Challenges for a QCD Axion at the 10 Mev Scale JHEP05(2021)138 , 5 10 QCD Θ Comes ]

JHEP05(2021)138 Springer , g,h May 17, 2021 April 30, 2021 April 30, 2021 March 8, 2021 : : : : Revised Received Published Accepted and Xiao-Ping Wang [email protected] , d,e,f Published for SISSA by https://doi.org/10.1007/JHEP05(2021)138 [email protected] Carlos E.M. Wagner , c,d . 3 2102.10118 The Authors. c Beyond Standard Model, Higgs Physics

We report on an interesting realization of the QCD axion, with mass in the MeV. It has previously been shown that although this scenario is stringently , Navin McGinnis, [email protected] (10) a,b O Beijing 100083, China Beijing Key Laboratory of AdvancedBeijing Nuclear 100191, Materials China and Physics, BeihangE-mail: University, [email protected] Argonne, IL 60439, U.S.A. Physics Department and EnricoChicago, Fermi Institute, IL University 60637, of U.S.A. Chicago, Kavli Institute for Cosmological Physics,Chicago, IL University 60637, of U.S.A. Chicago, School of Physics, Beihang University, Beijing 100871, China Center for High EnergyBeijing Physics, 100871, Peking China University, TRIUMF, 4004 Westbrook Mall, Vancouver, BCHigh V6T Energy 2A3, Physics Canada Division, Argonne National Laboratory, School of Physics andPeking State University, Key Laboratory of Nuclear Physics and Technology, b c e g d a h f Open Access Article funded by SCOAP sector appearing in this Standard ModelModel-like extension. Higgs In boson particular, the into decayboson two of signature the light Standard that axions may may be be searched relevantKeywords: for and at leads the to LHC in a the novelArXiv near Higgs ePrint: future. study the compatibility of theof allowed parameter the space with most the recentfine one structure leading measurements to constant. of consistency We further theand provide show electron an the anomalous ultraviolet conditions completion under magneticmixing of which angles, moment this it and axion and may remain variant lead consistent the with to experimental the constraints observed on quark the masses extended and scalar CKM Abstract: range constrained from multiple sources, theleads model remains to viable an for a explanationmore range detail of of the parameters the that additional Atomki constraints experiment proceeding from anomaly. recent low In energy this experiments article and we study in Jia Liu, Challenges for a QCD axion at the 10 MeV scale JHEP05(2021)138 , 5 10 QCD θ comes ]. 1 QCD θ 14 ]. The gauge interactions of the theory have 1 – 1 – ]. The axion interactions lead to a field dependent 7 – 4 3 ], which leads to a severe fine tuning problem in the SM [ 3 [ 8 10 − 1 17 10 10 e parameter. Even in the absence of a tree-level value, a non-vanishing value of 2) ]. The experiment measuring neutron EDM has found that such CP phase should 2 − angle, and the strong interactions induce a non-trivial potential which is minimized would be generated via the chiral anomaly, by the chiral phase redefinition associated QCD g One elegant way to solve the neutron EDM problem is to introduce a chiral symmetry, Although the gluon interactions with quarks preserve the CP symmetry, there is a CP θ 5.1 The generation5.2 of CKM matrix Additional and massive the scalar couplings and to pseudo-scalar first states generation fermions ( , which has been called the axion [ QCD QCD be smaller than the so-called PQ symmetry, whicha is spontaneously broken, leadingθ to a Goldstone boson, θ with making the quarkfrom masses the real. addition In ofmasses, general, the and hence, tree-level is the value naturally physicalhowever, and of the value order the of neutron one. phase electric dipole ofvalue In moment [ the the (EDM) presence determinant would of of acquire an an the unsuppressed unobserved quark value sizable of sufficient to explain allneutrino CP-violating experiments. phenomena observed in B and Kviolating meson, interaction in as the wellthe SM as QCD sector that is related to the interactions induced by been tested withwith great the precision, recently while discoveredcollider Higgs the (LHC). boson Yukawa In are interactions the beingon SM, of currently these the tested quarks Yukawa interactions diversity at and lead of thequark to leptons Large and quark a lepton Hadron rich and sector, flavor respectively. structure lepton These based masses matrices and include CP the violating CKM phases that and are PMNS matrices in the 1 Introduction The Standard Model (SM) provideson a a consistent local description and of renormalizable particle gauge interactions, theory based [ 6 Conclusions 3 4 Atomki anomaly 5 UV model Contents 1 Introduction 2 Effective low energy model JHEP05(2021)138 ], ]. ]. ]. 16 21 12 30 – , , , ] sug- 13 20 9 29 , 33 is related 8 , a scale is not 1 f a f He, which de- . On the other 4 σ , associated with e ]. ]. Recently, it has 4 axion scenario has . a 2 ] revealed that there 26 ], where ∆ 19 , 28 7 , 18 Be and 6 [ 8 visible a f , an axion mass in the 10 MeV , proportional to the vacuum a a ] to save it from experimental f /f 19 π – f π 17 m axion scenario [ ]. The discrepancy, ' much larger than electroweak scale, where a 32 a , m , can span many orders of magnitude. Thus, f a 31 visible ]. It may also lead to significant dark matter – 2 – /f 1 25 . In this scenario, the mixing with the neutral pion and with positive sign. Since the axion has to decay to MeV produced in the de-excitation and later decay into , which can be interpreted as an intermediate pseudo- e + a 17 e ∆ ]. However, further theoretical and experimental analyses − e 27 ]. The original , therefore leading to the disappearance of the CP interactions axion, there are efforts [ 12 pion-phobic – axion scenarios, with QCD 8 , θ 1 GeV. For this scenario to survive the current experimental constraints, visible ]. This model may be tested with multi-lepton signatures when light 1 24 ' – invisible a f 22 , 19 , 18 [ The recent accurate measurement of the fine structure constant [ Regarding the Being associated with a Goldstone boson, the axion field has an approximate shift + e − compared to the SM theoretical calculationthis [ measurement used to behand, negative a and very had a recent,gests significance more a of smaller accurate about discrepancy measurement for electron-positron of pairs the promptly in fine the structure Atomki experiment, constant it has [ a sizable coupling to elec- resonant signal were absent. Inrange general, implies since the axion must couplecouplings only determined to by their first masses, generation their quarks QCD and charges and chargedis leptons a with mild suitable discrepancy with the electron magnetic dipole moment measurements [ by the Atomki experimentare [ needed to determine whether oreffects. not In the observed this peak work maypseudo-scalar we indeed particle be shall accounted assume with by that SM athe this constraints 17 MeV is on not QCD the the axion. proposed case QCD and We axion identify will, at the the however, associated 10 comment MeV scale on would how be modified if its scalar particle with mass around e mesons decay to multipleelectronic axion scattering cross-section states in [ thebeen dark suggested matter that higher direct order detection SM [ effects may lead to an effect similar to the one observed from the low energy quarkbeen mass combined with and the coupling recent parameters.The experimental anomalies This experiment from Atomki looks collaboration forexcite [ into high ground excitation states statesin and the of emit angular nuclei a correlation pair from of of electron and positron. A peak was observed the axion remains hidden due toof its these ultralight invisible mass axions and are ultra given small in couplings. the so-called A realization KSVZ andconstraints DFSZ by axion making scenarios [ it is suppressed by choosing appropriate PQ charges and an accidental cancellation arising necessarily related to the weak orgauge QCD scales, bosons, the which axion mass are and proportionalthere couplings is to to fermions a and rich phenomenologyexperimental to setups explore [ this wide regionto of the parameter space weak with scale, different There has are been also severely constrained by laboratory experiments [ in the strong sector in the physical vacuum andsymmetry, the thus solution it of can the besmall strong naturally due CP light. to problem. Its the couplingsexpectation suppression to value of other from the particles large field may that decay be breaks constant, rendered the chiral PQ symmetry. Since the at vanishing values of JHEP05(2021)138 . . e at 5 a e and , we ∆ (2.1) e 2) 5 2) − g ( − g ( h.c., + is the axion decay constant, which, R a f f L GeV. For the following discussion, it ¯ f , we review the properties of this visible 1 a 2 , and ' a/f f f a f iQ e – 3 – f ]. From the ultraviolet (UV) perspective, for the m meson mixing, may lead to a positive value of η 19 , e,u,d, X 18 = f quarks in the infrared (IR), the PQ breaking mechanism ], it has recently been discussed how this scenario remains = d , we consider the electron and photon couplings to the axion 35 3 int , L and 17 , what leads to a relation between the axion electron and photon u α , we further show how it can survive the constraints coming from ]. Although positive correction would be therefore in tension with the 4 34 and e 2) limit. In section − g denotes the PQ charge of the fermion ( for our conclusions. f 6 Q From the IR perspective, the relevant low-energy interactions are simply written as This article is organized as follows. In section In addition to experimental constraints from precision measurement of mesons, this where as emphasized in thewill introduction be must convenient to be work with the linear axion couplings to fermions. For instance, the axion to couple onlymust to allow for theCKM generation matrix. of We the discuss appropriate how this quark is and achieved lepton in a masses particular as UV well model as later the in section We consider the effective theorythe first for generation a fermions variantappeared of in some the the time QCD SM. ago axion Whilerobust [ which the to couples low-energy a mostly structure variety to of of this constraints setup [ has generation fermions while successfullyadditional generating constraints implied the by the CKM newsection matrix. physics associated We with this also scenario. discuss We the reserve 2 Effective low energy model values of couplngs. In section low energy electron collidersto and an beam explanation dump ofconstruct experiments, the a Atomki while concrete experimntal at UV constraints. the model same Furthermore, and time in show lead section how this scenario can couple to only the first a 10 MeV axion and study the associated constraints onaxion model this and model. how the mostpion-phobic relevant experimental constraints may beand avoided show under the the region of parameters which can lead to a consistency between the measured Therefore, it is interesting toimental constraints ask and if also this bethe 17 MeV fine consistent visible structure with axion constant. the can It currentaxion. evade is measurements all The also of most important current natural to exper- realizations findare are a therefore associated field subject with theoretical new to realization physicsenergy further of at this axion constraints the model. beyond weak scale those In and associated this with article, the we will effective low present an extension of the SM which leads to the one-loop level [ one-loop corrections induced by therections 17 MeV that, axion depending particle, on there the are axion- relevant two loop cor- scenario also is constrained by low energy electron collider and beam dump experiments. tron. As a pseudo-scalar, it can naturally give a negative contribution to electron JHEP05(2021)138 . , d aπ θ Q (1) 2 (2.4) (2.5) (2.6) (2.2) (2.3) ' are the 'O u d MeV, this Q quarks will ud,s ,Q PT are given d aη u ]. (10) θ χ Q O 18 [ and ) = 2 u demands a − 4 m 10 − − 10 , . Thus, this variant of the 3 1 . ! − 2 π ]. For s f ' 2 a aπ aη 2 π 36 . f ) (10 θ θ , will require the axion width into f . with respect to the PQ charges. m − 2 O a π ) e e 3 2 a m f a f √ ) − + f f f ) 2) d e e and hence an accidental cancellation d u Q + + 4 m − 3 e ) m m → − d = ud g − u u + ( a 10 → f aη a m u Q m 10 ]. The same mixing angles can be used to θ a × m + 5 3 − ( BR( 1 19 u d 2 is quite severe [ , + ) – 4 – f, g BR( m m d 5 ( 18 d 10 aπ p Q − ¯ θ PT) techniques. For detailed explanations and re- ], a cancellation of Q fγ ( 1 χ +

[ are in the range of . 10 ia | u π s f ' a × g 06 Q aπ aη α . ( πf 5 θ aπ θ 0 . | 4 f θ 0 X ' ± = 2 a < and ], in the sense that the mixing of the axion with the pion is 47 m . γγ a )) 0 ud g + 19 , e aη ' θ − 18 d e [ /m → u a ( m e ν ]. For the purpose of this work, it is important to note that for + 18 is the mixing angle between the axion and neutral pion, and e pion-phobic → aπ θ + π Searches for axions in the decay products of pions presents the most stringent con- At energies below the QCD scale, the couplings of the axion to ( Since the ratio Even assuming this relationbecomes between naturally the of quark the PQbetween order the charges, leading of order the contribution a associated value fewquark with of masses the times the precise and value mixing the of the higher up order and contributions down must occur for this scenario to be viable. and where we have chosen an arbitrary normalization of photons to be subdominantto with SM respect particles to are theaxion considered, one one is into expects electrons.below Hence, its if natural decays values. only Let us emphasize that, in leading order of perturbation theory translates to a bound on the mixing angle as As we will see the range of couplings needed for also in ref. [ the natural ranges for straints for the setupBR we consider. In particular, the bound on the charged pion decay where mixing angles with thethese parameters eta-mesons and in other the bases light-heavy for the basis. meson octect The in relationships leading between order of In this regime, thestandard physical chiral axion perturbation state theorysults ( and of meson this mixing procedure anglesparameterize we the can refer effective be to operator determined refs. controlling the by [ axion coupling to photons induce mixing of the axion in particular to the pion as well as other pseudo-scalar mesons. coupling to first generation quark and leptons in this basis is simply given by JHEP05(2021)138 1 (3.3) (3.1) (3.2) ]. For this 19 , 18 comes from the e is that it leads to a a 4 . ∆ 2 − ) e 10 . /m 14 a 3 − ) m ( x 10 x ) − . × b + , and therefore this scenario does 14 4 2 (1 ] ) − − 36) x 33 10 10 ± − Missing Energy). Indeed, considering a × ] is . 88 below but close to MeV and a coupling to electrons of order (1 + ] extracted from the fine structure constant 28 from a pseudo-scalar with couplings to the first − + aπ 30) aπ 17 dx e π θ 32 θ ( , 1 ± = ( 2) 0 – 5 – ' Z 31 − → a 2 SM e g ) ( m a + e a g = (48 K − ( 0 e 2 a )( 1 π . The measured deviation of the electron magnetic dipole exp e a 8 ∆ ( 2 a / − e ≡ GeV contributes in a relevant way to the electron anomalous 2) = e 1 a − ' . Apart from the KTeV anomaly, however, the phenomenological ∆ g 4 a 1-loop e f − a = ( 10 e ∆ for a × 4 7 − . ] from the SM prediction [ ). 10 e 30 = 0 , × 2.3 2) 29 5 . 1- and 2-loop contributions to aπ θ − ' g a In the present case, the largest contribution of the model to However, more recently the deviation inferred from a new, independent measurement One interesting aspect of a mixing angle One could in principle alleviate this aspect of the model assuming that the axion width ( /f e tree-level coupling of the axion to electrons, induced by the one-loop diagram in figure of the fine-structure constant has been reported as [ A pseudo-scalar particle withm a mass magnetic moment moment [ measured in recent cesium recoil experiments [ bound, properties of this modelconsistent with do the not Kaon change decay bounds. by setting this3 mixing angle to any other value not lead to a relaxation of the pion axionpossible mixing resolution of bound. the so-calledneutral KTeV anomaly, pion related into to pairs a of decay electronsreason, branching larger ratio for than of the the the one rest expected of in this the article, SM [ we will fix the pion mixing to values close to the upper is dominated by invisible decays,into allowing the electrons. reduction of This the possibility,constraints, axion however, in decay is branching particular strongly ratio the constrainedneutral decay by pion charged state Kaon with decays leads a to relevant a mixing bound with on an the axion axion-pion with mixing dominant invisible decays Figure 1 generation fermions. Theangles, effective eq. vertex ( is generated at low energies through the meson mixing JHEP05(2021)138 . e a MeV ∆ (3.4) (3.5) = 17 a ) the values of m 0 from the KLOE for e → g e , where the effective γγ a a g γγ a ∆ , g e a ]. However, those bounds g ) ]. Note that while we have x 43 18 – 2 , − z 39 (1 π a x ], we have verified that the chiral πf as in [ m 4 37 π at the 95% CL according to the values log πf e 2 PS 4 z a f e 2 ∆ − π m 2 ) / ]. A lower limit can be derived from various x 2 in the non-linear basis agrees with our results γγ a we show an upper limit on – 6 – z 34 g − ). This contribution is given by e ]. e a 2 have the same sign, the 2-loop contribution can g 2) (1 44 2.3 x = − γγ a ]. There, one trades the linear coupling of the axion to g g dx ( 37 1 0 2-loop e Z ). , we show the total contribution to a and ∆ 2 e a 3.2 ] = g z [ PS f . We see that without the 2-loop contribution (or ), whereas the blue shaded region shows the region of parameters which . In figure ]. It is important to note that both bounds have been derived assuming e 3.1 a 38 ) = 1 ∆ is assumed. Thus, in figure − GeV with respect to the electron and photon effective couplings. The cyan e e has been presented in [ a + µ e ∆ = 1 2) → a − would be negative and therefore the new determination of the fine structure constant f Let us stress that the values of the axion coupling to electron leads to a constraint on Relevant constraints on the values of the electron coupling are extracted from the It is clear that when At the 2-loop level, however, the magnetic moment receives an additional contribu- g a ( e a model in which the dominantaxion axion decaying decay to is electron intobe pairs electron feasible are pairs. at difficult future Although at runs searches for LEP of an the due LHC to [ the large ratio backgrounds, of this the may PQ charges of the first generation quark and leptons. For instance, since BR( ∆ demands sizable two loop corrections forUpper the bounds axion on contributions the to couplings bebeen of consistent explored the with axion in to various vector realizationsare bosons of based from on axions LEP the and and assumption LHC ALPS of have [ also an axion which mostly decay into photons, contrary to our couplings to electrons, thement constraints of will remain theexperiment same in regardless the of purple whichbeam measure- shaded dump region experiments. [ Weshaded show region the [ strongest available bound, from NA64, in the red reported in eq. ( can explain the newmoment measurement, measurement eq. of ( the deviation of thedecays electron of anomalous the magnetic axion to electron-positron pairs. As these constraints are placed on the partially cancel the 1-loop result.prediction of Thus, both couplingsand will have a relevant impactregion to shows the the range of couplings predicting fermions with a derivative coupling andthat a di-photon the coupling. corresponding We have result checkedin numerically for the linear basis.lagrangian obtained In from fact, the linear using couplingsdue the matches to that appendices the obtained in in specific the [ choice non-linear of basis interactions in our model. where and we have taken anchosen effective to cutoff work at in the the scale for linear basis of the axion couplings to fermions, a similar calculation tion from a Barr-Zeecoupling type to diagram photons proportional is to defined the by product eq. ( JHEP05(2021)138 are (3.6) (3.7) (3.8) 2 . The purple e 2) -7 − g ]. The cyan region is ( 5.×10 38 , ). The blue region shows 34 , which from figure 3.1 e -7 2) ), is given by 1 MeV 17 = − a 2.×10 NA64 2.2 g m ( ] -7 -1 . . . 2 1.×10 e − m obtained from eq. ( GeV -8 [MeV 28 e e d . 1 GeV a γγ a Q Q ∆ – 7 – ∼ g 5.×10 = 0 KLOE = d a e d e a f Q g Q Q -8 , one obtains 3 ]. − 2.×10 33 10 , from the expression of the axion mass one obtains that -8 × d 1 Q 2 -4 -4 -4 1.×10 ∼ and 0.002 0.001 u

2.×10 1.×10 5.×10

−

Q a g e 10 × . 4 . 5 . Parameter space for the 17 MeV axion which can accommodate 1 In particular, if the above ratio of PQ charges takes the values 1/3, 1/2 or 1, the axion is free of experimentalvalues constraints of from the the ratio KLOEin and of section NA64 PQ experiments. charges will This play range an of important role in the UV model described Taking into account the rangebetween of values consistent with Therefore, the coupling of the axion to the electrons, eq. ( consistent at the 95% C.L.the with 95% the C.L. deviation regionstructure constant, consistent reported with in the [ value inferred from the recentin measurement this of scenario, the ﬁne Figure 2 and red shaded regions are excluded by KLOE and NA64 respectively [ JHEP05(2021)138 e ]. ], 2 2) 15) 01) 27 and sets . . 51 (4.1) (4.2) , − e in this g ]. The (18 (21 50 52 2) ( . ∗ ∗ 19 γγ a − g Be He g 8 4 ( = 0 ), but would , , 4 ), what would 4 d − 3.2 − or more speciﬁc 4.2 10 s 10 ]. In terms of the + ∆ aη × × θ u 49 , 3) , while for 3) . . ∆ q . 5 ), at the 95% CL. Thus, ) and ( 22 6 ] favored by the nuclear ud and − − aη 3.2 4.1 19 θ ud 1 ] with further studies aimed 58 . . aη . Thus, combining the regions ]. The relevant axion-nuclear θ , which are determined by the 48 (1 e (0 s – a , eq. ( 19 ' 0 e aη ' ∆ 45 θ a quarks to that of the electron, giving 15) ∆ . 01) d . and (18 (21 ∗ ∗ and ud Be He 8 u 4 aη

) θ ) s s ). Alternatively, there could be an approximate – 8 – ∆ ∆ s contributions to eqs. ( s 3.1 aη s aη θ θ aη 2 2 θ √ √ . The light gray region is excluded by bounds on the 2 and ) + ) + d d ud , the combined one- and two-loop contributions to which are consistent with aη + ∆ θ γγ e a + ∆ g g u branching ratio in the non octet-enhanced regime, see [ u ) (∆ − (∆ about an order of magnitude larger than e ud s ud + aη aη e aη θ θ θ ( we show the regions of parameters given in [ ( which leads to the correct prediction for → − , which are consistent with the lattice computations of these quantities [ 3 − e a g ( parametrizes the proton spin contribution from a quark, 022 + . q 0 π associated with the new fine structure constant determination, eq. ( ∆ − e → a In figure If SM effects are confirmed to be dominant feature of the Atomki anomaly, as in [ We note that since the axion-pion mixing must be small to remain acceptable from = ∆ + s transition anomalies. We include theplane correlation with between the the values predicted of valuethe of red andrespectively, purple as shaded shown regions inK are figure excluded by the NA64 and KLOE experiments, are difficult to realize, aof small photon axion coupling wouldremain be consistent inconsistent with with the the old values cancellation one, eq. between ( the imply a mixing this could imply furtherrelations constraints between on them. the mixingsibility For angles instance, would in be order thatleading to to those suppress a mixing the small resonant angles photon signal, axion are one coupling. much pos- Beyond smaller the than fact their that such natural small values, mixing values that for a given valuea of value for of mixing angles which favor theparametrically connects Atomki the anomalies PQ with charges the ofcomplementary requirement the to information satisfy on the viable region of the scenario. anomalies. For∆ the aim of the computations,pion we decay have observations, chosen theAtomki mixing anomaly, angles effectively fix the coupling of the axion to photons. We see in figure where they obtain where the R.H.S of each equation gives the range of possible values explaining the Atomki mixing angles of thenuclear axion transitions can to be mesons, parameterized the as predicted axion emission rate for Recently, it has been showncouplings that the only variant of to the theof QCD first axion the analyzed generation in anomalies of thistransition reported quarks work, rates with and by were leptons, the alsoat can Atomki considered generic lead experiment much pseudo-scalar to [ earlier couplings an to in explanation nucleons [ more recently in [ 4 Atomki anomaly JHEP05(2021)138 ], and 0.050 18 e at the 2) 0 e a , a ratio − . In both 1 MeV 17 = 0 ∆ g 3 ( a 0.010 > s m >0, aη s 0.005 the light and dark θ aη | s ) mixing parameters η - a NA64 e θ η + | and θ 0, < Left: ud 0 aη (a→e θ + 0.001 < -4 . We show exclusion regions is consistent with →π , assuming the correlation of ) + ud s K 2 γγ a 5.×10 -enhanced) octet (not aη aη g θ θ ′ e ( Δa sgn -4 -4 -4 -5 -5 and 1/2, respectively. We see that for ) = 1.×10 1 0.010 0.005 0.001 . 3 , while in the right panel we show the ud ) leading to a suppression of the axion

) 0

5.×10 1.×10 5.×10 1.×10 /

ud aη η a | θ | θ MeV axion which can accommodate the Atomki also show the regions of parameter space 4.2 and Atomki anomalies. > aη ( = 1 θ e s 3 17 ( d 2) aη . Between the yellow regions the contributions that is much larger than its natural values. – 9 – transitions. θ − sgn 0.050 s /Q 3 g e , and hence, they are consistent with most of the ) and ( ( aη 2 ) 01) Q θ . and - − e 4.1 ) = 1 MeV 17 = + 0 at the 95% C.L. Light gray regions are excluded from kaon 10 a (21 ud 0 e ∗ < (a→e a same parameter space when aη m ), + 0.010 s θ ∆ He ud ( aη →π we ﬁnd that there is no mutual parameter space for the . 4 + aη 0 K 0.005 2) θ -enhanced) octet (not / | < s Right: η and a s sgn(θ = ) and a few θ NA64 | 3 (1 ud aη 3 / θ He, respectively, when sgn aη 15) − 4 cancel in eqs. ( . 0.001 = 1 s 10 sgn(θ -4 and (18 d aη ∗ 0 θ 5.×10 /Q > Be e leads to a mixing angle Be and 8 ′ e 8 Q 2 KLOE ud and / Δa aη -4 θ . Mutual parameter space for the ud = 1 -4 -5 -5 -4 aη 1.×10 d θ 0.010 0.005 0.001 The light and dark blue bands in ﬁgure It would be interesting to compare the allowed values of the axion-

When

1.×10 5.×10 1.×10 5.×10

1 ud η a | θ | e consistent with a ratio ofopposite PQ signs charges of theQ mixing angles, as represented in the right panel ofAtomki figure anomalies. naturally between allowed parameter space shownfrom in figure signal in the corresponding results when with the ones predicted inthis chiral is perturbation theory. not However,at as a emphasized next-to-leading simple in order. ref. task, [ since The these only firm mixing prediction parameters is receive that relevant these contributions mixing parameters are 95% C.L. for regions that wouldfirm be bounds, excluded are in indicatedbounds the by for octet gray the lines. enhanced case regime, In when the which sgn left are panel, therefore we not show the predictions and from NA64 and KLOEelectron in couplings red consistent with anddecays purple in respectively, the as non in octet-enhancedthe figure regime. octet-enhanced Gray regime. lines indicatepanels, the the region light (dark) that blue would be shaded contours excluded show in regions where Figure 3 yellow bands indicate the parameter spaceanomalies for the for JHEP05(2021)138 is 0.050 and , we from aγγ g 4 ud e a ), at the aη θ 1 MeV 17 = ∆ and a 3.1 0.010 e we see that, g 2 m >0, s 0.005 aη . In figure | ] s ) e η - a a e θ + | θ 0, < ∆ , from eq. ( ud e aη (a→e σ, a θ + 0.001 2 ). In figure -4 ∆ →π + − K 3.2 e 5.×10 -enhanced) octet (not a e and Atomki anomalies assuming [∆ Δa CL. The bound from NA64 inferred e -4 2) -4 -4 -5 -5 95% 1.×10 − 0.010 0.005 0.001 g

5.×10 1.×10 5.×10 1.×10

( . In this case, natural regions of

η a | θ | 3 assuming that the correlation of , at the e 3 a – 10 – 0.050 ∆ ) which does not differ significantly considering either - e 1 MeV 17 = + 2 a / (a→e m ), + 0.010 s = 1 aη →π + d K 0.005 is shown in the red dashed line. -enhanced) octet (not | /Q s e cover almost this whole region. However, this is not the case for inferred from NA64. Hence, this constraint on the meson-mixing η e a a sgn(θ = ) close to or larger than the central value of the measurement, there 3 θ Q | ∆ ud / e aγγ aη a g ∆ 0.001 = 1 sgn(θ -4 d 5.×10 /Q e e Q KLOE Δa -4 . Same parameter space as in figure ), where the axion couples exclusively to the first generation fermions in the SM. ) is, however, quite different compared to that of eq. ( -4 -5 -5 -4 1.×10 fermions 0.010 0.005 0.001 CL. All color shading follows that of figure accounting for both anomalies are completely open. In fact, scenarios motivated by 2.1 3.1 The corresponding parameter space consistent with the determination of

1.×10 5.×10 1.×10 5.×10

ud η a | θ | aη Generating the effective interactions tobreaking the mechanism up- must and bein down-quarks carefully is a non-trivial intertwined way as with thatwe the electroweak reproduces consider PQ symmetry an the breaking extension correctHiggs of flavor the fields. structure SM in The by the three PQ additional CKM symmetry Higgs matrix. is doublets realized and To by three this assigning singlets end, charges to the additional Higgs 5.1 The generation of CKMIn matrix this and section, weeq. the present ( couplings a possible to UV first completion of generation the effective model presented in PQ charges scenarios motivated by determination of the electron magnetic moment. 5 UV model angles vanishes for couplingsshow consistent the with corresponding the parameter region spacethe correlation for of the electron and95% photon couplings consistent with θ eq. ( except for values of is no lower bound on Figure 4 consistent with the Berkeleyfrom measuremant, the central value of JHEP05(2021)138 and (5.6) (5.3) (5.4) (5.5) (5.1) (5.2) gives is the , right- uL f V R SM Yuk u H L V , h.c., R ,m h.c. † + . All other particles u 1 R 3 V u f + u f j R or 0 1 Q    φ H t 1 R − 1 He e 0 m e m = 2 ij respectively. The e . The particle content and c e H 1 Q n Y R u 0 0 R 1 1 i i u e m Q − e u e ¯ H L v Y m u , i 0 0 0 2 + ¯ m 1 3 d m L R R , with 1 √ j R and ~u d Q . − , and    + is not, we expect the axion field to /n R = 1 L uR H 1 R Hd . d u H V d u R L = 1 ij , V 2 3 1 ,m d d d is a global Peccei-Quinn-like symmetry and u Q 1 R e R = Y V H u = i u Q 1 L u R i ¯ † PQ d Q u    H Y V d,e i 1 v v v + d,e and 1 2 2 j ¯ Q u = Q U(1) , ~u 13 23 33 j R H u u u Y – 11 – − m to the first generation fermions, while + L = 1 ij ˜ ~u Hu v Y v Y v Y 1 R d CKM u ij L u 1 2 u u Q † uL 12 22 32 V u u u u u,d,e u 2 Q , Y , where V V H Y Y Y − i f , are given by . For simplicity, we work in a basis where H H − ¯ charges of the SM Higgs, additional Higgs doublets 1 φ Q = u u u T i i = 2 H u ) v v v L m Y u 3 PQ . Therefore, to connect to the effective model, this requires 1 2 , i 0 2 31 11 21 ~u H u u u Q Q ¯ L/R Q H Y Y Y =2 X j = , t U(1)    3 3 , , L 1 R 2 2 Y 2 × , , PQ u 1 L/R X X Y u √ =1 =1 , c i i H but not U(1) ≡ 1 SU(2) U(1) ), i Particles u U(1) u u L/R Y m ⊃ − ⊃ − u i H × M are the vacuum expectation values of ¯ Q L u v Yuk PQ Yuk SM = ( gives the couplings of L L is charged under the PQ symmetry while SU(2) . The PQ charges are couples only to the first generation up-quark in the mass eigenstate basis, and Yuk PQ L/R u . u ~u L v H H matrices given the rotation between the flavor- and mass-eigenstate basis (denoted After diagonalization of both up- and down-type quark sectors, the CKM matrix is The relevant Yukawa interactions allowed by the PQ symmetry of the Higgs doublets, u, d, e , and those of the SM Higgs, f = uR Since be contained in that identity matrix. The diagonalization of the down-type quarks followsgiven similarly. by V with superscript where where where the couplings of the second andof third generation PQ fermions and to electroweak the symmetry SM Higgs. breaking Below the the up-quark scales mass matrix is then given by their PQ charges of the model is summarized inH table handed fermions, and Higgs singlets f are considered to be PQ singlets. bosons as well as the right-handed SM fermions Table 1 JHEP05(2021)138 2 ⊥ ) 1 (5.7) (5.8) (5.9) j (5.14) (5.11) (5.12) (5.13) (5.10) Y ). This ( 5.3 and , , allowed by h.c., 1    dia ⊥ + ) 0 0 V 1 j n e 12 Y φ 12 s ( ∗ d c . − φ    φ 12 12 0 0 1 B 12 c s 12 0 s + c we obtain    . − , 2 d L . is an auxiliary rotation angle φ =    d       ∗ u T . V 1 2 1 x d 2 d    φ T k T k 0) T ⊥ T ⊥ T ⊥ v ) T ⊥ φ ) can be decomposed in terms of the 1 2 m ) ) , ) ) 1 1 T k 1 1 1 T ⊥ T ⊥ 0 2 A j 1 j ) L j j u j d ) ) j , u u d 1 , d u 1 1 Y √ Y j + Y Y Y j j d ( Y V ( (1 d d ( ( ( ( e Y = Y Y u ( = 0 u ( (    H    1 v † j m d          2 H x x y ∗ e y √ , y c s c s , φ e ,Y 23 ). Similarly for – 12 – x = can be reconstructed according to eq. ( y θ    x s y A s    1 c d c , and diagonal scalar potential, 5.7 j − 13 − 13 u = Y + 13 c 13 s 0 Y 1 00 0 0 PQ 1 00 0 0 x d c , s 0 0 V ij 2    H       and † 13 L u u † = Φ u = 13 0 1 0 s u H † Y v c , the unitary matrix ∗ d m V L L − † Φ † u φ T d 2 d V V    are given by, √ Φ A 31 u 1 λ = j , and two perpendicular normalized vectors = d + k ,Y 1 Y )    u j 1 u 21 1 2 j u Φ + H T k Y T ⊥ T ⊥ † ) · Y ) ) angles are the CKM mixing angles in the SM. Then, the explicit forms ,Y 1 and ( Φ 1 1 j j j u H 11 2 Φ 1 u u u 23 j Y ∗ u u µ Y Y θ ( Y ( ( φ Y , − u    13 = A Φ θ X 1 represents the transposed column vector, and , j = = 12 Y T θ dia PQ Besides the Yukawa interactions, the scalar potential needs to be studied to single We choose the auxiliary angles explicitly as V V symmetries are procedure of the mixinganalogous in way. the lepton sector. However, thisout may the be physical accomplished axion inThe field an in off-diagonal the scalar model potential, as well as its mixing with other pseudo-scalars. The rest of the Yukawa matrix completes the realization of the CKM matrix in the UV model. We omit details of the where of the vectors and for the Yukawas we take where which does not affect the equality eq. ( Taking normalized vector which is equivalent to JHEP05(2021)138 I u u h = − which (5.16) (5.17) (5.18) (5.15) f leading ]. If we 7 − 18 for , carrying [ γa u 10 1 ˜ H . → × , f , it is clear that 5 φ f Ψ ≡ − GeV) e v / F, ≈ φ , v f 5 a J/ v f f e v 1) ( eff ¯ F γ 2 f − φ − ( PQ F, ,Q ia , the axion is contained v d f Q v 10 F φ a v f H m d × eigenvector) and the global 8 , it is contained with a double . 3rd ,Q , 0 H u , . SM φ . 2 X f ~ v G | v ( u =2nd 0 f F , PQ b Y Q 0 2 f ,Q f Q e , GeV, we have v 2 | v 0 f v 1 1) e e U(1) Q − ≈ f ( at leading order in 2 ,Q f × , v a v 1) d d f v L P − PQ d – 13 – ( , v ~ f G u . In the doublet Higgs leading to and I f ,Q ≡ − P u φ SU(2) v . The two massless pseudoscalars correspond to the . We assume that all the coefficients are real. In v v, v e γa e − eff u provides all the diagonal terms which do not provide H × f Q , φ , while for the SM Higgs , of which five will be massive, where we have chosen PQ F, 2 e ) → 5 d f v T − f and the second term gives the axion couplings to the 2nd Q φ ) 2 ¯ . For example, if we further assume φ dia Υ , fγ , φ I e ) + v a and V 2 f /v u f ia v 2 d . The last two terms reflect the PQ charge assignments of 2 f φ , φ d . + f f v PQ . v v ) I d , φ and Q e 2 H f e f ~ Q G f + v φ φ + 100 MeV , φ u,d,e 1 f 1 ( v a 1) 2 I u u 2 f ,H ⊃ 2 f f is the associated PQ charge, and we define H vv v m − ≈ d v ( ( I ( Q , φ f gives the mixing between the physical axion states among the seven f / f GeV) I e + and 2 f ~ Φ f . We have expressed 2 f v / ,H Q 2 P v Q a u u,d,e d , h , v P X PQ f I d f = φ − d, e ~ f q q G , eigenvector) symmetries P , h = 25( u I u . H,H = ≈ q φ 0 h f u, d, e PQ − ≡ ~ . G PQ SM = , ), the first three terms generate the couplings of axion to first generation fermions ( for | I a ~ ~ G G Φ = f f h ( PQ c PQ +1 5.13 The couplings of the QCD axion to the 2nd and 3rd generation fermions are constrained After rotating to the physical basis, the couplings of axion to SM fermions are given by Note that We require that the potential has a minimum, which determines the values of the Q ≡ | ’s. After applying this condition, we solve the mixing between the seven pseudo-scalars, I Φ ~ take the hierarchy is quite safe from the above constraints. from the exotic decaysto of heavy mesons. The relevant constraints are where and 3rd generationgenerates fermions, an generated effective PQ by charge mixing to with heavy fermions, the namely SM Higgs. Note that this with the suppressed factor suppressed factor where and pseudo-scalars, e.g. the axion is dominantly composed of the same hypercharge as Goldstone bosons afterU(1) breaking of will be sufficientrelevant for for a our discussion. complete description of theµ physical axion andΦ the interactions since it is associated with the imaginary part of the neutral component of eq. ( through mixing with the scalars mixing, but provide massescombinations to of CP-even the scalars. scalar fields We allowed omit by other the operators imposed found symmetries. by The other above potential where JHEP05(2021)138 . , is φ = 0 = 3 B , (5.23) (5.19) (5.20) (5.21) (5.22) u n . As a o A e ) . In this , mainly d GeV and , H 2 φ = v is explicitly = 0 φ I light e φ + A = 1 φ and 2 d B 1 GeV v e ( I light φ U(1) e ≈ φ φ . In this case, GeV, and therefore f v m and an even smaller φ 3 v 10 I e − , the – , ≡ 1 H ) e (1)GeV 6= 0 2 φ is dominantly composed of v φ (taking u,d,e φ B + from ≈ O I light 14 2 e a f φ states and may have a mass close v − f φ ( , v d 10 , which we denote as /v φ I u,d 2 f φ much smaller than the uncertainty of × v , v 0 e 1 , , . becomes a pseudo-goldstone boson with a f GeV ) 1 . 20 MeV , d 2 ∆ φ for scalar masses 2 φ − f /v ∼ v ≈ , φ v f 4 φ I light v φ 2 φ is f o − φ φ + B v v f vv e – 14 – φ 2 d φ A 10 f a v v ≡ B ] have converted this constraint to scalars, which ( 3 A × ∆ e v − 5 54 , 3 , u,d,e f − φ ∼ 53 , ) states, with masses given by , v e , v 0 2 φ I f , v symmetry and associated charged scalars h f and not related to any other dimensionful trilinear couplings. v e + 3 f 2 e 2 φ − v ]. Refs. [ v 20 GeV , ( φ U(1) d f 52 [ B ≈ . This coupling can be constrained using the Dark photon search at , v , v 0 4 f 0 0 . Moreover, it has a mixing of − , , A ) making its contribution to f 0 0 γA 4 φ . Additionally, there is one mass of the form . Therefore, this state mainly couples to the electron with a coupling of 10 n n v ≡ − I d , one can only decouple four heavy massive pseudo-scalars leaving one light . The lightness of this state can be understood in the limit → 3 × ≈ ≈ I e 10 H / 5 φ ) − u,d,e u, d, e × e f ∼ A = 1 5 v + = I light e φ φ f ( PQ e /v φ ~ω e The light pseudo-scalar with mass Q since A m I e requires a coupling smallerthis light than pseudo-scalar coupling wouldcorresponding be 1-loop close contribution to the to coupling current experimental bounds. The the experiment. where we have omittedφ the normalization factor.mixing Thus, from ∼ BaBar, In this case, we obtain comes from case, there is aresult, global there is one additionalbroken exact in goldstone the boson. scalarmass With potential. proportional to Therefore, The associated eigenvector can be easily represented with the simplficiation to 100 GeV, and one pseudo-scalar of mass where which dominantly comes from linear combination of where the last term determinesa the axion dimensionless decay parameter. constant There areof then linear three combinations massive of pseudo-scalars, the composed mostly In addition to the twoe.g. Goldstone bosons, there arepseudo-scalar. five massive More pseudo-scalars. specifically, we For assume the following parameters 5.2 Additional massive scalar and pseudo-scalar states JHEP05(2021)138 (5.25) (5.26) (5.27) (5.24) . Thus, . In this φ 2 v v and suffers φ H e B . λ φ 2 avoids existing ,    or /v 2 e e φ 2 φ v m ha v I light φ f e φ f + ∼ φ φ A v v v 2 e is a linear combination f v . There are two massive f A q 2 H . These states are mainly , I light 2 2 0 √ φ , which can also further raise , e 0 , H e † d ≈ − 2 φ   2 v I f H e φ , which are mostly composed of the e + ha φ I f , whose eigenvector is given by 2 v 1 f 2 2 (500 GeV) e h ) φ v f A ) the light pseudo-scalar is still viable but Similar to the pseudo-scalar sector, there f v , the five massive pseudo-scalars can be , f ∼ A φ q f 2 φ 2 f f v f v . , large enough such that φ v ( v f f 0 v = 2 which may induce a second minimum in the scalar = 3 1) φ , φ + A v 0 − φ n B n 2 f f 2 ( f , ∼ O A – 15 – (100 GeV) v e Q A . The interactions which determine the decay of ( 2 φ f 2 f v ' ) which are irrelevant to the main issues in this work and a H u,d,e and 1) X Q = f e φ + f − φ φ 5.13 , the light scalar masses become 2 ( e A v v 2 v e φ 1 u,d,e v √ q A = e = 2 u,d,e f A − = n SM ∼ the mass eigenstate of the SM Higgs is almost exactly given f P 2 I 2 h, f P v m 2 λvh 2 , there are seven massive CP-even scalars. Under the assumption    √   ≈ h f = 3 φ ) couples dominantly to the electron with coupling is dimensionful. In this case, the mass of v ⊃ − = n , and are all on the order of . One can choose φ φ GeV, this requires values for R light int B , we find that there is one SM-like Higgs with mass squared v R light φ L f φ , f φ ( v , B = 1 ~ω A u, d, e f = 2 φ = I light v f n and φ φ f φ v v Finally, we come to the phenomenology related to the SM Higgs decay. Working again Having dealt with the pseudo-scalar sector, we briefly discuss the seven massive CP- For φ Since 2 A f potential away from the EWthe one, EW particularly vacuum in must be the inwe direction a have where metastable omitted the configuration doublet additional just fieldsfull as terms vanish. in evaluation in the of In eq. SM. the this ( However, case, potential as and mentioned its previously vacuum structure is beyond the present discussion. in the limit by the neutral CP-eventhe component SM of Higgs to two axions are given by Just as from similar constraints. For in this case the massesenergy for phenomenology. CP-even scalars are also heavy and can be decoupled from low CP-even components of singlet Higgs bosons is still one light scalar with mass squared where composed of the neutral CP-evenscalars components of with doublet masses Higgs squared even scalars. For A limit, there are three CP-even masses squared given by of constraints. Moreover, one can alsoits add mass. the As term ais result, subject we conclude to that strongheavy for and constraints, completely while decoupled for from the low energy phenomenology. JHEP05(2021)138 and (5.30) (5.28) (5.29) 2 / 10 GeV, ∼ = 1 T exotic Higgs p and width of e ) Q 6% a . ]. Therefore, it is 0 m for 42 (2 [ , which is too close to can be reconstructed, / 2 h , as defined above. We a . is the radius for the EM m cm r d, e decay) and primary vertex 65 cm 3 = 0 indeed looks similar to the . − a = 1 R 025 MeV − . 10 f e , ∆ 0 ≈ a , + ∼ e 2 a ≈ m a R , where for d 2 e 0 2 , while in SM events it has to be in 2 a )) 2 h MeV (leading to d a 2 . This is similar to the signature of a m γcτ R 4 m m +1 ≈ 2 e f has a width of 4 decay will be highly collimated with a (2 Q R − (cm) − π r/ aa 1 and − e 8 1 O 2 a + ], where the converted photon has a large impact pa- u s d e , we see ≈ 55 f = ) + 2 φ decaying into – 16 – − → v f 2 2 f radian at the decay vertex. With the 3.8 Tesla e h a (cm) 2 arcsin( v R a + 2 f 4 meter. The separation angle between two tracks at e for ≈ − q A πm 1 ∼ O 88 10 → = 16 . sep radian and the two tracks can in principle be recognized 0 a θ 0 a × d d ≡ − 11 × Γ( 3 . ) = f 0 aa ≈ 1) and obtain the momentum for the converted photon. Extrap- − a GeV) → ( − is pretty light, the positron and electron pair (we will refer to / e h /E T . The SM Higgs decay to a a p f Γ( φ m , and and v = ( | ∼ + ) e θ B f v × u, d, e as q is the distance between the displaced vertex (where Therefore, the converted photon has zero impact parameter. In the case of the ( MeV. = − / a e 3 f T d + p | e Since the axion = 17 This is different from the case analyzed in ref. [ 3 = a → converted photon in SMvertex event. for But the there signal isthe depends one detector only material. critical on difference the in lifetime that of the conversion rameter. where in the transverse plane.measure. Since Therefore, a highly boosted momentum of olating the direction ofvertex. the momentum fromaxion, the since it vertex, will it beThe highly will electron boosted, tracks go we can can back have assume to non-zero the impact electrons the parameters, in primary its decay are parallel. still smaller than thelikely cone to size be constructed of as thewhich an typical is EM EM cluster. displaced cluster The toa displaced the converted vertex photon primary of in vertexdetector SM by has events, been where converted the into photon an passing electron-positron pair. through the In material that in case, one the can sum the R the EM calorimeter cells willcalorimeter cells be located in the transversethis plane. angle Assuming will the be electrons as have as large electron as and positron with the correct charge assignment. However, the separation is we obtain them lifetime of axion in the labthem as frame electrons collectively)separation in of the magnetic field in the tracker, the two tracks will separate with the curvature given by branching ratio). Assuminga the boost factor for the axion is also assume which is far smaller than SM Higgs total width of where JHEP05(2021)138 ] γγ 69 is an → 2 h χ cm for the MeV is still 65 , which decays . 0 to decay before 1 (10) A O ∼ MeV. However, this 87% both reconstructed as ≈ 100 . There, a constraint is a ] focused on the di-muon − decay location. If it decays ≥ e 68 0 0 + – 65cm) e A A . 64 (1 m / → is the DM, recognized as missing is the dark photon, and 0 1 ], where the lepton jets come from for 4cm 0 A . ] further pointed out that whether it χ 3 searches because the electrons in the 2 68 A . − 58 – ]. The ATLAS and CMS collaboration 0 − e e in the lab is about 64 with 63 . + − , and – e 0 1 − for an axion with mass 1 e A χ 60 0 → MeV and the topology is different from our + , where 0 aa jets) A e h A – 17 – 0 − can be reconstructed as converted photon, as we → → (10) → A 0 e decay. Ref. [ 1 O A h a − χ GeV. Therefore, with two → will be negligible in the contribution to the 1 e χ + h 20 − e ( e → ∼ + XX,X → decay is displaced but refs. [ . Such e 2 0 − a χ → e A ], such event is also classified as “ambiguous”. Thus, as the true 2 T → probability to decay after the first layer of the pixel detector. + h χ e E 59 a → → 13% 0 h A with ∼ ] have considered the case of a light and highly boosted aa 58 → – ], the two Si tracks (SCT tracks) have an efficiency of 0.35 to be reconstructed h 56 59 decays after the first layer of the pixel detector but before the 3rd-to-the-last layer of The lepton-jet signature has been generally discussed and also specifically for two In our scenario, the lifetime of Refs. [ 0 A particle physics. It canthe be presence naturally of solved a by new theexperimental pseudo-scalar introduction particle constraints, in of the the an spectrum. axionthe axion field, Generically, weak in decay implying scale, order constant to implying avoid the is a suggestion assumed very that light to axion in be particle. spite much of In larger these this than constraints, article, the we have axion investigated may be as heavy as 17 MeV, model. Therefore, weviable conclude and that provides an interesting electron-jet signature for future searches. 6 Conclusions The strong CP problem is one of the most intriguing aspects of the Standard Model of energy at the collider.channel The only. The prompt electron-jetfocusing signature has on been the studied in topology theset ATLAS on search [ the electron-jetssearch decay does BR not cover lower massess lepton-jets from the SM Higgshave decay searched in for refs. lepton [ jetsthe from decay a topology light bosonexcited fermion [ DM, which decay promtly to as converted photon for converted photons, the probabilitythe is signal as smallbranching ratio. as It 0.002. alsosignal does As is not not fit a to isolated. result, the we conclude that benchmark. Therefore, itthe has first the layer probability ofevent. the pixel There detector. isFrom a As ref. [ a result, it will dominantly look like a lepton-jet layer of pixel detector.event cannot In be this reconstructed case,of as since a electrons the converted conversion or photon. occurs photonselectrons In outside cannot [ the the pass flowchart the material for isolationIf the criteria, reconstruction this will besilicon-strip identified detectors as (SCT), a it lepton-jet can signature. be identified as a converted photon. into electron pairs, previously discussed for light is reconstructed as a converted photonbefore highly depends the on first the layerdetector of in the the pixel barrel tracker region), (about the 3.4 electrons (including cm positrons) away will from leave the hits central in axis the of first the JHEP05(2021)138 (1GeV). This scenario O = a f . 2 – 28 . = 0 d . /Q e = 2 Q – 18 – d doublets and singlets, associated with the up and /Q L u Q SU(2) with the recent determinations of the fine structure constraint. This . Moreover, the corresponding range of couplings leads to PQ charges η e 2) and − π g ( The model we constructed generates the right quark and charged lepton masses and is Building a realistic model leading to such a heavy axion is a non-trivial task, and One of the most relevant constraints on this scenario is imposed by the modifications rissey, and Tim Tait for usefulsupported discussions and by comments. the CW U.S. andat NM Department Argonne have of National been partially Energy Laboratory.also under The supported work contracts of by No. CW thea at DEAC02-06CH11357 DOE contribution the grant agreement University DE-SC0013642. with of the Chicago TRIUMF National has receives Research been federal Council of funding Canada. via The work of JL the large boost and itsin corresponding ways lifetime, that may are be not searched yet for studied in by the experiments. electronAcknowledgments channel We would like to thank Wolfgang Altmannshofer, Daniele Alves, Stefania Gori, David Mor- be too large, leadingmasses naturally of to the a order relatively of light several spectrum hundreds or of tens doubletconsistent of and with GeV, the singlets respectively. observed with CKMleads mixing. naturally It to also a avoids decay all mode experimental of constraints the and standard model Higgs into two axions, that due to leads naturally to smallfirst first generation generation fermions quark dominantlygenerations with and through suppressed lepton the effective masses. mixing PQ withdecays charge The SM of to axion Higgs. heavy 2nd couples Thus, mesons and searches to Higgs are 3rd for to two the safely axions, axion the evaded. Higgs in trilinear the In couplings exotic with order the to new singlets avoid and a doublets cannot large coupling of the SM down quarks and the electron sectors,values respectively. partly These fields induced acquire vacuum by expectation vevs interactions being with much the smaller Standardwith than Higgs a the doublet, combination singlet with of ones. thethe the doublet The order singlet axion of pseudo-scalar field components, 1 is GeV and then to their mostly generate vevs associated the should axion be decay of constant of order one and that take values between demands a more precise relationConcentrating between on the the PQ charged chargesintroduction in lepton of the and three lepton additional quark and masses, quark sectors. we build a model based on the to the anomalous magneticthe moment existence of of the relevant contributions electron.the at electron the In two-loop this level work, mayimplies lead we a correlation to demonstrated between a that the compatibility electronPQ, of coupling and to the the axion, coupling andlight to hence mesons, its photons charge at under low energies, induced mostly by the mixing with the resonance observed in nuclearthe transitions axion at should the couple Atomki onlysmall experiment. to mixing For the with this first the to generation pion,PQ happen, quark something charges of and that up leptons, may and be and down should achieved quarks for have a values of the ratio of the opening the possibility that this axion particle may lead to an explanation of the di-lepton JHEP05(2021)138 , (1979) Phys. 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