Jarlskog-like invariants for theories with scalars and fermions

Within the framework of theories where both scalars and fermions are present, we develop a systematic prescription for the construction of CP-violating quantities that are invariant under basis transformations of those matter fields. In theories with Spontaneous Symmetry Breaking, the analysis involves the vevs' transformation properties under a scalar basis change, with a considerable simplification of the study of CP violation in the scalar sector. These techniques are then applied in detail to the two Higgs-doublet model with quarks. It is shown that there are new invariants involving scalar-fermion interactions, besides those already derived in previous analyses for the fermion-gauge and scalar-gauge sectors.Comment: 12 pages, Latex, no figure

Flavour Changing Higgs Couplings in a Class of Two Higgs Doublet Models

We analyse various flavour changing processes like $t\to hu,hc$, $h\to \tau e,\tau\mu$ as well as hadronic decays $h\to bs,bd$, in the framework of a class of two Higgs doublet models where there are flavour changing neutral scalar currents at tree level. These models have the remarkable feature of having these flavour-violating couplings entirely determined by the CKM and PMNS matrices as well as $\tan\beta$. The flavour structure of these scalar currents results from a symmetry of the Lagrangian and therefore it is natural and stable under the renormalization group. We show that in some of the models the rates of the above flavour changing processes can reach the discovery level at the LHC at 13 TeV even taking into account the stringent bounds on low energy processes, in particular $\mu\to e\gamma$.Comment: 33 pages, 8 figures; matches version accepted for publicatio

Spontaneous CP Violation in the Next-to-Minimal Supersymmetric Standard Model Revisited

We re-examine spontaneous CP violation at the tree level in the context of the next-to-minimal supersymmetric standard model (NMSSM) with two Higgs doublets and a gauge singlet field. We analyse the most general Higgs potential without a discrete Z_3 symmetry, and derive an upper bound on the mass of the lightest neutral Higgs boson consistent with present experimental data. We investigate, in particular, its dependence on the admixture and CP-violating phase of the gauge singlet field, as well as on tan(beta). To assess the viability of the spontaneous CP violation scenario, we estimate epsilon_K by applying the mass insertion approximation. We find that a non-trivial flavour structure in the soft-breaking A terms is required to account for the observed CP violation in the neutral kaon sector. Furthermore, combining the minimisation conditions for spontaneous CP violation with the constraints coming from K0-K0bar mixing, we find that the upper bound on the lightest Higgs-boson mass becomes stronger. We also point out that the electric dipole moments of electron and neutron are a serious challenge for SUSY models with spontaneous CP violation.Comment: 19 pages, LaTeX2e, 5 figures; matches the published versio

What if the Masses of the First Two Quark Families are not Generated by the Standard Higgs?

We point out that, in the context of the SM, $|V^2_{13}| + | V^2_{23}|$ is expected to be large, of order one. The fact that $|V^2_{13}| + |V^2_{23}| \approx 1.6 \times 10^{-3}$ motivates the introduction of a symmetry S which leads to $V_{CKM} ={1\>\!\!\!\mathrm{I}}$, with only the third generation of quarks acquiring mass. We consider two scenarios for generating the mass of the first two quark generations and full quark mixing. One consists of the introduction of a second Higgs doublet which is neutral under S. The second scenario consists of assuming New Physics at a high energy scale , contributing to the masses of light quark generations, in an effective field theory approach. This last scenario leads to couplings of the Higgs particle to $s\overline s$ and $c \overline c$ which are significantly enhanced with respect to those of the SM. In both schemes, one has scalar-mediated flavour- changing neutral currents which are naturally suppressed. Flavour violating top decays are predicted in the second scenario at the level \mbox{Br} (t \rightarrow h c ) \geq 5\times 10^{-5}.Comment: 11 pages, 1 figur

Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology

We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of non-contractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/lagrangian and their spontaneous violation from a wider perspective than usual.Comment: 27 pages, 5 figure

Small violations of unitarity, the phase in Bs mixing and visible t->cZ decays at the LHC

We show that it is possible to accommodate the observed size of the phase in $B^0_s$--$\bar B^0_s$, mixing in the framework of a model with violation of $3\times 3$ unitarity. This violation is associated to the presence of a new $Q=2/3$ isosinglet quark $T$, which mixes both with $t$ and $c$ and has a mass not exceeding 500 GeV. The crucial point is the fact that this framework allows for $\chi\equiv\arg(-V_{ts}V_{cb}V_{tb}^*V_{cs}^*)$ of order $\lambda$, to be contrasted with the situation in the Standard Model, where $\chi$ is constrained to be of order $\lambda^2$. We point out that this scenario implies rare top decays $t\to cZ$ at a rate observable at the LHC and $|V_{tb}|$ significantly different from unity. In this framework, one may also account for the observed size of $D^0$--$\bar D^0$ mixing without having to invoke long distance contributions. It is also shown that in the present scenario, the observed size of $D^0$--$\bar D^0$ mixing constrains $\chi^\prime\equiv\arg(-V_{cd}V_{us}V_{cs}^*V_{ud}^*)$ to be of order $\lambda^4$, which is significantly smaller than what is allowed in generic models with violations of $3\times 3$ unitarity.Comment: 20 pages. References added. Additional observables considered, updated numerical examples, conclusions unchange

Flavour Physics and CP Violation in the Standard Model and Beyond

We present the invited lectures given at the Third IDPASC School which took place in Santiago de Compostela in January 2013. The students attending the school had very different backgrounds, some of them were doing their Ph.D. in experimental particle physics, others in theory. As a result, and in order to make the lectures useful for most of the students, we focused on basic topics of broad interest, avoiding the more technical aspects of Flavour Physics and CP Violation. We make a brief review of the Standard Model, paying special attention to the generation of fermion masses and mixing, as well as to CP violation. We describe some of the simplest extensions of the SM, emphasising novel flavour aspects which arise in their framework.Comment: Invited talk at the Third IDPASC School 2013, January 21st - February 2nd 2013, Santiago de Compostela, Galiza, Spain; 36 pages, 8 figures, 2 tables; version with few misprints correcte