Unusual Sources of CP violation in Two-Higgs Doublet Models Pedro Ferreira ISEL and CFTC, UL SCALARS 2011, 27/08/2011 P.F. and J.P. Silva, Eur.Phys.J. C69 (2010) 45 P.F., L. Lavoura and J.P. Silva, arXiv:1106.0034, submitted to PLB
The Two-Higgs doublet model (2HDM) (Lee, 1973) Most general SU(2) × U(1) scalar potential: m212, λ5, λ6andλ7complex - seemingly 14 independent real parameters Rich mass spectrum: a charged Higgs, three neutral scalars. Possibility of spontaneous CP Violation (CPV).
“Usual” CP violation • In the SM, CP violation is achieved by including, in the Lagrangian, complex Yukawa couplings. • These are dimension-4 terms in the fields, and as such CP breaking in the SM is an example of a HARD EXPLICIT BREAKING. • CP is not a symmetry respected by the Lagrangian, even before SSB. • If you use this same mechanism in the 2HDM, you would have • (at tree-level) well-defined scalar states – • scalars h and H, a pseudoscalar A. • For instance, no vertex ZZA exists, but ZZh and ZZH do.
In the 2HDM, CP violation can also be achieved through spontaneous symmetry breaking – a vacuum with a complex phase is generated by the potential. • CP is a symmetry respected by the whole lagrangian, BUT it’s the vacuum that breaks it. • It’s even possible to do it in a theory without tree-level FCNC, introducing a real soft breaking term. (Branco and Rebelo, 1985) • CP is respected by the Lagrangian, before SSB. But it is spontaneously broken. • After SSB there are no well-defined scalar states – • the “scalars” h and H and the “pseudoscalar” A mix among • themselves – there is CP violation in the scalar sector. • For instance, the vertices ZZA, ZZh and ZZH are all possible.
Using remarkable geometric arguments, Ivanov was able to show that THERE ARE ONLY SIX POSSIBLE SYMMETRIES IN THE 2HDM! 7 6 3 9 5 4 Each of these models has very different physical implications. The 2HDM allows for two exotic possibilities for CPV: - Spontaneous CP breaking, without mixing in the scalar sector. - Explicit CP breaking, but soft, not hard like in the SM. - In both cases tree-level scalar FCNC occurs, but are “naturally” small.
The CP3 model(P.F. and J.P. Silva, Eur.Phys.J. C69 (2010) 45) • Based on a generalized CP transformation of the form (0 < θ < π/2) (θ =π/2: CP2/MCPM model; see Markos Maniatis’ talk!) • Only θ = π/3 permits six massive quarks, and three massive charged leptons!! • The CP3 symmetry is imposed on the full lagrangian => the theory preserves CP before SSB. • A complex vacuum can be generated by the potential.
The Yukawa terms mix scalars and fermions. Most general terms for quarks: down-type quarks up-type quarks CP3 imposes heavy constraints on the form of the 3×3 Yukawa matrices Γ and Δ: Analogous form for the up-quark matrices. The fact that both matrices are non-zero implies the existence of tree-level scalar FCNC.
Why this is new and unusual: • The lagrangian is explicitly CP conserving. • The complex vacuum implies a non-zero value for the Jarlskog invariant => • CP breaking occurs, and is spontaneous! • Despite a complex vacuum, no mixing occurs in the scalar sector => • scalars preserve CP! None of the other 5 2HDM potentials has this feature. • The model has only (<) 12 independent parameters, and still manages to fit the 6 quark masses and CKM matrix elements. • Tree-level scalar FCNC usually screws up very sensitive CP-breaking observables, such as the mass differences in the K0, Bs and Bd mesons, the εK parameter, etc – the model manages to easily fit almost all of them. • - The reason is a “natural” cancellation that occurs in the model, the scalar and pseudoscalar contributions having opposite signs.
In short, a new type of CP violation: • - Lagrangian preserves CP before SSB (no explicit CPV as in the SM); • CP is broken spontaneously, but the scalar sector remains CP-conserving (unlike usual CPV in the 2HDM); • Tree-level FCNC occurs, but kept “naturally” small, so that most CPV observables can be fitted by the model…. … unfortunately not all observables; the model’s fit to the data implies that the unitarity triangle angles α and β are almost equal (leading to a value for the Jarlskog invariant 1000 times below its tabled value). Thus, the model seems to be excluded on experimental grounds.
The Z3 model(P.F., L. Lavoura and J.P. Silva, arXiv:1106.0034, submitted to PLB) The model is based on a Z3 symmetry imposed on the whole lagrangian complemented with a CP symmetry. The Yukawa matrices are of the form (real coefficients): Since the quarks couple to both doublets, there are tree-level FCNC…
This model – Z3 + CP – obviously preserves CP, and it has no vacua which violates CP! - In order to have CPV, we introduce a complex soft breaking term to the scalar potential: a dimension TWO term: This means that, in this model, CP is EXPLICITLY broken, but in a SOFT manner – not HARD, as in the SM. However, the scalar sector STILLpreserves CP – no mixing between states with different CP numbers.
Modelhasonly 11 parameterswithwhich to fitallquarkobservables. • Manages to fitquarkmasses, CKM matrixelements, K0, BsandBdmassdifferences, heavymesondecay rates, etc. • FCNC “undercontrol”: scalarandpseudoscalarcontributionsofoppositesign, andsimilar magnitude. • Even more astonishing, FCNC couplings are all real inthismodel! No “extra” contributions to CPV from FCNC. • Thismodel does as good a job as the SM inwhatconcerns CP violation, butwith a completelydifferentorigin for a complex CKM: nothardbreakingterms, butrather a quadraticsoftterm.
meff– combination of the masses of the CP-even scalars. • The model achieves this with scalar masses which can be as small as ~100 GeV. • The model’s parameters can also fit all LEP Higgs exclusion data and oblique parameter constraints.
Conclusions • The 2HDM still has surprises up its sleeve. • Two unusual sources of CP violation were found: • One, a spontaneous violation of CP which leaves the scalar sector CP conserving. • An explicit breaking of CP but via a complex soft breaking term, not a hard one. • In both cases tree-level scalar FCNC occur – but they can be kept under control without fine-tuning. • The second model does as good a job as the SM in fitting CP observables, arguably with a simpler Yukawa structure.