Cabibbo-Kobayashi-Maskawa Matrix, Unitarity Triangle and Geometry Origin of the Weak CP Phase

TL;DR

This paper explores the geometric origin of the weak CP phase in the CKM matrix, proposing it is determined by three mixing angles and predicting specific values for the unitarity triangle angles, consistent with current experiments.

Contribution

It introduces a geometric postulation that the weak CP phase arises from mixing angles, enabling determination of the CKM matrix and unitarity triangle from experimental data.

Findings

Angle gamma is approximately pi/2.

Weak CP phase delta exists only in the first or fourth quadrant.

Predictions align with current experimental results.

Abstract

In this work, the postulation that weak CP phase originates in a certain geometry, is further discussed. According to this postulation, the weak CP phase is determined by three mixing angles. So, if we can determine experimentally three elements of the Cabibbo-Kobayashi-Maskawa matrix, we can then determine the whole CKM matrix and correspondingly, the unitarity triangle. We find that the angle gamma is about pi/2 and the weak CP phase delta (delta_{13}) only can exist in the first or fourth quadrant. The conclusions coincide with the relevant analysis. Some other predictions are given in this paper, the comparison of the predictions based on the postulation to the relevant experimental and theoretical results is listed. All the predictions are consistent with the present experimental results.