$A_4$ modular invariance and the strong CP problem (2404.00858v2)
Abstract: We present simple effective theory of quark masses, mixing and CP violation with level $N=3$ ($A_4$) modular symmetry, which provides solution to the strong CP problem without the need for an axion. The vanishing of the strong CP-violating phase $\bar \theta$ 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 $\tau$. This provides the requisite large value of the CKM CP-violating phase while the strong CP phase $\bar \theta$ 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 $A_4$ singlets ${\bf 1}$, ${\bf 1'}$ and ${\bf 1''}$ with appropriate weights. The VEV of $\tau$ is restricted to reproduce the observed CKM parameters. We discuss cases in which the modulus VEV is close to the fixed points $i$, $\omega$ and $i\infty$. In particular, we focus on the VEV of $\tau$, which gives the absolute minima of the supergravity-motivated modular- and CP-invariant potentials for the modulus $\tau$, so called, modulus stabilisation. We present a successful model, which is consistent with the modulus stabilisation close to $\tau=\omega$.
- R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37 (1976) 172-175.
- G. ’t Hooft, Phys. Rev. Lett. 37 (1976) 8-11.
- C. Jarlskog, Phys. Rev. Lett. 55 (1985) 1039.
- R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38 (1977) 1440-1443.
- A. E. Nelson, Phys. Lett. B 136 (1984) 387-391.
- S. M. Barr, Phys. Rev. Lett. 53 (1984) 329.
- M. Dine and P. Draper, JHEP 08 (2015) 132 [arXiv:1506.05433 [hep-ph]].
- G. Hiller and M. Schmaltz, Phys. Lett. B 514 (2001) 263-268 [arXiv:hep-ph/0105254 [hep-ph]].
- K. S. Babu and R. N. Mohapatra, Phys. Rev. D 41 (1990) 1286.
- R. Kuchimanchi, Phys. Rev. Lett. 76 (1996) 3486-3489. [arXiv:hep-ph/9511376 [hep-ph]].
- L. Vecchi, JHEP 04 (2017) 149 doi:10.1007/JHEP04(2017)149 [arXiv:1412.3805 [hep-ph]].
- J. T. Penedo and S. T. Petcov, Nucl. Phys. B939 (2019) 292 [arXiv:1806.11040].
- J. C. Criado and F. Feruglio, SciPost Phys. 5 (2018) 042 [arXiv:1807.01125 [hep-ph]].
- H. Okada and M. Tanimoto, Phys. Lett. B 791 (2019) 54-61 [arXiv:1812.09677 [hep-ph]].
- H. Okada and M. Tanimoto, Eur. Phys. J. C 81 (2021) 52 [arXiv:1905.13421 [hep-ph]].
- H. Okada and M. Tanimoto, Phys. Dark Univ. 40 (2023) 101204 [arXiv:2005.00775 [hep-ph]].
- H. Okada and M. Tanimoto, Phys. Rev. D 103 (2021) 015005 [arXiv:2009.14242 [hep-ph]].
- H. Okada and M. Tanimoto, JHEP 03 (2021) 010 [arXiv:2012.01688 [hep-ph]].
- S. T. Petcov and M. Tanimoto, Eur. Phys. J. C 83 (2023) 579 [arXiv:2212.13336 [hep-ph]].
- S. T. Petcov and M. Tanimoto, JHEP 08 (2023) 086 [arXiv:2306.05730 [hep-ph]].
- X. G. Liu and G. J. Ding, JHEP 08 (2019) 134 [arXiv:1907.01488 [hep-ph]].
- G. Altarelli and F. Feruglio, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211 [hep-ph]].
- D. Hernandez and A. Y. Smirnov, Phys. Rev. D 86 (2012) 053014 [arXiv:1204.0445 [hep-ph]].
- S. F. King and C. Luhn, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340 [hep-ph]].
- M. Tanimoto, AIP Conf. Proc. 1666 (2015) 120002.
- S. F. King, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413 [hep-ph]].
- S. T. Petcov, Eur. Phys. J. C 78 (2018) 709 [arXiv:1711.10806 [hep-ph]].
- J. R. Ellis and M. K. Gaillard, Nucl. Phys. B 150 (1979) 141.
- I. B. Khriplovich, Phys. Lett. B 173 (1986) 193.
- D. Zhang, Nucl. Phys. B 952 (2020) 114935 [arXiv:1910.07869 [hep-ph]].
- S. Antusch and V. Maurer, JHEP 1311 (2013) 115 [arXiv:1306.6879 [hep-ph]].
- S. Weinberg, Trans. New York Acad. Sci. 38 (1977) 185.
- H. Fritzsch, Phys. Lett. B 73 (1978) 317.
- H. Fritzsch, Nucl. Phys. B 155 (1979) 189.
- Z. z. Xing and Z. h. Zhao, Nucl. Phys. B 897 (2015) 302 [arXiv:1501.06346 [hep-ph]].
- H. Fritzsch and Z. z. Xing, Phys. Lett. B 555 (2003) 63-70 [arXiv:hep-ph/0212195 [hep-ph]].
- G. C. Branco and J. I. Silva-Marcos, Phys. Lett. B 331 (1994) 390.
- M. Tanimoto and T. T. Yanagida, PTEP 2016 (2016) 043B03 [arXiv:1601.04459 [hep-ph]].