1204.6604 (Xinyi Zhang et al.)

On the CP violating phase $δ_{\rm CP}$ in fermion mixing matrix    [PDF]

Xinyi Zhang, Bo-Qiang Ma

The recent established large $\theta_{13}$ in neutrino mixing provides an optimistic possibility for the investigation of the CP violation, therefore it is necessary to study the CP violating phase $\delta_{\rm CP}$ in detail. Based on the maximal CP violation hypothesis, i.e., $\delta_{\rm KM}=90^\circ$, we calculate $\delta_{\rm CK}$ for both quarks and leptons and find that $\delta^{\mathrm{quark}}_{\mathrm{CK}}=(68.67^{+0.17}_{-0.09})^\circ$ and $\delta^{\mathrm{lepton}}_{\mathrm{CK}}=(85.38^{+0.80}_{-0.74})^\circ$, provided with three mixing angles to be given. We also examine the sensitivity of $|V_{ij}|$ and $|U_{ij}|$ to $\delta_{\rm CK}$ and $\delta_{\rm KM}$. As a convention-independent investigation, we discuss the $\Phi$ matrix, which has elements correspond to angles of the unitarity triangles. We demonstrate the $\Phi$ matrices for both quark and lepton sectors and discuss the implications as well as the variations of the $\Phi$ matrix elements with $\delta_{\rm CP}$.

View original: http://arxiv.org/abs/1204.6604