CP violation of quarks in \(A_{4}\) modular invariance

DOI10.1016/J.PHYSLETB.2019.02.028zbMATH Open1411.81226arXiv1812.09677OpenAlexW2906249388WikidataQ128346779 ScholiaQ128346779MaRDI QIDQ1738768

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Publication date: 18 April 2019

Published in: (Search for Journal in Brave)

Abstract: We discuss the quark mass matrices in the $A_4$ modular symmetry, where the $A_4$ triplet of Higgs is introduced for each up-quark and down-quark sectors, respectively. The model has six real parameters and two complex parameters in addition to the modulus $au$. By inputting six quark masses and three CKM mixing angles, we can predict the CP violation phase $delta$ and the Jarlskog invariant $J_{CP}$. The predicted ranges of $delta$ and $J_{CP}$ are consistent with the observed values. The absolute value of $V_{ub}$ is smaller than $0.0043$, while $V_{cb}$ is lager than $0.0436$. In conclusion, our quark mass matrices with the $A_4$ modular symmetry can reproduce the CKM mixing matrix completely with observed quark masses.

Full work available at URL: https://arxiv.org/abs/1812.09677

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