Related papers: Wolfenstein Parametrization Re-examined
We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity bound with respect to dimension as $O(\sqrt{d})$. We show…
We study leptonic CP violation from a new perspective. For Majorana neutrinos, a new parametrization for leptonic mixing of the form $V=O_{23} O_{12} K_{a}^{i}\cdot O$ reveals interesting aspects that are less clear in the standard…
We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of lepton number violating process responsible for leptogenesis, the upper bound of branching ratio of lepton flavor violating decay,…
In the Standard Model of elementary particles, quark-mixing is expressed in terms of a 3 x 3 unitary matrix V, the so called Cabibbo-Kobayashi-Maskawa (CKM) matrix. Significant unitarity checks are so far possible for the first row of this…
The new measurement of $W$-boson mass by the CDF collaboration revealed a remarkable $7\sigma$ disagreement with the Standard Model (SM) prediction. If confirmed by other experiments, then the disagreement strongly indicates the existence…
We develop for the CKM and PMNS matrices a new representation with special properties. It is obtained by splitting each of these matrices into two rotations by the angle ${\sim}2\pi/3$ and a universal diagonal matrix with elements, which…
In this letter, we obtain a rephasing invariant formula for the CP phase in the Kobayashi--Maskawa parameterization $\delta_{\rm KM} = \arg [ - { V_{ud} \det V_{\rm CKM} / V_{us} V_{ub} V_{cd} V_{td}} ]$. General perturbative expansion of…
We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent…
We investigate how the Fritzsch ansatz for the quark mass matrices can be modified in the least possible way to accommodate the observed large top quark mass and the measured values of the CKM elements. As one of the solutions, we find that…
These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss…
We analyse the present experimental evidence for a complex CKM matrix, even allowing for New Physics contributions to $\epsilon_{K}$, $a_{J/\Psi K_{S}}$%, $\Delta M_{B_{d}}$, $\Delta M_{B_{s}}$, and the $\Delta I=1/2$ piece of $% B\to \rho…
The dodeca symmetry is designed to obtain the Cabibbo angle $\theta_C^{\rm CKM}$ approximately $15^{\rm o}$ and the (11) element of $\Vp$ as $\cos 30^{\rm o}$, leading to $\theta_1^{\rm PMNS}+\theta_C^{\rm CKM}\simeq 45^{\rm o}$. This…
We propose a parametrization for two-body nonleptonic $B$ meson decays, in which the various topologies of amplitudes are counted in terms of powers of the Wolfenstein parameter $\lambda\sim 0.22$. The weak phases and the amplitudes are…
We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix…
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…
We propose a realistic A4 extension of the Standard Model involving a particular quark-lepton mass relation, namely that the ratio of the third family mass to the geometric mean of the first and second family masses are equal for down-type…
The value of the V_{ud} matrix element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can be derived from nuclear superallowed beta decays, neutron decay, and pion beta decay. We survey current world data for all three. Today, the most…
I discuss some general aspects of diagonalizing the quark mass matrices and list all possible parametrizations of the Cabibbo-Kobayashi-Maskawa matrix (CKM) in terms of three rotation angles and a phase. I systematically study the relation…
Within a specific texture of the quark mass matrix the notion of a maximal violation of the $CP$ symmetry can be defined. The experimental constraints from weak decays imply that in reality one is close to the case of maximal $CP$…