# Effective field theory, electric dipole moments and electroweak baryogenesis

- 95 Downloads
- 6 Citations

## Abstract

Negative searches for permanent electric dipole moments (EDMs) heavily constrain models of baryogenesis utilising various higher dimensional charge and parity violating (CPV) operators. Using effective field theory, we create a model independent connection between these EDM constraints and the baryon asymmetry of the universe (BAU) produced during a strongly first order electroweak phase transition. The thermal aspects of the high scale physics driving the phase transition are paramaterised by the usual kink solution for the bubble wall profile. We find that operators involving derivatives of the Higgs field yield CPV contributions to the BAU containing derivatives of the Higgs vacuum expectation value (vev), while non-derivative operators lack such contributions. Consequently, derivative operators cannot be eliminated in terms of non-derivative operators (via the equations of motion) if one is agnostic to the new physics that leads to the phase transition. Thus, we re-classify the independent dimension six operators, restricting ourselves to third generation quarks, gauge bosons and the Higgs. Finally, we calculate the BAU (as a function of the bubble wall width and the cutoff) for a derivative and a non-derivative operator, and relate it to the EDM constraints.

## Keywords

Cosmology of Theories beyond the SM CP violation Effective field theories Thermal Field Theory## 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]ATLAS collaboration,
*Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC*,*Phys. Lett.***B 716**(2012) 1 [arXiv:1207.7214] [INSPIRE]. - [2]CMS collaboration,
*Observation of a new boson at a mass of*125*GeV with the CMS experiment at the LHC*,*Phys. Lett.***B 716**(2012) 30 [arXiv:1207.7235] [INSPIRE]. - [3]G.A. White,
*A pedagogical introduction to electroweak baryogenesis*, IOP Concise Physics, Morgan & Claypool, (2016) [INSPIRE]. - [4]ATLAS and CMS collaborations,
*Combined measurement of the Higgs boson mass in pp collisions at*\( \sqrt{s}=7 \)*and*8*TeV with the ATLAS and CMS experiments*,*Phys. Rev. Lett.***114**(2015) 191803 [arXiv:1503.07589] [INSPIRE]. - [5]K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M.E. Shaposhnikov,
*The universality class of the electroweak theory*,*Nucl. Phys.***B 532**(1998) 283 [hep-lat/9805013] [INSPIRE]. - [6]M.B. Gavela, P. Hernández, J. Orloff and O. Pene,
*Standard Model CP-violation and baryon asymmetry*,*Mod. Phys. Lett.***A 9**(1994) 795 [hep-ph/9312215] [INSPIRE]. - [7]T. Konstandin, T. Prokopec and M.G. Schmidt,
*Axial currents from CKM matrix CP-violation and electroweak baryogenesis*,*Nucl. Phys.***B 679**(2004) 246 [hep-ph/0309291] [INSPIRE]. - [8]Planck collaboration, P.A.R. Ade et al.,
*Planck*2015*results. XIII. Cosmological parameters*,*Astron. Astrophys.***594**(2016) A13 [arXiv:1502.01589] [INSPIRE]. - [9]A. Kobakhidze, L. Wu and J. Yue,
*Electroweak baryogenesis with anomalous Higgs couplings*,*JHEP***04**(2016) 011 [arXiv:1512.08922] [INSPIRE].ADSGoogle Scholar - [10]D. Bödeker, L. Fromme, S.J. Huber and M. Seniuch,
*The baryon asymmetry in the Standard Model with a low cut-off*,*JHEP***02**(2005) 026 [hep-ph/0412366] [INSPIRE]. - [11]L. Fromme and S.J. Huber,
*Top transport in electroweak baryogenesis*,*JHEP***03**(2007) 049 [hep-ph/0604159] [INSPIRE]. - [12]F.P. Huang, P.-H. Gu, P.-F. Yin, Z.-H. Yu and X. Zhang,
*Testing the electroweak phase transition and electroweak baryogenesis at the LHC and a circular electron-positron collider*,*Phys. Rev.***D 93**(2016) 103515 [arXiv:1511.03969] [INSPIRE].ADSGoogle Scholar - [13]J. Engel, M.J. Ramsey-Musolf and U. van Kolck,
*Electric dipole moments of nucleons, nuclei and atoms: the Standard Model and beyond*,*Prog. Part. Nucl. Phys.***71**(2013) 21 [arXiv:1303.2371] [INSPIRE].ADSCrossRefGoogle Scholar - [14]T. Chupp and M. Ramsey-Musolf,
*Electric dipole moments: a global analysis*,*Phys. Rev.***C 91**(2015) 035502 [arXiv:1407.1064] [INSPIRE].ADSGoogle Scholar - [15]Y.T. Chien, V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti,
*Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions*,*JHEP***02**(2016) 011 [arXiv:1510.00725] [INSPIRE].ADSCrossRefGoogle Scholar - [16]J. Brod, U. Haisch and J. Zupan,
*Constraints on CP-violating Higgs couplings to the third generation*,*JHEP***11**(2013) 180 [arXiv:1310.1385] [INSPIRE].ADSCrossRefGoogle Scholar - [17]A. Noble and M. Perelstein,
*Higgs self-coupling as a probe of electroweak phase transition*,*Phys. Rev.***D 78**(2008) 063518 [arXiv:0711.3018] [INSPIRE].ADSGoogle Scholar - [18]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 - [19]V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti,
*Is there room for CP-violation in the top-Higgs sector?*,*Phys. Rev.***D 94**(2016) 016002 [arXiv:1603.03049] [INSPIRE].ADSGoogle Scholar - [20]V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti,
*Constraining the top-Higgs sector of the Standard Model effective field theory*,*Phys. Rev.***D 94**(2016) 034031 [arXiv:1605.04311] [INSPIRE].ADSGoogle Scholar - [21]C. Grojean, G. Servant and J.D. Wells,
*First-order electroweak phase transition in the Standard Model with a low cutoff*,*Phys. Rev.***D 71**(2005) 036001 [hep-ph/0407019] [INSPIRE]. - [22]K. Fuyuto, J. Hisano and E. Senaha,
*Toward verification of electroweak baryogenesis by electric dipole moments*,*Phys. Lett.***B 755**(2016) 491 [arXiv:1510.04485] [INSPIRE].ADSCrossRefGoogle Scholar - [23]S.J. Huber, M. Pospelov and A. Ritz,
*Electric dipole moment constraints on minimal electroweak baryogenesis*,*Phys. Rev.***D 75**(2007) 036006 [hep-ph/0610003] [INSPIRE]. - [24]J. Shu and Y. Zhang,
*Impact of a CP-violating Higgs sector: from LHC to baryogenesis*,*Phys. Rev. Lett.***111**(2013) 091801 [arXiv:1304.0773] [INSPIRE].ADSCrossRefGoogle Scholar - [25]X. Zhang and B.L. Young,
*Effective Lagrangian approach to electroweak baryogenesis: Higgs mass limit and electric dipole moments of fermion*,*Phys. Rev.***D 49**(1994) 563 [hep-ph/9309269] [INSPIRE]. - [26]F.P. Huang and C.S. Li,
*Electroweak baryogenesis in the framework of the effective field theory*,*Phys. Rev.***D 92**(2015) 075014 [arXiv:1507.08168] [INSPIRE].ADSGoogle Scholar - [27]P.H. Damgaard, A. Haarr, D. O’Connell and A. Tranberg,
*Effective field theory and electroweak baryogenesis in the singlet-extended Standard Model*,*JHEP***02**(2016) 107 [arXiv:1512.01963] [INSPIRE].ADSCrossRefGoogle Scholar - [28]N. Bernal, F.-X. Josse-Michaux and L. Ubaldi,
*Phenomenology of WIMPy baryogenesis models*,*JCAP***01**(2013) 034 [arXiv:1210.0094] [INSPIRE].ADSCrossRefGoogle Scholar - [29]C. Zhang, N. Greiner and S. Willenbrock,
*Constraints on non-standard top quark couplings*,*Phys. Rev.***D 86**(2012) 014024 [arXiv:1201.6670] [INSPIRE].ADSGoogle Scholar - [30]J. Herrero-Garcia, N. Rius and A. Santamaria,
*Higgs lepton flavour violation: UV completions and connection to neutrino masses*,*JHEP***11**(2016) 084 [arXiv:1605.06091] [INSPIRE].ADSCrossRefGoogle Scholar - [31]J.M. Yang and B.-L. Young,
*Dimension-six CP-violating operators of the third family quarks and their effects at colliders*,*Phys. Rev.***D 56**(1997) 5907 [hep-ph/9703463] [INSPIRE]. - [32]K. Whisnant, J.-M. Yang, B.-L. Young and X. Zhang,
*Dimension-six CP conserving operators of the third family quarks and their effects on collider observables*,*Phys. Rev.***D 56**(1997) 467 [hep-ph/9702305] [INSPIRE]. - [33]J.A. Aguilar-Saavedra,
*A minimal set of top-Higgs anomalous couplings*,*Nucl. Phys.***B 821**(2009) 215 [arXiv:0904.2387] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [34]A.D. Sakharov,
*Violation of CP invariance, c asymmetry and baryon asymmetry of the universe*,*Pisma Zh. Eksp. Teor. Fiz.***5**(1967) 32 [*JETP Lett.***5**(1967) 24] [*Sov. Phys. Usp.***34**(1991) 392] [*Usp. Fiz. Nauk***161**(1991) 61] [INSPIRE]. - [35]D. Nomura,
*Effects of top-quark compositeness on Higgs boson production at the LHC*,*JHEP***02**(2010) 061 [arXiv:0911.1941] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [36]B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek,
*Dimension-six terms in the Standard Model Lagrangian*,*JHEP***10**(2010) 085 [arXiv:1008.4884] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [37]P.C. Martin and J.S. Schwinger,
*Theory of many particle systems.*1,*Phys. Rev.***115**(1959) 1342 [INSPIRE]. - [38]J.S. Schwinger,
*Brownian motion of a quantum oscillator*,*J. Math. Phys.***2**(1961) 407 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [39]L.V. Keldysh,
*Diagram technique for nonequilibrium processes*,*Zh. Eksp. Teor. Fiz.***47**(1964) 1515 [*Sov. Phys. JETP***20**(1965) 1018] [INSPIRE]. - [40]K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu,
*Equilibrium and nonequilibrium formalisms made unified*,*Phys. Rept.***118**(1985) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [41]K.T. Mahanthappa,
*Multiple production of photons in quantum electrodynamics*,*Phys. Rev.***126**(1962) 329 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [42]V. Cirigliano, C. Lee, M.J. Ramsey-Musolf and S. Tulin,
*Flavored quantum Boltzmann equations*,*Phys. Rev.***D 81**(2010) 103503 [arXiv:0912.3523] [INSPIRE].ADSGoogle Scholar - [43]V. Cirigliano, C. Lee and S. Tulin,
*Resonant flavor oscillations in electroweak baryogenesis*,*Phys. Rev.***D 84**(2011) 056006 [arXiv:1106.0747] [INSPIRE].ADSGoogle Scholar - [44]H.A. Weldon,
*Dynamical holes in the quark-gluon plasma*,*Phys. Rev.***D 40**(1989) 2410 [INSPIRE].ADSGoogle Scholar - [45]H.A. Weldon,
*Structure of the quark propagator at high temperature*,*Phys. Rev.***D 61**(2000) 036003 [hep-ph/9908204] [INSPIRE]. - [46]V.V. Klimov,
*Spectrum of elementary Fermi excitations in quark gluon plasma*,*Sov. J. Nucl. Phys.***33**(1981) 934 [*Yad. Fiz.***33**(1981) 1734] [INSPIRE]. - [47]C. Lee, V. Cirigliano and M.J. Ramsey-Musolf,
*Resonant relaxation in electroweak baryogenesis*,*Phys. Rev.***D 71**(2005) 075010 [hep-ph/0412354] [INSPIRE]. - [48]V. Cirigliano, M.J. Ramsey-Musolf, S. Tulin and C. Lee,
*Yukawa and tri-scalar processes in electroweak baryogenesis*,*Phys. Rev.***D 73**(2006) 115009 [hep-ph/0603058] [INSPIRE]. - [49]G.A. White,
*General analytic methods for solving coupled transport equations: from cosmology to beyond*,*Phys. Rev.***D 93**(2016) 043504 [arXiv:1510.03901] [INSPIRE].ADSMathSciNetGoogle Scholar - [50]M. Carena, M. Quirós, M. Seco and C.E.M. Wagner,
*Improved results in supersymmetric electroweak baryogenesis*,*Nucl. Phys.***B 650**(2003) 24 [hep-ph/0208043] [INSPIRE]. - [51]J.M. Cline, M. Joyce and K. Kainulainen,
*Supersymmetric electroweak baryogenesis*,*JHEP***07**(2000) 018 [hep-ph/0006119] [INSPIRE]. - [52]D. Bödeker, G.D. Moore and K. Rummukainen,
*Chern-Simons number diffusion and hard thermal loops on the lattice*,*Phys. Rev.***D 61**(2000) 056003 [hep-ph/9907545] [INSPIRE]. - [53]G.D. Moore and K. Rummukainen,
*Classical sphaleron rate on fine lattices*,*Phys. Rev.***D 61**(2000) 105008 [hep-ph/9906259] [INSPIRE]. - [54]G.D. Moore,
*Sphaleron rate in the symmetric electroweak phase*,*Phys. Rev.***D 62**(2000) 085011 [hep-ph/0001216] [INSPIRE]. - [55]ACME collaboration, J. Baron et al.,
*Order of magnitude smaller limit on the electric dipole moment of the electron*,*Science***343**(2014) 269 [arXiv:1310.7534] [INSPIRE]. - [56]L. Bian, T. Liu and J. Shu,
*Cancellations between two-loop contributions to the electron electric dipole moment with a CP-violating Higgs sector*,*Phys. Rev. Lett.***115**(2015) 021801 [arXiv:1411.6695] [INSPIRE].ADSCrossRefGoogle Scholar - [57]A. Crivellin, S. Najjari and J. Rosiek,
*Lepton flavor violation in the Standard Model with general dimension-six operators*,*JHEP***04**(2014) 167 [arXiv:1312.0634] [INSPIRE].ADSCrossRefGoogle Scholar - [58]B.C. Regan, E.D. Commins, C.J. Schmidt and D. DeMille,
*New limit on the electron electric dipole moment*,*Phys. Rev. Lett.***88**(2002) 071805 [INSPIRE].ADSCrossRefGoogle Scholar - [59]W.C. Griffith, M.D. Swallows, T.H. Loftus, M.V. Romalis, B.R. Heckel and E.N. Fortson,
*Improved limit on the permanent electric dipole moment of*^{199}*Hg*,*Phys. Rev. Lett.***102**(2009) 101601 [INSPIRE].ADSCrossRefGoogle Scholar - [60]J.M. Pendlebury et al.,
*Revised experimental upper limit on the electric dipole moment of the neutron*,*Phys. Rev.***D 92**(2015) 092003 [arXiv:1509.04411] [INSPIRE].ADSGoogle Scholar - [61]C.A. Baker et al.,
*An improved experimental limit on the electric dipole moment of the neutron*,*Phys. Rev. Lett.***97**(2006) 131801 [hep-ex/0602020] [INSPIRE]. - [62]S.M. Barr and A. Zee,
*Electric dipole moment of the electron and of the neutron*,*Phys. Rev. Lett.***65**(1990) 21 [*Erratum ibid.***65**(1990) 2920] [INSPIRE]. - [63]
- [64]N. Yamanaka, T. Sato and T. Kubota,
*A reappraisal of two-loop contributions to the fermion electric dipole moments in R-parity violating supersymmetric models*,*Phys. Rev.***D 85**(2012) 117701 [arXiv:1202.0106] [INSPIRE].ADSGoogle Scholar - [65]D. Stöckinger,
*The muon magnetic moment and supersymmetry*,*J. Phys.***G 34**(2007) R45 [hep-ph/0609168] [INSPIRE]. - [66]R.G. Leigh, S. Paban and R.M. Xu,
*Electric dipole moment of electron*,*Nucl. Phys.***B 352**(1991) 45 [INSPIRE].ADSCrossRefGoogle Scholar - [67]T. Abe, J. Hisano, T. Kitahara and K. Tobioka,
*Gauge invariant Barr-Zee type contributions to fermionic EDMs in the two-Higgs doublet models*,*JHEP***01**(2014) 106 [*Erratum ibid.***04**(2016) 161] [arXiv:1311.4704] [INSPIRE]. - [68]M. Jung and A. Pich,
*Electric dipole moments in two-Higgs-doublet models*,*JHEP***04**(2014) 076 [arXiv:1308.6283] [INSPIRE].ADSCrossRefGoogle Scholar - [69]D. Bowser-Chao, D. Chang and W.-Y. Keung,
*Electron electric dipole moment from CP-violation in the charged Higgs sector*,*Phys. Rev. Lett.***79**(1997) 1988 [hep-ph/9703435] [INSPIRE]. - [70]W. Altmannshofer, J. Brod and M. Schmaltz,
*Experimental constraints on the coupling of the Higgs boson to electrons*,*JHEP***05**(2015) 125 [arXiv:1503.04830] [INSPIRE].ADSCrossRefGoogle Scholar - [71]S. Profumo, M.J. Ramsey-Musolf and G. Shaughnessy,
*Singlet Higgs phenomenology and the electroweak phase transition*,*JHEP***08**(2007) 010 [arXiv:0705.2425] [INSPIRE].ADSCrossRefGoogle Scholar - [72]H.H. Patel and M.J. Ramsey-Musolf,
*Baryon washout, electroweak phase transition and perturbation theory*,*JHEP***07**(2011) 029 [arXiv:1101.4665] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [73]H.H. Patel and M.J. Ramsey-Musolf,
*Stepping into electroweak symmetry breaking: phase transitions and Higgs phenomenology*,*Phys. Rev.***D 88**(2013) 035013 [arXiv:1212.5652] [INSPIRE].ADSGoogle Scholar - [74]S. Tulin and P. Winslow,
*Anomalous B meson mixing and baryogenesis*,*Phys. Rev.***D 84**(2011) 034013 [arXiv:1105.2848] [ INSPIRE].ADSGoogle Scholar