# Leptophilic dark matter from gauged lepton number: phenomenology and gravitational wave signatures

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## Abstract

New gauge symmetries often appear in theories beyond the Standard Model. Here we study a model where lepton number is promoted to a gauge symmetry. Anomaly cancellation requires the introduction of additional leptons, the lightest of which is a natural leptophilic dark matter candidate. We perform a comprehensive study of both collider and dark matter phenomenology. Furthermore we find that the model exhibits a first order lepton number breaking phase transition in large regions of parameter space. The corresponding gravitational wave signal is computed, and its detectability at *LISA* and other future GW detectors assessed. Finally we comment on the complementarity of dark matter, collider and gravitational wave observables, and on the potential reach of future colliders.

## Keywords

Beyond Standard Model Cosmology of Theories beyond the SM## Notes

### **Open Access**

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## References

- [1]P.J. Fox and E. Poppitz,
*Leptophilic dark matter*,*Phys. Rev.***D 79**(2009) 083528 [arXiv:0811.0399] [INSPIRE].ADSGoogle Scholar - [2]S. Chang, R. Edezhath, J. Hutchinson and M. Luty,
*Leptophilic effective WIMPs*,*Phys. Rev.***D 90**(2014) 015011 [arXiv:1402.7358] [INSPIRE].ADSGoogle Scholar - [3]N.F. Bell, Y. Cai, R.K. Leane and A.D. Medina,
*Leptophilic dark matter with Z*′*interactions*,*Phys. Rev.***D 90**(2014) 035027 [arXiv:1407.3001] [INSPIRE].ADSGoogle Scholar - [4]P. Schwaller, T.M.P. Tait and R. Vega-Morales,
*Dark matter and vectorlike leptons from gauged lepton number*,*Phys. Rev.***D 88**(2013) 035001 [arXiv:1305.1108] [INSPIRE].ADSGoogle Scholar - [5]R. Foot, G.C. Joshi and H. Lew,
*Gauged baryon and lepton numbers*,*Phys. Rev.***D 40**(1989) 2487 [INSPIRE].ADSGoogle Scholar - [6]P. Fileviez Perez and M.B. Wise,
*Baryon and lepton number as local gauge symmetries*,*Phys. Rev.***D 82**(2010) 011901 [*Erratum ibid.***D 82**(2010) 079901] [arXiv:1002.1754] [INSPIRE]. - [7]T.R. Dulaney, P. Fileviez Perez and M.B. Wise,
*Dark matter, baryon asymmetry and spontaneous B and L breaking*,*Phys. Rev.***D 83**(2011) 023520 [arXiv:1005.0617] [INSPIRE].ADSGoogle Scholar - [8]P. Fileviez Perez and M.B. Wise,
*Breaking local baryon and lepton number at the TeV scale*,*JHEP***08**(2011) 068 [arXiv:1106.0343] [INSPIRE].CrossRefzbMATHGoogle Scholar - [9]M. Duerr, P. Fileviez Perez and M.B. Wise,
*Gauge theory for baryon and lepton numbers with leptoquarks*,*Phys. Rev. Lett.***110**(2013) 231801 [arXiv:1304.0576] [INSPIRE].ADSCrossRefGoogle Scholar - [10]W. Chao,
*Pure leptonic gauge symmetry, neutrino masses and dark matter*,*Phys. Lett.***B 695**(2011) 157 [arXiv:1005.1024] [INSPIRE].ADSCrossRefGoogle Scholar - [11]W.-F. Chang and J.N. Ng,
*Study of gauged lepton symmetry signatures at colliders*,*Phys. Rev.***D 98**(2018) 035015 [arXiv:1805.10382] [INSPIRE].ADSGoogle Scholar - [12]W.-F. Chang and J.N. Ng,
*Alternative perspective on gauged lepton number and implications for collider physics*, arXiv:1808.08188 [INSPIRE]. - [13]P. Fileviez Perez, S. Ohmer and H.H. Patel,
*Minimal theory for lepto-baryons*,*Phys. Lett.***B 735**(2014) 283 [arXiv:1403.8029] [INSPIRE].ADSCrossRefGoogle Scholar - [14]S. Ohmer and H.H. Patel,
*Leptobaryons as Majorana dark matter*,*Phys. Rev.***D 92**(2015) 055020 [arXiv:1506.00954] [INSPIRE].ADSGoogle Scholar - [15]P. Agrawal, Z. Chacko and C.B. Verhaaren,
*Leptophilic dark matter and the anomalous magnetic moment of the muon*,*JHEP***08**(2014) 147 [arXiv:1402.7369] [INSPIRE].ADSCrossRefGoogle Scholar - [16]Y. Bai and J. Berger,
*Lepton portal dark matter*,*JHEP***08**(2014) 153 [arXiv:1402.6696] [INSPIRE].ADSCrossRefGoogle Scholar - [17]A. Freitas and S. Westhoff,
*Leptophilic dark matter in lepton interactions at LEP and ILC*,*JHEP***10**(2014) 116 [arXiv:1408.1959] [INSPIRE].ADSCrossRefGoogle Scholar - [18]H.-S. Lee,
*Muon g*− 2*anomaly and dark leptonic gauge boson*,*Phys. Rev.***D 90**(2014) 091702 [arXiv:1408.4256] [INSPIRE].ADSGoogle Scholar - [19]Q.-H. Cao, C.-R. Chen and T. Gong,
*Leptophilic dark matter confronts AMS-02 cosmic-ray positron flux*,*Chin. J. Phys.***55**(2017) 10 [arXiv:1409.7317] [INSPIRE].CrossRefGoogle Scholar - [20]J. Kile, A. Kobach and A. Soni,
*Lepton-flavored dark matter*,*Phys. Lett.***B 744**(2015) 330 [arXiv:1411.1407] [INSPIRE].ADSCrossRefGoogle Scholar - [21]A. Aranda, E. Jiménez and C.A. Vaquera-Araujo,
*Electroweak phase transition in a model with gauged lepton number*,*JHEP***01**(2015) 070 [arXiv:1410.7508] [INSPIRE].ADSCrossRefGoogle Scholar - [22]Y.S. Jeong, C.S. Kim and H.-S. Lee,
*Constraints on the*U(1)_{L}*gauge boson in a wide mass range*,*Int. J. Mod. Phys.***A 31**(2016) 1650059 [arXiv:1512.03179] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [23]L.A. Cavasonza et al.,
*Constraints on leptophilic dark matter from the AMS-02 experiment*,*Astrophys. J.***839**(2017) 36 [*Erratum ibid.***869**(2018) 89] [arXiv:1612.06634] [INSPIRE]. - [24]F. D’Eramo, B.J. Kavanagh and P. Panci,
*Probing leptophilic dark sectors with hadronic processes*,*Phys. Lett.***B 771**(2017) 339 [arXiv:1702.00016] [INSPIRE].ADSCrossRefGoogle Scholar - [25]S. Dutta, D. Sachdeva and B. Rawat,
*Signals of leptophilic dark matter at the ILC*,*Eur. Phys. J.***C 77**(2017) 639 [arXiv:1704.03994] [INSPIRE].ADSCrossRefGoogle Scholar - [26]G.H. Duan et al.,
*Simplified TeV leptophilic dark matter in light of DAMPE data*,*JHEP***02**(2018) 107 [arXiv:1711.11012] [INSPIRE].ADSCrossRefGoogle Scholar - [27]C.-Y. Chen, J. Kozaczuk and Y.-M. Zhong,
*Exploring leptophilic dark matter with NA64-μ*,*JHEP***10**(2018) 154 [arXiv:1807.03790] [INSPIRE].ADSGoogle Scholar - [28]B. Fornal, Y. Shirman, T.M.P. Tait and J.R. West,
*Asymmetric dark matter and baryogenesis from*SU(2)_{ℓ},*Phys. Rev.***D 96**(2017) 035001 [arXiv:1703.00199] [INSPIRE].ADSGoogle Scholar - [29]P. Schwaller,
*Gravitational waves from a dark phase transition*,*Phys. Rev. Lett.***115**(2015) 181101 [arXiv:1504.07263] [INSPIRE].ADSCrossRefGoogle Scholar - [30]J. Jaeckel, V.V. Khoze and M. Spannowsky,
*Hearing the signal of dark sectors with gravitational wave detectors*,*Phys. Rev.***D 94**(2016) 103519 [arXiv:1602.03901] [INSPIRE].ADSGoogle Scholar - [31]M. Chala, G. Nardini and I. Sobolev,
*Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures*,*Phys. Rev.***D 94**(2016) 055006 [arXiv:1605.08663] [INSPIRE].ADSGoogle Scholar - [32]A. Addazi,
*Limiting first order phase transitions in dark gauge sectors from gravitational waves experiments*,*Mod. Phys. Lett.***A 32**(2017) 1750049 [arXiv:1607.08057] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar - [33]I. Baldes,
*Gravitational waves from the asymmetric-dark-matter generating phase transition*,*JCAP***05**(2017) 028 [arXiv:1702.02117] [INSPIRE].ADSGoogle Scholar - [34]A. Addazi and A. Marciano,
*Gravitational waves from dark first order phase transitions and dark photons*,*Chin. Phys.***C 42**(2018) 023107 [arXiv:1703.03248] [INSPIRE].ADSCrossRefGoogle Scholar - [35]K. Tsumura, M. Yamada and Y. Yamaguchi,
*Gravitational wave from dark sector with dark pion*,*JCAP***07**(2017) 044 [arXiv:1704.00219] [INSPIRE].ADSCrossRefGoogle Scholar - [36]M. Aoki, H. Goto and J. Kubo,
*Gravitational waves from hidden QCD phase transition*,*Phys. Rev.***D 96**(2017) 075045 [arXiv:1709.07572] [INSPIRE].ADSMathSciNetGoogle Scholar - [37]D. Croon, V. Sanz and G. White,
*Model discrimination in gravitational wave spectra from dark phase transitions*,*JHEP***08**(2018) 203 [arXiv:1806.02332] [INSPIRE].ADSCrossRefGoogle Scholar - [38]I. Baldes and C. Garcia-Cely,
*Strong gravitational radiation from a simple dark matter model*, arXiv:1809.01198 [INSPIRE]. - [39]M. Breitbach, J. Kopp, E. Madge, T. Opferkuch and P. Schwaller,
*Dark, cold and noisy: constraining secluded hidden sectors with gravitational waves*, arXiv:1811.11175 [INSPIRE]. - [40]K.S. Babu, C.F. Kolda and J. March-Russell,
*Implications of generalized Z-Z*′*mixing*,*Phys. Rev.***D 57**(1998) 6788 [hep-ph/9710441] [INSPIRE]. - [41]A. Alloul et al.,
*FeynRules 2.0 — A complete toolbox for tree-level phenomenology*,*Comput. Phys. Commun.***185**(2014) 2250 [arXiv:1310.1921] [INSPIRE]. - [42]G. Bélanger et al.,
*MicrOMEGAs5.0: freeze-in*,*Comput. Phys. Commun.***231**(2018) 173 [arXiv:1801.03509] [INSPIRE]. - [43]Planck collaboration,
*Planck 2015 results. XIII. Cosmological parameters*,*Astron. Astrophys.***594**(2016) A13 [arXiv:1502.01589] [INSPIRE]. - [44]XENON collaboration,
*Dark matter search results from a one ton-year exposure of XENON1T*,*Phys. Rev. Lett.***121**(2018) 111302 [arXiv:1805.12562] [INSPIRE]. - [45]LUX-ZEPLIN collaboration,
*Projected WIMP sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment*, arXiv:1802.06039 [INSPIRE]. - [46]DARWIN collaboration,
*DARWIN: towards the ultimate dark matter detector*,*JCAP***11**(2016) 017 [arXiv:1606.07001] [INSPIRE]. - [47]CTA collaboration,
*Prospects for indirect dark matter searches with the Cherenkov Telescope Array (CTA)*,*PoS***ICRC2015**(2016) 1203 [arXiv:1508.06128] [INSPIRE]. - [48]MAGIC, Fermi-LAT collaboration,
*Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies*,*JCAP***02**(2016) 039 [arXiv:1601.06590] [INSPIRE]. - [49]H.E.S.S. collaboration,
*Search for dark matter annihilations towards the inner Galactic halo from 10 years of observations with H.E.S.S*,*Phys. Rev. Lett.***117**(2016) 111301 [arXiv:1607.08142] [INSPIRE]. - [50]Fermi-LAT collaboration,
*Updated search for spectral lines from Galactic dark matter interactions with pass 8 data from the Fermi Large Area Telescope*,*Phys. Rev.***D 91**(2015) 122002 [arXiv:1506.00013] [INSPIRE]. - [51]HESS collaboration,
*Dark matter gamma-ray line searches toward the Galactic Center halo with H.E.S.S. I*, PoS(ICRC2017)893 [arXiv:1708.08358] [INSPIRE]. - [52]Fermi-LAT collaboration,
*Sensitivity projections for dark matter searches with the Fermi Large Area Telescope*,*Phys. Rept.***636**(2016) 1 [arXiv:1605.02016] [INSPIRE]. - [53]A. Olivares-Del Campo, C. Bœhm, S. Palomares-Ruiz and S. Pascoli,
*Dark matter-neutrino interactions through the lens of their cosmological implications*,*Phys. Rev.***D 97**(2018) 075039 [arXiv:1711.05283] [INSPIRE].ADSGoogle Scholar - [54]I. Esteban et al.,
*Updated constraints on non-standard interactions from global analysis of oscillation data*,*JHEP***08**(2018) 180 [arXiv:1805.04530] [INSPIRE].ADSCrossRefGoogle Scholar - [55]M. Carena, A. Daleo, B.A. Dobrescu and T.M.P. Tait,
*Z*′*gauge bosons at the Tevatron*,*Phys. Rev.***D 70**(2004) 093009 [hep-ph/0408098] [INSPIRE]. - [56]Particle Data Group collaboration,
*Review of particle physics*,*Chin. Phys.***C40**(2016) 100001.Google Scholar - [57]ALEPH, DELPHI, L3, OPAL, LEP Electroweak collaboration,
*Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP*,*Phys. Rept.***532**(2013) 119 [arXiv:1302.3415] [INSPIRE]. - [58]A. Belyaev, N.D. Christensen and A. Pukhov,
*CalcHEP 3.4 for collider physics within and beyond the Standard Model*,*Comput. Phys. Commun.***184**(2013) 1729 [arXiv:1207.6082] [INSPIRE]. - [59]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]. - [60]CMS collaboration,
*Search for high-mass resonances in dilepton final states in proton-proton collisions at*\( \sqrt{s}=13 \)*TeV*,*JHEP***06**(2018) 120 [arXiv:1803.06292] [INSPIRE]. - [61]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 - [62]CMS collaboration,
*Combined measurements of the Higgs boson’s couplings at*\( \sqrt{s}=13 \)*TeV*, CMS-PAS-HIG-17-031 (2017). - [63]A. Djouadi,
*The Anatomy of electro-weak symmetry breaking. I: the Higgs boson in the standard model*,*Phys. Rept.***457**(2008) 1 [hep-ph/0503172] [INSPIRE]. - [64]P. Bechtle et al.,
*HiggsBounds-4: improved tests of extended Higgs sectors against exclusion bounds from LEP, the Tevatron and the LHC*,*Eur. Phys. J.***C 74**(2014) 2693 [arXiv:1311.0055] [INSPIRE].ADSCrossRefGoogle Scholar - [65]ALEPH, DELPHI, L3, OPAL, LEP Working Group for Higgs Boson Searches collaboration,
*Search for neutral MSSM Higgs bosons at LEP*,*Eur. Phys. J.***C 47**(2006) 547 [hep-ex/0602042] [INSPIRE]. - [66]OPAL collaboration,
*Decay mode independent searches for new scalar bosons with the OPAL detector at LEP*,*Eur. Phys. J.***C 27**(2003) 311 [hep-ex/0206022] [INSPIRE]. - [67]CMS collaboration,
*Update on the search for the standard model Higgs boson in pp collisions at the LHC decaying to W*^{+}*W*^{−}*in the fully leptonic final state*, CMS-PAS-HIG-13-003 (2013). - [68]CMS collaboration,
*Properties of the Higgs-like boson in the decay H*→*ZZ*→ 4*ℓ in pp collisions at*\( \sqrt{s}=7 \)*and*8*TeV*, CMS-PAS-HIG-13-002 (2013). - [69]CMS collaboration,
*Search for a Higgs boson in the mass range from 145 to 1000 GeV decaying to a pair of W or Z bosons*,*JHEP***10**(2015) 144 [arXiv:1504.00936] [INSPIRE]. - [70]ATLAS collaboration,
*Search for an additional, heavy Higgs boson in the H*→*ZZ decay channel at*\( \sqrt{s}=8 \)*TeV in pp collision data with the ATLAS detector*,*Eur. Phys. J.***C 76**(2016) 45 [arXiv:1507.05930] [INSPIRE]. - [71]CMS collaboration,
*Combination of standard model Higgs boson searches and measurements of the properties of the new boson with a mass near*125*GeV*, CMS-PAS-HIG-12-045 (2012). - [72]ATLAS collaboration,
*Measurement of the Higgs boson coupling properties in the H*→*ZZ*^{*}→ 4*ℓ decay channel at*\( \sqrt{s}=13 \)*TeV with the ATLAS detector*,*JHEP***03**(2018) 095 [arXiv:1712.02304] [INSPIRE]. - [73]ATLAS collaboration,
*Measurements of Higgs boson properties in the diphoton decay channel with*36*fb*^{−1}*of pp collision data at*\( \sqrt{s}=13 \)*TeV with the ATLAS detector*,*Phys. Rev.***D 98**(2018) 052005 [arXiv:1802.04146] [INSPIRE]. - [74]ATLAS, CMS collaboration,
*Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at*\( \sqrt{s}=7 \)*and*8*TeV*,*JHEP***08**(2016) 045 [arXiv:1606.02266] [INSPIRE]. - [75]L3 collaboration,
*Search for heavy neutral and charged leptons in e*^{+}*e*^{−}*annihilation at LEP*,*Phys. Lett.***B 517**(2001) 75 [hep-ex/0107015] [INSPIRE]. - [76]ATLAS collaboration,
*Search for electroweak production of supersymmetric particles in final states with two or three leptons at*\( \sqrt{s}=13 \)*TeV with the ATLAS detector*,*Eur. Phys. J.***C 78**(2018) 995 [arXiv:1803.02762] [INSPIRE]. - [77]CMS collaboration,
*Combined search for electroweak production of charginos and neutralinos in proton-proton collisions at*\( \sqrt{s}=13 \)*TeV*,*JHEP***03**(2018) 160 [arXiv:1801.03957] [INSPIRE]. - [78]C. Han et al.,
*Probing light higgsinos in natural SUSY from monojet signals at the LHC*,*JHEP***02**(2014) 049 [arXiv:1310.4274] [INSPIRE].ADSCrossRefGoogle Scholar - [79]P. Schwaller and J. Zurita,
*Compressed electroweakino spectra at the LHC*,*JHEP***03**(2014) 060 [arXiv:1312.7350] [INSPIRE].ADSCrossRefGoogle Scholar - [80]H. Baer, A. Mustafayev and X. Tata,
*Monojets and mono-photons from light higgsino pair production at LHC14*,*Phys. Rev.***D 89**(2014) 055007 [arXiv:1401.1162] [INSPIRE].ADSGoogle Scholar - [81]Z. Han, G.D. Kribs, A. Martin and A. Menon,
*Hunting quasidegenerate Higgsinos*,*Phys. Rev.***D 89**(2014) 075007 [arXiv:1401.1235] [INSPIRE].ADSGoogle Scholar - [82]M. Low and L.-T. Wang,
*Neutralino dark matter at*14*TeV and*100*TeV*,*JHEP***08**(2014) 161 [arXiv:1404.0682] [INSPIRE].ADSCrossRefGoogle Scholar - [83]R. Mahbubani, P. Schwaller and J. Zurita,
*Closing the window for compressed dark sectors with disappearing charged tracks*,*JHEP***06**(2017) 119 [*Erratum ibid.***10**(2017) 061] [arXiv:1703.05327] [INSPIRE]. - [84]M. D’Onofrio and K. Rummukainen,
*Standard model cross-over on the lattice*,*Phys. Rev.***D 93**(2016) 025003 [arXiv:1508.07161] [INSPIRE].ADSGoogle Scholar - [85]A.D. Sakharov,
*Violation of CP invariance, C asymmetry and baryon asymmetry of the universe*,*Pisma Zh. Eksp. Teor. Fiz.***5**(1967) 32 [INSPIRE].Google Scholar - [86]A.D. Linde,
*Decay of the false vacuum at finite temperature*,*Nucl. Phys.***B 216**(1983) 421 [*Erratum ibid.***B 223**(1983) 544] [INSPIRE]. - [87]M. Quirós,
*Finite temperature field theory and phase transitions*, in the proceedings of the*Summer School in High-energy physics and cosmology*, June 29–July 17, Trieste, Italy (1999), hep-ph/9901312 [INSPIRE]. - [88]C. Caprini et al.,
*Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions*,*JCAP***04**(2016) 001 [arXiv:1512.06239] [INSPIRE].ADSCrossRefGoogle Scholar - [89]L. Dolan and R. Jackiw,
*Symmetry behavior at finite temperature*,*Phys. Rev.***D 9**(1974) 3320 [INSPIRE].ADSGoogle Scholar - [90]D. Curtin, P. Meade and H. Ramani,
*Thermal resummation and phase transitions*,*Eur. Phys. J.***C 78**(2018) 787 [arXiv:1612.00466] [INSPIRE].ADSCrossRefGoogle Scholar - [91]S.R. Coleman and E.J. Weinberg,
*Radiative corrections as the origin of spontaneous symmetry breaking*,*Phys. Rev.***D 7**(1973) 1888 [INSPIRE].ADSGoogle Scholar - [92]C. Delaunay, C. Grojean and J.D. Wells,
*Dynamics of non-renormalizable electroweak symmetry breaking*,*JHEP***04**(2008) 029 [arXiv:0711.2511] [INSPIRE].ADSCrossRefGoogle Scholar - [93]C.L. Wainwright,
*CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields*,*Comput. Phys. Commun.***183**(2012) 2006 [arXiv:1109.4189] [INSPIRE].ADSCrossRefGoogle Scholar - [94]
- [95]L. Leitao and A. Megevand,
*Gravitational waves from a very strong electroweak phase transition*,*JCAP***05**(2016) 037 [arXiv:1512.08962] [INSPIRE].ADSCrossRefGoogle Scholar - [96]D.J. Weir,
*Gravitational waves from a first order electroweak phase transition: a brief review*,*Phil. Trans. Roy. Soc. Lond.***A 376**(2018) 20170126 [arXiv:1705.01783] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [97]C. Caprini and D.G. Figueroa,
*Cosmological backgrounds of gravitational waves*,*Class. Quant. Grav.***35**(2018) 163001 [arXiv:1801.04268] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [98]D. Bödeker and G.D. Moore,
*Can electroweak bubble walls run away?*,*JCAP***05**(2009) 009 [arXiv:0903.4099] [INSPIRE].CrossRefGoogle Scholar - [99]D. Bödeker and G.D. Moore,
*Electroweak bubble wall speed limit*,*JCAP***05**(2017) 025 [arXiv:1703.08215] [INSPIRE].MathSciNetCrossRefGoogle Scholar - [100]S.J. Huber and T. Konstandin,
*Gravitational wave production by collisions: more bubbles*,*JCAP***09**(2008) 022 [arXiv:0806.1828] [INSPIRE].ADSCrossRefGoogle Scholar - [101]M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir,
*Numerical simulations of acoustically generated gravitational waves at a first order phase transition*,*Phys. Rev.***D 92**(2015) 123009 [arXiv:1504.03291] [INSPIRE].ADSGoogle Scholar - [102]C. Caprini, R. Durrer and G. Servant,
*The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition*,*JCAP***12**(2009) 024 [arXiv:0909.0622] [INSPIRE].ADSCrossRefGoogle Scholar - [103]A. Kosowsky and M.S. Turner,
*Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions*,*Phys. Rev.***D 47**(1993) 4372 [astro-ph/9211004] [INSPIRE]. - [104]J.R. Espinosa, T. Konstandin, J.M. No and G. Servant,
*Energy budget of cosmological first-order phase transitions*,*JCAP***06**(2010) 028 [arXiv:1004.4187] [INSPIRE].ADSCrossRefGoogle Scholar - [105]P. Binetruy, A. Bohe, C. Caprini and J.-F. Dufaux,
*Cosmological backgrounds of gravitational waves and eLISA/NGO: phase transitions, cosmic strings and other sources*,*JCAP***06**(2012) 027 [arXiv:1201.0983] [INSPIRE].ADSCrossRefGoogle Scholar - [106]S. Isoyama, H. Nakano and T. Nakamura,
*Multiband gravitational-wave astronomy: observing binary inspirals with a deciHertz detector, B-DECIGO*,*PTEP***2018**(2018) 073E01 [arXiv:1802.06977] [INSPIRE]. - [107]N. Seto, S. Kawamura and T. Nakamura,
*Possibility of direct measurement of the acceleration of the universe using*0*.*1*Hz band laser interferometer gravitational wave antenna in space*,*Phys. Rev. Lett.***87**(2001) 221103 [astro-ph/0108011] [INSPIRE]. - [108]J. Crowder and N.J. Cornish,
*Beyond LISA: exploring future gravitational wave missions*,*Phys. Rev.***D 72**(2005) 083005 [gr-qc/0506015] [INSPIRE]. - [109]
- [110]E. Thrane and J.D. Romano,
*Sensitivity curves for searches for gravitational-wave backgrounds*,*Phys. Rev.***D 88**(2013) 124032 [arXiv:1310.5300] [INSPIRE].ADSGoogle Scholar - [111]T. Robson, N. Cornish and C. Liu,
*The construction and use of LISA sensitivity curves*, arXiv:1803.01944 [INSPIRE]. - [112]K. Yagi, N. Tanahashi and T. Tanaka,
*Probing the size of extra dimension with gravitational wave astronomy*,*Phys. Rev.***D 83**(2011) 084036 [arXiv:1101.4997] [INSPIRE].ADSGoogle Scholar - [113]K. Yagi,
*Scientific potential of DECIGO pathfinder and testing GR with space-borne gravitational wave interferometers*,*Int. J. Mod. Phys.***D 22**(2013) 1341013 [arXiv:1302.2388] [INSPIRE].ADSCrossRefGoogle Scholar - [114]J. Ellis,
*TikZ-Feynman: Feynman diagrams with TikZ*,*Comput. Phys. Commun.***210**(2017) 103 [arXiv:1601.05437] [INSPIRE].ADSCrossRefGoogle Scholar - [115]
- [116]G. Passarino and M.J.G. Veltman,
*One loop corrections for e*^{+}*e*^{−}*annihilation into μ*^{+}*μ*^{−}*in the Weinberg model*,*Nucl. Phys.***B 160**(1979) 151 [INSPIRE].ADSCrossRefGoogle Scholar - [117]R. Mertig, M. Böhm and A. Denner,
*FEYN CALC: computer algebraic calculation of Feynman amplitudes*,*Comput. Phys. Commun.***64**(1991) 345 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [118]V. Shtabovenko, R. Mertig and F. Orellana,
*New developments in FeynCalc 9.0*,*Comput. Phys. Commun.***207**(2016) 432 [arXiv:1601.01167] [INSPIRE]. - [119]T. Hahn and M. Pérez-Victoria,
*Automatized one loop calculations in four-dimensions and D-dimensions*,*Comput. Phys. Commun.***118**(1999) 153 [hep-ph/9807565] [INSPIRE]. - [120]G.J. van Oldenborgh and J.A.M. Vermaseren,
*New algorithms for one loop integrals*,*Z. Phys.***C 46**(1990) 425 [INSPIRE].MathSciNetGoogle Scholar - [121]
- [122]A. Denner,
*Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200*,*Fortsch. Phys.***41**(1993) 307 [arXiv:0709.1075] [INSPIRE].ADSGoogle Scholar - [123]T. Konstandin, G. Nardini and I. Rues,
*From Boltzmann equations to steady wall velocities*,*JCAP***09**(2014) 028 [arXiv:1407.3132] [INSPIRE].ADSCrossRefGoogle Scholar - [124]G.C. Dorsch, S.J. Huber and T. Konstandin,
*Bubble wall velocities in the Standard Model and beyond*,*JCAP***12**(2018) 034 [arXiv:1809.04907] [INSPIRE].ADSCrossRefGoogle Scholar - [125]P.J. Steinhardt,
*Relativistic detonation waves and bubble growth in false vacuum decay*,*Phys. Rev.***D 25**(1982) 2074 [INSPIRE].ADSGoogle Scholar - [126]