https://doi.org/10.1140/epjc/s10052-024-13272-w
Regular Article - Theoretical Physics
modular invariance and the strong CP problem
1
INFN/SISSA, Via Bonomea 265, 34136, Trieste, Italy
2
Kavli IPMU (WPI), UTIAS, The University of Tokyo, 277-8583, Kashiwa, Chiba, Japan
3
Department of Physics, Niigata University, Ikarashi 2, 950-2181, Niigata, Japan
4
Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria
b
morimitsutanimoto@yahoo.co.jp
Received:
1
July
2024
Accepted:
19
August
2024
Published online:
10
September
2024
We present simple effective theory of quark masses, mixing and CP violation with level () modular symmetry, which provides solution to the strong CP problem without the need for an axion. The vanishing of the strong CP-violating phase is ensured by assuming CP to be a fundamental symmetry of the Lagrangian of the theory. The CP symmetry is broken spontaneously by the vacuum expectation value (VEV) of the modulus . This provides the requisite large value of the CKM CP-violating phase while the strong CP phase remains zero or is tiny. Within the considered framework we discuss phenomenologically viable quark mass matrices with three types of texture zeros, which are realized by assigning both the left-handed and right-handed quark fields to singlets , and with appropriate weights. The VEV of is restricted to reproduce the observed CKM parameters. We discuss cases in which the modulus VEV is close to the fixed points i, and . In particular, we focus on the VEV of , which gives the absolute minima of the supergravity-motivated modular- and CP-invariant potentials for the modulus , so called, modulus stabilisation. We present a successful model, which is consistent with the modulus stabilisation close to .
© The Author(s) 2024
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