PHYSICAL REVIEW D 102, 036016 (2020)
Dynamical evidence for a fifth force explanation of the ATOMKI nuclear anomalies
† ‡ Jonathan L. Feng ,* Tim M. P. Tait , and Christopher B. Verhaaren Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA
(Received 18 June 2020; accepted 30 July 2020; published 17 August 2020)
Recent anomalies in 8Be and 4He nuclear decays can be explained by postulating a fifth force mediated by a new boson X. The distributions of both transitions are consistent with the same X mass, 17 MeV, providing kinematic evidence for a single new particle explanation. In this work, we examine whether the new results also provide dynamical evidence for a new particle explanation, that is, whether the observed decay rates of both anomalies can be described by a single hypothesis for the X boson’s interactions. We consider the observed 8Be and 4He excited nuclei, as well as a 12C excited nucleus; together these span the possible JP quantum numbers up to spin 1 for excited nuclei. For each transition, we determine whether scalar, pseudoscalar, vector, or axial vector X particles can mediate the decay, and we construct the leading operators in a nuclear physics effective field theory that describes them. Assuming parity conservation, the scalar case is excluded and the pseudoscalar case is highly disfavored. Remarkably, however, the protophobic vector gauge boson, first proposed to explain only the 8Be anomaly, also explains the 4He anomaly within experimental uncertainties. We predict signal rates for other closely related nuclear measurements, which, if confirmed by the ATOMKI group and others, would provide overwhelming evidence that a fifth force has been discovered.
DOI: 10.1103/PhysRevD.102.036016
I. INTRODUCTION them to probe extremely rare processes mediated by particles with very weak interactions. In the standard model of particle physics, particles In 2015, researchers working at the ATOMKI pair interact through the electromagnetic, strong, and weak spectrometer experiment reported a 6.8σ anomaly in the forces. Following tradition, if we include gravity, but not decays of an excited beryllium nucleus to its ground state, the force mediated by the Higgs boson, there are four 8 8 − Beð18.15Þ → Beeþe [9]. The observed anomaly is an known forces. The discovery of a fifth force and the particle excess of events at opening angles θeþe− ≈ 140°, suggesting that mediates it would have profound consequences for 8 the production of a new X boson through Beð18.15Þ → fundamental physics. 8BeX, followed by the decay X → eþe−, with best- Nuclear physics provides a fruitful hunting ground for fit parameters m ¼ 16.7 0.35ðstatÞ 0.5ðsystÞ MeV new forces. This was obviously true in the past, given the X and Γð8Beð18.15Þ → 8BeXÞ¼1.1 × 10−5 eV, assuming central role of nuclear physics in elucidating the strong and BðX → eþe−Þ¼1. weak forces, but it remains true today. In particular, nuclear In 2016, this possibility was analyzed in detail in experiments are well suited to discovering light and weakly Refs. [10,11]. All possible spin-parity assignments for interacting particles [1–4], which have many particle and the X particle were examined, several explanations were astrophysical motivations [5–8]. These particles may be excluded, and the possibility that the X particle is a vector light enough to be produced in nuclear decays, and the gauge boson mediating a protophobic fifth force was shown extraordinary event rates of nuclear experiments allow to be a viable explanation. Following these studies, other new physics explanations were examined in detail, with a host of implications for nuclear, particle, and astrophysical – *[email protected] observations; see, for example, Refs. [12 25] and Ref. [26] † [email protected] for a brief review. A follow-up study from nuclear theory ‡ [email protected] was also shown to disfavor a nuclear form factor as an explanation [27]. Follow-up measurements of the nuclear Published by the American Physical Society under the terms of transitions have not been reported by other groups, but the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to other experimental collaborations have provided new con- the author(s) and the published article’s title, journal citation, straints on X boson couplings to electrons that exclude part and DOI. Funded by SCOAP3. of the viable parameter space in some models [28,29].
2470-0010=2020=102(3)=036016(19) 036016-1 Published by the American Physical Society FENG, TAIT, and VERHAAREN PHYS. REV. D 102, 036016 (2020)
8 4 Since 2016, the ATOMKI experimentalists have rebuilt anomalous Be and He decay rates have a consistent new their spectrometer and confirmed the 8Beð18.15Þ anomaly physics interpretation. with the new detector. A refined analysis yields best-fit On the experimental side, the width measurement of parameters [30] Eq. (4) requires careful differentiation of signal and back- ground. The leading backgrounds include external pair 3 → 4 γ → þ − mX ¼ 17.01 0.16 MeV; ð1Þ creation (p þ H He þð e e Þ) and internal pair creation from the E0 transition 4Heð20.21Þ → 4Heeþe−.By Γð8Beð18.15Þ → 8BeXÞ¼ð6 1Þ fitting to the expected opening angle distributions for the Γ =Γ 0 10−6Γ 8 18 15 → 8 γ signal and these backgrounds, the ratio X E was × ð Beð . Þ Be Þ determined. The collaboration has noted, however, that ¼ð1.2 0.2Þ × 10−5 eV: ð2Þ an additional background from the E1 transition may also be significant [36]. Including this contribution will modify They have also considered the decays of other excited the best-fit width. With this in mind, we consider models beryllium and carbon nuclei [31,32]. Most remarkably, in that predict widths that differ by orders of magnitude from recent months they have reported the observation of a 7.2σ Eq. (4) to be highly disfavored, whereas models that predict 4 excess at θeþe− ≈ 115° in the transitions of Heð20.49Þ → roughly similar widths are considered viable. These pre- 4Heeþe−, where the proton beam energy was tuned to dictions will be tested once a refined experimental analysis produce a resonance that sits within the Breit-Wigner peaks including a separate determination of the E1 background is of both the 4Heð20.21Þ and 4Heð21.01Þ excited states. available. Assuming the production of a new particle, the best fit We begin examining the fifth force explanation for parameters are reported to be [33,34] the ATOMKI results in Sec. II, where we consider the production and decay kinematics for the observed 8Be and 4He processes and also for a 12C excited state, which mX ¼ 16.98 0.16ðstatÞ 0.20ðsystÞ MeV; ð3Þ completes the possible nuclei JP assignments up to spin 1. Γ 4 20 49 → 4 0 12Γ 4 20 21 → 4 þ − In Sec. III we determine how the observation or exclusion ð Heð . Þ HeXÞ¼ . ð Heð . Þ Hee e ÞE0 of various decays constrains the possible X spin-parity 4 0 1 2 10−5 ¼ð . . Þ × eV; ð4Þ assignments. This is developed further in Sec. IV, where for each of these possibilities we determine the leading where the width uncertainty includes only the uncertainty interactions in an effective field theory (EFT) that describes Γ 4 20 21 → 4 þ − 3 3 1 0 10−4 from ð Heð . Þ Hee e ÞE0 ¼ð . . Þ× eV low-energy nuclear transitions. Using this EFT, the decay [35], the decay width of the standard model E0 transition. rates for the pseudoscalar, axial vector, and vector cases The fact that this excess is at a different angle eliminates are calculated in Secs. V, VI, and VII, respectively. some experimental systematic explanations of both anoma- Remarkably, we find that in the vector case, the proto- lies. At the same time, the fact that the excess is found at the phobic gauge boson, previously advanced as an explan- same X mass provides striking supporting evidence that a ation of the 8Be anomaly, also provides a viable explanation new particle is being produced. for the new 4He observations within experimental uncer- Of course, it would be clarifying if these nuclear decays tainties. In Sec. VIII, we suggest further nuclear measure- were examined by another collaboration. It is important to ments that can provide incisive tests of the new particle note, however, that the observation of a second signal hypothesis, and we summarize our conclusions in Sec. IX. provides an opportunity for another highly nontrivial check of the new physics interpretation beyond simply the II. PRODUCTION AND DECAY KINEMATICS consistency of the best-fit masses. The description in terms of a new particle requires not just kinematic consistency, We consider the production of new X particles in the but also dynamical consistency; that is, the rates for the decays of excited states of 8Be, 12C, and 4He nuclei. anomalous decays must also be consistent with the same set Although the states of interest have different quantum of interaction strengths between the X and quarks. The numbers, leading to different decay dynamics, the kine- best-fit widths are similar numerically, but it is far from matic features of the relevant processes are very similar. 8 4 obvious that this implies consistency: the Be and He In each case, a beam of protons with kinetic energy P excited states have different J quantum numbers and Ebeam collides with nuclei A at rest to form excited nuclei 8 → different excitation energies, and the Be measurement was through the process p þ A N . The excited nuclei N 4 on resonance, while the He measurement was between two decay to the corresponding ground state nuclei N0 through → → þ − resonances. The decays therefore take place through N N0X, and the X bosons further decay via X e e . operators with different dimensions and different partial In this section we review the experimental results and the waves, and these differences may lead to disparate decay kinematics of these processes. We examine the kinematics widths. A priori, then, it is not at all clear that the observed of resonance production in Sec. II A, and we consider the X
036016-2 DYNAMICAL EVIDENCE FOR A FIFTH FORCE EXPLANATION … PHYS. REV. D 102, 036016 (2020)
TABLE I. Production and decay kinematic parameters. Beams of protons with kinetic energy Ebeam collide with → nuclei A at rest to form excited nuclei N , which then decay to the ground state nucleus N0 through N N0X.We m 17 E m m v N fix X ¼ MeV, and for each of the relevant processes, we give the values of beam, A, N , N (the velocity θmin þ − 4 20 49 in the lab frame), vX (the X velocity in the N rest frame), and eþe− (the minimum e e opening angle). Heð . Þ indicates the resonance energy probed in Ref. [33], which sits between the 4Heð21.01Þ and 4Heð20.21Þ states.
min p þ A → N E [MeV] m [MeV] m [MeV] v =c v =c θ − beam A N N X eþe p þ 7Li → 8Beð18.15Þ 1.03 6533.83 7473.01 0.0059 0.350 139° p þ 7Li → 8Beð17.64Þ 0.45 6533.83 7472.50 0.0039 0.267 149° p þ 11B → 12Cð17.23Þ 1.40 10252.54 11192.09 0.0046 0.163 161° p þ 3H → 4Heð21.01Þ 1.59 2808.92 3748.39 0.0146 0.587 108° p þ 3H → 4Heð20.49Þ 0.90 2808.92 3747.87 0.0110 0.557 112° p þ 3H → 4Heð20.21Þ 0.52 2808.92 3747.59 0.0084 0.540 115°
4 boson decay and the electron-positron opening angle θeþe− For the He anomaly [33], the experiment ran between in Sec. II B. the broad 0þ 4Heð20.21Þ and 0− 4Heð21.01Þ resonances. The proton beam energy was tuned to produce 4He nuclei A. Resonance production with an excitation energy of E ¼ 20.49 MeV, which is well within the widths of both excited states; see Fig. 1. For resonance production, the required proton energy is B. X boson decay 2 2 2 m − m − mp N A Once produced, the excited nucleus decays through Ep ¼ 2 ; ð5Þ mA → N N0X. In the N rest frame, the X boson is produced with energy where m and m are the nuclear (not atomic) masses. A N 2 2 2 The proton beam energy, or proton kinetic energy, is m þ m − m E N X N0 ≈ m − m ; 6 − ’ X ¼ N N0 ð Þ Ebeam ¼ Ep mp, the proton s momentum is pp ¼ 2m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N 2 − 2 Ep mp, and the N nucleus is created with velocity where the last expression exploits the fact that m , m − pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX N vN ¼ pp=ðEp þ mAÞ in the lab frame. The values of Ebeam, ≪ 1 − 2 mN0 mN , mN0 . The X velocity is vX ¼ ðmX=EXÞ m m v A, N , and N for the considered processes are given in Table I, and the properties of the relevant excited nuclear Ebeam (MeV) states are summarized in Table II. 0 0.5 1 2 8 The anomaly observed in the Be system is unambig- + uously associated with the 8Beð18.15Þ state [9]. The 0 0 8Beð18.15Þ and 8Beð17.64Þ resonances do not overlap significantly, and the anomaly was found to appear and disappear as the proton beam energy was varied to scan through the 8Beð18.15Þ resonance.
P TABLE II. Nuclear excited states N and their spin-parity J , T Γ isospin , total decay width N , and photon branching fraction [37–42] [or, in the case of 4Heð20.21Þ, the branching fraction for þ − the E0 decay into e e [35] ]. The N states are labeled by their 8 energy above the nuclear ground state N0 in MeV. The Be 19.5 20.0 20.5 21.0 21.5 22.0 excited states mix; we list the dominant isospin component. E (MeV) P N T Γ [keV] BðN → N0γÞ J N FIG. 1. The Breit-Wigner resonance curves of the 4 − 4 8Beð18.15Þ 1þ 0 138 1.4 × 10−5 0þ Heð20.21Þ and 0 Heð21.01Þ excited states as a function 8Beð17.64Þ 1þ 1 10.7 1.4 × 10−3 of the excitation energy E above the helium ground state (bottom) 12 − −5 Cð17.23Þ 1 1 1150 3.8 × 10 and the proton beam energy Ebeam (top). The solid and dashed − 4Heð21.01Þ 0 0 840 0 vertical lines at beam energies of 0.90 MeV and 0.52 MeV 4Heð20.21Þ 0þ 0 500 6.6 × 10−10 (E0) correspond to the beam energy used in Ref. [33] and the beam energy required to maximize the 0þ resonance, respectively.
036016-3 FENG, TAIT, and VERHAAREN PHYS. REV. D 102, 036016 (2020) and is shown in Table I for the various processes, assuming 180 17 → þ − mX ¼ MeV. The X boson decays through X e e .In C 17.23 the X rest frame, the electron and positron velocities 160 are ve ≈ 0.998.
All of the processes of interest have the hierarchies deg Be 18.15 140 ≲ 0 01 ≪ ≈ 1 e v v