JOURNAL OF HIGH ENERGY PHYSICS | Volume 2019 ,Issue 5 ,2019-05-07 |
Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter | |
Regular Article - Theoretical Physics | |
Xin Wang ^{1} , ^{2} Shun Zhou ^{1} , ^{2} | |
Show affiliations | |
DOI：10.1007/JHEP05(2019)035 | |
Received 2019-2-7, accepted for publication 2019-4-29, Published 2019-4-29 | |
摘要
Neutrino oscillations in matter can be fully described by six effective parameters, namely, three neutrino mixing angles , one Dirac-type CP-violating phase , and two neutrino mass-squared differences and . Recently, a complete set of differential equations for these effective parameters have been derived to characterize their evolution with respect to the ordinary matter term , in analogy with the renormalization-group equations (RGEs) for running parameters. Via series expansion in terms of the small ratio αc ≡ Δ21/Δc with Δc ≡ Δ31 cos2 θ12+Δ32 sin2θ12, we obtain approximate analytical solutions to the RGEs of the effective neutrino parameters and make several interesting observations. First, at the leading order, and are given by the simple formulas in the two-flavor mixing limit, while and are not changed by matter effects. Second, the ratio of the matter-corrected Jarlskog invariant to its counterpart in vacuum approximates to , where with A∗ ≡ a/Δ21 and with Ac ≡ a/Δc have been defined. Finally, after taking higher-order corrections into account, we find compact and simple expressions of all the effective parameters, which turn out to be in perfect agreement with the exact numerical
关键词
Renormalization Group;Neutrino Physics
授权许可
© The Author(s) 2019
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通讯作者
Xin Wang.Theoretical Physics Division, Institute of High Energy Physics, 19B Yuquan Road, Shijingshan District, 100049, Beijing, China;School of Physical Sciences, University of Chinese Academy of Sciences, 19B Yuquan Road, Shijingshan District, 100049, Beijing, China.wangx@ihep.ac.cn
推荐引用方式
Xin Wang,Shun Zhou. Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter. JOURNAL OF HIGH ENERGY PHYSICS ,Vol.2019, Issue 5(2019)
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