Related papers: Jarlskog Invariant of the Neutrino Mapping Matrix
We propose that the smallness of the light quark masses is related to the smallness of the T violation in hadronic weak interactions. Accordingly, for each of the two quark sectors ("upper" and "lower") we construct a 3\times 3 mass matrix…
The relation between low energy CP violating phases, and the CP asymmetry of leptogenesis, $\epsilon$, is investigated. Although it is known that in general those are independent, there may be a relation when a model is specified. We…
The neutrino mixing matrix is expanded in powers of a small parameter $\lambda$, which approximately equals to 0.1. The meaning of every order of the expansion is discussed respectively, and the range of $\lambda$ is carefully calculated.…
We present the first complete calculation of the Jarlskog invariant, a working measure of the strength of CP violation in the flavor oscillations of three light neutrino species, with the help of a full Euler-like block parametrization of…
Even if quark and lepton masses are not uniquely predicted by the fundamental theory, as may be the case in the string theory landscape, nevertheless their pattern may reveal features of the underlying theory. We use statistical techniques…
We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant…
For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two…
If we impose the $\mu-\tau$ symmetry, as a constraint into neutrino mass matrix, one find that the Jarlskog rephasing invariant: $J_{\rm CP}=0$ which implies that CP violation cannot be accommodated in the $\mu-\tau$ symmetry scheme. By…
The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact…
In this paper, we show that the ratio of the effective Jarlskog invariant $\widetilde{\cal J}$ for leptonic CP violation in three-flavor neutrino oscillations in matter to its counterpart ${\cal J}$ in vacuum $\widetilde{\cal J}/{\cal J}…
Terrestrial matter effects in neutrino propagation are T-invariant, so that any observed T violation when neutrinos pass through the Earth, such as an asymmetry between the transition probabilities P(nu_mu -> nu_e) and P(nu_e -> nu_mu),…
We describe calculations of Jarlskog's determinant in the case of n=3,4 in detail. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations of them.
We discuss the relation between the CP violation of the quark mixing and that of the lepton mixing by investigating a CP violating observable, the Jarlskog invariant, as well as the CP violating Dirac phase. The down-type quark mass matrix…
In the quark sector, Jarlskog rephasing invariant $\rm{J_{CP}}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to the…
In fermion mixing phenomenology, the matrix of moduli squared, P=(|U|^2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The…
An asymmetry between the probabilities P(\nu_{\mu}\to\nu_{e}) and P(\bar{\nu_{\mu}}\to\bar{\nu_{e}}) would be direct indication of CP violation at the fundamental level. Planck scale effects on neutrino mixing, we have derived the mixing…
The neutrino mixing matrix is expanded in powers of a small parameter $\lambda$ in tri-bimaximal mixing pattern. We also present some applications of this parametrization, such as to the expression of the Jarlskog parameter $J$. Comparing…
Recent work on F-theory GUTs has shown that the predicted masses, and magnitudes of the mixing matrix elements in the quark and lepton sectors are in close accord with experiment. In this note we estimate the CP violating phase of the…
In the quark sector, Jarlskog rephasing invariant parameter $J_{CP}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to…
Current experimental data on neutrino oscillations are consistent with the tri-bimaximal mixing. If future experimental data will determine a non-zero $V_{e3}$ and/or find CP violations in neutrino oscillations, there is the need to modify…