https://doi.org/10.1140/epjc/s10052-023-12303-2
Regular Article - Theoretical Physics
Quark masses and CKM hierarchies from 
modular flavor symmetry
1
Department of Physics, University of Wisconsin-Madison, 53706, Madison, WI, USA
2
Department of Physics, Keio University, 223-8522, Yokohama, Japan
3
Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), 34051, Daejeon, Korea
4
Department of Physics, Hokkaido University, 060-0810, Sapporo, Japan
Received:
4
October
2023
Accepted:
27
November
2023
Published online:
15
December
2023
We propose models to explain the hierarchies of the quark masses and mixing by utilizing the 
modular flavor symmetry. The hierarchy is realized by the modulus 
stabilized at 
, where the residual 
symmetry is approximately unbroken and the Froggatt–Nielsen mechanism works. It is found that the quark hierarchies are realized only in a few cases of quark representations. We study two models with assigning the modular weights, so that the observed quark hierarchies are explained in the cases of both small and large ratios of the top to bottom Yukawa couplings. We also argue that 
hierarchies of the 
coefficients and the spontaneous CP violation can be realized by imposing another 
modular symmetry.
© The Author(s) 2023
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