Estimate of Wolfenstein's Parameters rho and eta Based on a Geometry Viewpoint to the Weak CP Phase

TL;DR

This paper proposes a geometric approach to estimate Wolfenstein's parameters rho and eta, providing bounds and a linear relation between them, which can be tested with future data.

Contribution

It introduces a geometric viewpoint on the weak CP phase to constrain and relate Wolfenstein's parameters rho and eta.

Findings

Positive rho is asserted based on geometry.

Allowed ranges for eta and rho are identified.

A linear relation between eta and rho is found.

Abstract

Based on a geometric postulation on the weak CP phase in Cabibbo-Kobayashi-Maskawa (CKM) matrix, a positive rho is asserted. Besides, 0.18<eta<0.54 and 0.048<rho<0.140 are permitted by the present data. The corresponding geometric constraint on Wolfenstein's parameters is also worked out. We find that, according to the geometry viewpoint, eta and rho satisfy an approximate linear relation. These results can be put to the more precisely tests in near future.