Explanation of the 17 MeV Atomki Anomaly in a U(1)^\prime-Extended 2-Higgs Doublet Model
aa r X i v : . [ h e p - ph ] F e b Explanation of the 17 MeV Atomki Anomaly in a U (1) ′ -Extended 2-Higgs Doublet Model Luigi Delle Rose,
1, 2
Shaaban Khalil, and Stefano Moretti
1, 2 School of Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK Particle Physics Department, Rutherford Appleton Laboratory,Chilton, Didcot, Oxon OX11 0QX, United Kingdom Center for Fundamental Physics, Zewail City of Science and Technology, 6 October City, Giza 12588, Egypt (Dated: February 16, 2018)Motivated by an anomaly observed in the decay of an excited state of Beryllium ( Be) by theAtomki collaboration, we study an extension of the Standard Model with a gauged U (1) ′ symmetryin presence of a 2-Higgs Doublet Model structure of the Higgs sector. We show that this scenariocomplies with a variety of experimental results and is able to explain the potential presence of aresonant spin-1 gauge boson, Z ′ , with a mass of 17 MeV in the Atomki experimental data, forappropriate choices of U (1) ′ charges and Yukawa interactions. The Atomki pair spectrometer experiment [1] was setup for searching e + e − internal pair creation in the decayof excited Be nuclei (henceforth, Be ∗ ), the latter beingproduced with the help of a beam of protons directed ona Lithium ( Li) target. The proton beam was tuned insuch a way that the different Be excitations could beseparated with high accuracy.In the data collection stage, a clear anomaly was ob-served in the decay of Be ∗ with spin-parity J P = 1 + into the ground state Be with spin-parity 0 + (both withisospin T = 0), where Be ∗ had an excitation energyof 18.15 MeV. Upon analysis of the electron-positronproperties, the spectra of both their opening angle θ and invariant mass M presented the characteristics ofan excess consistent with an intermediate boson X be-ing produced on-shell in the decay of the Be ∗ state,with the X object subsequently decaying into e + e − pairs.The best fit to the mass M X of X was given as [1] M X = 16 . ± .
35 (stat) ± . , in correspon-dence of a ratio of Branching Ratios (BRs) obtained asBR( Be ∗ → X + Be)BR( Be ∗ → γ + Be) × BR( X → e + e − ) = 5 . × − . This combination yields a statistical significance of theexcess of about 6 . σ [1].An explanation of the X nature was attempted by [2,3], in the form of models featuring a new vector boson Z ′ with a mass M Z ′ of about 17 MeV, with vector-likecouplings to quarks and leptons. Constraints on such anew state, notably from searches for π → Z ′ + γ by theNA48/2 experiment [4], require the couplings of the Z ′ to up and down quarks to be ‘protophobic’, i.e., that thecharges eǫ u and eǫ d of up and down quarks – written asmultiples of the positron charge e – satisfy the relation2 ǫ u + ǫ d < ∼ − [2, 3]. Subsequently, further studies ofsuch models have been performed in [5–13] . An alternative explanation was given in [14], wherein the X was In the footsteps of this literature, we consider here anextension of the SM described by a generic U (1) ′ groupwith a light gauge boson [15–20]. Due to the presence oftwo such Abelian symmetries, U (1) Y × U (1) ′ , the mostgeneral kinetic Lagrangian of the corresponding fields,ˆ B µ and ˆ B ′ µ , respectively, allows for a gauge invariantmixing of the two field-strengths L kin = −
14 ˆ F µν ˆ F µν −
14 ˆ F ′ µν ˆ F ′ µν − κ F ′ µν ˆ F µν , (1)where κ is the kinetic mixing parameter between U (1) Y and U (1) ′ . A diagonal form for this Lagrangian can beobtained by transformation of the Abelian fields suchthat the gauge covariant derivative becomes D µ = ∂ µ + .... + ig Y B µ + i (˜ gY + g ′ z ) B ′ µ , (2)where Y and z are the hypercharge and U (1) ′ charge,respectively, and ˜ g the gauge coupling mixing betweenthe two Abelian groups.We also consider the presence of two SU (2)(pseudo)scalar doublets, embedded in a 2-Higgs DoubletModel (2HDM) scalar potential, Φ and Φ , with thesame hypercharge Y = 1 / z Φ and z Φ under the extra U (1) ′ . The new Abeliansymmetry replaces the discrete Z one usually imposedin 2HDMs to avoid tree-level flavour changing neutralcurrents [21, 22]. Alongside spontaneous Electro-WeakSymmetry Breaking (EWSB) of the SM gauge symme-try through the Vacuum Expectation Values (VEVs) ofthe two Higgs doublets h Φ , i = v , , with v = v + v and tan β = v /v , one may in principle also have a con-tribution to U (1) ′ symmetry breaking through the VEV h χ i = v ′ of an extra SM-singlet scalar χ , indeed con-nected to the mass term m B ′ = g ′ z χ v ′ . The diagonalisa-tion of the mass matrix of neutral gauge bosons implies identified with a light pseudoscalar state with couplings to upand down type quarks about 0.3 times those of the StandardModel (SM) Higgs boson. the following mixing angle, θ ′ , between the SM Z andnew Z ′ : tan 2 θ ′ = 2 g Φ g Z g Φ + 4 m B ′ /v − g Z , (3)where g Z = p g + g is the EW coupling. The parame-ters g Φ and g Φ are defined as g Φ = (˜ g + 2 g ′ z Φ ) cos β + (˜ g + 2 g ′ z Φ ) sin βg Φ = (˜ g + 2 g ′ z Φ ) cos β + (˜ g + 2 g ′ z Φ ) sin β . (4)The Z − Z ′ mixing θ ′ is generated by both the kineticmixing ˜ g and the mass mixing induced by the Z ′ gaugeinteractions with the two Higgs doublets. The generalexpressions of the masses of the Z and Z ′ gauge bosonsare M Z,Z ′ = g Z v (cid:20) (cid:18) g Φ + 4 m B ′ /v g Z + 1 (cid:19) ∓ g Φ sin 2 θ ′ g Z (cid:21) (5)and, for g ′ , ˜ g ≪ m B ′ ≪ v , the Z ′ mass is given by M Z ′ ≃ m B ′ + v g ′ ( z Φ − z Φ ) sin (2 β ) , (6)which is non-vanishing even when m B ′ → U (1) ′ charges of the scalar dou-blets z Φ and z Φ . In the m B ′ ≃ v ′ ≃ χ , one finds, for M Z ′ ≃
17 MeV and v ≃
246 GeV, g ′ ∼ − . Here, two comments are in order. Firstly, incase of one Higgs doublet (which is obtained from Eq. (6)by neglecting the second term), the limit m B ′ ≪ v leadsto M ′ Z ≃ m B ′ and the SM Higgs sector does not play anyrole in the generation of the Z ′ mass. Secondly, in the2HDM case with z Φ = z Φ , the symmetry breaking ofthe U (1) ′ can actually be realised without the extra SM-singlet χ , namely with v ′ = 0. In this paper we focus onthe latter scenario in which the contribution of the SM-singlet χ can be completely neglected. In this case, thetypical CP-odd state of the 2HDM extensions representsthe longitudinal degree of freedom of the Z ′ .Having discussed the spontaneous symmetry breakingof the U (1) ′ , we now briefly comment on the fermion sec-tor and the constraints imposed by the new gauge sym-metry. The conditions required by the cancellation ofgauge and gravitational anomalies, which strongly con-strain the charge assignment of the SM spectrum under the extra U (1) ′ gauge symmetry, are here imposed. Thisimplies the introduction of SM-singlet fermions, s i , whichcould be exploited, in some scenarios, for implementing aseesaw mechanism generating light neutrino masses. Theactual charges and masses of these new states, if present,strongly depend on the specific realisation of the fermionsector. These SM-singlet states are irrelevant for the ex-planation of the Atomki anomaly and will not be ad-dressed in this paper. The general charge assignmentsof the spectrum in our extension of the SM are given in SU (3) SU (2) U (1) Y U (1) ′ Q L z Q u R z u d R z Q − z u L − z Q e R − z Q − z u s i z s i TABLE I. Flavour universal charge assignment in the U (1) ′ extension of the SM. Tab. I, where the z s i ’s are chosen to cancel the anomalyin the U (1) ′ U (1) ′ U (1) ′ and U (1) ′ GG triangle diagrams, G being the gravitational current.The interactions between the SM fermions and the Z ′ gauge boson are described by the corresponding La-grangian, L int = − J µZ ′ Z ′ µ , where the gauge current isgiven by J µZ ′ = X f ¯ ψ f γ µ ( C f,L P L + C f,R P R ) ψ f (7)with left- and right-handed coefficients C f,L = − g Z s ′ (cid:0) T f − s W Q f (cid:1) + (˜ gY f,L + g ′ z f,L ) c ′ ,C f,R = g Z s W s ′ Q f + (˜ gY f,R + g ′ z f,R ) c ′ . (8)In these equations we have adopted the shorthand no-tations s W ≡ sin θ W , c W ≡ cos θ W , s ′ ≡ sin θ ′ and c ′ ≡ cos θ ′ . We have also introduced Y f the hypercharge, z f the U (1) ′ charge, T f the third component of the weakisospin and Q f the electric charge of a generic fermion f .Analogously, the vector and axial-vector components ofthe Z ′ interactions are C f,V = C f,R + C f,L (cid:2) − g Z s ′ ( T f − s W Q f ) + c ′ ˜ g (2 Q f − T f ) + c ′ g ′ ( z f,L + z f,R ) (cid:3) ,C f,A = C f,R − C f,L (cid:2) ( g Z s ′ + ˜ gc ′ ) T f − c ′ g ′ ( z f,L − z f,R ) (cid:3) , (9)where we have exploited the relation Y f = Q f − T f . These equations can considerably be simplified by real-ising that g Z s ′ is of the same order of ˜ g for g ′ , ˜ g ≪ C f,V ≃ ˜ gc W Q f + g ′ (cid:2) z Φ ( T f − s W Q f ) + z f,V (cid:3) ,C f,A ≃ g ′ (cid:2) − z Φ T f + z f,A (cid:3) , (10)where we have introduced the vector and axial-vector U (1) ′ charges z f,V/A = 1 / z f,R ± z f,A ). Notice that z Φ can be either z H for a single Higgs doublet ( H )model or a combination of z Φ and z Φ , namely z Φ = z Φ cos β + z Φ sin β , for a 2HDM. The z Φ charge arisesfrom the small gauge coupling expansion of the Z − Z ′ mixing angle θ ′ which implies c ′ ≃ s ′ ≃ − g Φ /g Z = − ˜ g − g ′ z Φ . The Z ′ couplings are characterised by thesum of three different contributions. The kinetic mixing˜ g induces a vector-like term proportional to the Electro-Magnetic (EM) current which is the only source of inter-actions when all the SM fields are neutral under U (1) ′ .In this case the Z ′ is commonly dubbed dark photon .The second term is induced by z Φ , the U (1) ′ charge inthe Higgs sector, and leads to a dark Z , namely a gaugeboson mixing with the SM Z boson. Finally, there is thestandard gauge interaction proportional to the fermionic U (1) ′ charges z f,V/A .We can now delineate two different scenarios depend-ing on the structure of the axial-vector couplings of the Z ′ boson. In particular, when only a SU (2) doublet istaken into account, the C f,A coefficients are suppressedwith respect to the vector-like counterparts (see [23]).This is a direct consequence of the gauge invariance ofthe Yukawa interactions which forces the U (1) ′ charge ofthe Higgs field to satisfy the conditions z H = z Q − z d = − z Q + z u = z L − z e . Inserting the previous relations intoEq. (10), we find C f,A ≃
0, which describes a Z ′ withonly vector interactions with charged leptons and quarks.We stress again that the suppression of the axial-vectorcoupling is only due to the structure of the scalar sec-tor, which envisions only one SU (2) doublet, and to thegauge invariance of the Yukawa Lagrangian. This featureis completely unrelated to the U (1) ′ charge assignmentof the fermions, the requirement of anomaly cancellationand the matter content potentially needed to account forit. In the scenario characterised by two Higgs doublets,the axial-vector couplings of the Z ′ are, in general, ofthe same order of magnitude as the vector ones and thecancellation between the two terms of C f,A in Eq.(10)is not achieved regardless of the details of the YukawaLagrangian, namely, of the type of the 2HDM consid-ered. Notice that, unlike the pure vector-like case, it isextremely intricate to build up a model of a Z ′ with onlyaxial-vector interactions and, in general, both C V and C A are present.A well-known realisation of the scalar sector with twoHiggs doublets is the so-called type-II in which the up-type quarks couple to one Higgs doublet (convention-ally chosen to be Φ ) while the down-type quarks cou- ple to the other (Φ ). The anomaly cancellation con-dition arising from the U (1) ′ SU (3) SU (3) diagram andthe gauge invariance of the Yukawa Lagrangian require2 z Q − z d − z u = z Φ − z Φ = 0, which necessarily calls forextra coloured states when z Φ = z Φ . These new statesmust be vector-like under the SM gauge group and chiralunder the extra U (1) ′ [23].A far more interesting scenario is realised when thescalar sector reproduces the structure of the type-I2HDM in which only one (Φ ) of the two Higgs doubletsparticipates in the Yukawa interactions. The correspond-ing Lagrangian is the same as the SM one and its gaugeinvariance simply requires z Φ = − z Q + z u = z Q − z d = z L − z e , without constraining the U (1) ′ charge of Φ . Dif-ferently from the type-II scenario in which extra colouredstates are required to build an anomaly-free model, inthe type-I case the UV consistency of the theory can beeasily satisfied introducing only SM-singlet fermions asdemanded by the anomaly cancellation conditions of the U (1) ′ U (1) ′ U (1) ′ and U (1) ′ GG correlators. Nevertheless,the mismatch between z Φ and z f,A = ± z Φ / C f,A to be suppressed and the Z ′ interactions are given by C u,V = 23 ˜ gc W + g ′ (cid:20) z Φ (cid:18) − s W (cid:19) + z u,V (cid:21) ,C u,A = − g ′ β ( z Φ − z Φ ) ,C d,V = −
13 ˜ gc W + g ′ (cid:20) z Φ (cid:18) −
12 + 23 s W (cid:19) + z d,V (cid:21) ,C d,A = g ′ β ( z Φ − z Φ ) ,C e,V = − ˜ gc W + g ′ (cid:20) z Φ (cid:18) −
12 + 2 s W (cid:19) + z e,V (cid:21) ,C e,A = g ′ β ( z Φ − z Φ ) ,C ν,V = − C ν,A = g ′ z Φ + z L ) . (11)We now show that the structure of the couplings dis-cussed above is able to explain the presence of a Z ′ reso-nance in the Be ∗ decay. As pointed out in [3], the contri-bution of the axial-vector couplings to the Be ∗ → Be Z ′ decay is proportional to k/M Z ′ ≪
1, where k is themomentum of the Z ′ , while the vector component issuppressed by k /M Z ′ . Therefore, in our case, being C f,V ∼ C f,A , we can neglect the effects of the vectorcouplings of the Z ′ and their interference with the axialcounterparts. The relevant matrix elements for the Be ∗ transition mediated by an axial-vector boson have beencomputed in [24]. Notice that the axial couplings of thequarks and, therefore, the width of the Be ∗ → Be Z ′ decay are solely controlled by the product g ′ cos β whilethe kinetic mixing ˜ g only affects the BR( Z ′ → e + e − )since the Z ′ → νν decay modes are allowed (we assumethat the Z ′ → s i s j decays are kinematically closed). Fordefiniteness, we consider a U (1) dark charge assignmentwith z f = 0 and z Φ = 0 and we choose z Φ = 1 andtan β = 1. Analogue results may be obtained for dif-ferent U (1) ′ charge assignments and values of tan β . Weshow in Fig. 1 the parameter space explaining the Atomkianomaly together with the most constraining experimen-tal results. The orange region, where the Z ′ gauge cou-plings comply with the best-fit of the Be ∗ decay ratein the mass range M Z ′ = 16 . − . Be ∗′ [1] . The horizontal greyband selects the values of g ′ accounting for the Z ′ massin the negligible m B ′ case in which the U (1) ′ symmetrybreaking is driven by the two Higgs doublets. Further-more, among all other experimental constraints involvinga light Z ′ that may be relevant for this analysis we haveshown the most restrictive ones. The parity-violatingMøller scattering measured at the SLAC E158 experi-ment [26] imposes a constraint on the product C e,V C e,A of the Z ′ , namely | C e,V C e,A | . − for M Z ′ ≃
17 MeV[23]. The strongest bound comes from the atomic par-ity violation in Cesium (Cs), namely from the measure-ment of its weak nuclear charge ∆ Q W [27, 28], whichrequires | ∆ Q W | . .
71 at 2 σ [29]. It represents a con-straint on the product of C e,A and a combination of C u,V and C d,V . This bound can be avoided if the Z ′ haseither only vector or axial-vector couplings but in thegeneral scenario considered here, it imposes severe con-straints on the gauge couplings g ′ , ˜ g thus introducing afine-tuning in the two gauge parameters. Also shownis the constraint from neutral pion decay, π → Z ′ γ ,from the NA48/2 experiment [30]. The bound is propor-tional to the anomaly factor | C u,V Q u − C d,V Q d | whichdepends on the vector coupling of the Z ′ and is givenby | C u,V + C d,V | . . × − / p BR( Z ′ → e + e − ) for M Z ′ ≃
17 MeV. The contribution of the axial compo-nents is induced by chiral symmetry breaking effects andis, therefore, suppressed by the light quark masses. Thelight-boson contribution to the anomalous magnetic mo-ment of the electron has also been taken into account,as it is required to be within the 2 σ uncertainty of thedeparture of the SM prediction from the experimentalresult [31]. We now analyse the contribution of a verylight gauge boson Z ′ to the muon anomalous magneticmoment [32] which has been measured at BrookhavenNational Laboratory to a precision of 0 .
54 parts per mil-lion. The current average of the experimental results is The Atomki collaboration has recently presented evidences of anexcess, compatible with a 17 MeV boson mediation, in the Be ∗′ transition at the “International Symposium: Advances in DarkMatter and Particle Physics 2016” [25]. Since this result is notpublic we do not account for it, but we ought to mention it. FIG. 1. Allowed parameter space (orange region) explain-ing the anomalous Be ∗ decay. The white region above isexcluded by the non-observation of the same anomaly in the Be ∗′ transition. Also shown (shaded regions) is the allowedparameter space by the g − g ′ and ˜ g compatible with the weak nuclear charge measure-ment of Cesium. The horizontal grey band delineates valuesof g ′ for which the Z ′ mass is solely generated by the SM vev. given by [33–35] a exp µ = 11659208 . . × − , (12)which is different from the SM prediction by 3 . σ to 3 . σ :∆ a µ = a exp µ − a SM µ = (28 . ± . . ± . × − . From the interaction Lagrangian described above onefinds a new contribution to ( g − µ generated by a one-loop diagram with Z ′ exchange as shown in Fig. 2, whichleads to µ µ µ µZ ′ γ FIG. 2. The new contribution to the muon anomalous mag-netic moment in a U (1) ′ extension of the SM. δa Z ′ µ = r m µ π (cid:2) C µ,V g V ( r m µ ) − C µ,A g A ( r m µ ) (cid:3) , (13)where r m µ ≡ ( m µ /M Z ′ ) and g V , g A are given by g V ( r ) = Z dz z (1 − z )1 − z + rz , (14) g A ( r ) = Z dz ( z − z )(4 − z ) + 2 rz − z + rz . (15)For M Z ′ ≃
17 MeV one finds δa Z ′ µ ≃ . C µ,V − C µ,A .We require again that the contribution of the Z ′ to ( g − µ , which is mainly due to its axial-vector component, isless than the 2 σ uncertainty of the discrepancy betweenthe SM result and the experimental measure.We finally comment on the constraints imposedby neutrino-electron scattering processes [36–38], thestrongest one being from ¯ ν e e scattering at the TEXONOexperiment [37], which affect a combination of C e,V/A and C ν,V . In the protophobic scenario, in which the Z ′ hasonly vector interactions, the constrained ν coupling to the Z ′ boson is in high tension with the measured Be ∗ decayrate since C ν,V = − C n,V , where C n,V = C u,V + 2 C d,V is the coupling to neutrons, and a mechanism to suppressthe neutrino coupling must be envisaged [3]. This boundis, in general, alleviated if the one attempts to explainthe Atomki anomaly with a Z ′ boson with axial-vectorinteractions since the required gauge couplings g ′ , ˜ g aresmaller than the ones needed in the protophobic case.Neutrino couplings are also constrained by meson decays,like, for instance K ± → π ± νν which has been studied in[39] and where it has been shown that the correspondingconstraint is relaxed by a destructive interference effectinduced by the charged Higgs. As the results presentedin [39] relies on the Goldstone boson equivalence approx-imation, we have computed the full one-loop correctionsto the K ± → π ± Z ′ process in the U (1) ′ -2HDM scenario.The details will be presented in a forthcoming work andthe results are in agreement with the estimates in [39]. Inour setup, for g ′ ∼ − and tan β = 1, M H ± ∼
600 GeVcan account for the destructive interference quoted abovebetween the W ± and H ± loops. For instance, we findBR( K ± → π ± Z ′ → π ± νν ) ≃ . K ± → π ± νν ) exp for M H ± ∼
615 GeV with BR( Z ′ → νν ) ≃
30% which isthe maximum value for the invisible Z ′ decay rate in theallowed region (orange and grey shaded area) shown inFig. 1. A similar constraint arises from the B meson de-cay to invisible but is less severe than the one discussedabove [42]. The B ± → K ± Z ′ process is characterisedby the same loop corrections appearing in K ± → π ± Z ′ ,with the main difference being the dependence on theCKM matrix elements. Therefore, the suppression effectinduced by the charge Higgs mass affects both processesin the same region of the parameter space, thus ensuringthat the bound from the invisible B decays is satisfiedonce the constraint from the analogous K meson decayis taken into account.In summary, we have come to an exciting conclusion.The model that we have constructed, which minimallydeparts from the SM, in both the gauge sector (whereina dark U (1) ′ is added) and Higgs framework (wherein asecond doublet is added with a type-I Yukawa configura-tion), with the two intertwined as it is the pseudoscalarstate of the latter that spontaneously breaks the sym-metry of the former, has the potential to explain theanomaly in the decays of the Beryllium. Notably, the ballpark of values of the g ′ coupling reproducing the Beinternal pair creation excess also predicts the mass of the Z ′ from EWSB and, therefore, as for the masses of the Z and W gauge bosons, the M Z ′ = 17 MeV could begenerated by the same EW mass scale v ≃
246 GeV.
ACKNOWLEDGEMENTS
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