Naumov-and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

Zhi-zhong Xing; Shun Zhou

doi:10.1088/1674-1137/42/10/103105

Chinese Physics C> 2018, Vol. 42> Issue(10) : 103105 DOI: 10.1088/1674-1137/42/10/103105

Naumov-and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

Zhi-zhong Xing ^1,2,3 ,
Shun Zhou ^1,2

1.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Center for High Energy Physics, Peking University, Beijing 100871, China

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Abstract：
In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalization-group (RG) equations in the tau-dominance approximation, and for the running behaviors of up-and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.
- fermion flavor mixing ,
- CP violation ,
- renormalization-group equations

References

[1]	T. Ohlsson and S. Zhou, Nature Commun., 5:5153 (2014)[arXiv:1311.3846]
[2]	S. H. Chiu and T. K. Kuo, Phys. Rev. D, 97:055026 (2018), arXiv:1712.08487
[3]	Z. z. Xing, S. Zhou, and Y. L. Zhou, JHEP, 1805:015 (2018), arXiv:1802.00990 arXiv:1802.00990
[4]	V. A. Naumov, Int. J. Mod. Phys. D, 1:379 (1992)
[5]	S. Toshev, Mod. Phys. Lett. A, 6:455 (1991)
[6]	C. Patrignani et al (Particle Data Group), Chin. Phys. C, 40:100001 (2016)
[7]	P. F. Harrison and W. G. Scott, Phys. Lett. B, 476:349 (2000)[hep-ph/9912435]
[8]	Z. z. Xing, Phys. Lett. B, 487:327 (2000)[hep-ph/0002246]
[9]	Z. z. Xing, Phys. Rev. D, 64:033005 (2001)[hep-ph/0102021]
[10]	H. Fritzsch and Z. z. Xing, Phys. Lett. B, 413:396 (1997)[hep-ph/9707215]
[11]	H. Fritzsch and Z. z. Xing, Phys. Lett. B, 440:313 (1998)[hep-ph/9808272]
[12]	Z. z. Xing and S. Zhou, Springer-Verlag, Berlin Heidelberg (2011)
[13]	M. Lindner, M. Ratz, and M. A. Schmidt, JHEP, 0509:081 (2005)[hep-ph/0506280]
[14]	S. Antusch, J. Kersten, M. Lindner, and M. Ratz, Nucl. Phys. B, 674:401 (2003)[hep-ph/0305273]
[15]	S. Antusch, J. Kersten, M. Lindner, M. Ratz, and M. A. Schmidt, JHEP, 0503:024 (2005),[hep-ph/0501272]
[16]	J. w. Mei, Phys. Rev. D, 71:073012 (2005)[hep-ph/0502015]
[17]	Z. z. Xing and Z. h. Zhao, Rept. Prog. Phys., 79:076201 (2016), arXiv:1512.04207
[18]	P. Minkowski, Phys. Lett. B, 67:421 (1977)
[19]	T. Yanagida, Conf. Proc. C, 7902131:95 (1979)
[20]	S. L. Glashow, NATO Sci. Ser. B, 61:687 (1980)
[21]	M. Gell-Mann, P. Ramond and R. Slansky, Conf. Proc. C, 790927:315 (1979), arXiv:1306.4669
[22]	R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett., 44:912 (1980)
[23]	Z. z. Xing, D. Zhang and J. y. Zhu, JHEP, 1711:135 (2017), arXiv:1708.09144
[24]	Z. z. Xing, H. Zhang and S. Zhou, Phys. Rev. D, 86:013013 (2012), arXiv:1112.3112
[25]	C. Jarlskog, Phys. Rev. Lett., 55:1039 (1985)
[26]	H. Fritzsch and Z. z. Xing, Phys. Rev. D, 57:594 (1998)[hep-ph/9708366]
[27]	H. Fritzsch and Z. z. Xing, Prog. Part. Nucl. Phys., 45:1 (2000)[hep-ph/9912358]

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Zhi-zhong Xing and Shun Zhou. Naumov-and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos[J]. Chinese Physics C, 2018, 42(10): 103105. doi: 10.1088/1674-1137/42/10/103105

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Received: 2018-04-09
Revised: 2018-06-15

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Supported by the National Natural Science Foundation of China (11775231) and (11775232), the National Youth Thousand Talents Program, and the CAS Center for Excellence in Particle Physics.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Naumov-and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

3. Center for High Energy Physics, Peking University, Beijing 100871, China

Received Date: 2018-04-09

Accepted Date: 2018-06-15

Available Online: 2018-10-05

Fund Project: Supported by the National Natural Science Foundation of China (11775231) and (11775232), the National Youth Thousand Talents Program, and the CAS Center for Excellence in Particle Physics.

Abstract: In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalization-group (RG) equations in the tau-dominance approximation, and for the running behaviors of up-and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.

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Naumov-and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

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