Dark Matter Interpretation of the Neutron Decay Anomaly Bartosz Fornal and Benjam´ın Grinstein Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA (Dated: May 10, 2018) There is a long-standing discrepancy between the neutron lifetime measured in beam and bottle experiments. We propose to explain this anomaly by a dark decay channel for the neutron, involving one or more dark sector particles in the final state. If any of these particles are stable, they can be the dark matter. We construct representative particle physics models consistent with all experimental constraints. INTRODUCTION In this paper we focus on the latter possibility. We as- sume that the discrepancy between the neutron lifetime mea- The neutron is one of the fundamental building blocks of surements arises from an incomplete theoretical description matter. Along with the proton and electron it makes up most of neutron decay and we investigate how the Standard Model of the visible universe. Without it, complex atomic nuclei sim- (SM) can be extended to account for the anomaly. ply would not have formed. Although the neutron was discov- ered over eighty years ago [1] and has been studied intensively thereafter, its precise lifetime is still an open question [2, 3]. NEUTRON DARK DECAY The dominant neutron decay mode is β decay − Since in beam experiments neutron decay is observed by n ! p + e +ν ¯e ; detecting decay protons, the lifetime they measure is related described by the matrix element to the actual neutron lifetime by 1 µ M = p GF Vud gV [p ¯ γµn − λ p¯ γ5γµn ] [e ¯ γ (1 − γ5)ν ] : 2 beam τn τn = : (1) The theoretical estimate for the neutron lifetime is [4–7] Br(n ! p + anything) 4908:7(1:9) s In the SM the branching fraction (Br), dominated by β decay, τn = 2 2 : jVudj (1 + 3 λ ) is 100% and the two lifetimes are the same. The neutron decay rate obtained from bottle experiments is The Particle Data Group (PDG) world average for the axial- −28 vector to vector coupling ratio is λ = −1:2723 ± 0:0023 [8]. Γn ' 7:5 × 10 GeV: Adopting the PDG average jVudj = 0:97417 ± 0:00021 gives τn between 875:3 s and 891:2 s within 3 σ. The discrepancy ∆τn ' 8:4 s between the values measured in There are two qualitatively different types of direct neutron bottle and beam experiments corresponds to [18] lifetime measurements: bottle and beam experiments. exp bottle beam −30 In the first method, ultracold neutrons are stored in a con- ∆Γn = Γn − Γn ' 7:1 × 10 GeV : tainer for a time comparable to the neutron lifetime. The re- maining neutrons that did not decay are counted and fit to a We propose that this difference be explained by the exis- tence of a dark decay channel for the neutron, which makes decaying exponential, exp(−t/τn). The average from the five bottle experiments included in the PDG [8] world average is Br(n ! p + anything) ≈ 99% : [9–13] τ bottle = 879:6 ± 0:6 s : n There are two qualitatively different scenarios for the new arXiv:1801.01124v3 [hep-ph] 9 May 2018 Recent measurements using trapping techniques [14, 15] yield dark decay channel, depending on whether the final state con- a neutron lifetime within 2:0 σ of this average. sists entirely of dark particles or contains visible ones: In the beam method, both the number of neutrons N in a beam and the protons resulting from β decays are counted, (a) n ! invisible + visible ; and the lifetime is obtained from the decay rate, dN=dt = (b) n ! invisible : −N/τn. This yields a considerably longer neutron lifetime; the average from the two beam experiments included in the Here the label “invisible” includes dark sector particles, as PDG average [16, 17] is well as neutrinos. Such decays are described by an effective beam operator O = Xn, where n is the neutron and X is a spin τn = 888:0 ± 2:0 s : 1=2 operator, possibly composite, e.g. X = χ1χ2...χk, with The discrepancy between the two results is 4:0 σ. This sug- the χ’s being fermions and bosons combining into spin 1=2. gests that either one of the measurement methods suffers from From an experimental point of view, channel (a) offers a de- an uncontrolled systematic error, or there is a theoretical rea- tection possibility, whereas channel (b) relies on higher order son why the two methods give different results. radiative processes. We provide examples of both below. 2 Proton decay constraints One can also have a scalar DM particle φ with mass mφ < The operator O generally gives rise to proton decay via 938:783 MeV and χ being a Dirac right-handed neutrino. ∗ + Trivial model-building variations are implicit. The scenarios p ! n + e + νe ; with a Majorana fermion χ or a real scalar φ are additionally followed by the decay of n∗ through the channel (a) or (b) constrained by neutron-antineutron oscillation and dinucleon and has to be suppressed [19]. Proton decay can be elimi- decay searches [23, 24]. nated from the theory if the sum of masses of particles in the minimal final state f of neutron decay, say Mf , is larger than MODEL-INDEPENDENT ANALYSIS mp − me. On the other hand, for the neutron to decay, Mf must be smaller than the neutron mass, therefore it is required that Based on the discussed experimental constraints, the avail- mp − me < Mf < mn : able channels for the neutron dark decay are: n ! χ γ ; n ! χ φ ; n ! χ e+e− ; Nuclear physics bounds In general, the decay channels (a) and (b) could trigger nu- as well as those involving additional dark particle(s) and/or clear transitions from (Z; A) to (Z; A−1). If such a transition photon(s). is accompanied by a prompt emission of a state f 0 with the 0 sum of masses of particles making up f equal to Mf 0 , it can Neutron ! dark matter + photon be eliminated from the theory by imposing Mf 0 > ∆M = M(Z; A) − M(Z; A − 1) : Of course Mf 0 need not be the This decay is realized in the case of a two-particle interac- 0 same as Mf , since the final state f in nuclear decay may tion involving the fermion DM χ and a three-particle interac- not be available in neutron decay. For example, Mf 0 < Mf tion including χ and a photon, i.e., χ n ; χ n γ. Equations (2) 0 when the state f consists of a single particle, which is not and (3) imply that the DM mass is an allowed final state of the neutron decay. If f 0 = f then f 0 must contain at least two particles. The requirement becomes, 937:900 MeV < mχ < 938:783 MeV therefore, and the final state photon energy ∆M < min Mf 0 ≤ Mf < mn : 0:782 MeV < E < 1:664 MeV : (4) The most stringent of such nuclear decay constraints comes γ from the requirement of 9Be stability, for which ∆M = We are not aware of any experimental constraints on such 937:900 MeV, thus monochromatic photons. The search described in [25–27] measured photons from radiative β decays in a neutron beam, 937:900 MeV < min M 0 ≤ M < 939:565 MeV : (2) f f however, photons were recorded only if they appeared in co- The condition in Eq. (2) circumvents all nuclear decay limits incidence with a proton and an electron, which is not the case listed in PDG [8], including the most severe ones [20–22]. in our proposal. To describe the decay n ! χ γ in a quantitative way, we Dark matter consider theories with an interaction χ n, and an interaction Consider f to be a two-particle final state containing a dark χ n γ mediated by a mixing between the neutron and χ. An sector spin 1=2 particle χ. Assuming the presence of the in- example of such a theory is given by the effective Lagrangian teraction χ n, the condition in Eq. (2) implies that the other eff gne µν L =n ¯ i@= − mn + σ Fµν n particle in f has to be a photon or a dark sector particle φ with 1 2mn mass mφ < 1:665 MeV (we take it to be spinless). The decay +χ ¯ i@= − m χ + " (¯nχ +χn ¯ ) ; (5) − χ χ ! p + e +ν ¯e is forbidden if where gn '−3:826 is the neutron g-factor and " is the mixing mχ < mp + me = 938:783 MeV : (3) parameter with dimension of mass. The term corresponding Provided there are no other decay channels for χ, Eq. (3) en- to n ! χ γ is obtained by transforming Eq. (5) to the mass sures that χ is stable, thus making it a DM candidate. On the eigenstate basis and, for " mn − mχ, yields − other hand, if χ ! p + e +ν ¯e is allowed, although this pre- eff gne " µν χ Ln!χγ = χ¯ σ Fµν n : (6) vents from being the DM, its lifetime is still long enough to 2mn (mn − mχ) explain the neutron decay anomaly. In both scenarios φ can be a DM particle as well. Therefore, the neutron dark decay rate is Without the interaction χ n, only the sum of final state g2 e2 m2 3 m "2 masses is constrained by Eq. (2). Both χ and φ can be DM n χ n ∆Γn!χγ = 1 − 2 2 candidates, provided 8π mn (mn − mχ) 2 exp 1+x 3 1−x " [GeV] jmχ − mφj < mp + me : ≈ ∆Γn 2 1:8×10−3 9:3×10−14 ; (7) 3 where x = mχ=mn.