Exploring the Origin of CP Violation in the Standard Model
C Lin - arXiv preprint arXiv:2010.08245, 2020 - arxiv.org
C Lin
arXiv preprint arXiv:2010.08245, 2020•arxiv.orgIn this article, we present a very general but not ultimate solution of CPV problem in the
standard model. Our study starts from a naturally Hermitian ${\bf M^ 2}\equiv M^ q\cdot
M^{q\dagger} $ rather than the previously assumed Hermitian $ M^ q $. The only
assumption employed here is that the real part and imaginary part of $\bf M^ 2$ can be,
respectively, diagonalized by a common $\bf U^ q $ matrix. Such an assumption leads to a
$\bf M^ 2$ pattern which depends on only five parameters and can be diagonalized …
standard model. Our study starts from a naturally Hermitian ${\bf M^ 2}\equiv M^ q\cdot
M^{q\dagger} $ rather than the previously assumed Hermitian $ M^ q $. The only
assumption employed here is that the real part and imaginary part of $\bf M^ 2$ can be,
respectively, diagonalized by a common $\bf U^ q $ matrix. Such an assumption leads to a
$\bf M^ 2$ pattern which depends on only five parameters and can be diagonalized …
In this article, we present a very general but not ultimate solution of CPV problem in the standard model. Our study starts from a naturally Hermitian rather than the previously assumed Hermitian . The only assumption employed here is that the real part and imaginary part of can be, respectively, diagonalized by a common matrix. Such an assumption leads to a pattern which depends on only five parameters and can be diagonalized analytically by a matrix which depends on only two of the parameters. Two of the derived mass eigenvalues are predicted degenerate if one of the parameters in up- (down-) quark sector is zero. As the patterns are obtained, thirty-six candidates are yielded and only eight of them, classified into two groups, fit empirical data within the order of . One of the groups is further excluded in a numerical test, and the surviving group predicts that the degenerate pair in a quark type are the lightest and the heaviest generations rather than the lighter two generations assumed in previous researches. However, there is still one unsatisfactory prediction in this research, a quadruple equality in which four CKM elements of very different values are predicted to be equal. It indicates the pattern studied here is still oversimplified by that employed assumption and the ultimate solution can only be obtained by diagonalizing the unsimplified matrix containing nine parameters directly. The presented here is already very close to such an ultimate CPV solution.
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