Particle Physics Models for the ATOMKI Beryllium-8 Anomaly Tim M.P . Tait University of California, Irvine Work with: J. Feng, B. Fornal, S. Gardner, I. Galon, J. Smolinsky, TMPT, P . Tanedo Bormio arXiv:1604.07411 & PRL; arXiv:1608.03591 & PRD January 26, 2017
ATOMKI Experiment 18.15 MeV 138 keV width 1.03 MeV ~10 keV spread • Since Attila already told us about the experiment and results yesterday, I will focus on interpretation.
Be-8 Levels • The Be-8 ground state is a 0 + isosinglet. arXiv:1608.03591 • There are a variety of excited states with different spins and isospins. • For today, interested in the 1 + 17.64 Be*’ and 18.15 Be * states. There is some evidence that these states are actually admixtures of isotriplet and isosinglet. Pastore et al, PRC90 (2014) [1406.2343]
Experimental Results Fixed E p = 1.10 MeV -1 10 m=15.6 MeV Counts, N ee [per 0.5 MeV] A.J. Krasznahorkay, et al. 800 dN/d θ PRL116, 042501 (2016) m=16.6 MeV symmetric e + e - 700 m=17.6 MeV 600 500 m=16.6 MeV 400 background 300 a 200 s y m m e -2 t r i ÷1.9 c 10 100 signal e + e - 0 9 10 11 12 13 14 15 16 17 18 80 90 100 110 120 130 140 150 160 170 Invariant Mass, m ee [MeV] Opening Angle [Deg] • Note that in the bump region ~14 - 18 MeV, the signal is a pretty large fraction of the total number of events (though it is a small fraction of the total integrated over all m ee ).
So What’s Going On? • Obviously, one should be cautious. In the very least we would like to see these results repeated, preferably by a different group. • Logically, we should consider the possibilities of: • Experimental error/Miscalibration/Etc: • Nothing is obviously wrong with the experiment: the angles and energies all seem self-consistent and pass the sanity checks; • Up until now unknown nuclear physics effect: • Nuclear physicists so far haven’t come up with an obvious explanation for a bump (but they continue to work on it!) This is crucial; • Physics Beyond the Standard Model. • My attitude here: Let’s see what kind of new physics can explain it and see what other constraints/opportunities there are to learn more.
BSM Interpretation • A BSM interpretation requires a new particle, X. • The ATOMKI group fits a hypothesis consisting of the expected M1 IPC background (and also allows for a contribution of E1 pollution) plus signal: m X = 16 . 7 ± 0 . 35 (stat) ± 0 . 5 (sys) MeV Γ ( 8 Be ∗ → 8 Be X ) Γ ( 8 Be ∗ → 8 Be γ ) Br( X → e + e − ) = 5 . 8 × 10 − 6 • A few things are clear: • It must be a boson coupled to leptons in order to decay into e+e- • It must couple to quarks and/or gluons so that it can appear in beryllium transitions. • It has a short life-time such that it decays within about 1 cm so that its decay is prompt compared to the detector geometry.
Effective Field Theory • We can capture the essential features of the decay in terms of arXiv:1604.07411 and arXiv:1608.03591 a low energy effective field L V = g V Be G µ ν F ( V ) ρσ ✏ µ νρσ theory. Λ V L S = g S • ( @ µ s )( @ ν Be) G ρσ ✏ µ νρσ The deBroglie wavelength of the Λ 2 S emitted particle is m 2 L A = g A Be G µ ν F ( A ) A Be A µ Be ⇤ µ µ ν + λ ~ 1/ (6 MeV), Λ A g A Λ 0 A whereas the size of the nucleus L P = g P Be ( @ µ a ) Be ⇤ µ . is r ~ 1/(100 MeV). • G µ ν ≡ ∂ µ Be ∗ ν − ∂ ν Be ∗ We can treat the nucleus as µ point-like, expanding in The leading operators are dimension- r / λ ~ 1 / 20. four (pseudo-scalar), -five (vector and • axial-vector), and -six (scalar). We assume parity conservation to avoid getting bogged down The scalar 0 + operator vanishes upon with strong APV constraints, but applying the equation of motion. this assumption can be relaxed.
0 + Scalar Particle NAIVELY ISOVIOLATING We expect our finding for the NAIVELY ISOCONSERVING scalar operator is more general. ANGULAR MOMENTUM ` = 1 PARITY P = ( − ) ` P Be P X - + + The decay is forbidden if parity is conserved. 0+
Axion-like Particle • The EFT dictates that a pseudo scalar L P = g P Be ( @ µ a ) Be ⇤ µ . particle can couple Be* to the ground state. 10 - 1 SLAC 141 LEP • We initially discarded this possibility 10 - 2 Y -> invisible because of strong ALP constraints on 10 - 3 e + e - -> inv. + γ this mass range. g a γ [ GeV - 1 ] 10 - 4 CHARM NuCal • However, these bounds are relaxed 10 - 5 HB Cosmo SLAC 137 because of the prompt decay to e+e-. 10 - 6 SN1987a • 10 - 7 Ellwanger and Moretti followed this up 10 - 8 in 1609.01669. 10 - 4 10 - 3 10 - 2 10 - 1 10 0 m a [ GeV ] • They use a nuclear shell model to estimate transition matrix elements. m f X ξ f g P = • v They conclude that it works provided f ξ q ∼ 0 . 7 ξ ` ∼ 4 O(10%) cancellations in some FCNCs.
Spin One L V = g V Be G µ ν F ( V ) ρσ ✏ µ νρσ • For a vector particle, the EFT Λ V m 2 L A = g A g corresponds to a dimension-5 operator Be G µ ν F ( A ) A Be A µ Be ⇤ µ µ ν + Λ A g A Λ 0 A (two operators for axial-vectors). e = 10 - 3 Family Non - Universal Couplings, c V • For a massless vector, this EFT also 10 - 2 e + e - → γ A' BaBar - e describes EM transitions, and the + e → r η e dimension 5 nature of the operator l l o M 10 - 3 reflects the fact that this is an M1 ( g - 2 ) e Allowed ( g - 2 ) μ favored transition. e | | c A Beam Dumps • π 0 → e + e - For axial-vector couplings, the nuclear 10 - 4 Favored Anomalon matrix elements only have recently been computed. Kozaczuk, Morrissey, Stroberg arXiv:1612.01525 10 - 5 • 10 2 1 10 The results seem promising to fit the m A ' [ MeV ] signal and evade constraints. Kahn, Krnjaic, Mishra-Sharma, TMPT arXiv:1609.09072 • There is a wider menu of constraints 17 MeV is an interesting hole in the low energy and UV worries such as anomalies. constraints, but naively probed by UV physics at the LHC!
Dark Photon 2 • KLOE ε For a dark photon, the nuclear WASA physics is identical to the usual EM ) σ (3 transition, and cancels out of the 2) e − (g -5 ratio of partial widths. 10 HADES APEX Br( 8 Be ∗ → X ) p X | 3 Br( 8 Be ∗ → � ) ∼ " 2 | ~ (g 2) − µ A1 | ~ p γ | 3 -6 10 BaBar • Fitting the size of the signal requires ε ~ 0.1, which is ruled out by E774 π 0 → γ X NA48/2 E141 NA48/2’s search for π 0 γ X. -7 10 2 10 10 2 m (MeV/c ) A’ NA46/2 1504.00607
Proto-phobic Vectors • We choose to focus from here on at vector (rather than axial vector) interactions. • We’d like to engineer away the bounds from NA48/2 without turning off couplings to first generation quarks altogether, which drives us to ``proto-phobic” couplings: To avoid NA46/2, prohibit π decay to X 훾 X X π 0 = ✓ p ◆ π 0 Goldstone 1 u − d ¯ � � u ¯ d of SU (2) L × SU (2) R √ 2 γ γ STEINBERGER CALCULATION FROM QUARK CONTENT Q u Q 0 u − Q d Q 0 ✓ ◆ d = 0 p N = Q 0 d = − 2 Q 0 n u • Note that axial vectors will naturally evade NA48/2, since their couplings to π 0 do not go through the anomaly, and are thus suppressed by the small quark masses.
Isospin Violation • To identify the target region for generalized up and down quark ISOVIOLATING charges, we need to address the evidence for isospin mixing in the ISOCONSERVING Be* and Be*’ states. Pastore, et al. Phys. Rev. C 90 [1406.2343]; Phys. Rev. C 88 [1308.5670] • Pastore et al infer that these states are mixed by looking at their hadronic decays, which find that the physical states {a,b} are related to eigenstates of isospin by: Ψ a = α 1 Ψ T =0 + β 1 Ψ T =1 Ψ b = β 1 Ψ T =0 − α 1 Ψ T =1 • with mixing parameters: α 1 ∼ 0 . 21(3) β 1 ∼ 0 . 98(1)
Results = | ( ε p + ε n ) β 1 M 1 1 ,T =0 + ( ε p � ε n )( � α 1 M 1 1 ,T =1 + β 1 κ M 1 1 ,T =1 ) | 2 | k X | 3 Γ X | β 1 M 1 1 ,T =0 � α 1 M 1 1 ,T =1 + β 1 κ M 1 1 ,T =1 | 2 | k γ | 3 Γ γ arXiv:1609.07411 BEST FIT NA48/2 g i ≡ e × ε i 16 10 PROTOPHOBIC 11 To explain the ATOMKI BEST FIT 5 results, one would like a 7 coupling ε to neutrons 5.8 of order 10 -2 and one to protons < about 10 -3 . 4 DARK PHOTON 2 0 1 0.25 0.05 0 5 10
Why nothing from 17.64 ? • The large isospin mixing between the 17.64 and 18.15 MeV states argues ISOVIOLATING that it is difficult to use iso-spin structure to explain why no signal is ISOCONSERVING seen in the Be*’ state. • Of course, this possibility was also closed because protophobic couplings imply an equal admixture of isosinglet and isotriplet currents. • Thus, the best prospect to explain why the new boson is produced in Be* but not Be*’ decays is the fact that the phase space is close to saturated. • That said, the kinematics and isospin structure is such that eventually this decay must happen in any reasonable particle physics explanation.
Electron Couplings • The electron couplings are bounded from below by the need to decay promptly before the ATOMKI detectors, ~ cm from the target. e α m 2 X + 2 m 2 q e Γ ( X ! e + e − ) = ε 2 1 � 4 m 2 e /m 2 X 3 m X • This requirement places the mild constraint that the electron couplings be: ~ cm ε e & 1 . 4 × 10 − 5 • It doesn’t particularly care whether these couplings are vector or axial, but we choose vector couplings to avoid running into APV and other parity-odd observable constraints.
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