Light Axial Vectors, Nuclear Transi6ons, and the 8 Be Anomaly Jonathan Kozaczuk (UMass Amherst) U.S. Cosmic Visions: New Ideas in Dark Ma8er 3/23/17
Some References Primarily based on JK, D. Morrissey, and S.R. Stroberg , arXiv:1612.01525 [hep-ph] See also: Krasznahorkay et al , PRL 116 (2016) no.4, 042501 Feng et al , PRL 117 (2016) no.7, 071803 PRD 95 (2017) no.3, 035017 Kahn et al , arXiv:1609.09072 [hep-ph] This workshop: I\ah Galon’s slides Subsequent talks by Xilin Zhang, Rafael Lang, and Kyle Leach Kozaczuk 2
The Atomki Experiment in a Nutshell Search for internal pair crea6on ( e + e - produc6on) in excited states of 8 Be Target Telescope detectors MWPC Gulyas et al, 2015 Feng et al, 2016 1.0 µ A proton beam from Van de Graaf generator impinge on LiF 2 , LiO 2 targets e + e - energies and angles determined by 5 plas6c telescope detectors (scin6llator + PMT) and mul6-wire propor6onal chambers Kozaczuk 3
The Atomki Experiment in a Nutshell Proton beam energy tuned to excite J=1 8 Be states Feng et al, 2016 Detector calibrated using internal pair crea6on in 12 C and 16 O One week-long experiments at each bombarding energy, targets periodically changed Kozaczuk 4
The Atomki Results Krasznahorkay et al, 2016 Isoscalar transi6on features significant bump-like excess in e + e - opening angle and invariant mass spectrum ( 6.8 σ ) Feng et al, 2016 No corresponding excess in the isovector ( 8 Be *’ ) transiJon Kozaczuk 5
The Atomki Interpreta6on Krasznahorkay et al, 2016 Interpreta6on put forward by collabora6on: light gauge boson m = 16 . 7 ± 0 . 35(stat) ± 0 . 5(syst) MeV Γ ( 8 Be 0 → 8 Be X ) Γ ( 8 Be 0 → 8 Be γ ) Br( X → e + e � ) = 5 . 8 × 10 � 6 NA48/2 Collabora6on, 2015 In the Atomki PRL the collabora6on claimed this to be consistent with a standard dark photon featuring ε 2 ~ 10 -7 Feng et al (2016) pointed out that explaining the Atomki result actually requires , ✏ ≈ 0 . 011 which is excluded, in par6cular by NA48/2 Kozaczuk 6
A Protophobic Vector Explana6on Feng et al, 2016 (PRL + PRD) Assume more general vector setup L = � 1 4 X µ ν X µ ν + 1 , X X µ X µ � X µ J µ t J µ = P f e " f ¯ 2 m 2 f � µ f , The NA48/2 constraint arises from decays. Rate π 0 → X γ propor6onal to axial anomaly trace factor ⌘ ( " u q u � " d q d ) 2 . 2 General setup can work provided X is protophobic, | 2 ε u + ε d | = | ε p | . (0 . 8 − 1 . 2) × 10 � 3 (NA48/2 bound) p Br( X → e + e � ) (large enough rate; some caveats here) | ε n | = (2 − 10) × 10 � 3 (prompt decays) | ε e | & 1 . 3 ⇥ 10 − 5 p Br( X ! e + e − ) See I\ah Galon’s slides for more details Kozaczuk 7
An Axial Vector Explana6on Another poten6al explana6on: light axial vector JK, D. Morrissey, S. Stroberg , 2016 X q � µ � 5 q , � L � X µ g q ¯ q Axial anomaly does not contribute to in this case and so π 0 → X γ X does not have to be protophobic Also, less momentum suppression ( L=0 vs L=1 in vector case) L ! p X | 2 g 2 3 + 2 | ~ g A M 2 8 Be ∗ → 8 Be X = 4 8 Be G µ ν F ( A ) Λ 2 M 2 m 2 A = L A X µ ν m 2 3 Λ A X g Leading term for vector Challenge: have to do some nuclear physics Kozaczuk 8
An Axial Vector Explana6on In the vector case, nuclear matrix elements cancel (in the pure isospin limit) � 8 Be ∗ i X | 8 Be ∗ i Γ ( 8 Be ∗ ! 8 Be X ) � ¯ Γ ( 8 Be ∗ ! 8 Be γ ) / h 8 Be | J µ � � = ( ε p + ε n ) h 8 Be N γ µ N = ε p + ε n EM | 8 Be ∗ i � 8 Be ∗ i h 8 Be | J µ � ¯ � � h 8 Be N γ µ N Cancella6on does not hold in the axial vector case � 8 Be ∗ i X | 8 Be ∗ i Γ ( 8 Be ∗ ! 8 Be X ) � ¯ Γ ( 8 Be ∗ ! 8 Be γ ) / h 8 Be | J µ = a 0 h 8 Be � N γ µ γ 5 N � Need matrix element EM | 8 Be ∗ i � 8 Be ∗ i h 8 Be | J µ � ¯ � � h 8 Be N γ µ N Here relates nucleon to quark operators, with current a 0 = 2( ∆ u + ∆ d )( ✏ u + ✏ d ) + 4 ∆ s ✏ s X J X ε f ¯ f γ µ γ 5 f µ = f Kozaczuk 9
An Axial Vector Explana6on How large do the couplings have to be? X q � µ � 5 q , X q � µ � 5 q | N i = � µ i � i X g q ∆ q ( N ) � L � X µ g q ¯ h N | g q ¯ q q q Quark-level interac6on Nucleon-level operators Decay width for J = 1 � 0 transi6ons (at leading order in k/m N expansion): 2 + E 2 ✓ ◆ k | a n h 0 || σ n || 1 i + a p h 0 || σ p || 1 i | 2 k Γ = m 2 18 π X Reduced matrix elements of spin operators ac6ng on all nucleons of a given type in the nucleus Need to compute for the 8 Be states of interest h 0 || � p,n || 1 i . 3 Kozaczuk 10
Matrix Elements Full ab-iniFo calcula6on of the matrix elements U6lizes the In-Medium Similarity Renormaliza6on Group (IM-SRG) with forces derived from chiral effec6ve theory (NN + 3N) and including effects from meson exchange currents (MECs) Fix isospin mixing frac6on from M1 isoscalar transi6on to extract predic6ons for the other matrix elements Kozaczuk 11
Matrix Elements Results: Matrix element Prediction h 0 + k M 1 k V i ( µ N ) 0 . 76(12) h 0 + k σ p k V i 0 . 102(28) h 0 + k σ n k V i � 0 . 073(29) h 0 + k σ p k S i � 0 . 047(29) h 0 + k σ n k S i � 0 . 132(33) Things to note: -Rela6ve sign between the proton and neutron matrix elements for the 8 Be *’ transi6on, but not for 8 Be * , results in suppression of isovector rate -Significant error bars (can be improved in the future) but results enough to begin scru6ny of the axial vector scenario Kozaczuk 12
Implica6ons for the 8 Be Anomaly Obtain range of couplings required to explain the Atomki result Requirements depend on precise mass (need more info from experimentalists) From Feng et al, 2016: Γ 8 Be ∗ ! 8 Be X ' 5 . 8 ⇥ 10 � 6 m X ' 16 . 7 MeV , Γ 8 Be ∗ ! 8 Be γ Γ 8 Be ∗ ! 8 Be X ' 2 . 3 ⇥ 10 � 6 m X ' 17 . 3 MeV , Γ 8 Be ∗ ! 8 Be γ Γ 8 Be ∗ ! 8 Be X ' 5 . 0 ⇥ 10 � 7 . m X ' 17 . 6 MeV , Γ 8 Be ∗ ! 8 Be γ 14 Demand that the corresponding isovector transi6on rate is not too large to conflict with null results (Feng et al, 2016) Γ 8 Be ⇤ ! 8 Be X > 5 ⇥ Γ 8 Be ⇤0 ! 8 Be X Γ 8 Be ⇤ ! 8 Be γ Γ 8 Be ⇤0 ! 8 Be γ Kozaczuk 13
Other Constraints What about other constraints? And UV comple6on? Impact of other constraints depend on UV comple6on. Our assump6ons: -Purely axial genera6on-independent quark couplings -Both axial- and vector-like couplings to leptons: i � µ + g A ¯ X � g V i � µ � 5 � L ⊃ X µ ` i ` i i -Vanishing couplings to neutrinos -100% branching frac6on into electron-positron pairs These assump6ons can be relaxed if so desired Kozaczuk 14
Other Constraints See also Kahn et al, 2016 for detailed discussion of constraints on light axial vectors Dominant constraints on lepton couplings: e ) 2 + ( g A p Decays inside Atomki detector: ( g V e ) 2 & 1 . 3 × 10 − 5 e ⇥ ' Muon (g-2): µ ) 2 + 9 ⇥ 10 − 3 ( g V � . 1 . 6 ⇥ 10 − 9 . � � � ( g A µ ) 2 � e ) 2 + ( g V p Electron beam dumps (SLAC E141): ( g A e ) 2 & 2 ⇥ 10 − 4 e e ) 2 + ( g V Electron-positron colliders (KLOE2): p ( g A e ) 2 . 2 ⇥ 10 � 3 e Parity-viola6ng Moller scatering (SLAC E158): / � . 1 ⇥ 10 � 8 � � g V e g A � e Dominant constraints on quark couplings: g A µ ( g u + g d � 1 . 5 g s ) η � µ + µ - : . 4 ⇥ 10 � 10 . ( m X / MeV) 2 Proton fixed target experiments ( ν - Cal I) (also depends on coupling to electrons) Kozaczuk 15
Puung it all together A light axial vector can be a viable explana6on of the 8 Be anomaly Detailed results depend on rela6onship between leptonic and quark couplings Dominant constraints on this scenario depend on leptonic couplings and are highly UV-dependent The Atomki null result for 8 Be *’ places the strongest model-independent constraint on the quark couplings Relaxing our ini6al assump6ons could poten6ally open up more parameter space Kozaczuk 16
A UV Comple6on Rela6onship of couplings shown can arise in a UV comple6on involving a dark U(1) RH and two Higgs doublets (see Kahn et al, 2016) Purely axial quark couplings + vanishing neutrino couplings (there’s tuning here) results in: g A g V g u = � 2 g d , e,µ = g d , e,µ = 2 g d Also require vector-like fermions (+ dark Higgses) to cancel anomalies. LHC limits on “anomalons” yield upper bound on couplings (subdominant to 8 Be *’ limit) [Kahn et al, 2016] Results stress importance of complementarity and of probing both quark and leptonic couplings Kozaczuk 17
Future Experiments Many planned experiments should have an impact on the light (axial) vector scenario See e.g. Feng et al, 2016; Kahn et al, 2016 Lepton Couplings : VEPP-3, DarkLight, MESA, Belle II, HPS, APEX, PADME… Quark couplings : LHCb, ShiP, SeaQuest … Other nuclear decay experiments (including independent verifica6on of the Atomki result!) Kozaczuk 18
Takeaways -A light vector axially coupled to quarks can explain the 8 Be anomaly and exist in a viable UV-complete theory -If the anomaly goes away, we have a new constraint on light axially-coupled vectors (already have a new constraint from 8 Be*’) -Important to target both lepton and quark couplings -Are there other nuclear systems that can be useful in discovering or constraining light new vectors that are otherwise difficult to probe? Kozaczuk 19
Backup Kozaczuk 20
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