks of reconstructed x and y with the “ADC saturation cut”

79 mean [keV] σ [keV] resolution [%] Real data Full volume 664.7 ( 0.7) 37.0 ( 0.6) 5.57 ( 0.09) 20cm FV 666.2 (1.1) 36.4 (0.8) 5.47 (0.13) 10cm FV 669.9 (1.8) 34.8 (1.4) 5.20 (0.21) Simulation Full volume 655.9 ( 0.3) 38.3 ( 0.4) 5.83 ( 0.07) 20cm FV 657.3 (1.1) 37.6 (0.7) 5.71 (0.11) 10cm FV 657.7 (1.9) 36.8 (1.3) 5.59 (0.20)

Table 7.6: Energy resolution of the prototype detector for 662-keV γ rays (137Cs from Hole A).

, “1000 < Ereconst. < 1400 keV” and “ 10 < reconstructed z < 10 cm” are ﬁt with an asymmetric gaussian (pink line)−as shown in Fig. 7.21and 7.22, and the ﬁt results are summarized in Table 7.7. Here σ in Table 7.7 is not the vertex resolution of the prototype detector because the γ rays spread in the x-y plane as shown in Fig. 7.23 and 7.24.

reconstructed x reconstructed y mean [cm] σ [cm] mean [cm] σ [cm] Real data Hole A 1.17 ( 0.04) 1.63 ( 0.03) 1.52 ( 0.03) 1.44 ( 0.03) Hole B −6.46 (0.06) 1.42 (0.05) 1.85 (0.08) 1.68 (0.07) − Simulation Hole A 0.04 ( 0.06) 1.92 ( 0.05) 1.58 ( 0.04) 1.53 ( 0.03) Hole B −6.40 (0.05) 1.43 (0.04) 1.25 (0.04) 1.40 (0.04) −

Table 7.7: Reconstructed vertex of prototype detector for 1173 and 1333 keV γ rays (60Co from Hole A, B). Here σ is not the vertex resolution of the prototype detector because the γ rays spread in the x-y plane as shown in Fig. 7.23 and 7.24.

80 60Co from Hole A 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 reconstructed energy (keV) 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 reconstructed energy (keV)

Figure 7.19: Reconstructed energy spectrum of 60Co from Hole A with the “ADC saturation cut” and “maximum PMT ratio cut”. Events around photoelectric absorption peaks (1000 < Ereconst. < 1400 keV) are used to check the vertex resolution.

81 60Co from Hole B 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 reconstructed energy (keV) 10 4 10 3 10 2 arbitrary unit 10 1 0 250 500 750 1000 1250 1500 1750 2000 reconstructed energy (keV)

Figure 7.20: Reconstructed energy spectrum of 60Co from Hole B with the “ADC saturation cut” and “maximum PMT ratio cut.” Events near the photoelectric absorption peak (1000 < Ereconst. < 1400 keV) are used to check the vertex resolution.

82 60Co from Hole A 4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 arbitrary unit 1500 arbitrary unit 1500 1000 1000 500 500 0 0 -10 -5 0 5 10 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm) 4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 arbitrary unit 1500 arbitrary unit 1500 1000 1000 500 500 0 0 -10 -5 0 5 10 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm)

Figure 7.21: Reconstructed x and y distribution of 60Co from Hole A with the “ADC saturation cut,” “1000 < Ereconst. < 1400 keV” and “ 10 < reconstructed z < 10 cm.” Peaks of reconstructed x and y are ﬁtted− with an asymmetric gaussian (pink line), and the ﬁt results are summarized in Table 7.7.

83 60Co from Hole B 2500 2500

2000 2000

1500 1500

arbitrary unit 1000 arbitrary unit 1000

500 500

0 0 -15 -10 -5 0 5 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm) 2500 2500

2000 2000

1500 1500

arbitrary unit 1000 arbitrary unit 1000

500 500

0 0 -15 -10 -5 0 5 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm)

Figure 7.22: Reconstructed x and y distribution of 60Co from Hole B with the “ADC saturation cut,” “1000 < Ereconst. < 1400 keV” and “ 10 < reconstructed z < 10 cm.” Peaks of reconstructed x and y are ﬁt with− an asymmetric gaussian (pink line), and the ﬁt results are summarized in Table 7.7

84 60Co from Hole A 4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 arbitrary unit 1500 arbitrary unit 1500 1000 1000 500 500 0 0 -10 -5 0 5 10 -10 -5 0 5 10 x of light barycenter (cm) y of light barycenter (cm) 4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 arbitrary unit 1500 arbitrary unit 1500 1000 1000 500 500 0 0 -10 -5 0 5 10 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm)

Figure 7.23: Comparison between light barycenter and reconstructed vertex of the simulation (60Co from Hole A) with the “ADC saturation cut,” “1000 < Ereconst. < 1400 keV” and “ 10 < reconstructed z < 10 cm.” Peaks are ﬁt with asymmetric gaussians (pink− line).

85 60Co from Hole B 3000 3000 2500 2500 2000 2000 1500 1500 arbitrary unit arbitrary unit 1000 1000 500 500 0 0 -15 -10 -5 0 5 -10 -5 0 5 10 x of light barycenter (cm) y of light barycenter (cm) 3000 3000 2500 2500 2000 2000 1500 1500 arbitrary unit arbitrary unit 1000 1000 500 500 0 0 -15 -10 -5 0 5 -10 -5 0 5 10 reconstructed x (cm) reconstructed y (cm)

Figure 7.24: Comparison between light barycenter and reconstructed vertex of the simulation (60Co from Hole B) with the “ADC saturation cut,” “1000 < Ereconst. < 1400 keV” and “ 10 < reconstructed z < 10 cm.” Peaks are ﬁt with asymmetric gaussians (pink− line).

86 7.9 Self-shielding power of liquid xenon

The self-shielding power of liquid xenon is evaluated with γ-ray calibration data, 137Cs (662 keV) and 60Co (1117 and 1333 keV) from Hole A. The reconstructed vertex along the γ-ray incident direction (reconstructed z) is checked after applying the following cuts: Reconstructed vertex is in 10 cm square from the origin on the xy plane • (“10cm square cut on xy plane”). “ADC saturation cut” • Environmental background is mixed in γ-ray calibration data, so it is subtracted from the data as shown in Fig. 7.25 and 7.26. The reconstructed z of real data agrees well with that of simulation as shown in Fig. 7.27 and 7.28,, so the self-shielding of liquid xenon works as expected.

-1 10

-2

arbitrary unit 10

-3 10

-4 10

-5 10

-6 10 -20 -15 -10 -5 0 5 10 15 20 reconstructed z (cm)

Figure 7.25: Subtraction of environmental background (green line) from γ-ray calibration data with 137Cs source (red line). Black line is background subtracted data.

7.10 Non-proportionality of scintillation yield

Reconstructed energy spectra of the following γ-ray source runs are compared with that of simulation:

87 1

-1 10 arbitrary unit -2 10

-3 10

-4 10

-5 10

-6 10

-7 10 -20 -15 -10 -5 0 5 10 15 20 reconstructed z (cm)

Figure 7.26: Subtraction of environmental background (green line) from γ-ray calibration data with 60Co source (red line). Black line is background subtracted data.

131mXe uniformly inside the detector (164 keV). • 137Cs from Hole A (662 keV). • 40K source inside the radiation shield (1461 keV). • 208Th source inside the radiation shield (2615 keV). • Photoelectric absorption peak of each source run are ﬁt with an asymmetric gaussian after the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV.

7.10.1 131mXe uniformly inside the detector (Neutron activation) As discussed in Section 7.11, neutrons from an Am/Be source irradiated the xenon of the prototype detector for 8 hours at the last stage of data taking. As a result of this irradiation, the xenon∼ was activated uniformly inside the detector. A photoelectric absorption peak of 164 keV γ rays generated by isomer shift of 131mXe was found in the data after neutron irradiation (Live time = 2.74 days) as shown in Fig. 7.29. Peaks of real data and simulation are ﬁtted with asymmetric gaussians, and the ﬁt results are summarized in Table 7.8.

88 -1 10

arbitrary unit -2 10

-3 10

-4 10

-5 10 -20 -15 -10 -5 0 5 10 15 20 reconstructed z (cm)

Figure 7.27: Reconstructed vertex along the γ-ray incident direction (reconstructed z) (137Cs from Hole A). Distribution of real data (black line) agrees well with that of simulation (red line), so self-shielding of liquid xenon works as expected. Both ends of distribution is chipped by the “ADC saturation cut.”

7.10.2 137Cs from Hole A Photoelectric absorption peaks of 662-keV γ rays (137Cs from Hole A) are ﬁt with an asymmetric gaussian as shown in Fig. 7.30, and the ﬁt results are summarized in Table 7.8.

7.10.3 40K inside the radiation shield 40 As a K source, 5kg of AlK(SO4)2 12H2O was placed inside the radiation shield as shown in Fig 7.31. Photoelectric· absorption peaks of 1461 keV γ ray are ﬁt with an asymmetric gaussian (see Fig. 7.32), and the ﬁt results are summarized in Table 7.8.

7.10.4 208Th inside the radiation shield As a 208Th source, lantern mantles (camp supplies) were placed inside the radiation shield as shown in Fig 7.33. The photoelectric absorption peaks of 2615 keV γ ray are ﬁt with an asymmetric gaussian (see Fig. 7.34), and the ﬁt results are summarized in Table 7.8.

89 -1 10

arbitrary unit -2 10

-3 10

-4 10

-5 10 -20 -15 -10 -5 0 5 10 15 20 reconstructed z (cm)

Figure 7.28: Reconstructed vertex along the γ-ray incident direction (reconstructed z) (60Co from Hole A). Distribution of real data (black line) agrees well with that of simulation (red line), so self-shielding of liquid xenon works as expected. Both ends of distribution is chipped by the “ADC saturation cut.”

90 131mXe (neutron activation) 50 40 30 20 arbitrary unit 10 0 -10 0 25 50 75 100 125 150 175 200 225 reconstructed energy (keV) 2000 1750 1500 1250 1000 arbitrary unit 750 500 250 0 0 25 50 75 100 125 150 175 200 225 reconstructed energy (keV)

Figure 7.29: Reconstructed energy spectrum of 131mXe (164 keV) with the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV. Peaks of real data (Live time = 2.74 days) and simulation are ﬁt with asymmetric gaussians (pink line), and the ﬁt results are summarized in Table 7.8.

91 137Cs from Hole A 1400 1200 1000 800

arbitrary unit 600 400 200 0 0 100 200 300 400 500 600 700 800 reconstructed energy (keV) 1400 1200 1000 800

arbitrary unit 600 400 200 0 0 100 200 300 400 500 600 700 800 reconstructed energy (keV)

Figure 7.30: Reconstructed energy spectrum of 137Cs (662keV) from Hole A with the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV. Peaks of real data and simulation are ﬁt with asymmetric gaussians (pink line), and the ﬁt results are summarized in Table 7.8.

92 40 Figure 7.31: Location of K source (5 kg of AlK(SO4)2 12H2O) inside the radiation shield. ·

93 40K inside the radiation shield 100 90 80 70 60 50 arbitrary unit 40 30 20 10 0 0 200 400 600 800 1000 1200 1400 1600 reconstructed energy (keV) 100 90 80 70 60 50 arbitrary unit 40 30 20 10 0 0 200 400 600 800 1000 1200 1400 1600 reconstructed energy (keV)

Figure 7.32: Reconstructed energy spectrum of 40K (1461 keV) inside the radiation shield with the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV. Peaks of real data and simulation are ﬁt with asymmetric gaussians (pink line), and the ﬁt results are summarized in Table 7.8.

94 Figure 7.33: Location of 208Th source (lantern mantles inside SUS container) inside the radiation shield.

95 208Tl (Thorium series) inside the radiation shield 80 70 60 50 40 arbitrary unit 30 20 10 0 0 500 1000 1500 2000 2500 reconstructed energy (keV) 50 45 40 35 30 25 arbitrary unit 20 15 10 5 0 0 500 1000 1500 2000 2500 reconstructed energy (keV)

Figure 7.34: Reconstructed energy spectrum of 208Th (2615 keV) inside the radiation shield with the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV. Peaks of real data and simulation are ﬁt with asymmetric gaussians (pink line), and the ﬁt results are summarized in Table 7.8.

96 7.10.5 Non-proportionality of scintillation yield and energy resolution The ﬁt results of the photoelectric absorption peaks of various γ-ray sources are summarized in Table 7.8.

mean (keV) resolution (%) 131mXe Real data 181.8 ( 2.0) 7.3 ( 1.3) (164 keV) Simulation 178.6 (0.2) 7.3 (0.2) 137Cs Real data 666.2 ( 1.1) 5.5 ( 0.1) (662 keV) Simulation 657.3 (1.1) 5.7 (0.1) 40K Real data 1386 ( 15) 5.1 ( 1.1) (1461 keV) Simulation 1363 (12) 4.9 (0.7) 208Tl Real data 2312 ( 15) 4.6 ( 0.6) (2615 keV) Simulation 2373 (18) 3.6 (0.6)

Table 7.8: Fit results of the photoelectric absorption peaks of various γ-ray sources. Reconstruction is done with the reconstruction parameters, Eq. (7.10), (7.11) and (7.12) calibrated with 662-keV γ rays. Peaks are ﬁt with asymmetric gaussians.

Real data has a non-proportionality of scintillation yield (see Fig. 7.35) and the simulation reproduces that well by introducing LET dependence of the scintillation yield (Eq. ((4.3) and (4.4)). Reconstructed energy resolution for various γ rays is shown in Fig. 7.36, and simulation reproduces real data well again.

97 1.2 1.1 1 0.9 0.8

0.7 -1

Relative scintillation yield 10 1 10 γ-ray energy (MeV) 1.2 1.1 1 0.9 0.8

0.7 -1

Relative scintillation yield 10 1 10 γ-ray energy (MeV)

Figure 7.35: Relative scintillation yield for various γ rays. Vertical axis is normalized with 662-keV γ ray (137Cs). Both real data and simulation have a non-proportionality, 10 % from 662 keV. The simulation reproduces real data well by introducing∼ LET dependence of scintillation yield (Eq. ((4.3) and (4.4)).

98 ) 10

% 9 8 7 6 5 4 3 2 1 Energy resolution ( 0 -1 10 1 10 γ-ray energy (MeV)

) 10

% 9 8 7 6 5 4 3 2 1 Energy resolution ( 0 -1 10 1 10 γ-ray energy (MeV)

Figure 7.36: Reconstructed energy resolution of the prototype detector for various γ rays. Simulation reproduces real data well again by introducing LET dependence of the scintillation yield (Eq. ((4.3) and (4.4)).

99 7.11 Trigger and event selection eﬃciency for Dark Matter search

The global trigger of the prototype detector is fired when the number of hit PMTs within 100 ns is larger than 3. The trigger efficiency of the prototype detector as a function of deposited energy (keVee) is calculated with the detector simulation (see Fig. 7.37). Trigger efficiency is calculated as follows, Generate events uniformly inside the chamber with the detector simulation • for each bin of deposited energy. Trigger efficiency = (num. of events with > 3 hits) / (num. of generated • events) Calculated trigger efficiency at 5 < E < 6 keV is 94( 1) %. deposit ) % 100

80 trigger efficiency ( 60

0 0 2 4 6 8 10 12 14 16 18 20 deposit energy (keVee)

Figure 7.37: Trigger eﬃciency of the prototype detector calculated with the detector simulation. Trigger eﬃciency at 5 < E < 6 keV is 94( 1) %. deposit

The trigger and event selection eﬃciency as a function of deposited energy (keVee) is calculated with the detector simulation as shown in Fig. 7.38. The “Noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” are applied for 15cm FV. The trigger and event selection eﬃciency is calculated as follows, Generate events uniformly inside the chamber with the detector simulation • for each bin of deposited energy.

100 Efficiency = (num. of events in each reconstructed fiducial volume with • cuts) / (num. of events in each fiducial volume with generated vertex)

The calculated trigger and event selection eﬃciency at 5 < Edeposit < 10 keVee is 17( 1) % for 15cm FV. ) % 100

60 event selection efficiency ( & 40 trigger

0 0 10 20 30 40 50 60 70 80 deposit energy (keVee)

Figure 7.38: Trigger and event selection eﬃciency of prototype detector calculated with detector simulation. The calculated eﬃciency at 5 < Edeposit < 10 keVee is 17( 1) % for 15cm FV.

The trigger and event selection eﬃciency is conﬁrmed with an Am/Be neutron source run. The Am/Be source was placed inside the radiation shield as shown in Fig 7.39. As discussed in Section 7.3, the GEANT4 package is used for Am/Be source simulation and tracking of scintillation photons is done with GEANT3. The energy spectrum of neutrons from the Am/Be source used for simulation is shown in Fig. 7.40. The reconstructed energy spectrum of the nuclear recoil peak for the Am/Be source run is shown in Fig. 7.41. The ratio of mass normalized counts of Full volume with “noise cut” to that of 15cm FV with “noise cut” and “maximum PMT ratio cut” is 9.1( 1.6) % for real data and 11.6( 1.0) % for simulation in the dark matter search window 5 < Erecon. < 10 keVee; the systematic error to select 15cm FV with “maximum PMT ratio cut” is set as 27.5 %.

101 Figure 7.39: Location of Am/Be neutron source inside the radiation shield.

12 arbitrary unit

0 0 2 4 6 8 10 12 neutron energy (MeV)

Figure 7.40: Energy spectrum of neutron from Am/Be source used for detector simulation.

102 Am/Be neutron source run 50 45 40 35

counts/kg 30 25 20 15 10 5 0 0 5 10 15 20 25 30 reconstructed energy (keV) 180 160 140 120 counts/kg 100 80 60 40 20 0 0 5 10 15 20 25 30 reconstructed energy (keV)

Figure 7.41: Reconstructed energy spectrum of the nuclear recoil peak for the Am/Be neutron source run. The upper ﬁgure is real data and lower ﬁgure is simulation. Vertical axis is counts normalized to target mass. The black line is Full volume with “noise cut” and the red line are 15cm FV with “noise cut” and “maximum PMT ratio cut”. The ratios of mass normalized counts of Full volume with “noise cut” (black line) to that of 15cm FV with “noise cut” and “maximum PMT ratio cut” (red line) are 9.1( 1.6) % for real data and 11.6( 1.0) % for simulation in the dark matter search window 5 < Erecon. < 10 keVee; the systematic error to select 15cm FV with “maximum PMT ratio cut” is set as 27.5 %.

103 Chapter 8

Dark Matter search by prototype detector

The prototype detector is not optimized for a dark matter search because of its small photo coverage, large dead angle region from PMTs and small self- shielding volume, therefore it originally didn’t have sensitivity to a dark matter search. We made the following improvements to the prototype detector to in- crease the photoelectron yield and lower the energy threshold as discussed in Sec. 6.1.4: Installed mirror on the inner wall of the detector. • Filled the gap between the MgF2 window and the PMT with a high re- • fractive index material. We search for a dark matter signal with this improved prototype detector.

8.1 Measurements

With the prototype detector described in Chapters 6 and 7, a dark matter search experiment was performed at Kamioka Observatory. The measurement was started on November 22, 2006 and halted in December 21, 2006, and the live time of the dark matter search run was 17.98 days. During the measurement, calibration of the detector was performed about once a day. The stability of the detector is discussed with these daily calibration data in Section 8.2.

8.2 Stability of detector

Daily γ-ray calibration data (137Cs and 60Co from Hole A) are checked as shown in Fig. 8.1, and stability within 3 % is conﬁrmed during the measurement. With a stability collection, the stabilit∼ y of the dark matter search run becomes 0.5 %.

104 1.05

1.04

1.03

1.02

1.01

0.99

0.98

0.97

relative charge of photoelectric absorption peak 0.96

0.95 0 5 10 15 20 25 30 time (day) from 2006/11/21 0:00

Figure 8.1: Relative charge of photoelectric peak of daily γ-ray calibration with the “ADC saturation cut,” “maximum PMT ratio cut” and 20cm FV. Relative charge is normalized to the average during the measurement. Stability within 3 % is conﬁrmed during 1 month measurement. With a stability collection, the∼ stability of the dark matter∼ search run becomes 0.5 %.

8.3 Trigger rate and event selection 8.3.1 Noise cut Electrical noise events were mixed in with the dark matter search data. An event display of typical electrical noise is shown in Fig. 8.2; it has a large number of TDC hits despite low total charge. By applying the following cut, these noise events can be removed as shown in Fig. 8.3. “number of PMTs with charge > 0.4 p.e.” > 0.65 (8.1) “number of TDC hits”

8.3.2 Trigger rate The trigger eﬃciency for the dark matter search was discussed in Section 7.11. The trigger rate of dark matter search runs with a “noise cut” is shown in Fig. 8.4; some high rate runs caused by electrical noise exist even with a “noise cut.” Runs with “trigger rate < 1.15 Hz” are used for the dark matter search

105 Figure 8.2: Event display of typical electrical noise. These noise events have a large number of TDC hits despite low total charge.

(live time = 17.98 days), and the mean trigger rate of the dark matter search runs with the “noise cut” is 1.093( 0.001) Hz.

106 10 3

10 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 num. of hit (ADC) / num. of hit (TDC)

Figure 8.3: Distribution of “(number of PMTs with charge > 0.4 p.e.)/(number of TDC hits)” of the dark matter search run with the “maximum PMT ratio cut” and “0 < Ereconst < 50 keV”. Blue and red lines correspond to Full volume and 15cm FV. By selecting the events with “(number of PMTs with charge > 0.4 p.e.)/(number of TDC hits) > 0.65”, electrical noise events can be removed.

107 2.5 2.25 2 1.75 1.5 1.25 1

trigger rate (Hz) 0.75 0.5 0.25 0 0 5 10 15 20 25 30 time (day) from 2006/11/21 0:00 1.2 1.175 1.15 1.125 1.1 1.075 trigger rate (Hz) 1.05 1.025 1 0 5 10 15 20 25 30 time (day) from 2006/11/21 0:00

Figure 8.4: Trigger rate of dark matter search runs ( 2 hours for each run) with “noise cut.” The upper ﬁgure is trigger rate of all dark∼ matter search runs, and some high rate runs, which were caused by electrical noise, exist even with “noise cut.” Runs with “trigger rate < 1.15 Hz” are used for the dark matter search (lower ﬁgure), and the mean trigger rate is 1.093( 0.001) Hz.

108 8.3.3 Event selection

The sealing parts of the MgF2 windows (U-tight seal) are made with In, and 95.71 % of In is a radioactive isotope, 115In. β decays of 115In have the following characteristics. τ = 4.41 1014 year • 1/2 × Q = 496 keV • β β decays of 115In make background events below 500 keV. Backgrounds from 115In can be cut with the “ADC saturation cut” and the “maximum PMT ratio cut,” as shown in Fig 8.5 and 8.6, because these events occurred near PMTs. The deﬁnition of the “maximum PMT ratio cut” is “(Maximum charge in the 54 PMTs)/(Total charge of the 54 PMTs) < 0.3”. Cherenkov photons emitted at quartz window of the PMTs or the MgF2 windows make background events below 50 keV. Backgrounds from Cherenkov photons can be cut with the “maximum PMT ratio cut,” as shown in Fig 8.5 and 8.6, because these events also occur near the PMTs. After applying the “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut,” events in 15cm FV are selected with reconstructed vertex as shown in Fig. 8.7, 8.8 and 8.9.

109 10 5 10 4 10 3 10 2

number of events 10 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Maximum charge in 54 PMTs / Total chage of 54 PMTs 10 5 10 4 10 3 10 2

number of events 10 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Maximum charge in 54 PMTs / Total chage of 54 PMTs

Figure 8.5: Distribution of “(Maximum charge in the 54 PMTs) /(Total charge of the 54 PMTs)” of the dark matter search run with the “noise cut” and “ADC saturation cut” (0 < Ereconst. < 500 keV (upper figure) and 0 < Ereconst. < 50 keV (lower figure)). Blue and red lines correspond to Full volume, and 15cm FV. By selecting events with “(Maximum charge in 54 PMTs)/(Total charge of 54 PMTs) < 0.3”, background events from β decay of 115In and Cherenkov photons, which make peaks around 1 in the above figures, can be removed.

110 10

1 event rate(counts/day/kg/keV)

-1 10

0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV)

Figure 8.6: Reconstructed energy spectrum of Full volume for the dark matter search run (0 < Ereconst. < 500 keV). The black line is the spectrum with the “noise cut,” and the peak around 110 keV is made by ADC saturation. The pink line is the spectrum with an additional “ADC saturation cut” on the black line, and the peak around 110 keV disappears. Blue line is the spectrum with additional “maximum PMT ratio cut” for pink line. Background events near PMTs can be removed with the “ADC saturation cut” and “maximum PMT ratio cut.”

111 1 -1 10 -2 10

counts/day/kg/keV -3 10

0 500 1000 1500 2000 2500 3000 reconstructed energy (keV) 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 counts/day/kg/keV 0.04 0.02 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

Figure 8.7: Reconstructed energy spectrum of the dark matter search run (0 < Ereconst. < 3000 keV). Red line corresponds to 15cm FV with the “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut.”

112 1 -1 10 -2 10

counts/day/kg/keV -3 10

0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV) 0.14 0.12 0.1 0.08 0.06

counts/day/kg/keV 0.04 0.02 0 0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV)

Figure 8.8: Reconstructed energy spectrum of the dark matter search run (0 < Ereconst. < 500 keV). Red line corresponds to 15cm FV with the “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut.”

113 1 -1 10 -2 10

counts/day/kg/keV -3 10

0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV) 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 counts/day/kg/keV 0.02 0.01 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 8.9: Reconstructed energy spectrum of dark matter search run (0 < Ereconst. < 100 keV). Red line corresponds to 15cm FV with the “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut.”

114 8.4 Results 8.4.1 Obtained spectrum The reconstructed energy spectrum of the dark matter search run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut” and 15cm FV after the eﬃciency collection is shown in Fig. 8.10, and 5 < Ereconst. < 10 keV is used as the dark matter search window. Twenty-two events remain in this dark matter search window and these events are used to calculate a constraint on the neutralino-nucleus cross section σχ−N in Section 8.4.4. The eﬃciency for this event selection is discussed in Section 7.11.

0.3

0.25

counts/day/kg/keV 0.2

0.15

0.1

0.05

0 0 5 10 15 20 25 30 35 40 45 50 reconstructed energy (keV)

Figure 8.10: Reconstructed energy spectrum of the dark matter search run after the eﬃciency collection with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut” and 15cm FV. Twenty-two events remain in dark matter search window, 5 < Ereconst. < 10 keV.

8.4.2 Expected dark matter signal The expected dark matter signal is derived as described in Chapter 3 with the astrophysical parameters listed in Table 8.1. As discussed in Section 4.4, the following quenching factor fQ is used for liquid xenon.

fQ = 0.2 (8.2)

115 The expected deposited energy of a dark matter signal for natural xenon is shown in Fig. 8.11, and the reconstructed energy spectrum of a dark matter signal is calculated with detector simulation as shown in Fig. 8.12.

−2 −3 ρD (Dark Matter density) 0.3 GeV c cm Velocity distribution Maxwellian −1 v0 (Most probable velocity of the Maxwellian) 220 km s −1 vE (Earth velocity) 244 km s −1 vesc (Escape velocity) 450 km s

Table 8.1: Astrophysical parameters used to derive the limit.

116 10

-1 10event rate(counts/day/kg/keV)

-2 10

0 2 4 6 8 10 12 14 16 18 20 deposit energy (keVee)

Figure 8.11: Expected deposited energy of a dark matter signal for natural −5 xenon (Spin independent interaction and σχ−p = 1.0 10 pb). Red, blue and × 2 green lines are for the cases of Mχ = 50, 100 and 200 GeV/c , respectively.

117 0.3

0.25

0.2

0.15 event rate(counts/day/kg/keV)

0.1

0.05

0 0 5 10 15 20 25 30 35 40 45 50 reconstructed energy (keV)

Figure 8.12: Reconstructed energy spectrum of a dark matter signal after the eﬃciency collection calculated with the detector simulation (Spin independent −5 2 interaction , σχ−p = 1.0 10 pb and Mχ = 100 GeV/c ). Red line is 15cm FV with the “noise cut”,× “ADC saturation cut” and “maximum PMT ratio cut.”

118 8.4.3 Systematic errors As shown in Fig. 8.13, a event rate of a dark matter signal simulation in 5 < Ereconst. < 10 keV with “maximum PMT ratio cut” and 15cm FV change 0.2 % with “noise cut”, then the systematic error for “noise cut” in the dark matter search window, 5 < Ereconst. < 10 keV, is set as 0.2 %.

0.3

0.25

0.2

0.15 event rate(counts/day/kg/keV)

0.1

0.05

0 0 5 10 15 20 25 30 35 40 45 50 reconstructed energy (keV)

Figure 8.13: Reconstructed energy spectrum of a dark matter signal with “maximum PMT ratio cut.” and 15cm FV after the eﬃciency collection calculated −5 with the detector simulation (Spin independent interaction , σχ−p = 1.0 10 2 × pb and Mχ = 100 GeV/c ). Blue and red lines are the spectrum without and with “noise cut”. By comparing the event rate of blue and red lines, the systematic error for “noise cut” in the dark matter search window, 5 < Ereconst. < 10 keV, is set as 0.2 %.

As discussed in Section 7.11, the systematic error for “maximum PMT ratio cut” and 15cm FV in the dark matter search window, 5 < Ereconst. < 10 keV, is set as 27.5 %. As discussed in Section 4.4, the smallest quenching factor of liquid xenon in Table 4.4 , fQ = 0.2, is used to derive the constraint on the neutralino- nucleus cross section conservatively. Here we assume that the quenching factor, fQ = 0.2, has 10 % error. As shown in Fig. 8.14, a event rate of a dark matter signal simulation in 5 < Ereconst. < 10 keV with “noise cut”, “maximum PMT ratio cut” and 15cm FV change 0.2 % with 10 % reduction of the quenching factor, then the systematic error for the quenching factor in the dark matter

119 search window, 5 < Ereconst. < 10 keV, is set as 25.4 %.

0.3

0.25

0.2

0.15 event rate(counts/day/kg/keV)

0.1

0.05

0 0 5 10 15 20 25 30 35 40 45 50 reconstructed energy (keV)

Figure 8.14: Reconstructed energy spectrum of a dark matter signal with “noise cut”, “maximum PMT ratio cut.” and 15cm FV after the eﬃciency collection calculated with the detector simulation (Spin independent interaction , σχ−p = −5 2 1.0 10 pb and Mχ = 100 GeV/c ). Blue and red lines are the spectrum without× and with 10 % reduction of the quenching factor. The event rates of blue and red lines in the dark matter search window 5 < Erecon. < 10 keVee; are 0.143( 0.004) and 0.114( 0.004); the systematic error to the quenching factor is set as 25.4 %.

Combining the systematic errors for “noise cut”, “maximum PMT ratio cut”, 15cm FV and the quenching factor, the total systematic error for the dark matter search with “noise cut”, “maximum PMT ratio cut” and 15cm FV in the dark matter search window, 5 < Ereconst. < 10 keV, is set as 37.4 % as shown in Table 8.2.

120 Item Systematic error (%) “noise cut” 0.2 “maximum PMT ratio cut” 27.5 and 15cm FV Quenching factor (fQ) 25.4 Total 37.4

Table 8.2: Systematic errors to derive the constraint on the neutralino-nucleus cross section from the dark matter search run.

121 8.4.4 Constraint on Neutralino-Nucleus cross section σχ−N We conservatively assumed that all the remaining events in the dark matter search window are caused by the neutralino, and the limit of σχ−N was calculated by comparing these remaining events with the expected dark matter signal by detector simulation. The 90 % conﬁdence level upper limit count, Nlim. is deﬁned by the observed events, Nobs., and the total systematic error, errsys = 0.374, as

N = N (1 + err ) + 1.28 N (1 + err ) (8.3) lim. obs. sys · obs. sys q for Nobs.(1 + errsys) > 10. As shown in Fig. 8.15 and 8.16, respectively, we obtained the upper limits, 1.70 10−5 pb for the spin-independent neutralino-proton cross section with neutralino× mass 62 GeV/c2, and 6.74 pb for the spin-dependent neutralino- proton cross section with neutralino mass 60 GeV/c2. The limit of the spin- SD dependent cross section, σχ−p, is calculated on the basis of the odd group model as discussed in Section 3.3.4. We also follow a “model-independent” framework described in Section 3.3.4 for the interpretation of the remaining events in terms of spin-dependent interactions. The obtained limits of σSD in the cases of pure proton coupling (an = 0) and pure neutron coupling (ap = 0) are shown in Fig. 8.17 and 8.18, respectively.

122 -2 10 (pb) -p χ

SI -3

σ 10

-4 10

-5 10

-6 10

-7 10

-8 10 2 3 10 10 10 -2 Mχ (GeVc )

SI Figure 8.15: Limits of spin-independent cross section, σχ−p, as a function of Mχ. The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment is shown by the red (This work) line. DAMA’s allowed region is shown by the pink line[28]. The limits by EDELWEISS [30] and CDMS II [31] with cryogenic germanium detectors are shown by the blue and light-blue line. The world’s current lowest limit by XENON10 with a dual phase xenon detector is shown by the green line [32]. MSSM predictions are shown by the black line.

123 10 3 (pb) -p

χ 2

SD 10 σ

-1 10

-2 10

-3 10

-4 10 2 3 10 10 10 -2 Mχ (GeVc )

SD Figure 8.16: Limits of spin-dependent cross section, σχ−p, as a function of Mχ on the basis of the odd group model. The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment is shown by the red (This work) line. The limits by UKDMC [27] and DAMA [29] with NaI(Tl) detectors are shown by the blue and green lines. The limit by CRESST with cryogenic Al2O3 detector is shown by the pink dotted line [33]. The limit by the Tokyo group with CaF2 scintillator is shown by the light-blue line [34]. MSSM predictions are shown by the black line.

124 10 5 (pb) -p

χ 4

SD 10 σ

10 3

10 2

-1 10

-2 10 2 3 10 10 10 -2 Mχ (GeVc )

SD Figure 8.17: Limits of spin-dependent cross section, σχ−p, as a function of Mχ in the cases of pure proton coupling (an = 0). The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment is shown by the red (This work) line. The limit by CDMS II with cryogenic germanium detector is shown by green line [73]. The limit by the Tokyo group with CaF2 scintillator is shown by the blue line [34]. The world’s current lowest limit by UKDMC with NaI(Tl) detectors is shown by the pink line [27].

125 10 4 (pb) -n

χ 3

SD 10 σ

10 2

-1 10

-2 10

-3 10 2 3 10 10 10 -2 Mχ (GeVc )

SD Figure 8.18: Limits of spin-dependent cross section, σχ−n, as a function of Mχ in the cases of pure neutron coupling (ap = 0). The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment is shown by the red (This work) line. The limit by the Tokyo group with CaF2 scintillator is shown by the blue line [34]. The world’s current lowest limit by CDMS II with cryogenic germanium detector is shown by green line [73].

126 Chapter 9

Discussions

In this chapter, we will discuss the remaining background in the dark matter search data.

9.1 Background from outside the liquid xenon

γ rays and neutrons are the major background from outside the liquid xenon, and these backgrounds are estimated with the detector simulation as discussed in Section 9.1.1 and 9.1.2.

9.1.1 γ rays from PMTs, the lead shield and the ambient The contents of radioactive impurities in the PMT, R8778ASSY, are shown in Table 6.2. γ-ray backgrounds from these impurities were estimated with the detector simulation as shown in Fig. 9.1, 9.2 and 9.3. γ rays were generated uniformly from the positions of the PMTs in the simulation. A simulation package for particle decay, DECAY4 [74], was used to decide the initial energy of a γ ray from U-chains and Th-chains. The count rate of each γ-ray background spectrum was adjusted to that of the dark matter search run by multiplying fac- tors as shown in Table 9.1, because we did not measure the content of impurities for all of the PMTs by HPGe.

U-chain Th-chain 40K 60Co factor 1.6 1.4 0.8 0.7

Table 9.1: Multiplicative factor for the count rate to reproduce the estimated γ-ray background from the PMTs in the dark matter search run.

The decay rate of 210Pb in the lead shield was measured to be 250 Bq/kg with the HPGe detector, and γ rays are generated through bremsstrahlung as shown in Fig. 9.4. The background from these γ rays was estimated with the detector simulation as shown in Fig 9.5. The ambient γ-ray ﬂux in the Kamioka Observatory calculated with HPGe measurement and GEANT3 simulation is shown in Fig. 9.6. Ambient γ rays reaches the detector through holes in the radiation shield for gas lines and

127 PMT cables. Background from ambient γ rays was estimated with the detector simulation, as shown in Fig. 9.7. The reconstructed energy spectrum of the combined γ-ray backgrounds from outside the liquid xenon (U-chain, Th-chain, 40K and 60Co in the PMTs, the lead shield, and ambient γ rays) is compared with that of the dark matter search run, as shown in Fig. 9.8, 9.9, and 9.10. A peak below 100 keV exists in the energy spectrum of the dark matter search run, but it does not exist in that of the estimated γ-ray background.

128 Background from the PMTs (Simulation) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 1000 2000 3000 0 1000 2000 3000 reconstructed energy (keV) reconstructed energy (keV) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 1000 2000 3000 0 1000 2000 3000 reconstructed energy (keV) reconstructed energy (keV)

0.14 0.14 0.12 0.12 0.1 0.1 0.08 0.08 0.06 0.06

counts/day/kg/keV 0.04 0.04 0.02 0.02 0 0 0 1000 2000 3000 0 1000 2000 3000 reconstructed energy (keV) reconstructed energy (keV) 0.14 0.14 0.12 0.12 0.1 0.1 0.08 0.08 0.06 0.06

counts/day/kg/keV 0.04 0.04 0.02 0.02 0 0 0 1000 2000 3000 0 1000 2000 3000 reconstructed energy (keV) reconstructed energy (keV)

Figure 9.1: Reconstructed energy spectrum of γ-ray background from the PMTs estimated with the detector simulation (0 < Ereconst. < 3000 keV). Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line.

129 Background from the PMTs (Simulation) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 200 400 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 200 400 0 200 400 reconstructed energy (keV) reconstructed energy (keV)

0.05 0.05 0.045 0.045 0.04 0.04 0.035 0.035 0.03 0.03 0.025 0.025 0.02 0.02 0.015 0.015 counts/day/kg/keV 0.01 0.01 0.005 0.005 0 0 0 200 400 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 0.05 0.05 0.045 0.045 0.04 0.04 0.035 0.035 0.03 0.03 0.025 0.025 0.02 0.02 0.015 0.015 counts/day/kg/keV 0.01 0.01 0.005 0.005 0 0 0 200 400 0 200 400 reconstructed energy (keV) reconstructed energy (keV)

Figure 9.2: Reconstructed energy spectrum of γ-ray background from the PMTs estimated with the detector simulation (0 < Ereconst. < 500 keV). Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line.

130 Background from the PMTs (Simulation) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV)

0.006 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.001counts/day/kg/keV 0.001 0 0 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV) 0.006 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.001counts/day/kg/keV 0.001 0 0 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV)

Figure 9.3: Reconstructed energy spectrum of γ-ray background from the PMTs estimated with the detector simulation (0 < Ereconst. < 100 keV). Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line.

131 Figure 9.4: Decay chain of 210Pb.

132 Background from the lead shield (Simulation) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 1000 2000 3000 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 1 -1 10 -2 10 -3 10

counts/day/kg/keV -4 10 0 20 40 60 80 100 reconstructed energy (keV)

0.008 0.008 0.007 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.003 0.003

0.002counts/day/kg/keV 0.002 0.001 0.001 0 0 0 1000 2000 3000 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 0.008 0.007 0.006 0.005 0.004 0.003

0.002counts/day/kg/keV 0.001 0 0 20 40 60 80 100 reconstructed energy (keV)

Figure 9.5: Reconstructed energy spectrum of γ-ray background from the lead shield with the detector simulation. Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red lines.

133 Figure 9.6: Calculated ﬂux of ambient γ rays in the Kamioka Observatory [75].

134 Background from the ambient γ (Simulation) 1 1 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10

counts/day/kg/keV -4 -4 10 10 0 1000 2000 3000 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 1 -1 10 -2 10 -3 10

counts/day/kg/keV -4 10 0 20 40 60 80 100 reconstructed energy (keV)

0.03 0.03 0.025 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005counts/day/kg/keV 0.005 0 0 0 1000 2000 3000 0 200 400 reconstructed energy (keV) reconstructed energy (keV) 0.03 0.025 0.02 0.015 0.01 0.005counts/day/kg/keV 0 0 20 40 60 80 100 reconstructed energy (keV)

Figure 9.7: Reconstructed energy spectrum of γ-ray background from ambient γ rays with the detector simulation. Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line.

135 1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 counts/day/kg/keV 0.04 0.02 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV) 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 counts/day/kg/keV 0.04 0.02 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

Figure 9.8: Reconstructed energy spectrum of the dark matter search run and that of the combined γ-ray backgrounds from outside the liquid xenon (U-chain, Th-chain, 40K and 60Co in the PMTs, the lead shield, and ambient γ rays) estimated with the detector simulation (0 < Ereconst. < 3000 keV). Energy spectrum of 15 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line.

136 1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV)

1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV)

0.16 0.14 0.12 0.1 0.08 0.06

counts/day/kg/keV 0.04 0.02 0 0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV) 0.16 0.14 0.12 0.1 0.08 0.06

counts/day/kg/keV 0.04 0.02 0 0 50 100 150 200 250 300 350 400 450 500 reconstructed energy (keV)

Figure 9.9: Reconstructed energy spectrum of the dark matter search run and that of the combined γ-ray backgrounds from outside the liquid xenon (U-chain, Th-chain, 40K and 60Co in the PMTs, the lead shield, and ambient γ rays) estimated with the detector simulation (0 < Ereconst. < 500 keV). Energy spectrum of 10 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line. There is a peak below 100 keV in the dark matter search run, but it does not exist in the estimated γ-ray background.

137 1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

1 -1 10 -2 10 -3 10 counts/day/kg/keV -4 10 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 counts/day/kg/keV 0.02 0.01 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV) 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 counts/day/kg/keV 0.02 0.01 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.10: Reconstructed energy spectrum of the dark matter search run and that of the combined γ-ray backgrounds from outside the liquid xenon (U- chain, Th-chain, 40K and 60Co in the PMTs, the lead shield, and ambient γ rays) estimated with the detector simulation (0 < Ereconst. < 100 keV). Energy spectrum of 10 cm FV with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut” is shown by the red line. A peak below 100 keV exists in the dark matter search run, but it does not exist in the estimated γ-ray background.

138 9.1.2 Ambient neutrons The neutron ﬂux inside the radiation shield in the Kamioka Observatory was measured with a 3He proportional counter as shown in Table 9.2 [76]. Since the shield has the same composition as that of the prototype detector, the same neutron ﬂux is expected for the prototype detector.

Location thermal neutron non-thermal neutron Inside of the radiation shield < 4.8 10−7 < 3.4 10−6 in the Kamioka Observatory × ×

Table 9.2: Neutron ﬂux (neutron cm−2 s−1) inside the radiation shield in the Kamioka Observatory measured with a 3He proportional counter [76]. Since the shield has the same composition as that of the prototype detector, the same neutron ﬂux is expected for the prototype detector.

Xenon captures thermal neutrons, and it becomes a radioactive isotope as shown in Table 9.3. The expected background spectrum from thermal neutrons is shown in Fig. 9.11 [77].

before abun. after cross section (b) τ1/2 disinteg. mode E (keV) 124Xe 0.10 125mXe 28 57.8 sec IT 140.8 (γ) 111.8 (γ) 124Xe 0.10 125Xe 165 16.9 hour EC 243.4 (γ) 188.4 (γ) 126Xe 0.09 127mXe 0.45 69.2 sec IT 124.7 (γ) 172.4 (γ) 126Xe 0.09 127Xe 3.5 36.4 day EC 375.0 (γ) 202.9 (γ) 128Xe 1.91 129mXe 0.48 8.88 day IT 39.58 (γ) 196.6(γ) 130Xe 4.1 131mXe 0.45 11.8 day IT 163.9 (γ) 132Xe 26.9 133mXe 0.05 2.19 day IT 233.2 (γ) 132Xe 26.9 133Xe 0.45 5.24 day β− 346.0 (β) 81.0 (γ) 134Xe 10.4 135mXe 0.003 15.3 min IT 526.6 (γ) 134Xe 10.4 135Xe 0.265 9.14 hour β− 910.0 (β) 249.8.0 (γ) 136Xe 8.9 137Xe 0.26 3.8 min β− 4170.0 (β) 3720.0 (β) 455.5 (γ)

Table 9.3: Thermal neutron capture by xenon.

When the ﬂux of thermal neutrons is = 4.8 10−7 neutron cm−2 s−1, the expected background level is 2 10−7 counts/da× y/kg/keV below 10keVee. Then the background from thermal∼ × neutron is negligible for the dark matter search with the prototype detector.

139 -1 10

-2 10

-3

counts/day/kg/keV 10

-4 10

-5 10

-6 10

-7 10

0 10 20 30 40 50 60 70 80 90 100 deposit energy (keVee)

Figure 9.11: Expected background spectrum from thermal neutrons [77] for thermal neutron ﬂux = 4.8 10−7 neutron cm−2 s−1. Background level is 2 10−7 counts/day/kg/k×eV below 10keVee; the background from thermal ∼neutrons× is negligible for the dark matter search with the prototype detector.

If the following conditions are satisfied, the energy spectrum of non-thermal neutrons is represented by the “1/E law”. Neutron sources are distributed uniformly inside a boueless moderator. • The moderater rarely absorbs neutrons. • The Kamioka Observatory satisfies the above conditions. Because the laboratory is surrounded by a base rock which contains a small amount of water, the “1/E law” was assumed to calculate the non-thermal neutron flux in the laboratory. Since we couldn’t measure the energy spectrum of non-thermal neutrons with a 3He proportional counter, the “1/E law” was used for the energy spectrum of non-thermal neutrons inside the shield to calculate the non-thermal flux in Table 9.2. An expected background spectrum from non-thermal neutrons is calculated with GEANT4 (for the tracking of neutrons) and GENAT3 (for the tracking of scintillation photons) as shown in Fig. 9.12. The “1/E law” is used for the energy spectrum of non-thermal neutrons. The peak around 50 keV exists in the spectrum, but it does not exist in the dark matter search run (see Fig. 8.10). The expected background spectrum from neutrons with monochromatic

140 energies, 1 MeV and 10 MeV, are shown in Fig. 9.13 and 9.14, and the inelastic peaks still exist. From these results, we conclude that the low energy peak of the dark matter search run is not made by the non-thermal neutron background.

Background from non-thermal neutrons (Simulation) 0.06

0.05

counts/day/kg/keV 0.04

0.03

0.02

0.01

0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.12: Expected background spectrum from non-thermal neutrons for non-thermal neutron ﬂux = 3.4 10−6 neutron cm−2 s−1. The “1/E law” is used for the energy spectrum of×non-thermal neutrons inside the shield. The peak around 50 keV made by inelastic scattering of the neutrons exists.

141 Background from non-thermal neutrons (Simulation) 0.16

0.14

0.12 counts/day/kg/keV 0.1

0.08

0.06

0.04

0.02

0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.13: Expected background spectrum from non-thermal neutrons for non-thermal neutron ﬂux = 3.4 10−6 neutron cm−2 s−1. Neutrons have the monochromatic energy, 1 MeV.×The peak around 50 keV made by inelastic scattering of the neutrons also exists.

142 Background from non-thermal neutrons (Simulation) 0.1

0.09

0.08

0.07 counts/day/kg/keV 0.06

0.05

0.04

0.03

0.02

0.01

0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.14: Expected background spectrum from non-thermal neutrons for non-thermal neutron ﬂux = 3.4 10−6 neutron cm−2 s−1. Neutrons have the monochromatic energy, 10 MeV.×The peak around 50 keV made by inelastic scattering of the neutrons also exists.

143 9.2 Background from inside the liquid xenon

In a low background experiment, contamination within the detector often de- termines the background level. We will start the estimation of the remaining backgrounds with the contaminations within the liquid xenon.

9.2.1 Uranium series inside xenon 238U has the long half life, 4.468 109 year, and it continuously decays into a stable nucleus, 206Pb, as shown in× Fig. 9.15. The content of 238U was measured by the delayed coincidence signal of 214Bi (see Fig. 9.16). A radioactive equilibrium of the uranium series was assumed for this calculation, but it was possibly broken between 226Ra and 222Rn because the half-lives of the nuclei before 226Ra are longer than those of the nuclei after 222Rn. Data taking for the uranium series search was done twice. First and second data were taken on 2006/11/25 (live time = 0.853 days) and 2006/12/15 (live time = 0.786 days), respectively. Alpha rays from delayed coincidence events have relatively high energy, so the nominal gain of the 54 PMTs was set to 0.35 106 to measure these events without causing ADC saturation. After× collecting primary data, the data acquisition system waits for a delayed event during 1000 µs. We treat the delayed events as subevents which are attached to the primary events. A distribution of the number of subevents is shown in Fig. 9.17. The following cut is applied for events which have more than one subevent: 15< ∆T<1000 µs (Eﬃciency = 94 %) • Here, ∆T is the time diﬀerence from a primary event to a subevent. Re- constructed energy spectra of subevents in the 214Bi search run with “15< ∆T<1000 µs” are shown in Fig. 9.18. Events with “Esub. >5 MeV” are selected as the delayed coincidence events (Esub.: reconstructed energy of subevents). Distributions of ∆t of the delayed coincidence events are shown in Fig. 9.19. Distributions of the distance between the primary event and a subevent for the delayed coincidence events are shown in Fig. 9.20. Vertex distributions of the delayed coincidence events are shown in Fig. 9.21 and 9.22; they are distributed uniformly inside the detector. Reconstructed energy spectra of primary events in the 214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV” are shown in Fig. 9.23. Comparing the spectrum of the primary events with that of the simulation, the contents of 238U in xenon are calculated to be:

238U/Xe = 47( 9) 10−14 [g/g] in 2006/11/25 (9.1) × = 11( 4) 10−14 [g/g] in 2006/12/15 (9.2) × If we assume that the origin of the delayed coincidence events is 222Rn which exists inside the xenon from the begining, the expected content of 238U in 222 2006/12/15 is calculated with a half life of Rn (τ1/2 = 3.8 day) as follows,

19.15 [days] 238U/Xe = 47( 9) 10−14 exp × × −3.8 [days]/ ln 2 = 1.4( 0.3) 10−14 [g/g] ×

144 If the calculated value does not agree with the measured value in 2006/12/15 to within the error, then some part of the delayed coincidence events may have a diﬀerent origin. When the content of 238U inside xenon is 238U/Xe = 100 10−14 [g/g], the estimated background level is 2 10−4 counts/day/kg/keV× below 10keVee. Thus the background from the∼uranium× series is negligible for the dark matter search with the prototype detector. To achieve the target sensitivity of the single phase detector with 800 kg of liquid xenon (which is discussed in Chapter 10), a content of 238U inside xenon, 238U/Xe = 1 10−14 [g/g], is required. We are developing a distillation system to achieve the×above requirement with about one order of magnitude reduction of 238U inside xenon.

145 Figure 9.15: Uranium series.

τ 1/2= 164.3µs 214Bi 214Po 210Pb β (99.98%) α (100%) Q β = 3.27MeV 7.687 MeV

Figure 9.16: Decay scheme of 214Bi.

146 10 5 10 4 10 3 10 2 10 1 0 1 2 3 4 5 number of subevent 10 5 10 4 10 3 10 2 10 1 0 1 2 3 4 5 number of subevent

Figure 9.17: Distribution of the number of subevents (214Bi search run). Up- per and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15 and the events which have more than one subevent are 73 events and 45 events, respectively.

147 10 3 10 2 10

number of event 1 -1 10 0 2 4 6 8 10 12 reconstructed energy of subevent (MeV) 10 3 10 2 10

number of event 1 -1 10 0 2 4 6 8 10 12 reconstructed energy of subevent (MeV)

Figure 9.18: Reconstructed energy spectra of subevents (214Bi search run with “15< ∆T<1000 µs”). Real data are shown by the black points. Accidental events estimated from the real data are shown by the red line. Simulated events 214 of α ray from Po are shown by the blue line. The events with “Esub. >5 MeV” are selected as the delayed coincidence events. Upper and lower ﬁgures are the data taken on2006/11/25 and 2006/12/15 and the number of events with “Esub. >5 MeV” are 35 and 7, for each data run, respectively.

148 14 12 10 8 6 number of event 4 2 0 0 200 400 600 800 1000 time difference between primary and subevent (µs) 6 5 4 3

number of event 2 1 0 0 200 400 600 800 1000 time difference between primary and subevent (µs)

Figure 9.19: Distributions of ∆t (214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV”). Upper and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15. Distributions of the real data are shown by the black lines, and the expected distributions with τ1/2 = 164 µs are shown by the red lines.

149 14 12 10 8 6 number of event 4 2 0 0 5 10 15 20 25 30 distance between primary and subevent (cm) 8 7 6 5 4 3 number of event 2 1 0 0 5 10 15 20 25 30 distance between primary and subevent (cm)

Figure 9.20: Distributions of the distance between a primary event and a subevent calculated with the reconstructed vertex (214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV”). Upper and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15. Distributions of the real data are shown by the black points, and those of the simulation are shown by the blue lines.

150 10 9 8 7 6 5 4 number of event 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 volume from center by reconstructed vertex (subevent) (kg) 5 4.5 4 3.5 3 2.5 2 1.5number of event 1 0.5 0 0 10 20 30 40 50 60 70 80 90 100 volume from center by reconstructed vertex (subevent) (kg)

Figure 9.21: Vertex distribution at each volume from the center of the detector calculated with the reconstructed vertex of the subevents (214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV”). Upper and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15. Distributions of the real data and the simulation are shown by the black points and the blue line.

151 1.2 1 0.8 0.6 0.4

integrated fraction 0.2 0 0 10 20 30 40 50 60 70 80 90 100 volume from center by reconstructed vertex (subevent) (kg) 1.2 1 0.8 0.6 0.4

integrated fraction 0.2 0 0 10 20 30 40 50 60 70 80 90 100 volume from center by reconstructed vertex (subevent) (kg)

Figure 9.22: Integrated fraction at each volume from the center of the detector calculated with the reconstructed vertex of the subevents (214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV”). Upper and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15. Distributions of the real data and the simulation are shown by the black points and the blue line.

152 20 18 16 14 12 10 8 number of event 6 4 2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 reconstructed energy of primary event (MeV) 10 9 8 7 6 5 4 number of event 3 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 reconstructed energy of primary event (MeV)

Figure 9.23: Reconstructed energy spectra of primary events (214Bi search run with “15< ∆T<1000 µs” and “Esub. >5 MeV”). Upper and lower ﬁgures are the data taken on 2006/11/25 and 2006/12/15. Distributions of the real data and the simulation are shown by the black points and the blue line, respectively. By comparing the spectrum of the primary events with that of the simulation, the contents of 238U in xenon are calculated.

153 9.2.2 Thorium series inside xenon 232Th has a long half life, 1.405 1010 years, and it continuously decays into a stable nucleus, 208Pb, as shown×in Fig. 9.24. The content of 232Th was measured by the delayed coincidence signal of 212Bi (see Fig. 9.25). A radioactive equilibrium of the thorium series was assumed for this calculation.

Figure 9.24: Thorium series.

The content of the thorium series was measured with the prototype detector in August 2004. The details of the measurement are shown in [69]. No delayed coincidence events of 212Bi were found, and the following upper limit is achieved: 232Th/Xe < 23 10−14 [g/g] (90 % CL) (9.3) × When the content of 232Th inside xenon is 232Th/Xe = 23 10−14 [g/g], the estimated background level is 1 10−4 counts/day/kg/keV× below 10keVee. ∼ ×

154 τ 1/2= 299 ns 212Bi 212Po 208Pb β (64.0%) α (100%) Q β= 2.25MeV 8.785 MeV

Figure 9.25: Decay scheme of 232Th.

Thus the background from the thorium series is negligible for the dark matter search with the prototype detector. To achieve the target sensitivity of the single phase detector with 800 kg of liquid xenon (which is discussed in Chapter 10), a content of 232Th inside xenon, 232Th/Xe = 2 10−14 [g/g], is required. We are developing a distillation system to achieve the×above requirement with about one order of magnitude reduction of 232Th inside xenon.

155 9.2.3 Krypton inside xenon 85Kr has a relatively long half life, 10.756 years, and it decays into a stable nucleus, 85Rb, as shown in Fig. 9.26. 10.756y 9/2+ 0 85 36Kr

Q β− =687.0

0.434% 9/2+ 514.0083 1.015 µs

514.0keV

99.563% 5/2− 0 85 Stable 37Rb

Figure 9.26: Decay scheme of 85Kr.

85Kr originally doesn’t exist in nature, but it has been generated through the burning process of uranium fuel with a light-water reactor in recent years. The present abundance of 85Kr in Kr was measured by a HPGe detector as follows,

85Kr/Kr = 1.15 10−11 (9.4) × 95.563 % of 85Kr decays into the ground state of 85Rb through β decay with Qβ = 687.0 keV. The expected background spectrum from this β decay for the case of Kr/Xe = 10 ppt and 85Kr/Kr = 1.15 10−11 is shown in Fig. 9.27. The krypton concentration in the processed× xenon gas measured by gas chromatography and a photoionization detector was 3.3( 1.1) ppt as discussed in Section 6.2.1. When the content of krypton inside xenon is Kr/Xe = 5 ppt (mol/mol), the estimated background level is 1 10−4 counts/day/kg/keV below 10keVee. Then the background from krypton∼ ×is negligible for the dark matter search with the prototype detector. To achieve the target sensitivity of the single phase detector with 800 kg of liquid xenon (which is discussed in Chapter 10), a content of krypton inside xenon, Kr/Xe = 1ppt (mol/mol), is required. We are developing a distillation system to achieve the above requirement with factor three reduction of krypton inside xenon.

156 -3 10

-4

counts/day/kg/keV 10

-5 10

-6 10

0 200 400 600 800 1000 deposit energy (keVee)

Figure 9.27: Expected background spectrum from the β decay of 85Kr for the case of Kr/Xe = 10 ppt and 85Kr/Kr = 1.15 10−11. ×

157 9.3 Background caused by the detector geometry

Reconstructed energy spectra of γ rays from a 232Th source (lantern mantles) inside the radiation shield (see Section 7.10.4) are shown in Fig. 9.28. Recon- structed energy spectra of the ambient γ-ray run are shown in Fig. 9.29. (The door of the radiation shield was open to introduce the ambient γ rays inside the radiation shield as shown in Fig. 6.4.) Low energy peaks below 30 keV, which exists only in the real data, are found. The shape of these peaks in the real data are similar to to that of the low energy peak of the dark matter search run (see Fig. 8.10). These low energy peaks of the γ-ray calibration data can be caused by the events which happened in the small gaps of the detector. If an interaction happened in the gap, only a small fraction of scintillation photons can come out from it. Then these events pile up at low energy and some fraction of them are mis-reconstructed into the ﬁducial volume. Pictures of the gaps are shown in Fig. 9.30.

158 Thorium series inside the radiation shield 600 500 400 300 200 counts/day/kg/keV 100 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV) 600 500 400 300 200 counts/day/kg/keV 100 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

140 120 100 80 60 40 counts/day/kg/keV 20 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV) 140 120 100 80 60 40 counts/day/kg/keV 20 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.28: Reconstructed energy spectrum of γ rays from 232Th source (lantern mantles) inside the radiation shield with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut.” 15cm FV is shown by the red line. A peak below 30 keV, which exists only in the real data, is found.

159 Ambient γ rays (Door of the radiation shield is open) 20 18 16 14 12 10 8 6 counts/day/kg/keV 4 2 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV) 20 18 16 14 12 10 8 6 counts/day/kg/keV 4 2 0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

3 2.5 2 1.5 1 counts/day/kg/keV 0.5 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV) 3 2.5 2 1.5 1 counts/day/kg/keV 0.5 0 0 10 20 30 40 50 60 70 80 90 100 reconstructed energy (keV)

Figure 9.29: Reconstructed energy spectrum of the ambient γ-ray run with “noise cut”, “ADC saturation cut” and “maximum PMT ratio cut.” 15cm FV is shown by the red line. (The door of the radiation shield was open to introduce the ambient γ rays inside the radiation shield as shown in Fig. 6.4.) A peak below 30 keV, which exists only in the real data, is found.

160 Figure 9.30: Pictures of small gaps in the prototype detector. The low energy peaks can be caused by the events which happened in these gaps.

161 9.4 Wave form analysis

In this section, wave forms of the dark matter search data were checked to understand the origin of its low energy peak. Wave forms were evaluated with “mean hit timing” which is deﬁnied in Section 9.4.1.

9.4.1 Deﬁnition of “mean hit timing” The “mean hit timing” is deﬁned as follows,

54 ∆t “mean hit timing” = i=1 i (9.5) “number of hit PMT” 1 P − where 0 for non hit PMTs ∆t = (9.6) i “Hit time of PMT from ﬁrst hit” for hit PMTs i If the decay time of the scintillation light is ﬁxed, “mean hit timing” changes with total photoelectron. Relations between the decay time of scintillation light and “mean hit timing” are calculated with a Monte Carlo simulation as shown in Fig. 9.31. Here, the following conditions are assumed in the simulation. The rising time of the scintillation light is 15 ns. • Probabilities to detect scintillation photons are equal for 54 PMTs. • Fistest hit time of each PMT is adopted as “hit time”. •

9.4.2 “mean hit timing” of the dark matter search run “mean hit timing”-“reconstructed energy” scatter plots of the dark matter search run, the Am/Be neutron source run, the ambient γ-ray run, and the 208Th source run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut” and 15cm FV are shown in Fig. 9.32. Projections of Fig. 9.32 to y axis for the events with “reconstructed energy < 30 keV” are shown in Fig. 9.33. In Fig. 9.33, about a half of the events of the dark matter search run exist in “mean hit timing” < 25 ns, but only a small fraction of the events of the ambient γ-ray run and 232Th source run exist in the same region. As disscussed in Section 9.3, a large fraction of the events below 30 keV of the ambient γ-ray run and 232Th source run can be caused by the events which happened in the small gaps of the detector, so the events with “mean hit timing > 25 ns” in Fig. 9.33 can be explained as the gap events. A number of gap events can be proportion to a number of high energy events. An reconstructed energy spectrum above 600 keV with “noise cut” of the ambient γ-ray run is similar to that of the dark matter search run, so the reconstructed energy spectrum of the dark matter search run is compared with that of the ambient γ-ray run as shown in Fig. 9.34. Here, the number of event above 600 keV of the ambinet γ-ray run is normalized to that of the dark matter search run. Reconstructed energy spectrums of each run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut” and 15cm FV are

162 60

40 mean hit timing (ns)

0 0 10 20 30 40 50 60 Decay time of scintillation light (ns)

Figure 9.31: Relation between the decay time of scintillation light and “mean hit timing” calculated with a Monte Carlo simulation. Black, red, green, blue and pink points corresponnd to 10, 20, 30, 40 and 50 total photoelectrons.

compared in Fig 9.35 and 9.36. From Fig. 9.35, the low energy peak with “mean hit timing > 25 ns” of the dark matter search run coincide with that of the ambient γ-ray run, so it can be explained with the events which happened in the small gaps of the detector. From Fig. 9.36, the low energy peak with “mean hit timing < 25 ns” of the dark matter search run is diﬀerent from that of the ambient γ-ray run, so it can’t be explained with the gap events. A deposit energy spectrum of Am/Be neutron source run with Geant4 simulation is shown in Fig 9.37. and a distribution of number of nuclear recoils of Am/Be neutron source run with Geant4 simulation is shown in Fig 9.38. From Fig. 9.37, most of the events below 30 keV of Am/Be neutron source run in Fig. 9.32 were made with nuclear recoils. From Fig. 9.38, more than 85 % of the events of Am/Be neutron source run in Fig. 9.33 have “number of nuclear recoil 2”. A time spread of nuclear recoil is evaluated with “spread of recoil time” ≥as follows. (deposit E) (∆t from ﬁrst recoil) “spread of recoil time” = i i × i (9.7) (deposit E) P i i Distribution of “spread of recoil time” of Am/BeP neutron source run with Geant4 simulation is shown in Fig 9.39. From Fig. 9.39, more than 54 % of the events

163 15cm FV 100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 mean hit timing (ns) 10 mean hit timing (ns) 10 0 0 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV) 100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 mean hit timing (ns) 10 mean hit timing (ns) 10 0 0 0 20 40 60 80 100 0 20 40 60 80 100 reconstructed energy (keV) reconstructed energy (keV)

Figure 9.32: “mean hit timing”-“reconstructed energy” scatter plots of the dark matter search run, the Am/Be neutron source run, the ambient γ-ray run, and the 208Th source run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut” and 15cm FV. of Am/Be neutron source run in Fig. 9.33 have “spread of recoil time > 10 ns”. Signal nuclear recoil events are expexted for the dark matter signal, so the districution of “mean hit timing” of the Am/Be source run is diﬀerent from that of the dark matter signal.

164 15cm FV, Ereconst < 30 keV 30 20 18 25 16 20 14 12 15 10

num. of events 8 10 6 5 4 2 0 0 0 10 20 30 40 50 0 10 20 30 40 50 mean hit timing (ns) mean hit timing (ns) 25 14 22.5 12 20 10 17.5 15 8 12.5

num. of events 6 10 4 7.5 5 2 2.5 0 0 0 10 20 30 40 50 0 10 20 30 40 50 mean hit timing (ns) mean hit timing (ns)

Figure 9.33: Distributions of “mean hit timing” of the dark matter search run, the Am/Be neutron source run, the ambient γ-ray run, and the 232Th source run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut”, 15cm FV and “reconstructed energy < 30 keV”.

165 x 10 10000

8000 num. of events

6000

4000

2000

0 0 500 1000 1500 2000 2500 3000 reconstructed energy (keV)

Figure 9.34: Reconstructed energy spectrum of the dark matter search run and the ambient γ-ray run with “noise cut”. Here, the number of event above 600 keV of the ambinet γ-ray run is normalized to that of the dark matter search run.

166 15cm FV, TDC mean > 25 ns 30

25 num. of events 20

0 0 10 20 30 40 50 60 70 80 90 100 reconst energy (keV)

Figure 9.35: Reconstructed energy spectrum of the dark matter search run and the ambient γ-ray run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut”, 15cm FV and “mean hit timing > 25 ns”. The spectrum of the dark matter search run is similar to that of the ambient γ-ray run, so it can be explained with the events which happened in the small gaps of the detector.

167 15cm FV, TDC mean < 25 ns 30

25 num. of events 20

0 0 10 20 30 40 50 60 70 80 90 100 reconst energy (keV)

Figure 9.36: Reconstructed energy spectrum of the dark matter search run and the ambient γ-ray run with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut”, 15cm FV and “mean hit timing < 25 ns”. The spectrum of the dark matter search run is diﬀerent from that of the ambient γ-ray run, so it can’t be explained with the events which happened in the small gaps of the detector.

168 2000

1750

num. of events 1500

1250

1000

750

500

250

00 5 10 15 20 25 30 deposit energy (keVee)

Figure 9.37: Deposit energy spectrum of Am/Be neutron source run with Geant4 simulation. Spectrums of all the events and the events made with only nuclear recoil are shown by the black and red lines. Most of the events below 30 keV are made with only nuclear recoil.

169 1000

800 num. of events

600

400

200

00 2 4 6 8 10 12 14 16 18 20 num. of nuclear recoil

Figure 9.38: Distribution of number of nuclear recoils in “5 < deposit energy < 30 keV” of Am/Be neutron source run with Geant4 simulation. More than 85 % of the events have “number of nuclear recoil 2”. ≥

170 1400

1200 num. of events 1000

800

600

400

200

0 0 10 20 30 40 50 60 70 80 90 100 spread of recoil time (ns)

Figure 9.39: Distribution of “spread of recoil time” in “5 < deposit energy < 30 keV” of Am/Be neutron source run with Geant4 simulation. More than 54 % of the events have “spread of recoil time 10 ns”. ≥

171 9.4.3 Tritium inside the liquid xenon 3T has the half life, 12.33 years, and it decays into 3He through β decay with Qβ = 18.6 keV. An energy spectrum of β-ray emitted with the decay is calculated with DECAY4 [74] as shown in Fig. 9.40. A background from 3T in liquid xenon is estimated with the detector simulation using the β spectrum.

6000

5000 arbitrary unit

4000

3000

2000

1000

00 2 4 6 8 10 12 14 16 18 20 β energy (keV)

Figure 9.40: Energy spectrum of β-ray emitted with β decay of 3T calculated with DECAY4 [74].

3T is contained in liquid xenon mainly as HTO or HT. A water concentration in the processed xenon gas was calculated as < 100 ppb (mol/mol) with the tuned absorption length of the liquid xenon, 66( 10) cm, and Fig. 9.41. HTO/H2O of the atomosphere in Fukuoka, Japan is reported −17 as 2 10 from 1984 to 1994 [78]. When the content of H2O is 100 ∼ × −17 ppb (mol/mol) and HTO/H2O is 2 10 , the estimated background level is 1 10−4 counts/day/kg/keV belo×w 10 keVee. Then the background from HTO∼ is×negligible for the dark matter search with the prototype detector. A hydrogen concentration in the processed xenon gas was measured as 30 ppb (g/g) with APIMS (Atomospheric Pressure Ionization Mass Spectroscopy) by Nippon API Co.. HT/H2 of the measured hydrogen is diﬃcult to estimate, because we don’t know when the xenon gas was contaminated with the hydrogen. HT/H2 changes more than 5 orders of magnitude with types of hydrogen gasses. For instance, HT/H2 of the atomosphere in Fukuoka, Japan is reported as 1 10−12 from 1984 to 1994 [78], and that of market hydrogen gasses processed∼ ×

172 Figure 9.41: Scintillation light intensity as a function of the distance from the light source for various concentrations of water in liquid xenon [79].

from water is < 1 10−17. The solubility of× hydrogen in liquid xenon is also unknown, so it is assumed that all the hydrogen was dissolved in the liquid xenon for the following calcu- −15 ation. If HT/H2 of the measured hydrogen in the xenon gas is 1.5 10 , the low energy peak of the dark matter search run with “mean hit timing× < 25 ns” can be reprodeced with the tritium simulation as shown in Fig 9.42.

173 15cm FV, TDC mean < 25 ns 40

num. of events 30

0 0 10 20 30 40 50 60 70 80 90 100 reconst energy (keV)

Figure 9.42: Reconstructed energy spectrum of the dark matter search run and the ambient γ-ray run + the tritium simulation with “noise cut”, “ADC saturation cut”, “maximum PMT ratio cut”, 15cm FV and “mean hit timing < 25 ns”. Low energy peak of the dark matter search run can be reproduced with the tritium simulation.

174 9.5 Summary

The low energy peak of the dark matter search run with “mean hit timing > 25 ns” can be explained with the evebts which happened in the small gaps of the detector. From Fig. 9.35, a number of the remaining events of the ambient γ-ray run in the dark matter search window is 17.4( 7.0) event, If the lower limit, 10.4 event, is subtracted from the ﬁnal sample of the dark matter search SI SD run, the limits of σχ−p and σχ−p are shown in Fig. 9.43 and 9.44, respectively. SD The limit of the spin-dependent cross section, σχ−p, is calculated on the basis of the odd group model as discussed in Section 3.3.4.

-2 10 (pb) -p χ

SI -3

σ 10

-4 10

-5 10

-6 10

-7 10

-8 10 2 3 10 10 10 -2 Mχ (GeVc )

SI Figure 9.43: Limits of spin-independent cross section, σχ−p, as a function of Mχ with the gap event subtraction. The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment with the gap event subtraction is shown by the red (This work with the subtraction) line. DAMA’s allowed region is shown by the pink line[28]. The limits by EDELWEISS [30] and CDMS II [31] with cryogenic germanium detectors are shown by the blue and light-blue line. The world’s current lowest limit by XENON10 with a dual phase xenon detector is shown by the green line [32]. MSSM predictions are shown by the black line.

Tritium inside liquid xenon is the candidate of the low energy peak of the dark matter search run with “mean hit timing < 25 ns”. HT/H2 of the processed xenon gas is hard to estimate, so a quantitative certiﬁcation is diﬃcult from the

175 10 3 (pb) -p

χ 2

SD 10 σ

-1 10

-2 10

-3 10

-4 10 2 3 10 10 10 -2 Mχ (GeVc )

SD Figure 9.44: Limits of spin-dependent cross section, σχ−p, as a function of Mχ with the gap event subtraction on the basis of the odd group model. The regions above the curves are excluded at 90 % conﬁdence level. The result from this experiment with the gap event subtraction is shown by the red (This work with the subtraction) line. The limits by UKDMC [27] and DAMA [29] with NaI(Tl) detectors are shown by the blue and green lines. The limit by CRESST with cryogenic Al2O3 detector is shown by the pink dotted line [33]. The limit by the Tokyo group with CaF2 scintillator is shown by the light-blue line [34]. MSSM predictions are shown by the black line.

hydrogen concentration in the processed xenon, 30 ppb (g/g).

176 Chapter 10

Future prospects

A single phase detector with 800 kg of liquid xenon is optimized for dark matter search, and it is under construction at Kamioka Observatory. Features of this detector are discussed in Section 10.1, and expected sensitivity is shown in Section 10.2.

10.1 Single phase detector with 800 kg of liquid xenon

A schematic view of the single phase detector with 800 kg of liquid xenon is shown in Fig. 10.1. Approximately 800 PMTs are immersed in the liquid xenon, and the distance from the center of the detector to the PMTs is 45 cm. ∼ 10.1.1 Larger photo coverage and small dead angle from PMTs The photo coverage of the 800-kg liquid xenon detector is 70 %, and the expected photoelectron yield is 5 p.e./keV for an event at the∼detector center. The photo coverage and photoelectron∼ yield of the detector is improved from that of the prototype detector, as shown in Table 10.1, and this improvement enables us to lower the energy threshold and achieve higher sensitivity for the dark matter search.

photo coverage (%) photoelectron yield (p.e./keV) prototype detector 16 1.93 800-kg liquid xenon detector 70 5 ∼ ∼

Table 10.1: Comparison between photo coverage and photoelectron yield of the prototype detector and those of the 800-kg liquid xenon detector. More than a factor of 4 and 2.5 improvements are expected for photo coverage and photoelectron yield, respectively.

Some fraction of events that occur at the dead angle of the PMTs in the outer region of detector are mis-reconstructed into the center region of detector,

177 Figure 10.1: Schematic view of the single phase detector with 800 kg of liquid xenon. 800 PMTs are immersed inside liquid xenon, and distance from the center of∼detector to PMTs is 45 cm. ∼ and these events become backgrounds in the ﬁducial volume. The dead angle from the PMTs also reduces with the improvement in photo coverage, so that mis-reconstructed background events are greatly reduced.

10.1.2 Thicker layer for self-shielding and larger ﬁducial volume The layer for self-shielding of the 800-kg liquid xenon detector is enlarged from that of the prototype detector, as shown in Table 10.2, and it enables stronger shielding for low energy γ-ray backgrounds. The ﬁducial volume of the 800-kg liquid xenon detector is also enlarged from that of the prototype detector, as shown in Table 10.2, and it enables higher sensitivity.

10.1.3 Further reduction of radioactive impurities in PMTs We developed a low background hexagonal PMT, R8778MOD, for the 800-kg liquid xenon detector in cooperation with Hamamatsu Photonics. A picture of the R8778MOD is shown in Fig. 10.2. The hexagonal shape of R8778MOD is suited for increasing the photo coverage and reducing the dead angle. The radioactive impurities, except for 60Co, in R8778MOD were reduced by about a factor 10 from that of R8778ASSY, as shown in Table 10.3. R8778ASSY

178 thickness of self-shielding layer (cm) ﬁducial volume (kg) prototype detector 7.5 9.73 800-kg liquid xenon detector 20 100 ∼ ∼

Table 10.2: Comparison between photo coverage and photoelectron yield of the prototype detector and those of the 800-kg liquid xenon detector. More than a factor of 2.5 and 10 improvements are expected for thickness of self-shielding layer and ﬁducial volume, respectively.

Figure 10.2: Picture of R8778MOD.

is the PMT that was used for the prototype detector as described in Section 6.1.2. The content of 60Co is diﬃcult to reduce because cobalt is used as the raw material of the side tube of R8778MOD, but this level of 60Co does not cause a problem for achieving the expected sensitivity of the 800-kg liquid xenon detector, which is shown in Section 10.2.

10.1.4 Radiation shield with water tank A water tank is used as the radiation shield of the single phase detector with 800 kg of liquid xenon, as shown in Fig. 10.3. Approximately 2 m thickness of water is needed to reduce backgrounds from ambient γ rays to that from PMTs, and it is also enough to reduce backgrounds from ambient fast neutrons to the target level. With a suﬃcient safety factor, the height and diameter of water tank are decided as 10 m and 11 m. We install 20-inch PMTs on the wall of the water tank to ∼detect Cherenk∼ ov photons generated by muons.

179 U (mBq/PMT) Th (mBq/PMT) K (mBq/PMT) 60Co (mBq/PMT) R8778ASSY 18( 2) 6.9( 1.3) 140( 20) 5.5( 0.9) R8778MOD < 1 < 0.94 < 9.68 4.5( 0.3)

Table 10.3: Radioactive impurities in R8778ASSY and R8778MOD measured by HPGe detector. R8778ASSY is the PMT used for the prototype detector as described in Section 6.1.2. About a factor of 10 improvement from R8778ASSY to R8778MOD is achieved for the content of radioactive impurity, except for 60Co. The content of 60Co is diﬃcult to reduce because cobalt is used as the raw material of the side tube of R8778MOD, but this level of 60Co does not cause a problem for achieving the expected sensitivity of the 800-kg liquid xenon detector.

10.2 Expected sensitivity

Expected sensitivities for a 3 σ discovery of WIMPs with the 800-kg liquid xenon detector are shown in Fig. 10.4 and 10.5. The following conditions are assumed for this sensitivity calculation. Exposure time is 5 years. • 100 kg of liquid xenon at the center region are used as the ﬁducial volume. • Energy threshold is 5 keVee. • The sensitivity to WIMP direct detection will be improved by 2 orders of magnitude for the spin-independent case, and 3 orders of magnitude for the spin- dependent case, from the world’s current limit.

180 Figure 10.3: Schematic view of water shield for single phase detector with 800 kg of liquid xenon. Approximately 2 m thickness of water is needed to reduce background from ambient γ rays and ambient neutrons to the target level. With a suﬃcient safety factor, the height and diameter of the water tank are decided as 10 m and 11 m. 20 inch PMTs are installed on the wall of the water tank to ∼detect Cherenk∼ ov photons generated by muons.

181 (pb) -p χ SI

σ -5 10

-6 10

-7 10

-8 10

-9 10 2 3 10 10 10 -2 Mχ (GeVc )

Figure 10.4: Expected sensitivity for a 3 σ discovery of WIMPs with the 800- kg liquid xenon detector using 100 kg of center ﬁducial volume with a 5 keVee energy threshold after 5 years exposure (spin-independent case). The sensitivity to WIMPs direct detection will be improved by 2 orders of magnitude from the world’s current limit [32].

182 10 3 (pb) -p

χ 2

SD 10 σ

-1 10

-2 10

-3 10

-4 10 2 3 10 10 10 -2 Mχ (GeVc )

Figure 10.5: Expected sensitivity for a 3 σ discovery of WIMPs with the 800-kg liquid xenon detector using 100 kg of center ﬁducial volume with a 5 keVee energy threshold after 5 years exposure (spin-dependent case). The sensitivity to WIMP direct detection will be improved by 3 orders of magnitude from the world’s current limit [27][29].

183 Chapter 11

Conclusion

The XMASS Collaboration is developing single phase liquid xenon detectors for the purpose of direct detection of dark matter. A single phase detector with 800 kg of liquid xenon is under construction at Kamioka Observatory. The expected sensitivity of this detector to the neutralino as dark matter is about 2 orders of magnitude higher than the present best limit in the world. A prototype detector was developed at Kamioka Observatory to check the performance of single phase liquid xenon detectors. With the detector, the physical properties of liquid xenon were measured, and the performance of energy and vertex reconstruction was conﬁrmed. We also search for the neutralinos with the detector though it was not optimized for a dark matter search. Al- though no dark matter signal was found, we obtained the upper limits for the neutralino-proton cross section as follows, σSI = 1.70 10−5 pb at M = 62 GeV/c2 (spin-independent case). • χ−p × χ σSD = 6.74 pb at M = 60 GeV/c2 (spin-dependent case). • χ−p χ These limits are nearly at the expected sensitivity of the detector within its restrictive conditions. From these measurements of the prototype detector, the feasibility of achieving the target sensitivity with the 800-kg liquid xenon detector was conﬁrmed.

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