The Randall-Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to epsilon_K, which is inversely proportional to the fundamental Yukawa scale. Hence the RS epsilon_K problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from epsilon'/ε_K, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV in the two-site limit. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.
I describe in detail the calculation of the coefficients eta_3 and eta_1 of the low-energy Delta S=2 -hamiltonian describing K^0-K^0-bar-mixing in the next-to-leading order of renormalization group improved (RG) perturbation theory. First a general introduction into the application of the operator expansion and of RG methods to weak processes is presented. This includes the RG formalism for Green's functions with two operator insertions. Second I discuss the elimination of unphysical operators with emphasis on evanescent operators. Then the two-loop calculations needed for eta_3 and eta_1 are …
Possible signals for indirect CPT violation arising in experiments with neutral kaons are considered in the context of a general CPT- and Lorentz-violating standard-model extension. Certain CPT observables can depend on the meson momentum and exhibit sidereal variations in time. Any leading-order CPT violation would be controlled by four parameters that can be separately constrained in appropriate experiments. Recent experiments bound certain combinations of these parameters at the level of about $10^{-20}$ GeV.
The problem of indirect violation of discrete symmeties CP, T and CPT in a neutral meson system can be described using two complex parameters epsilon and delta, which are invariant under rephasing of meson and quark fields. For the Bd system, where the width difference between the physical states is negligible, only Re(delta) and Im(epsilon) survive. As a consequence, the traditional observables constructed for kaons, which are based on flavour tag, are not useful for the analogous study in this system. We describe how using a CP tag and studying CP-to-flavour transitions of the B mesons, we m…
The amplitudes of $K \rightarrow πγ^* \rightarrow πe^+e^-$ and $K \rightarrow ππγ$ decays have been calculated within chiral Lagrangian approach including higher-order derivative terms and meson loops. The selfconsistency of the simultaneous description of the experimental data on the nonleptonic and radiative kaon decays have been demonstrated. We estimate the effects of ``indirect'' and ``direct'' $CP$-violation in $K^0_L \rightarrow π^0 e^+e^-$ decays and discuss $CP$-violating charge asymmetries in $K^{\pm} \rightarrow π^{\pm} π^0 γ$ decays.
Recently it was shown, within the mass insertion approximation (MIA), that the gluino mediated flavor changing neutral current (FCNC) interactions can saturate both epsilon_K and Re(epsilon'/epsilon_K) even for the real Cabibbo-Kobayashi-Maskawa (CKM) matrix through a single CP violating parameter (delta^d_12)_LL. In this work, we extend our previous analysis to the nonvanishing KM phase, and to the effective SUSY model where the MIA is no longer a good approximation. In our model, epsilon_K and B0 - B0 bar mixing can receive significant SUSY contributions. Therefore the usual constraints on r…
New precise data in B physics and theoretical developments in K physics lead us to reconsider the weak K^0-\bar{K}^0 transition from a large-N_c viewpoint, N_c being the number of colors. In this framework, we infer an upper limit on \hat{B}_K and the Kaon indirect CP violation.
CKM-unitarity, direct and indirect CP-violation and the ΔI=1/2 rule in full lattice QCD are the focus of this talk. To this end I will discuss and compare recent lattice results for leptonic, semi-leptonic and non-leptonic decays of the kaon and neutral kaon mixing and I will motivate current best estimates f_K/f_π=1.198(10), f_+^{Kπ}(0)=0.964(5) and \hat{B}_K=0.720(39). Moreover new theoretical advances that will improve the quality of these computations in the future will be discussed.
Experimental signals for indirect CPT violation in the neutral-meson systems are studied in the context of a general CPT- and Lorentz-violating standard-model extension. In this explicit theory, some CPT observables depend on the meson momentum and exhibit diurnal variations. The consequences for CPT tests vary significantly with the specific experimental scenario. The wide range of possible effects is illustrated for two types of CPT experiment presently underway, one involving boosted uncorrelated kaons and the other involving unboosted correlated kaon pairs.
Neutral Kaon mixing plays an important role in the phenomenology of the standard model and its extensions because of its sensitivity to high-energy scales. In particular epsilon_K, parameterising indirect CP violation in the neutral Kaon system, serves as an important constraint on models of new physics and is well suited for the indirect search for heavy new particles. In order to exploit this potential, a precise prediction of the standard-model background is crucial. I give a short summary of the standard-model prediction of epsilon_K, and present our recent NNLO QCD calculation of the char…
The framework of a warped extra dimension with the Standard Model (SM) fields propagating in it is a very well-motivated extension of the SM since it can address both the Planck-weak and flavor hierarchy problems of the SM. Within this framework, solution to the little hierarchy problem motivates extending the SM electroweak (EW) 5D gauge symmetry in such a way that its breakdown to the SM delivers the SM Higgs boson. We study signals at the large hadron collider (LHC) for the extra EW (called coset) gauge bosons, a fundamental ingredient of this framework. The coset gauge bosons, due to their…
We study a warped extra-dimension scenario where the Standard Model fields lie in the bulk, with the addition of a fourth family of fermions. We concentrate on the flavor structure of the Higgs couplings with fermions in the flavor anarchy ansatz. Even without a fourth family, these couplings will be generically misaligned with respect to the SM fermion mass matrices. The presence of the fourth family typically enhances the misalignment effects and we show that one should expect them to be highly non-symmetrical in the ${(34)}$ inter-generational mixing. The radiative corrections from the new …
We have calculated the short distance QCD coefficient η_3 of the effective |ΔS|=2-hamiltonian in the next-to-leading order. Since now all coefficients η_1, η_2 and η_3 are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of ε_K. The measured value for ε_K$ yields a lower bound on each of |V_{cb}|, |V_{ub}/V_{cb}|, the top quark mass $m_t$ and the non- perturbative parameter B_K as a function of the remaining three quantities. We discuss the implications on the CKM phase δ, |V_{td}| and the key quantity for all CP-violating processe…
I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)^2 of the CP eigenstates K^0_1, K^0_2, and for certain ranges of values of the CP-violating parameter, a negative (mass)^2 can arise in the CP-violating basis. Under certain conditions, …
Within the minimal Left-Right (LR) symmetric model we revisit the predictions for the kaon CP violating observables $\varepsilon$ and $\varepsilon'$ in correlation with the neutron electric dipole moment. We perform a complete study of the cross constraints on the model parameters, phases and the $M_{W_R}$ scale, considering the two cases of extended parity or charge conjugation as LR discrete symmetries, together with the possible presence of a Peccei-Quinn symmetry. We discuss in particular two scenarios: whether the Standard Model saturates the experimental value of $\varepsilon'/\varepsilo…
We investigate the issue of testing CPT invariance in the neutral-$D$ system, using $D$ events obtained either from fixed-target experiments or from a tau-charm factory. For both types of experiments we show that the expected suppression of mixing in the $D$ system, normally viewed as a disadvantage for CP tests, allows unsuppressed measurement of certain parameters describing CPT violation. Asymmetries are presented that permit the extraction of parameters for direct CPT violation in the $D$ system and for indirect CPT violation in the $K$ system. We also show that experiments on the neutral-…
In this short presentation I emphasize the increased importance of kaon flavour physics in the search for new physics (NP) that we should witness in the rest of this decade and in the next decade. The main actors will be the branching ratios for the rare decays $K^+\rightarrowπ^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$, to be measured by NA62 and KOTO, and their correlations with the ratio $\varepsilon'/\varepsilon$ on which recently progress by lattice QCD and large $N$ dual QCD approach has been made implying a new flavour anomaly. Further correlations of $K^+\rightarrowπ^+ν\barν$, $K_{L}\rig…
For the Bd meson system, CP, T and CPT indirect violation can be described using two physical parameters, epsilon and delta. The traditional observables based on flavour tag and used in the kaon system, are not helpful in the Bd case, and new asymmetries have to be introduced. Here such alternative observables, based on CP tag, are presented, together with the first estimation on the sensitivity that current asymmetric B-factories can achieve on their measurement.
Kaon physics provides a unique opportunity to identify new flavour and CP violating interactions beyond the Standard Model (SM). In the SM, implied by the hierarchical structure of the CKM matrix and the GIM mechanism, flavour changing neutral current processes are most strongly suppressed in the kaon sector while the suppression is much less effective in the B meson systems. Thus their theoretical cleanness makes rare K decays, in particular the K -> pi nu anti-nu system, extremely well suited to look for deviations from their tiny SM values. Despite the increasingly stringent constraints on …
We study the effect of charged-Higgs-induced chromomagnetic operator, $Q_{8G}(-) \equiv \bar s σ^{μν} T^a γ_5 d G^a_{μν}$, on the Kaon direct CP violation $Re(ε'/ε)$. Using the matrix element $\langle ππ| O_{8G}(-) | K^0 \rangle$ recently obtained by a large $N_c$ dual QCD approach, we find that if the Kobayashi-Maskawa phase is the origin of CP violation, the charged-Higgs-induced gluon penguin dipole operator in the type-III two-Higgs-doublet model can explain the measured $Re(ε'/ε)$ when the constraints from the relevant low energy flavor physics, such as $ΔB(K)=2$, $B\to X_s γ$, and Kaon i…
Data indicate that $ΔI=1/2$ transitions account for 4.5-4.7% of both CP conserving and CP violating $K \to 2π$ decays, as well as CP conserving radiative $K \to ππγ$ processes. Observed $K \to ππγ/ππ$ branching ratios are shown to scale near $α/π$ or $α/2π$. The $K_L$-$K_S$ mixing angle $ϕ$ and the semileptonic weak-rate asymmetry $δ$ are reviewed, and theory is shown to be consistent with data. Also, $K \to 2π$ $ΔI=1/2$ dominance is studied in the context of the chiral constituent quark model, displaying again excellent agreement with data. Finally, indirect and direct kaon CP violation are s…
We propose a model of soft CP violation that evades the strong CP problem and can describe observed CP violation in the neutral kaon sector, both direct and indirect. Our model requires two ``duark'' mesons carrying quark number two that have complex (CP-violating) bare masses and are coupled to quark pairs. Aside from the existence of these potentially observable new particles with masses of several hundred GeV, we predict a flat unitarity triangle ({\it i.e.,} no observable direct CP violation in the $B$-meson sector) and a possibly anomalous branching ratio for the decay mode $K^+\to π^++\b…
To measure the Yukawa couplings of the up and down quarks, Y_{u,d}, seems to be far beyond the capabilities of current and (near) future experiments in particle physics. By performing a general analysis of the potential misalignment between quark masses and Yukawa couplings, we derive predictions for the magnitude of induced flavor-changing neutral currents (FCNCs), depending on the shift in the physical Yukawa coupling of first-generation quarks. We find that a shift of -100% in the down-quark Yukawa Y_d would generically result in ds transitions in conflict with Kaon physics. This could alre…
The Kaon direct CP violation $Re(ε'_K/ε_K)$ below the experimental data of a $2σ$ in the standard model, which is calculated using the RBC-UKQCD lattice and a large $N_c$ dual QCD, indicates the necessity of a new physics effect. In order to resolve the insufficient $Re(ε'_K/ε_K)$, we study the charged-Higgs contributions in a generic two-Higgs-doublet model. If we assume that the origin of the CP-violation phase is uniquely from the Kobayashi-Maskawa (KM) phase when the constraints from the $B$- and $K$-meson mixings, $B\to X_s γ$, and Kaon indirect CP violating parameter $ε_K$ are simultaneo…
We propose a model of soft CP violation that evades the strong CP problem and can describe observed CP violation in the neutral kaon sector, both direct and indirect. Our model requires two ``duark'' mesons carrying quark number two that have complex (CP-violating) bare masses and are coupled to quark pairs. Aside from the existence of these potentially observable new particles with masses of several hundred GeV, we predict a flat unitarity triangle ({\it i.e.,} no observable direct CP violation in the $B$-meson sector) and a possibly anomalous branching ratio for the decay mode $K^+\to π^++\b…
I rebuild a conventional two-Higgs doublet model by relaxing the spontaneous CP violation and considering approximate global U(1) family symmetries. So that the domain-wall problem does not explicitly arise at the weak scale, but CP violation still solely originates from a single CP-phase in the vacuum after spontaneous symmetry breaking. With this phase four types of CP-violating mechanism are induced in the model. In particular, by a new type of the mechanism, both the indirect- and direct- CP violation (i.e. $ε$ and $ε'/ε$) in kaon decay and the neutron electric dipole moment can be consist…
We present results for $\varepsilon_K$, the indirect CP violation parameter, calculated in the Standard Model using inputs from lattice QCD: the kaon bag parameter $\hat{B}_K$, and the CKM matrix element $V_{cb}$ from the axial current form factor for the exclusive decay $\bar{B}\to D^*\ell\barν$ at zero-recoil. In addition, we take the coordinates of the unitarity triangle apex $(\barρ,\barη)$ from the angle-only fit of the UTfit Collaboration and use $V_{us}$ to fix $λ$. In order to estimate the systematic error, we also use Wolfenstein parameters from the CKMfitter and UTfit. We find a $3.3…
I give a pedagogical introduction into flavour-changing neutral current interactions of kaons and their role to reveal or constrain physics beyond the Standard Model (SM). Then I discuss the measure $ε_K^\prime$ of direct CP violation in $K\to ππ$ decays, which deviates from the SM prediction by $2.8σ$. A supersymmetric scenario with flavour mixing among left-handed squarks can accomodate the measured value of $ε_K^\prime$ even for very heavy sparticles, outside the reach of the LHC. The considered scenario employs mass splittings among the right-handed up and down squarks (to enhance $ε_K^\pr…
The characteristic property of the Z2XZ2 orbifold compactification is the cyclic permutation symmetry between the three twisted sectors. We discuss how this property, which is retained in a class of realistic free fermionic string models, may be instrumental in enabling fermion mass hierarchy while ensuring sfermion mass degeneracy, irrespective of the dominant source of supersymmetry breaking. The cyclic symmetry is reflected in some models in the existence of a family universal anomalous U(1)_A. We analyze the FCNC and CP violation effects in a model with a dominant U(1)_A SUSY breaking. In …
