# Search for a heavy dark photon at future *e*^{+}*e*^{−} colliders

- 64 Downloads
- 3 Citations

## Abstract

A coupling of a dark photon *A*^{′} from a U(1)_{A}′ with the standard model (SM) particles can be generated through kinetic mixing represented by a parameter *ϵ*. A non-zero ϵ also induces a mixing between *A*^{′} and *Z* if dark photon mass *m*_{A}′ is not zero. This mixing can be large when *m*_{A}′ is close to *m*_{Z} even if the parameter *ϵ* is small. Many efforts have been made to constrain the parameter *ϵ* for a low dark photon mass *m*_{A}′ compared with the *Z* boson mass *m*_{Z} . We study the search for dark photon in *e*^{+}*e*^{−} → γ*A*^{′} → γ*μ*^{+}*μ*^{−} for a dark photon mass *m*_{A}′ as large as kinematically allowed at future *e*^{+}*e*^{−} colliders. For large *m*_{A}′, care should be taken to properly treat possible large mixing between *A*^{′} and *Z*. We obtain sensitivities to the parameter *ϵ* for a wide range of dark photon mass at planed *e*^{+} *e*^{−} colliders, such as Circular Electron Positron Collider (CEPC), International Linear Collider (ILC) and Future Circular Collider (FCC-ee). For the dark photon mass 20 GeV ≲ *m*_{A}′ ≲ 330 GeV, the 2*σ* exclusion limits on the mixing parameter are *ϵ* ≲ 10^{−3}-10^{−2}. The CEPC with \( \sqrt{s}=240 \) GeV and FCC-ee with \( \sqrt{s}=160 \) GeV are more sensitive than the constraint from current LHCb measurement once the dark photon mass *m*_{A}′ ≳ 50 GeV. For *m*_{A}′ ≳ 220 GeV, the sensitivity at the FCC-ee with \( \sqrt{s}=350 \) GeV and 1*.*5 ab^{−1} is better than that at the 13 TeV LHC with 300 fb^{−1}, while the sensitivity at the CEPC with \( \sqrt{s}=240 \) GeV and 5ab^{−1} can be even better than that at 13TeV LHC with 3ab^{−1} for *m*_{A}′ ≳ 180 GeV. We also comment on sensitivities of *e*^{+}*e*^{−} → γ*A*^{′} with dark photon decay into several other channels at future *e*^{+}*e*^{−} colliders.

## Keywords

Beyond Standard Model e+-e- Experiments## Notes

### **Open Access**

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

## References

- [1]L.B. Okun,
*Limits of electrodynamics: paraphotons?*,*Sov. Phys. JETP***56**(1982) 502 [INSPIRE].Google Scholar - [2]
- [3]R. Foot and X.-G. He,
*Comment on Z Z-prime mixing in extended gauge theories*,*Phys. Lett.***B 267**(1991) 509 [INSPIRE]. - [4]R. Foot, X.G. He, H. Lew and R.R. Volkas,
*Model for a light Z-prime boson*,*Phys. Rev.***D 50**(1994) 4571 [hep-ph/9401250] [INSPIRE]. - [5]R. Foot and R.R. Volkas,
*Neutrino physics and the mirror world: How exact parity symmetry explains the solar neutrino deficit, the atmospheric neutrino anomaly and the LSND experiment*,*Phys. Rev.***D 52**(1995) 6595 [hep-ph/9505359] [INSPIRE]. - [6]M. Pospelov, A. Ritz and M.B. Voloshin,
*Secluded WIMP Dark Matter*,*Phys. Lett.***B 662**(2008) 53 [arXiv:0711.4866] [INSPIRE]. - [7]N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer and N. Weiner,
*A Theory of Dark Matter*,*Phys. Rev.***D 79**(2009) 015014 [arXiv:0810.0713] [INSPIRE]. - [8]J. Erler, P. Langacker, S. Munir and E. Rojas,
*Improved Constraints on Z-prime Bosons from Electroweak Precision Data*,*JHEP***08**(2009) 017 [arXiv:0906.2435] [INSPIRE].ADSCrossRefGoogle Scholar - [9]C.-R. Chen, F. Takahashi and T.T. Yanagida,
*Gamma rays and positrons from a decaying hidden gauge boson*,*Phys. Lett.***B 671**(2009) 71 [arXiv:0809.0792] [INSPIRE]. - [10]K. Petraki and R.R. Volkas,
*Review of asymmetric dark matter*,*Int. J. Mod. Phys.***A 28**(2013) 1330028 [arXiv:1305.4939] [INSPIRE]. - [11]R. Foot and S. Vagnozzi,
*Solving the small-scale structure puzzles with dissipative dark matter*,*JCAP***07**(2016) 013 [arXiv:1602.02467] [INSPIRE].ADSCrossRefGoogle Scholar - [12]P.-H. Gu and X.-G. He,
*Realistic model for a fifth force explaining anomaly in*^{8}*Be*^{∗}→^{8}*Be e*^{+}*e*^{−}*Decay*,*Nucl. Phys.***B 919**(2017) 209 [arXiv:1606.05171] [INSPIRE]. - [13]C.-F. Chang,
*Hidden Photon Compton and Bremsstrahlung in White Dwarf Anomalous Cooling and Luminosity Functions*, arXiv:1607.03347 [INSPIRE]. - [14]M. Cirelli, P. Panci, K. Petraki, F. Sala and M. Taoso,
*Dark Matter’s secret liaisons: phenomenology of a dark*U(1)*sector with bound states*,*JCAP***05**(2017) 036 [arXiv:1612.07295] [INSPIRE].ADSCrossRefGoogle Scholar - [15]J.D. Bjorken, R. Essig, P. Schuster and N. Toro,
*New Fixed-Target Experiments to Search for Dark Gauge Forces*,*Phys. Rev.***D 80**(2009) 075018 [arXiv:0906.0580] [INSPIRE]. - [16]H. Davoudiasl, H.-S. Lee and W.J. Marciano,
*Muon Anomaly and Dark Parity Violation*,*Phys. Rev. Lett.***109**(2012) 031802 [arXiv:1205.2709] [INSPIRE]. - [17]SHiP collaboration, M. Anelli et al.,
*A facility to Search for Hidden Particles (SHiP) at the CERN SPS*, arXiv:1504.04956 [INSPIRE]. - [18]P. Ilten, Y. Soreq, J. Thaler, M. Williams and W. Xue,
*Proposed Inclusive Dark Photon Search at LHCb*,*Phys. Rev. Lett.***116**(2016) 251803 [arXiv:1603.08926] [INSPIRE].ADSCrossRefGoogle Scholar - [19]LHCb collaboration,
*Search for Dark Photons Produced in*13*TeV pp Collisions*,*Phys. Rev. Lett.***120**(2018) 061801 [arXiv:1710.02867] [INSPIRE]. - [20]N. Blinov, E. Izaguirre and B. Shuve,
*Rare Z Boson Decays to a Hidden Sector*,*Phys. Rev.***D 97**(2018) 015009 [arXiv:1710.07635] [INSPIRE]. - [21]
- [22]M. He, X.-G. He and C.-K. Huang,
*Dark Photon Search at A Circular e*^{+}*e*^{−}*Collider*,*Int. J. Mod. Phys.***A 32**(2017) 1750138 [arXiv:1701.08614] [INSPIRE]. - [23]BaBar collaboration, J.P. Lees et al.,
*Search for a Dark Photon in e*^{+}*e*^{−}*Collisions at BaBar*,*Phys. Rev. Lett.***113**(2014) 201801 [arXiv:1406.2980] [INSPIRE]. - [24]J. Liu, X.-P. Wang and F. Yu,
*A Tale of Two Portals: Testing Light, Hidden New Physics at Future e*^{+}*e*^{−}*Colliders*,*JHEP***06**(2017) 077 [arXiv:1704.00730] [INSPIRE]. - [25]M. Karliner, M. Low, J.L. Rosner and L.-T. Wang,
*Radiative return capabilities of a high-energy, high-luminosity e*^{+}*e*^{−}*collider*,*Phys. Rev.***D 92**(2015) 035010 [arXiv:1503.07209] [INSPIRE]. - [26]ATLAS collaboration,
*Search for new high-mass phenomena in the dilepton final state using 36 fb*^{−1}*of proton-proton collision data at*\( \sqrt{s}=13 \)*TeV with the ATLAS detector*,*JHEP***10**(2017) 182 [arXiv:1707.02424] [INSPIRE]. - [27]F.A. Berends, G.J.H. Burgers and W.L. van Neerven,
*QED Radiative Corrections to the Reaction e*^{+}*e*^{−}→*Zγ*,*Phys. Lett.***B 177**(1986) 191 [INSPIRE]. - [28]V. Barger, P. Langacker and H.-S. Lee,
*Six-lepton Z-prime resonance at the LHC*,*Phys. Rev. Lett.***103**(2009) 251802 [arXiv:0909.2641] [INSPIRE].ADSCrossRefGoogle Scholar - [29]G. Altarelli, B. Mele and M. Ruiz-Altaba,
*Searching for New Heavy Vector Bosons in pp Colliders*,*Z. Phys.***C 45**(1989) 109 [*Erratum ibid.***C 47**(1990) 676] [INSPIRE]. - [30]D. Curtin, R. Essig, S. Gori and J. Shelton,
*Illuminating Dark Photons with High-Energy Colliders*,*JHEP***02**(2015) 157 [arXiv:1412.0018] [INSPIRE].ADSCrossRefGoogle Scholar - [31]CEPC-SPPC Study Group,
*CEPC-SPPC Preliminary Conceptual Design Report. 1. Physics and Detector*, [http://cepc.ihep.ac.cn/preCDR/volume.html] [INSPIRE]. - [32]TLEP Design Study Working Group collaboration, M. Bicer et al.,
*First Look at the Physics Case of TLEP*,*JHEP***01**(2014) 164 [arXiv:1308.6176] [INSPIRE]. - [33]A. Blondel, P. Janot, K. Oide, D. Shatilov and F. Zimmermann,
*FCC-ee parameter update*, in*FCC-ee polarization workshop*, https://indico.cern.ch/event/669194/attachments/1542823/2420244/FCC-ee_parameter_update_-_6_October_2017.pdf. - [34]H. Baer et al.,
*The International Linear Collider Technical Design Report — Volume 2: Physics*, arXiv:1306.6352 [INSPIRE]. - [35]
- [36]K. Fujii et al.,
*Physics Case for the 250 GeV Stage of the International Linear Collider*, arXiv:1710.07621 [INSPIRE]. - [37]J. Alwall et al.,
*The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations*,*JHEP***07**(2014)079 [arXiv:1405.0301] [INSPIRE]. - [38]T. Sjöstrand, S. Mrenna and P.Z. Skands,
*PYTHIA 6.4 Physics and Manual*,*JHEP***05**(2006) 026 [hep-ph/0603175] [INSPIRE]. - [39]DELPHES 3 collaboration, J. de Favereau et al.,
*DELPHES 3, A modular framework for fast simulation of a generic collider experiment*,*JHEP***02**(2014) 057 [arXiv:1307.6346] [INSPIRE]. - [40]D. Yu, M. Ruan, V. Boudry and H. Videau,
*Lepton identification at particle flow oriented detector for the future e*^{+}*e*^{−}*Higgs factories*,*Eur. Phys. J.***C 77**(2017) 591 [arXiv:1701.07542] [INSPIRE]. - [41]Z. Chen et al.,
*Cross Section and Higgs Mass Measurement with Higgsstrahlung at the CEPC*,*Chin. Phys.***C 41**(2017) 023003 [arXiv:1601.05352] [INSPIRE]. - [42]O. Cerri, M. de Gruttola, M. Pierini, A. Podo and G. Rolandi,
*Study the effect of beam energy spread and detector resolution on the search for Higgs boson decays to invisible particles at a future e*^{+}*e*^{−}*circular collider*,*Eur. Phys. J.***C 77**(2017) 116 [arXiv:1605.00100] [INSPIRE]. - [43]Linear Collider ILD Concept Group collaboration, T. Abe et al.,
*The International Large Detector: Letter of Intent*, arXiv:1006.3396 [INSPIRE]. - [44]M.-S. Chen and P.M. Zerwas,
*Equivalent-Particle Approximations in electron and Photon Processes of Higher Order QED*,*Phys. Rev.***D 12**(1975) 187 [INSPIRE]. - [45]I. Hoenig, G. Samach and D. Tucker-Smith,
*Searching for dilepton resonances below the Z mass at the LHC*,*Phys. Rev.***D 90**(2014) 075016 [arXiv:1408.1075] [INSPIRE]. - [46]CMS collaboration,
*Measurement of the differential and double-differential Drell-Yan cross sections in proton-proton collisions at*\( \sqrt{s}=7 \)*TeV*,*JHEP***12**(2013) 030 [arXiv:1310.7291] [INSPIRE]. - [47]J.M. Cline, G. Dupuis, Z. Liu and W. Xue,
*The windows for kinetically mixed Z’-mediated dark matter and the galactic center gamma ray excess*,*JHEP***08**(2014) 131 [arXiv:1405.7691] [INSPIRE].ADSCrossRefGoogle Scholar - [48]ATLAS collaboration,
*Search for high-mass dilepton resonances in*20*f b*^{−1}*of pp collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS experiment*, ATLAS-CONF-2013-017 (2013). - [49]ATLAS collaboration,
*Search for high-mass dilepton resonances in pp collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS detector*,*Phys. Rev.***D 90**(2014)052005 [arXiv:1405.4123] [INSPIRE]. - [50]B. Fuks and R. Ruiz,
*A comprehensive framework for studying W*^{′}*and Z*^{′}*bosons at hadron colliders with automated jet veto resummation*,*JHEP***05**(2017) 032 [arXiv:1701.05263] [INSPIRE]. - [51]A. Hook, E. Izaguirre and J.G. Wacker,
*Model Independent Bounds on Kinetic Mixing*,*Adv. High Energy Phys.***2011**(2011) 859762 [arXiv:1006.0973] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar - [52]J. Liu, L.-T. Wang, X.-P. Wang and W. Xue,
*Exposing Dark Sector with Future Z-Factories*, arXiv:1712.07237 [INSPIRE]. - [53]I. Chakraborty, S. Mondal and B. Mukhopadhyaya,
*Lepton flavor violating Higgs boson decay at e*^{+}*e*^{−}*colliders*,*Phys. Rev.***D 96**(2017) 115020 [arXiv:1709.08112] [INSPIRE].