Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the CP-violating phase $delta_{rm CP}$ in fermion mixing matrices
144
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 in the original Kobayashi-Maskawa (KM) scheme of neutrino mixing matrix, i.e., $delta_{rm KM}=90^circ$, we calculate $delta_{rm CK}$ for both quarks and leptons in the Chau-Keung (CK) scheme of the standard parametrization and find that $delta^{mathrm{quark}}_{mathrm{CK}}=(68.62^{+0.89}_{-0.81})^circ$ and $delta^{mathrm{lepton}}_{mathrm{CK}}=(85.39^{+4.76}_{-1.82})^circ$, 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 $delta_{rm CP}$.
rate research
Read More
A model independent analysis of the leptonic Dirac CP-violating phase ({delta}) is presented. The analysis uses the experimentally determined values of the mixing angles in the lepton mixing matrix in order to explore the allowed values for {delta} and possible general forms for the charged lepton mixing matrix. This is done under two general assumptions: 1) that the mixing matrix in the neutrino sector is the so-called tribimaximal matrix and hence the non zero value for {theta}13 arises due to the mixing matrix in the charged lepton sector and 2) the charged lepton mixing matrix is parametrized in terms of three angles and one phase. It is found that any value of {delta} is still consistent with the data and that, considering the assumptions above, regardless of the value for {delta}, the 1-3 mixing angle in the charged lepton sector is small but non zero and the 2-3 mixing angle can take values in only two possible small ranges around 0 and {pi}/2 respectively.
The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $delta_{rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^circ$ within $1sigma (3sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.
Natural 4 zeros texture mass matrices recently proposed by Fritzsch and Xing have been investigated by including `non-leadingcorrections in the context of latest data regarding m_t^{pole} and V_{CKM} matrix elements. Apart from accommodating m_t^{pole} in the range 175pm15 GeV, |V_{cb}| and |V_{ub}/V_{cb}|=0.08pm0.02, the analysis with maximal CP-violation predicts |V_{td}| = .005-.013. Further, the CP-violating phase angle delta can be restricted to the ranges (i) 22^o -45^o and (ii) 95^o - 130^o, concretizing the ambiguity regarding phase of CKM matrix. Furthermore, we find that non-leading calculations are important when `Cabibbo triangle is to be linked to unitarity triangle.
We study the CP-violating phase of the quark sector in the $U(8)$ flavor model on $T^2/Z_N , (N=2,3,4,6)$ with non-vanishing magnetic fluxes, where properties of possible origins of the CP violation are investigated minutely. In this system, a non-vanishing value is mandatory in the real part of the complex modulus parameter $tau$ of the two-dimensional torus. On $T^2$ without orbifolding, underlying discrete flavor symmetries severely restrict the form of Yukawa couplings and it is very difficult to reproduce the observed pattern in the quark sector including the CP-violating phase $delta_{rm CP}$. In cases of multiple Higgs doublets emerging on $T^2/Z_2$, the mass matrices of the zero-mode fermions can be written in the Gaussian textures by choosing appropriate configurations of vacuum expectation values of the Higgs fields. When such Gaussian textures of mass matrices are realized, we show that all of the quark profiles, which are mass hierarchies among the quarks, quark mixing angles, and $delta_{rm CP}$ can be simultaneously realized.
A bonus of the framed standard model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is asolution (without axions) of the strong CP problem by cancelling the theta-angle term $theta_I$ $Tr (H^{mu u} H^*_{mu u})$ in colour by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed. Extending here to flavour, one finds that there are two terms proportional to $Tr (G^{mu u}G^*_{mu u})$: (a) in the action from flavour instantons with unknown coefficient, say $theta_I$, (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient $theta_C$. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant $J$ in the PMNS matrix for leptons of order $10^{-2}$, as is hinted by experiment. But if the term $theta_I$ is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term $theta_C$ to be cancelled by the chiral transformation on leptons, then the following prediction results: $Jsim-0.012$ ($delta_{CP}sim(1.11)pi$) which is (i) of the right order, (ii) of the right sign, (iii) in the range favoured by present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
