An exact CKM matrix related to the approximate Wolfenstein form

Abstract

Noting the hierarchy between three mixing angles, ${\theta }_{2,3}=\mathcal{O}({\theta }_1^2)$, we present an exact form of the quark mixing matrix, replacing Wolfenstein's approximate form. In addition, we suggest to rotate the unitarity triangle, using the weak CP phase convention where the phase is located at the (31) element $\sin {\theta }_1\sin {\theta }_2{e}^{i\delta }$ while the (13) element $\sin {\theta }_1\sin {\theta }_3$ is real. For the $(ab)$ unitarity triangle, the base line (x-axis) is defined from the product of the first row elements, $V_{1a}{V}_{1b}^{\ast }$, and the angle between two sides at the origin is defined to be the phase $\delta$. This is a useful definition since every Jarlskog triangle has the angle $\delta$ at the origin, defined directly from the unitarity condition. It is argued that $\delta$ represents the barometer of the weak CP violation, which can be used to relate it to possible Yukawa textures.

5 pages with 2 figures

References in corpus (2)

• Quark and lepton mixing angles with a dodeca-symmetry
• A new simple form of quark mixing matrix

Cited by in corpus (16)

• Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D
• Axion Dark Matter Research with IBS/CAPP
• Final state interaction phases using data from CP asymmetries
• The CKM matrix with maximal CP violation from Z(12) symmetry
• A possible relation between leptogenesis and PMNS phases
• Theory of flavors: String compactification
• Unifying CP violations of quark and lepton sectors
• Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay-constant
• Parametrization of PMNS matrix based on dodeca-symmetry
• The CKM matrix from anti-SU(7) unification of GUT families
• Leptonic CP violation in flipped SU(5) GUT from $Z_{12-I}$ Orbifold Compactification
• On the progenitor quark mass matrix
• Jarlskog determinant and data on flavor matrices
• Axions, strong and weak CP, and KNP inflation
• Effective SUSY modified after LHC run
• Strong CP problem, axions, and cosmological implications of CP violation