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Potentialities of a Low-Energy Detector Based on He4 Evaporation to Observe Atomic Effects in Coherent Neutrino Scattering and P

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Potentialities of a Low-Energy Detector Based on He4 Evaporation to Observe Atomic Effects in Coherent Neutrino Scattering and P PHYSICAL REVIEW D 100, 073014 (2019) 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, C. Giunti ,3, K. A. Kouzakov ,4,§ E. Picciau ,1, and A. I. Studenikin5,6,¶ 1Universit`a degli 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 (Received 14 July 2019; published 29 October 2019) 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 been 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 sizably 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 yr 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, 160, and 500 g of tritium. In the latter scenario, the Standard Model (SM) value of the Weinberg angle can be measured with a statistical 2ϑSMþ0.015 2 ϑ uncertainty of sin W −0.016 . This would 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 and we find that using 60 g of tritium it is possible to set an upper −13 limit of about 7 × 10 μB at 90% C.L., that is more than one order of magnitude smaller than the current experimental limit. DOI: 10.1103/PhysRevD.100.073014 I. INTRODUCTION This observation triggered a lot of attention from the scientific community and unlocked a new and powerful Coherent elastic neutrino-nucleus scattering (CEνNS) tool to study many and diverse physical phenomena: has been recently observed by the COHERENT experi- – ment [1,2], after many decades from its prediction [3–5]. nuclear physics [6,7], neutrino properties [8 10], physics beyond the Standard Model (SM) [11–17], and electroweak interactions [18,19]. The experimental challenge related to ν *[email protected] the CE NS observation is due to the fact that in order † [email protected] to meet the coherence requirement qR ≪ 1 [20], where ‡ [email protected] q ¼jq⃗j is the three-momentum transfer and R is the nuclear §[email protected] ∥ radius, one has to detect very small nuclear recoil energies [email protected][email protected] ER, lower than a few keV. At even lower momentum transfers, such that Published by the American Physical Society under the terms of ≪ 1 qRatom , where Ratom is the radius of the target atom the Creative Commons Attribution 4.0 International license. including the electron shells, the reaction can be viewed Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, as taking place on the atom as a whole [21]. This effect 3 ∼ 1 and DOI. Funded by SCOAP . should be visible for qRatom , i.e., for momentum 2470-0010=2019=100(7)=073014(9) 073014-1 Published by the American Physical Society M. CADEDDU et al. PHYS. REV. D 100, 073014 (2019) ∼ 2 transfers q keV=Ratom½Å, where Ratom½Å is the atomic II. ATOMIC EFFECTS IN radius in angstroms. The corresponding atomic recoil COHERENT SCATTERING ∼ 2 2 energy is TR meV=ðARatom½ÅÞ, where A is the atomic In order to derive the cross section for a CEνAS process mass number of the recoiling atom. In the following we νl þ A → νl þ A, where A is an atom and l ¼ e, μ, τ,we consider helium atoms that have an atomic radius of start from the differential cross section of a CEνNS process about 0.5 Å, for which the effect is expected to be as a function of the recoil energy ER of the nucleus [21,25] observable at TR ∼ 2 meV. For much larger recoil energies O 100 of ð meVÞ the atomic effect becomes completely dσCEνNS G2 m E negligible. ¼ F C2 m 1 − N R ; ð1Þ dE π V N 2 2 In Ref. [21] it has been noted that, in the case of electron R Eν neutrino scattering, the interference between the electron where GF is the Fermi constant, mN is the nuclear mass, Eν cloud and the nucleus is destructive. As a consequence, the 2 scattering amplitude becomes null and changes sign as q2 is the neutrino energy and CV is the q -dependent matrix varies from large to small values, producing a sharp dip in element of the vector neutral-current charge the differential cross section. In practice, electrons tend to 1 screen the weak charge of the nucleus as seen by an C ¼ ½ð1 − 4 sin2 ϑ ÞZF ðq2Þ − NF ðq2Þ: ð2Þ electron neutrino probe. V 2 W Z N The small recoils needed for the observation of coherent elastic neutrino-atom scattering are well below the thresh- Here, Z and N are the number of protons and neutrons in 2 2 olds of detectability of currently available detectors, mak- the atom and FNðq Þ [FZðq Þ] is the nuclear neutron ing it very difficult to observe this effect. However, in (proton) form factor [6,26,27]. In principle, one should Ref. [22] a new technology based on the evaporation of also consider the axial coupling CA contribution, but helium atoms from a cold surface and their subsequent for even-even (spin zero) nuclei it is equal to zero. Since detection using field ionization has been proposed for the in this paper we take as a target a 4He detector, we have detection of low-mass dark matter particles. In this con- CA ¼ 0. figuration, the nuclear recoils induced by dark-matter As anticipated in the introduction, when the energy scattering produce elementary excitations (phonons and of the incoming neutrino is low enough, atomic effects CEνAS rotons) in the target that can result in the evaporation of arise. In the case of CEνAS processes, dσ =dTR can helium atoms, if the recoil energy is greater than the be derived starting from the formula in Eq. (1) with binding energy of helium to the surface. Given that the the inclusion of the electron contribution to the vector latter can be below 1 meV, this proposed technique coupling [21,25] represents an ideal experimental setup to observe atomic effects in coherent neutrino scattering. 1 2 2 CAtom ¼ C þ ð1 þ 4sin ϑ ÞZF ðq Þ; ð3Þ Here, we propose a future experiment that would V V 2 W e allow the observation of coherent elastic neutrino-atom 2 scattering (CEνAS) processes and we investigate its where Feðq Þ is the electron form factor and the þ sign ν ν¯ − sensitivity. Since this effect could be visible only for applies to e and e, while the sign applies to all the other extremely small recoil energies, in order to achieve a neutrino species. As explained in Ref. [21], the þ sign is sufficient number of low-energy CEνAS events, electron responsible for the destructive interference between the neutrinos with energies of the order of a few keV need electron and nuclear contributions. In principle, one should to be exploited. Unfortunately, there are not so many add also the axial contribution from the electron cloud, Atom available sources of such low-energy neutrinos. In this CA , that however becomes null when the number of spin paper, we investigate the possibility to use a tritium up and down electrons is the same, which applies to our β-decay source, that is characterized by a Q value of scenario. Moreover, at the low momentum transfers con- ν 2 18.58 keV. The PTOLEMY project [23,24], that aims to sidered in CE AS processes, one can safely put FNðq Þ¼ 2 1 develop a scalable design to detect cosmic neutrino FZðq Þ¼ . This allows one to derive physics properties background, is already planning to use about 100 g of from the analysis on CEνAS processes being independent tritium, so we can assume that a similar or even larger on the knowledge of the neutron distribution that is largely amount could be available in the near future. Moreover, unknown [6,28]. we show the potentialities of such a detector to perform As visible from Eq.
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