Unusual Sources of CP violation inTwo-Higgs Doublet Models

Pedro Ferreira

ISEL and CFTC, ULSCALARS 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)

m212, λ5, λ6 and λ7 complex - seemingly 14 independent real parameters

Rich mass spectrum: a charged Higgs, three neutral scalars.

Possibility of spontaneous CP Violation (CPV).

Most general SU(2) × U(1) scalar potential:

CP – What distinguishes matter from anti-matter

“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!

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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

2*

1*

2

1

cossinsincos

(0 < θ < π/2)

• 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.

(θ =π/2: CP2/MCPM model; see Markos Maniatis’ talk!)

The Yukawa terms mix scalars and fermions. Most general terms for 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.

down-type quarks up-type quarks

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 STILL preserves CP – no mixing between states with different CP numbers.

• Model has only 11 parameters with which to fit all quark observables.

• Manages to fit quark masses, CKM matrix elements, K0, Bs and Bd mass differences, heavy meson decay rates, etc.

• FCNC “under control”: scalar and pseudoscalar contributions of opposite sign, and similar magnitude.

• Even more astonishing, FCNC couplings are all real in this model! No “extra” contributions to CPV from FCNC.

• This model does as good a job as the SM in what concerns CP violation, but with a completely different origin for a complex CKM: not hard breaking terms, but rather a quadratic soft term.

• 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.

meff – combination of the masses of the CP-even scalars.

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.