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Potentialities of a Low-Energy Detector Based on $^ 4$ He Evaporation to Observe Atomic Effects in Coherent Neutrino Scattering and Physics Perspectives

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Potentialities of a Low-Energy Detector Based on $^ 4$ He Evaporation to Observe Atomic Effects in Coherent Neutrino Scattering and Physics Perspectives Potentialities of a low-energy detector based on 4He evaporation to observe atomic effects in coherent neutrino scattering and physics perspectives M. Cadeddu,1, ∗ F. Dordei,2, y C. Giunti,3, z K. A. Kouzakov,4, x E. Picciau,1, { and A. I. Studenikin5, 6, ∗∗ 1Universit`adegli studi di Cagliari and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Cagliari, Complesso Universitario di Monserrato - S.P. per Sestu Km 0.700, 09042 Monserrato (Cagliari), Italy 2Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Cagliari, Complesso Universitario di Monserrato - S.P. per Sestu Km 0.700, 09042 Monserrato (Cagliari), Italy 3Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via P. Giuria 1, I{10125 Torino, Italy 4Department of Nuclear Physics and Quantum Theory of Collisions, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia 5Department of Theoretical Physics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia 6Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia We propose an experimental setup to observe coherent elastic neutrino-atom scattering (CEνAS) using electron antineutrinos from tritium decay and a liquid helium target. In this scattering process with the whole atom, that has not beeen observed so far, the electrons tend to screen the weak charge of the nucleus as seen by the electron antineutrino probe. The interference between the nucleus and the electron cloud produces a sharp dip in the recoil spectrum at atomic recoil energies of about 9 meV, reducing sizeably the number of expected events with respect to the coherent elastic neutrino-nucleus scattering case. We estimate that with a 60 g tritium source surrounded by 500 kg of liquid helium in a cylindrical tank, one could observe the existence of CEνAS processes at 3σ in 5 years of data taking. Keeping the same amount of helium and the same data-taking period, we test the sensitivity to the Weinberg angle and a possible neutrino magnetic moment for three different scenarios: 60 g, 160 g, and 500 g of tritium. In the latter scenario, the Standard Model (SM) value 2 SM+0:015 of the Weinberg angle can be measured with a statistical uncertainty of sin #W −0:016. This would 2 represent the lowest-energy measurement of sin #W , with the advantage of being not affected by the uncertainties on the neutron form factor of the nucleus as the current lowest-energy determination. Finally, we study the sensitivity of this apparatus to a possible electron neutrino magnetic moment −13 and we find that using 60 g of tritium it is possible to set an upper limit of about 7 × 10 µB at 90% C.L., that is more than one order of magnitude smaller than the current experimental limit. I. INTRODUCTION as taking place on the atom as a whole. In Ref. [21] it has been noted that, in the case of electron neutrino scat- Coherent elastic neutrino-nucleus scattering (CEνNS), tering, the interference between the electron cloud and has been recently observed by the COHERENT experi- the nucleus becomes destructive. As a consequence, the 2 ment [1, 2], after many decades from its prediction [3{5]. scattering amplitude becomes null and changes sign as q This observation triggered a lot of attention from the sci- varies from large to small values, producing a sharp dip in entific community and unlocked a new and powerful tool the differential cross section. In practice, electrons tend to study many and diverse physical phenomena: nuclear to screen the weak charge of the nucleus as seen by an physics [6, 7], neutrino properties [8{10], physics beyond electron neutrino probe. This effect should be visible for 2 2 the Standard Model (SM) [11{17], and electroweak (EW) momentum transfers of the order of q ∼ 100 keV , cor- interactions [18, 19]. The experimental challenge related responding to atomic recoil energies TR ∼ 10 meV. For to the CEνNS observation is due to the fact that in order recoil energies of O(100 meV) this effect starts to become arXiv:1907.03302v2 [hep-ph] 11 Sep 2019 to meet the coherence requirement qR 1 [20], where completely negligible. The small recoils needed are well q = j~qj is the three-momentum transfer and R is the nu- below the thresholds of detectability of currently avail- clear radius, one has to detect very small nuclear recoil able detectors, making it very difficult to observe this effect. energies ER, lower than a few keV. At even lower momentum transfers, such that However, in Ref. [22] a new technology based on the qRatom 1, where Ratom is the radius of the target atom including the electron shells, the reaction can be viewed evaporation of helium atoms from a cold surface and their subsequent detection using field ionization has been pro- posed for the detection of low-mass dark matter parti- cles. In this configuration, the nuclear recoils induced by ∗ [email protected] dark-matter scattering produce elementary excitations y [email protected] z [email protected] (phonons and rotons) in the target that can result in x [email protected] the evaporation of helium atoms, if the recoil energy is { [email protected] greater than the binding energy of helium to the surface. ∗∗ [email protected] Given that the latter can be below 1 meV, this proposed 2 2 technique represents an ideal experimental setup to ob- where Fe(q ) is the electron form factor and the + sign serve atomic effects in coherent neutrino scattering. applies to νe andν ¯e, while the − sign applies to all the Here, we propose a future experiment that would allow other neutrino species. As explained in Ref. [21], the the observation of coherent elastic neutrino-atom scatter- + sign is responsible for the destructive interference be- ing (CEνAS) processes and we investigate its sensitivity. tween the electron and nuclear contributions. In princi- Since this effect could be visible only for extremely small ple, one should add also the axial contribution from the recoil energies, in order to achieve a sufficient number Atom electron cloud, CA , that however becomes null when of low-energy CEνAS events, electron neutrinos with en- the number of spin up and down electrons is the same, ergies of the order of a few keV need to be exploited. which applies to our scenario. Moreover, at the low mo- Unfortunately, there are not so many available sources of mentum transfers considered in CEνAS processes, one 2 2 such low-energy neutrinos. In this paper, we investigate can safely put FN(q ) = FZ(q ) = 1. This allows to de- the possibility to use a tritium β-decay source, that is rive physics properties from the analysis on CEνAS pro- characterized by a Q-value of 18.58 keV. The PTOLEMY cesses being independent on the knowledge of the neutron project [23, 24], that aims to develop a scalable design to distribution that is largely unknown [6, 28]. detect cosmic neutrino background, is already planning As visible from Eq. (3), in CEνAS processes a key role to use about 100 g of tritium, so we can assume that a is played by the electron form factor, that is defined as the similar or even larger amount could be available in the Fourier transform of the electron density of an atom. In near future. Moreover, we show the potentialities of such contrast to the case of atomic hydrogen, the He electron a detector to perform the lowest-energy measurement of density is not known exactly. In our present study we the weak mixing angle #W , also known as the Weinberg employ the following parameterisation of the He electron angle, a fundamental parameter in the theory of Standard form factor, that has proved to be particularly effective Model electroweak interactions, and to reveal a magnetic and accurate (see, for instance, Refs. [29{31]) moment of the electron neutrino below the current limit. 4 ! 2 2 X −bi(q=4π) Fe(q ) = A· ai · e + c : (4) II. ATOMIC EFFECTS IN COHERENT i=1 SCATTERING The parameters ai = f0:8734; 0:6309; 0:3112; 0:178g, bi = In order to derive the cross section for a CEνAS process f9:1037; 3:3568; 22:9276; 0:9821g and c = 0:0064, ex- tracted from Tab. 6.1.1.4 of Ref. [30], are given by a ν` + A ! ν` + A, where A is an atom and ` = e; µ, τ, 2 we start from the differential-scattering cross-section of close fit of the numerical calculations for Fe(q ) using a well-established theoretical model of the He electron a CEνNS process as a function of the recoil energy ER wave function. The normalization A is a scaling fac- of the nucleus [21, 25] 2 tor such that Fe(q ) ! 1 for q ! 0, as in the nuclear dσCEνNS G2 m E form factor definition. This parameterisation assumes = F C2 m 1 − N R ; (1) V N 2 that the electron density is spherically symmetric so that dER π 2Eν the value of the Fourier transform only depends on the where GF is the Fermi constant, mN is the nuclear mass, distance from the origin in reciprocal space. The moment E is the neutrino energy and C is the q2-dependent ν V transferp q is related to the atomic recoil energy through matrix element of the vector neutral-current charge 1 q = 2mATR, where mA ∼ mN is the atomic mass. 1 For various models of the He electron wave function that C = [(1 − 4 sin2 # )ZF (q2) − NF (q2)] : (2) V 2 W Z N give an accurate value of the electron binding energy, the numerical results for F (q2) are known to be practically Here, Z and N are the number of protons and neutrons e 2 2 identical in a wide range of q values.
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