Direct Detection Experiments at the Dipole Portal Frontier

Ian M. Shoemaker and Jason Wyenberg Department of , University of South Dakota, Vermillion, SD 57069, USA (Dated: December 3, 2018) Heavy sterile are typically invoked to accommodate the observed neutrino masses, by positing a new Yukawa term connecting these new states to the neutrinos in the electroweak doublet. However, given our ignorance of the neutrino sector, we should explore additional interactions such sterile neutrinos may have with the SM. In this paper, we study the dimension-5 operator which couples the heavy state to a light neutrino and the photon. We find that the recent XENON1T direct detection data can improve the limits on this “Neutrino Dipole Portal” by up to an order of magnitude over previous bounds. Future direct detection experiments may be able to extend these bounds down to the level probed by SN1987A.

I. INTRODUCTION Thus to achieve 1 event at XENON1T we would very roughly expect ∼ The fact that neutrinos are massive is one of the key obser- r 2 2 r vational facts indicating that the (SM) of par- GF QwmN ER 6 1 ER d 50 10− GeV− , (2) ticle physics is incomplete. Most models of neutrino masses ' 4παZ2 ∼ keV posit new right-handed states which are singlets under the SM gauge groups. These neutral fermion singlets have been pre- where the factor of 50 comes from needing a 50-fold in- dominantly studied in connection with neutrino masses via crease in the SM cross section for the “neutrino floor” to the Neutrino Portal interaction, L NHL, where N is the presently be detectable. We expect the estimate in Eq. 2 to singlet fermion, L is the SM ⊃ doublet, and H is the be valid up to singlet fermion masses of order Boron-8 en- Higgs doublet. For this reason, singlet fermions can play the ergies, m4 Eν 10 MeV. Although the above estimates ∼ ∼ role of a “sterile” neutrino (i.e. uncharged under the elec- are simplistic, they provide us with ample motivation to carry troweak symmetry), and they mix with the left-handed neu- out a more complete analysis. Indeed, a dipole strength at 6 1 trinos after the Higgs acquires a vacuum expectation value. the d 10− GeV− level is competitive with a variety of ' However, the standard neutrino portal interaction may not known constraints on the NDP [6, 8, 9]. We summarize our be the predominant interaction these states have with the SM. main findings in Fig. 1 which demonstrate that XENON1T al- They may also interact via a “Neutrino Dipole Portal” inter- ready provides the leading constraints up to 10 MeV masses, action, which after electroweak symmetry breaking can be and future high-exposure/low-threshold direct detection can written as improve the bounds down to the SN1987A region.

L d (¯ν σ F µν N) + h.c., (1) NDP ⊃ L µν where Fµν is the electromagnetic field strength, σρσ = 0.100 i 2 [γρ, γσ], νL is the SM neutrino, and the coefficient d with 1 units of (mass)− controls the strength of the interaction. Despite its simplicity and the wide interest in a “sterile” neu- 0.001 trino, this interaction has not received much attention. It has, however, been considered in the context of the MiniBooNE DONUT 10-5 ]

events [1–7], and has also been been studied in the context of - 1

IceCube data [8] and at the upcoming SHiP experiment [9]. Xenon 1T (this work)

In this paper we will study the neutrino dipole portal (NDP) d [ GeV -7

arXiv:1811.12435v1 [hep-ph] 29 Nov 2018 10 at the XENON1T direct detection experiment using their 1 IceCube ton-year exposure [10]. Despite not finding evidence of DM' SuperCDMS scattering, XENON1T is nearly at the level where they can 10-9

start seeing events from solar neutrinos. Many prior works SN-1987A have used neutrinos at direction detection experiments to study various beyond SM neutrino interactions [11–22]. At 10-11 the few keV recoil energies of XENON1T, the Boron-8 (B8) 1 5 10 50 100 500 1000

neutrinos make the largest contribution, comprising 0.02 m4 [MeV] background events in the 1 ton-year sample [10]. However,∼ if neutrinos have additional interactions beyond EW forces, this FIG. 1: These are the expected sensitivity curves for the -flavored rate could be larger and already detectable. To get an approx- NDP based on the XENON1T data [10] and a future SuperCDMS imate idea of the sensitivity to the NDP we can compare the exposure. The relevant previously published exclusion limits of 2 2 SN1987A [9], IceCube [8] and DONUT [8, 23] are also shown. SM cross section, dσ/dER GF QwmN /4π, with the NDP cross section, dσ/dE d2'αZ2/E . . R ' R + 2 e

incoming neutrino is unlikely to undergo much up-scattering ⌫ e N in the Earth prior to arrival at the detector. In Sec. III we look at what improvements can come in the near term, focusing

⇤ on a future run of SuperCDMS. Then in Sec. IV we discuss the nature of models giving rise to the NDP, along with po- tential ways in which future work could refine and extend the Xe Xe analysis carried out here.

µν FIG. 2: The neutrino dipole portal LNDP ⊃ d (¯νLσµνparticle-antiparticleF final state N) al- lows for a neutrino to up-scatter off a nucleus to a heavyThe electromagnetic vertex with neutral lep- II. NEUTRINO TRANSITION MAGNETIC MOMENT ton state N. This produces a distinctive recoil spectrum, while the RATES newly produced heavy neutral lepton decays outside the detector. A. Mechanism The remainder of this paper is organized as follows. In Sec. II we compute a realistic spectrum of nuclear recoil Incoming solar neutrinos may up-scatter to a heavy state

events at XENON1T from solar neutrinos mediated by the N through the NDP operator+ via the process shown in Fig. 2. µ

NDP interaction.(1) We find there that the new state will typi- The coherent cross section for neutrino-nucleus scattering via

cally decay outside the detector after it is produced and that an a NDP reads µ ,and fi erent way M ↵ " ! # A.J.Barr 2009-2013.

2 4 c dσνn Nn 2 2 2 1 m4 ER mN 1 m4(ER mN ) → (3) = d αZ F (ER) 1 + + 2 2− 2 erent reactions. dER ER − 2Eν ERmN − 2Eν 2Eν − Eν 8Eν ERmN ect the Feynman ↵ ↵

where Z is the atomic number, ER is the nuclear recoil en- recoil ER: ergy, E is the incident neutrino energy, m is the mass of ν N +

2 e the target nucleus, m4 is the mass of the heavy sterile neu- min m4 + 2mN ER Eν (ER) = h i. (5) trino, and F (E ) is the nuclear form factor. p e R 2 E (E + 2m ) E R R N − R .

+ The solar neutrino 8B flux provides the dominant contri- e B. Event Rates in Xenon1T Detector bution to NDP nuclear scattering in the XENON1T exper- + +

+ 8 iment. We normalize the B spectrum to the flux φ8B = 6 2 1

+ + 5.1 10 cm s− [36]. For illustration, in Fig. 3 we plot the

e e e e Neutrino e scattering at dark matter direct detection experi- × expected recoil spectrum for a range of possible ν4 masses. ments has been widely studied [16, 24–33] and depending on As one would expect, at low masses there is little dependence the range of energies may include contributions from solar,

on the recoil spectrum, while at masses around 10 MeV 4

! ! ! ! atmospheric! ! and the diffuse supernova background. In fact, ∼ the rate starts to get very suppressed. +

the original DM direct detection proposal from Goodman and µ µ

A detected: nuclear recoil event will create a signal of n Witten [34] was an extension of the detection method for so- + + photoelectrons (PEs) given by a poisson distribution with ex- e e e lar and reactor neutrinos via neutral currents by Drukier and pectationµ value n, given by: + + Stodolsky [35]. + + erent time-orderings, so each is just a di + The nuclear recoil spectrum of neutrino induced scattering  e e n = E L E g . (6) ↵

R y R 1 events can be computed via: + e µ  is the light yield as a function of as shown α α α Ly ER ER Z erent time ordering of the same fundamental vertex that dR dΦ dσ ! ν νn Nn  in [37], and detector photon gain is g1 = 0.144 0.007 [38]. = MT ↵ → (Eν ,ER dEν , (4) ± dER × Emin dEν dER The event rate is then given by:

ν e + α Z α + where α=e, µ, τ indexes the neutrino flavor, MT is the expo- dR   dR = Eff ER Poiss(n n) dER, (7) sure of the XENON1T experiment (equal to 1.3 Tonne 278.8 + dn dER × | days), and is the solar neutrino flux. The function× e Φν ! min   + Eν (ER) is the minimum energy of the incident neutrino to where Eff ER , the efficiency as a function of nuclear recoil e e up-scatter to the state of mass m4 while producing a nuclear energy, is given in Fig. 1 of Ref. [10]. Finally, we model the e + + e 2.3 Distinct diagrams anti-particle shows the arrowparticle going flow the is opposite ‘wrong’ to way that (here of right anti-particle. The to same left), basic since electromagnetic the Consider vertex each is of responsible the partial for reactions many di Each of these iscouples just an a electron di to a photon. 2.3 Distinct diagrams A Feynman diagram representsso all the positions possible of time thetwo orderings vertices diagrams within of for the the graph possible are arbitrary. vertices, Consider the following In the left diagram it appearsphoton, that which the incoming then particles annihilated splitit to to form appears a produce that virtual the theand outgoing muons that particles. and the On the photonnothing. the subsequently photon Changing right collided appeared the position diagram with outdiagram of the of – the electron the internal it vertices and vacuum stilland does positron, together, represents right not leaving the a side same justof represent contribution writing di to the the same amplitude. Feynman diagram. The left side On the other hand,to changing the one way another in whichprocess does the however lines result in a in diagram a are connected newIn diagram. the two Consider diagrams forway above to example the move the outgoing aroundthe photons the first. have vertices been The in swapped.must two the be diagrams There second added. therefore is diagram provide no so separate contributions that to it is the same as January 18, 2014 3 total signal rate as: 0.100 α ∞ α dR X dR II = GaussS1 n, √n 0.5 , (8) - dS1 | × dn Xenon 1T n=1 0.001

(this work CHARM with the 0.5 factor coming from the uncertainty of the 1 PE ) bin size. 10-5 NOMAD ]

- 1 MiniBooNE

C. Exclusion Curves d [ GeV 10-7 IceCube The result of the XENON1T experiment excludes a portion SuperCDMS -9 of the m4, d NTMM parameter space. Following a Bayesian 10 approach, with a signal s and background b an upper limit on SN-1987A s can be determined as: 10-11 1 1 sup = F −2 [p, 2(n + 1)] b, (9) 2 χ − 1 5 10 50 100 500 1000 m4 [MeV] 1 2 where Fχ−2 is the inverse cumulative χ distribution, and n is the number of observed events such that 2(n + 1) is the FIG. 4: Expected sensitivity to muon-flavored NDP at XENON1T number of degrees of freedom. The p factor is given by the and a future SuperCDMS exposure. Included are bounds from NO- expression: MAD [8, 41], CHARM [8, 42], MiniBooNE [9, 43], IceCube [8], and SN1987A [9].  p = 1 α F 2 [2b, 2(n + 1)] , (10) − χ where α is 1 CL, and CL is the confident limit [39]. An al- D. Up-scattering and Decay Considerations ternative statistical− analysis may employ the Likelihood Pro- file method [40] incorporating the binned energy data. A Notice that in principle the dipole interaction admits the check of the calculated exclusion curve for d for several val- possibility of ν N upscattering prior to the neutrino flux ues of m showed nearly identical results between a rudimen- 4 arriving at the detector.→ At minimum a neutrino traverses 1 tary likelihood profile method and the χ2 approach employed km to reach the underground detector. We will find that∼ the here. process of up-scattering in the Earth is irrelevant for the pa- For the XENON1T data, with 2 observed events and an rameters of interest. The total cross section for up-scattering expected background of 1.34 events, s = 6.53. Figure up is roughly estimated as [9] 1 shows the 90% confidence exclusion in the (m4, d) plane. Also shown are excluded regions from previously published  4E2  results (see caption for details). For reference we also show 2 2 ν (11) σν N αZ d log 4 2 the current and future direct detection sensitivity to the muon- → ' | | × m4Rnuc flavored NDP in Fig. 4. For an incoming solar neutrino with Boron-8 energies Eν 10 MeV while traversing a distance of 1 km through the' ν-N scattering Earth, we find that d would need to be, 109 νe,m 4 = 1 MeV m νe, 4 = 5 MeV v

] m 7 νe, 4 = 10 MeV u 1 - 1 10 m u (12) νμ/τ, 4 = 1 MeV d  2  ' t 2 4Eν keV νμ/τ,m 4 = 5 MeV (1km) n αZ log 4 2 - 1 ⊕ m4Rnuc 105 m yr νμ/τ, 4 = 10 MeV

- 1 1 0.14 GeV− 1000 ' [ Tonne r where we assumed that the dominant contribution to the ter- 10 restrial density is silicon. Dipole strengths this strong are al- dR / dE ready excluded by a number of independent probes including 0.1 DONUT and IceCube (ντ transitions) [8], and by CHARM-

0.01 0.05 0.10 0.50 1 5 10 II, MiniBooNE and LSND [9] (νµ transitions). Er [keV] Shortly after being produced through up-scattering in the detector the ν4 state will eventually decay. If this decay, FIG. 3: Event rates of nuclear scattering via a NDP in the Xenon ν4 ν +γ, happens inside the detector volume, the resultant −6 −1 → 1T detector with d = 10 GeV for masses m4 = 1 MeV (red), photon could potentially cause the signal to be thrown away m4 = 5 MeV (green), and m4 = 10 MeV (blue). Also shown is the as background. Of course if the initial nuclear energy depo- standard model ν-nucleus scattering rate (black curve). sition in the up-scattering ν+Xe ν +Xe is sufficiently far → 4 4

-7 from the final decay of the ν one may still be able to per- 5.×10 4 m = 1 MeV form a search using either only the nuclear recoil events or a 4 m4 = 5 MeV dedicated search aimed at the spatially/temporally correlated 2.×10 -7 m4 = 10 MeV nuclear and photon signals unique to the NDP model. Such an analysis is beyond the scope of this work, but could result ] 1.×10 -7 in stronger bounds than the analysis performed here. - 1

To ensure that the nuclear recoil events we model have not 5.×10 -8 been vetoed by the collaboration, we only exclude regions of d [ GeV parameter space where the newly produced ν4 state decays outside of the detector. To do this we impose a penalty factor 2.×10 -8 to account for the possibility that the heavy state decays in 1.×10 -8 the detector shortly after being produced. This penalty factor 10 100 1000 104 105 takes the form Exposure[kg yr]

ldet/`D PD = e− , (13) FIG. 5: Anticipated sensitivity of SuperCDMS as a function of ex- posure, eventually plateauing from systematic uncertainties. where ldet is a characteristic length scale of the detector which we take to be 100 cm, and the boosted decay length for a ν4 with energy E4 is energy of the relevant solar neutrino flux. For the exposure of the Xenon 1T data, this maximum energy is that of the solar s  2 neutrino B8 flux. To probe higher values of , the atmo- 16πE4 E4 m4 `D γβτ 1. (14) spheric neutrino flux could be employed, but this requires an ≡ ' d2m4 m − 4 4 exposure of 107 ton-year for a Xenon based experiment. ∼ For the decay N ν + γ to occur inside within 100 cm we → 4 1 would need d & 4 10− GeV− for E4 10 MeV and × ' IV. MODEL DISCUSSION m4 = 5 MeV.

Throughout the paper we have assumed that the NDP term, µν III. FUTURE DIRECT BOUNDS: SUPERCDMS LNDP d (¯νLσµν F N), dominates the phenomenology ULTRA-LOW THRESHOLDS of the heavy⊃ singlet lepton N, but have not commented on the implications of such an operator. As discussed in [9], if The SuperCDMS collaboration [44] anticipates detection N has a large Majorana mass the NDP interaction can gen- of low energy nuclear recoil events which could exclude val- erate a large active neutrino mass. However, this concern is ues of d several orders of magnitude lower than the Xenon mitigated if the Dirac mass is large compared to the Majorana 1T data. For an order of magnitude estimate, a 1-ton year mass. Moreover, it has been known that the Zee model [46] of exposure of the SuperCDMS experiment was modeled. Us- neutrino masses can naturally accommodate large magnetic ing the published efficiency curve of the SuperCDMS exper- moments [47]. Other models that have been shown to allow iment [45] (see their Fig. 4), the estimated background from for large magnetic moments consistently are the Barr, Freire, solar neutrino nuclear recoils is 460 events. For a 3σ dis- Zee (BFZ) spin-suppression mechanism [48] and horizontal covery signal above the statistical∼ uncertainty, 65 signal flavor symmetries [49] (see also [50]). events are required. Figure 1 includes a projected∼ exclusion curve of the SuperCDMS experiment. Worth noting is the fact that the SuperCDMS collaboration V. CONCLUSION may soon be probing the neutrino floor. For exposures much higher than 1-ton year, the detector reach plateaus and can- We have shown that the recent XENON1T data can be not probe any lower values of d. This is shown in Figure 5 used to constrain the neutrino dipole portal at new levels of as the neutrino background systematic uncertainty obscures a sensitivity. The solar neutrinos which are nearly detectable potential signal from the neutrino magnetic moment. at direct detection experiments would already have been Eventually pp solar neutrinos may contribute to the neu- observed if the NDP interaction was sufficiently large. Future trino background at direct detection experiments. This would improvements in searches such as these will come from large require very low-energy thresholds and would result in a large scale, low-threshold experiments which will be capable of enhancement of the event rate. For the mechanism of the neu- seeing large numbers of solar neutrino events. We note that trino transition magnetic moment discussed in this paper, we although we have focused on nuclear recoil events here, one estimate that a future detector would require a recoil energy could extend the analysis to include electron recoil events. threshold below 1 eV to observe the pp-flux, and only if Given the reduction in the CM energy from scattering on m is below 100∼ keV. electrons, this method will only allow sensitivity to sterile 4 ∼ The upper limit of m4 that could be excluded by the Xenon masses m4 . 0.5 MeV. 1T experiment is 10 MeV due to the maximum incoming ∼ 5

Lastly, we note that our computation of the bounds on the strengthening of the bounds found here. We leave such a NDP coupling from direct detection experiments has been in- study to future work. tentionally conservative. This is due to the imposition of the penalty factor Eq.13 which vetoes events in which the sin- glet fermion decay ν4 ν + γ occurs within the detector volume, and may therefore→ complicate discrimination from Acknowledgments e/γ backgrounds since it yields a nonstandard S1 and S2 sig- nal in XENON1T. A similar effect arising from DM-induced nuclear excitations which re-decay to photon final states on We are very grateful to Laura Baudis, Dongming Mei, short timescales was studied in [51]. A future analysis may Ryan Plestid, and Yu-Dai Tsai for helpful discussions. This be able to conduct a dedicated search for the non-standard work in supported by the U.S. Department of Energy under S1 and S2 signals associated with the NDP, resulting in a the award number DE-SC0019163.

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