Searching for axionlike particle at future ep colliders
SSearching for axionlike particles at future ep colliders Chong-Xing Yue, ∗ Ming-Ze Liu, † and Yu-Chen Guo ‡ Department of Physics, Liaoning Normal University, Dalian 116029, China
Abstract
We explore the possibility of searching for axionlike particle (ALP) at future ep colliders viathe subprocess e − γ → e − a → e − γγ . Sensitivities to the effective ALP-photon coupling g aγγ forits mass in the range of 10 GeV < M a < ep colliders are competitive and complementary to other colliders. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] a r X i v : . [ h e p - ph ] J u l . INTRODUCTION Axionlike particles (ALPs) were originally motivated by the axion, which results fromthe dynamical solution to the strong CP problem of the standard model (SM) [1]. ALPsare often defined as relatively light pseudoscalar particles and appear in many extensionsof the SM. Both axions and ALPs are optimal candidates to explain the dark matter(DM) of the Universe [2]. In general, any model with global U(1) symmetry, which isspontaneously broken, predicts the existences of ALPs and their masses and couplingsare independent parameters. They can couple to the SM fermions and electroweak gaugebosons via dimension-5 operators [3]. At tree level, there is no dimension-5 operatorcontributing to the couplings of ALP to the physical Higgs boson, which can be inducedat loop level or by the high dimension operators [4]. ALPs have anomalous couplingsto gluons as optional, and they are not required to solve the strong CP problem. Theexperimental constraints on the effective couplings of ALP to ordinary particles havebeen widely studied using various experimental data from particle physics, astroparticlephysics, and cosmology. Bounds obtained from the LEP and LHC in diphoton, triphoton,and monophoton final states have been summarized and partly updated in Refs.[5–9].In general, the couplings of ALP to photons or Z bosons can be considered indepen-dently and might be investigated separately. The present and future collider experimentscan be used to search for ALPs with masses in the broad range from eV to TeV [5–14]. At e + e − colliders, production of ALP can be studied via photon fusion and ALP-strahlung inassociation with a photon, Z , or Higgs boson [5]. At hadron colliders, exotic Higgs decaysand Z boson decays are the most promising search channels, which have been studied inRefs. [7, 11]. For GeV-scale ALP produced in photon-fusion, heavy-ion collisions at theLHC can provide strong constraints on ALP-photon couplings [12]. Reference [14] hasstudied the possibility of detecting ALP at the LHC via the process pp → ppγγ with thesubprocess γγ → γγ . A number of these constraints are model independent and tendto vanish at high masses. It is necessary to further study the possibility of searching forALP at upcoming or future collider experiments.At high energies, in addition to the electromagnetic exchange, the electroweak bosonsalso play important roles. The γ or Z boson exchange induces neutral current deepinelastic scattering, which has been extensively explored via ep collisions. In this article,2e consider the possibility of searching for ALP a at the LHeC [15] and FCC-eh [16] ina model-independent way. We assume that its mass is in the range of 10–3000 GeV andfocus on the subprocess e − γ → e − a → e − γγ , in which the initial photon comes from theinitial proton. The analysis of the relevant SM backgrounds and detection efficiencies ofthe signals are presented. Our numerical results demonstrate that, compared with othercolliders, the bounds given by the LHeC on the ALP free parameters for its mass in therange of 10–100 GeV are competitive and complementary. In addition, the FCC-eh canimprove the effective search limit up to 2.5 TeV.This paper is organized as follows. After reviewing the relevant couplings of ALP tophotons and Z bosons, we briefly describe the theory framework in Sec. II. In Sec. III, wecalculate the production cross sections of the process e − p → e − a at the LHeC and FCC-eh. Our analysis strategy is also discussed in this section. We finalize the prospectivesensitivities of ep collider experiments for the ALP parameter space before concluding inSec. IV. II. EFFECTIVE INTERACTIONS OF ALP
The ALPs we consider are gauge singlets under the SM gauge group and are oddunder CP . The effective interactions of ALP with the SM particles can be described bythe general effective Lagrangian [3]. Among them, those that are relevant for the process e − γ → e − a appear as L = 12 ( ∂ µ a )( ∂ µ a ) − M a a − C BB f a aB µν ˜ B µν − C W W f a aW iµν ˜ W i,µν , (1)where B µν and W iµν are the field strength tensors of the gauge groups U (1) Y and SU (2) L ,and we have defined the dual field strength tensors by ˜ B µν = (cid:15) µνρσ B ρσ . The ALP mass M a and the decay constant f a are supposed to be free parameters. After electroweaksymmetry breaking, Eq.(1) can give the couplings of ALP to the electroweak gauge bosons.The relevant terms, which are related to our calculation, are written as L ⊃ − g aγγ aF µν ˜ F µν − g aγZ aF µν ˜ Z µν , (2)where F µν and Z µν denote the field strength tensors of the electromagnetic field and Z field, respectively, and their duals are defined as above. The couplings g aγγ and g aγZ can3e written as a linear combination of the relevant free parameters g aγγ = C BB c W + C W W s W f a , g aγZ = 2 c W s W ( C W W − C BB ) f a , (3)where s W =sin θ W and c W =cos θ W , with θ W being the Weinberg angle. It is obvious thatthere is g aγγ (cid:29) g aγZ for C W W (cid:39) C BB . The loop-induced flavor changing processes like B → Ka can give strong constraints on the coupling parameter C W W [17]. Thus, it isparticularly interesting to consider the case C W W (cid:28) C BB . From Eq.(3) we can see thatthere is g aγZ (cid:39) − tanθ W g aγγ in this case. III. SEARCH FOR ALP AT ep COLLIDERS
Lepton-hadron scattering has played a crucial role in the exploration of the elementaryparticles over the past 60 years. After the last ep collider (HERA) with the center-of-massenergy √ s = 318 GeV, it is natural to consider the possibility of future ep colliders. Twoideas have been discussed: the LHeC [15] that uses the electron beam to collide withthe existing LHC beam and the FCC-eh [16] that is an option of the Future CircularCollider program. With upgrading of the LHC, the LHeC could upgrade into HE-LHeCby HE-LHC. The electron beam collides with the 7, 13.5, and 50 TeV p beams, whichcorrespond to the LHeC, HE-LHeC, and FCC-eh, respectively. A final LHeC run indedicated operation could bring the total integrated luminosity close to 1 ab − . For theHE-LHeC and FCC-eh, we assume that the total integrated luminosity could reach 2 and3 ab − , respectively.First, we give the production cross sections for the process e − p → e − γ → e − a at theLHeC with √ s = 1 . √ s = 3 . σ ( e − p → e − a ) = (cid:90) dx f γ/p ( x , µ ) · ˆ σ ( e − γ → e − a ) , (4)where the photon is emitted from the proton and can be described by the photon distribu-tion function f γ/p ( x, µ ). Considering the mass range possible to be explored, we assumethat the ALP mass is in the range of 10 GeV < M a < g aγZ ≈ g aγZ =42 tanθ W g aγγ . This is because the interference effects between the two kinds of Feynmandiagrams induced by γ and Z exchanges are negative which counteract contributions ofthe aγZ coupling. Thus, we only show the cross sections in final state e − a for the caseof g aγZ = − tanθ W g aγγ in Fig. 1 as functions of the ALP mass M a and the couplingconstant g aγγ . g a γγ = - GeV - g a γγ = - GeV - g a γγ = - GeV - - - - M a [ GeV ] σ ( e - p → e - a ) [ f b ] FCC - ehLHeC M a = M a = M a = - - - - - - - - - g a γγ [ GeV - ] FCC - ehLHeC FIG. 1: Cross sections of the process e − p → e − a at the LHeC and FCC-eh as functions of M a (left) and g aγγ (right). Now we consider the possibility of searching for ALP in diphoton decay channel e − p → e − a → e − γγ . The signature of the final state is characterized by the presence of a pairof photons with an invariant mass equal to the ALP mass and an isolated electron. Thefinal state could provide relatively high target efficiency. The SM backgrounds for thissignal are dominated by the QED subprocess e − γ → e − γγ with a real emission photonin the final state. Additional small backgrounds for small ALP mass may arise from thesubprocess e − γ → e − γ with the third photon candidate coming from the beam-inducedphoton. This kind of background is reduced using the very good time resolution O (ns) ofthe electromagnetic calorimeter at high photon energies [15]. Thus, we assume that beambackgrounds can be reduced to a negligible level without significantly affecting the signalselection efficiency.Our event selection requires the photon with energy E ( γ ) >
10 GeV and pseudorapidity | η ( γ ) | < .
5. The invariant mass of the two photons from decays of ALP peaks close to theALP mass. For the electron in the final state, transverse momentum p T ( e ) >
10 GeV and5 η ( e ) | < . E T [ GeV ] E v e n t s ( s c a l e d t oo n e ) M a =200GeVM a =400GeVM a =600GeVM a =800GeVM a =1000GeVBackground 0 100 200 300 400 500 600 p T ( ) [ GeV ] E v e n t s ( s c a l e d t oo n e ) M a =200GeVM a =400GeVM a =600GeVM a =800GeVM a =1000GeVBackground0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ( ) E v e n t s ( s c a l e d t oo n e ) M a =200GeVM a =400GeVM a =600GeVM a =800GeVM a =1000GeVBackground 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ( e) E v e n t s ( s c a l e d t oo n e ) M a =200GeVM a =400GeVM a =600GeVM a =800GeVM a =1000GeVBackground FIG. 2: Normalized distributions of E T , E ( γ ), θ ( γγ ), and θ ( γe ) from the signal and backgroundevents for different M a with g aγγ = 10 − at the LHeC with √ s = 1 . For the final state of the process e − p → e − a → e − γγ , the two photons from ALP decaycould be a powerful trigger. We choose to reconstruct the energy and angular distributionsof the photons in the lab frame. As a result, the following kinematic variables are exploitedto develop additional cuts: the angle θ ( γe ) between the photon momentum and electronmomentum, the angle θ ( γγ ) between two photon momenta, and transverse momentum p T of the photon. We also apply an important global observable, the total transverse energy E T . In Fig. 2, we display the normalized distributions of these observables for some6articular choices of the model parameters ( M a = 200 , , , , g aγγ =10 − ) using MadAnalysis 5 [22]. The signals are well distinguished from the correspondingbackgrounds by the angle θ ( γγ ). The electron momentum in the SM backgrounds ismostly along the photon direction, which is different from the signal. Just as expected,the distributions show that the p T ( γ ) spectrum peaks at around half of the ALP masswhile the electrons in the SM backgrounds tend to be soft. Considering the kinematics,we impose the following improved cuts: p T ( γ ) >
70 GeV , θ ( eγ ) > . ,E T >
160 GeV , θ ( γγ ) > . . (5)These cuts could effectively remove the SM backgrounds. The event selection efficiency hasbeen optimized with respect to the signal, and the statistical significance S = S/ √ S + B ,where S and B respectively denoting the numbers of signal and background events aresummarized. Here, some of the results are shown in Table I. TABLE I: Effect of individual kinematical cuts on the signals and backgrounds. The statisticalsignificance S is computed for a luminosity of 1 ab − , M a = 600 GeV and g aγγ = 10 − .LHeC, √ s = 1 . S/ √ S + B Initial (no cut) 126 34910 0.674Basic cuts 116.12 32147.7 0.6465 E T >
160 GeV 112.90 2144.3 2.3764 θ ( γe ) > . p T ( γ ) >
70 GeV 112.40 1839.1 2.5443 θ ( γ γ ) > . Several types of experiments are used to search for ALP, ranging from the searchesfor direct production at colliders to those from cosmological and astroparticle physicsexperiments. The constraints from these searches can be mapped into the M a - g aγγ plane,and are shown in green sectors in Fig.3. The most competitive bounds for very light ALPwith mass below the MeV scale come from the astrophysics and cosmology, but we consider7he ALP mass range here begin with M a ∼
10 GeV, for which collider experiments providethe best limits. Thus, in Fig.3, we do not show the constraints on the very light ALP.At GeV scale, Ref. [9] provided the excluded parameters region by data from BABAR[25] and LHCb [26], which are adopted here and labeled flavour. For about 10 to 100GeV, the bounds labeled L3 in Fig. 3 are from the analysis of Ref. [23], in which the L3collaboration looked for hadronic final states accompanied by a hard photon [24], thoughit is ultimately superseded by LHC exclusions. For the high ALP mass near the TeVscale, the limits from data of the LHC run 1 [27] are extremely strong and should beimproved with the addition of run 2 data, especially at higher energies.
LHeCHE - LHeCFCC - eh - - - - - - M a [ eV ] g a γγ [ G e V - ] L3 LHC F l av ou r FIG. 3: Projected ep colliders sensitivity at 95% CL and existing constraints on the couplingof ALP with photons. The green regions are experimentally excluded. The projected sensitivity contours at 95% CL for the process e − p → e − a → e − γγ atfuture ep colliders are summarized in Fig. 3. From this figure, one can see that, for thelight ALP (i.e., 10 GeV < M a <
100 GeV), diphoton searches for the LHeC and FCC-eh can push significantly beyond current constraints from existing experiments and canpotentially probe the ALP-photon coupling g aγγ with the order of g aγγ ∼ − to 10 − .Furthermore, the FCC-eh will be sensitive to ALP in a large range of the parameter spaceand can significantly improve over existing bounds on ALP from the LHC.8 V. CONCLUSIONS
The existence of ALPs is a generic feature of many extensions of the SM that extendwell beyond axions. Both axions and ALPs may be excellent candidates to explain thenature of DM. As pseudo-Goldstone bosons, ALPs can naturally and very weakly coupleto the SM particles dominantly by couplings to photons and electroweak gauge bosons.A particular interesting decay channel is ALP decaying into a pair of photons.In this paper, we have investigated the search for ALP diphoton signal at future ep colliders via the process e − p → e − a → e − γγ in a model-independent fashion. Consideringthe mass range to be possibly explored at the LHeC and FCC-eh, we focus on 10 GeV < M a < ep colliders might become an important handle on new physics scenarios,which are related to ALP. ACKNOWLEDGMENT
This work was supported in part by the National Natural Science Foundation of Chinaunder Grants No. 11875157, No. 11847303, and No. 11847019. [1] R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. , 1440(1977); S. Weinberg, Phys. Rev.Lett. , 223(1978); F. Wilczek, Phys. Rev. Lett. , 279(1978).[2] L. F. Abbott and P. Sikivie, Phys. Lett. , 133(1983); J. Preskill, M. B. Wise, and F.Wilczek, Phys. Lett. , 127(1983).[3] H. Georgi, D. B. Kaplan and L. Randall, Phys. Lett. , 73(1986).
4] M. Bauer, M. Neubert and A. Thamm, Phys. Rev. Lett. , 181801(2016).[5] M. J. Dolan, T. Ferber, C. Hearty, F. Kahlhoefer, and K. Schmidt-Hoberg, J. High EnergyPhys. 12(2017)094.[6] K. Choi, S. H. Im, C. B. Park, and S. Yun, J. High Energy Phys. 11(2017) 070; F. Arias-Aragon and L. Merlo, J. High Energy Phys. 10(2017)168.[7] M. Bauer, M. Neubert, and A. Thamm, J. High Energy Phys. 12(2017)044; I. Brivio, M.B. Gavela, L. Merlo, K. Mimasu, J. M. No, R. del Rey, and V. Sanz, Eur. Phys. J. C , 572(2017); M. B. Gavela, R. Houtz, P. Quilez, and R. Del Rey, Eur. Phys. J. C ,369(2019).[8] N. Craig, A. Hook, and S. Kasko, J. High Energy Phys. 09(2018)028; M. Bauer, M. Heiles,M. Neubert, and A. Thamm, Eur. Phys. J. C , 74(2019).[9] X. C. Vidal, A. Mariotti, D. Redigolo, et al. , J. High Energy Phys. 01(2019)113.[10] M. Kleban and R. Rabadan, arXiv:0510183; S. Chang, P. J. Fox, and N. Weiner, Phys.Rev. Lett. , 111802(2007).[11] K. Mimasu and V. Sanz, J. High Energy Phys. 06(2015)173; J. Jaeckel and M. Spannowsky,Phys. Lett. B , 482(2016).[12] S. Knapen, T. Lin, H. K. Lou, and T. Melia, Phys. Rev. Lett. , 171801(2017).[13] M. Bauer, M. Neubert and A. Thamm, Phys. Rev. Lett. , 031802(2017); J. Heeck andW. Rodejohann, Phys. Lett. B , 385(2018); G. Cacciapaglia, G. Ferretti, T. Flacke, andH. Serodio, Eur. Phys. J. C 78, 724(2018).[14] C. Baldenegro, S. Fichet, G. Von Gersdorff, et al. , J. High Energy Phys. 06(2018)131.[15] J. Abelleira Fernandez et al. , J. Phys. G , 075001(2012); F. Zimmermann, O. Bruningand M. Klein, Report No. C13-05-12, p.MOPWO054; O. Bruening and M. Klein, Mod.Phys. Lett. A , 1330011 (2013).[16] O. Bruning, J. Jowett, M. Klein, et al. , CERN-ACC-2017-0019 (2016).[17] E. Izaguirre, T. Lin, and B. Shuve, Phys. Rev. Lett. , 111802(2017); F. Bj¨orkeroth, E.J. Chun, and S. F. King, J. High Energy Phys. 08(2018)117.[18] J. Alwall, R. Frederix, S. Frixione, et al. , J. High Energy Phys. 07(2014)079.[19] C. Schmidt, J. Pumplin, D. Stump and C. P. Yuan, Phys. Rev. D , 114015(2016).[20] T. Sj¨ostrand, S. Mrenna and P. Skands, Comput. Phys. Commun. , 852(2008).
21] J. Conway, R. Culbertson, R. Demina, et al. ,http://conway.physics.ucdavis.edu/research/software/pgs/pgs4-general.htm.[22] E. Conte, B. Fuks, and G. Serret, Comput. Phys. Commun. , 222 (2013).[23] G. Alonso- ´Alvarez, M. B. Gavela, and P. Quilez, J. High Energy Phys. 01(2019)113.[24] O. Adriani et al. (L3 Collaboration), Phys. Lett. B , 472(1992).[25] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. , 221803(2011).[26] S. Benson and A. Puig Navarro, Report No. LHCb-PUB-2018-006.https://cds.cern.ch/record/2314368.[27] J. Jaeckel, M. Jankowiak, and M. Spannowsky, Phys. Dark Univ. , 111(2013); A. Mariotti,D. Redigolo, F. Sala, and K. Tobioka, Phys. Lett. B , 13(2018)., 13(2018).