A Pythagoras-like theorem for CP violation in neutrino oscillations

• Published in: Physics letters. B Vol. 845; p. 138142
• Main Authors: Luo, Shu, Xing, Zhi-zhong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 10.10.2023; Elsevier
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2023.138142

The probabilities of νμ→νe and ν‾μ→ν‾e oscillations in vacuum are determined by the CP-conserving flavor mixing factors Rij≡Re(UμiUejUμj⁎Uei⁎) and the universal Jarlskog invariant of CP violation Jν≡(−1)i+jIm(UμiUejUμj⁎Uei⁎) (for i,j=1,2,3 and i<j), where U is the 3×3 Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix. We show that Jν2=R12R13+R12R23+R13R23 holds as a natural consequence of the unitarity of U. This Pythagoras-like relation may provide a novel cross-check of the result of Jν that will be directly measured in the next-generation long-baseline neutrino oscillation experiments. Indirect non-unitarity effects and terrestrial matter effects on Jν and Rij are also discussed.