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Cosmic Neutrino Background Search Experiments As Decaying Dark Matter Detectors

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Cosmic Neutrino Background Search Experiments As Decaying Dark Matter Detectors PHYSICAL REVIEW D 100, 015028 (2019) Cosmic neutrino background search experiments as decaying dark matter detectors David McKeen* TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada (Received 1 April 2019; published 18 July 2019) We investigate the possibility that particles that are long-lived on cosmological scales, making up part or all of the dark matter, decay to neutrinos that have present-day energies around an eV. The neutrinos from these decays can potentially be visible at experiments that hope to directly observe the cosmic neutrino background through neutrino capture on tritium, such as PTOLEMY. In the context of a simple model that can realize such decays, we discuss the allowed signatures at a PTOLEMY-like experiment given current cosmological constraints. DOI: 10.1103/PhysRevD.100.015028 I. INTRODUCTION enormous density, scattering of CνB neutrinos is highly suppressed since their energies are minuscule and they Particles with lifetimes on cosmological scales that couple to matter only via the weak interaction. Further- decay to neutrinos arise in a number of new physics more, the tiny energies involved make distinguishing from contexts, such as lepton number violation and the gener- backgrounds very troublesome. Both of these facts mean ation of neutrino masses [1], and can even comprise some that detecting the CνB is extremely challenging. The most or all of the dark matter of the Universe [2–5]. The present- promising technique to detect the very low energy CνB— day energy of the neutrinos from these decays can span a − neutrino capture on β-decaying nuclei, ν þðA; ZÞ → e þ wide range, making them accessible at, e.g., existing dark ðA; Z þ 1Þ, where a nucleus, ðA; ZÞ, is labeled by its mass matter direct detection and neutrino experiments [4–6]. number, A, and atomic number, Z—was first proposed by In this paper we will consider the decays of long-lived Weinberg in 1962 [9] and more recently studied in [10,11]. particles to neutrinos that carry very little energy today, in This process benefits from the lack of a threshold energy the neighborhood of an eV. These neutrinos are slightly and its signature is the production of an electron with more energetic than the standard cosmic neutrino back- energy above the end point of natural β decay, ðA; ZÞ → ground (CνB)—the thermal relic neutrinos that decoupled − ν¯ þ e þðA; Z þ 1Þ. For a neutrino of mass mν and energy from the plasma when the Universe had a temperature of a Eν, the shift above the end point is ∼mν þ Eν. In the case of few MeV. The temperature of the CνBis∼10−4 eV today, nonrelativistic CνB neutrinos, this shift is roughly 2mν.Of less than the scale of the atmospheric and solar neutrino course, extremely good resolution on the e− energy is mass splittings, and therefore at least two mass eigenstates required to resolve this gap given the relatively large rate ν in the C B are now nonrelativistic; the most energetic of of β decay compared to capture of CνB neutrinos. ≃ ≳ 0 05 these neutrinos have energy ECνB mν . eV. There is Recently, the PTOLEMY experiment has proposed [12] an upper limit on the neutrino masses, hence on the energy to tackle these difficulties using a target of 100 g of tritium ν of the C B, from observations of the cosmic microwave (i.e., A ¼ 3, Z ¼ 1 in the expressions above) implanted on Pbackground (CMB) and baryon acoustic oscillations of a graphene substrate along with MAC-E (Magnetic 0 12 mν< . eV at 95% confidence level [7]. Terrestrial Adiabatic Collimation with Electrostatic) filtering, radio experiments, in comparison, limit the neutrino mass at frequency monitoring, and advanced calorimetry to mea- 95% confidence level to less than 2.8 eV [8]. sure the e− energy. Tritium has a relatively small rate for β The present-day number density of CνB neutrinos is very −1 decay, Γβ ≃ ð17 yrÞ and implanting it on graphene serves ≃ 330 −3 large, with a cosmic average nCνB cm . Despite this to reduce intrinsic broadening of the e− energy from molecular effects. This could potentially allow for energy *[email protected] resolution as small as 0.1 eV, which is needed to success- fully probe the CνB. Published by the American Physical Society under the terms of This paper is organized as follows. In Sec. II, we describe the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to a simple model containing a long-lived particle that the author(s) and the published article’s title, journal citation, decays to neutrinos, and discuss the number density and and DOI. Funded by SCOAP3. energy distribution of neutrinos allowed by cosmological 2470-0010=2019=100(1)=015028(8) 015028-1 Published by the American Physical Society DAVID MCKEEN PHYS. REV. D 100, 015028 (2019) observations. We see that decays that take place after matter, and h ≃ 0.68 is the Hubble constant today in units 100 Ω Ω recombination, when photons decouple, are the most prom- of km=s=Mpc. J= dm is the fraction of dark matter ising to be probed at experiments sensitive to eV-scale that J particles would comprise today if they did not decay, neutrinos, such as PTOLEMY. We discuss the signature of which we normalize here to 5%. In what follows, we will this scenario at a PTOLEMY-like experiment in detail in suppress the argument of the scale factor and set its value Sec. III, considering both the diffuse and local contributions today to unity, a0 ¼ aðt0Þ¼1. We will also require that to the flux, and compare the reach to that of cosmological the J’s and their decay products do not grossly disturb observations. In Sec. IV, we conclude. the evolution of the Universe from the standard cosmology, with radiation domination at redshifts z ¼ a−1 − 1≳ ≃ 3300 II. DENSITIES AND DISTRIBUTIONS zeq , followed by matter domination, then more recently vacuum energy domination. The simple model we consider involves only a long- The number density of neutrinos produced in J decays lived, real scalar particle J with mass mJ. It couples to the simply follows from Eq. (3), light neutrinos ν through an interaction of the form − τ 2Ω ρ 1 − t= J g ˜ ð Þ¼ J cr;0 e L ¼ − νν þ ð Þ nν t 3 int J H:c: 1 m a 2 J − τ 130 Ω Ω 1 − t= J J= dm eV e In this expression, ν is a two-component, left-chiral spinor ¼ ; ð4Þ cm3 0.05 m a3 field, and the interaction is gauge invariant if, e.g., it comes J from a sterile admixture of the light neutrinos. This → νν where we use a tilde to distinguish this population from the coupling leads to the decay J . Assuming that this standard neutrinos. is the only J decay mode at tree level, its lifetime is There are essentially three qualitatively different regimes 32π 10−15 2 for the J lifetime in terms of its cosmological effects: 9 eV τ ≃ 0 2 τ ¼ ¼ 2 × 10 yr : ð2Þ (i) before neutrino decoupling, J <tdec . s, (ii) after J jgj2m g m J J neutrino decoupling and before recombination, tdec < τ ∼ 4 105 J <trec × yr, and (iii) after recombination, Here and in what follows, we take the neutrino masses to be τ J >trec. Case (i) is not observable since the neutrinos negligible compared to mJ. A natural candidate for J is the simply thermalize with the plasma. Cases (ii) and (iii) can Majoron associated with the spontaneous breaking of potentially lead to a nonstandard population of neutrinos lepton number at a scale f. In this case, the coupling is ¼ today. Crucially, cases (ii) and (iii) affect the observation of g imν=f which could easily be tiny for f above the TeV the CMB in different ways which we discuss below. scale. We have normalized the J mass on an eV for later convenience. For now, we are agnostic about the flavor A. Decays before recombination (τJ < trec) structure of the couplings in Eq. (1) but will return to this point in Sec. III. In this case, the neutrinos from J decays contribute to the We assume that the J’s are produced nonthermally and energy density in relativistic species at early times. This is are nonrelativistic at cosmologically interesting times.1 We constrained by the observation of the CMB which is record can then simply write down their number density, of the Universe at around trec. The extra contribution from J decays can be conven- ρ 3 cr;0 aðt0Þ − τ iently parametrized by a shift of the effective number of ð Þ¼Ω t= J nJ t J e Δ m aðtÞ relativistic degrees of freedom (d.o.f.), Neff, with J 63 Ω Ω ð Þ 3 J= dm eV a t0 − τ 4=3 ¼ t= J ð Þ 8 11 ρ˜ν 3 e : 3 Δ ¼ ð Þ cm 0.05 m aðtÞ Neff ; 5 J 7 4 ργ In this expression, aðtÞ is the scale factor of the Universe, where ργ and ρ˜ν are the energy densities in photons and t0 ¼ 13.8 Gyr is its age, Ω is the J energy density in units J neutrinos from J decay, respectively. A nonzero ΔN can of the critical energy density of the Universe today, eff 2 3 −2 affect the CMB by changing the expansion rate around the ρ 0 ¼ 10.5h keV=cm , Ω ¼ 0.12h is that of dark cr; dm time of last scattering from its standard value.
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