We investigate the quark Wigner distributions in a light-cone spectator model. The Wigner distribution, as a quasi-distribution function, provides the most general one-parton information in a hadron. Combining the polarization configurations, unpolarized, longitudinal polarized or transversal polarized, of the quark and the proton, we can define 16 independent Wigner distributions at leading twist. We calculate all these Wigner distributions for the $u$ quark and the $d$ quark respectively. In our calculation, both the scalar and the axial-vector spectators are included, and the Melosh-Wigner rotation effects for both the quark and the axial-vector spectator are taken into account. The results provide us a very rich picture of the quark structure in the proton.
The constancy of light speed is a basic assumption in Einsteins special relativity, and consequently the Lorentz invariance is a fundamental symmetry of space-time in modern physics. However, it is speculated that the speed of light becomes energy-dependent due to the Lorentz invariance violation~(LV) in various new physics theories. We analyse the data of the energetic photons from the gamma-ray bursts (GRBs) by the Fermi Gamma-Ray Space Telescope, and find more events to support the energy dependence in the light speed with both linear and quadratic form corrections. We provide two scenarios to understand all the new-released Pass~8 data of bright GRBs by the Fermi-LAT Collaboration, with predictions from such scenarios being testable by future detected GRBs.
The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the $mu$-$tau$ exchange symmetry are observed. Six types of texture non-zeros are shown. Implications for flavor models are discussed.
With the progress of increasingly precise measurements on the neutrino mixing angles, phenomenological relations such as quark-lepton complementarity (QLC) among mixing angles of quarks and leptons and self-complementarity (SC) among lepton mixing angles have been observed. Using the latest global fit results of the quark and lepton mixing angles in the standard Chau-Keung scheme, we calculate the mixing angles and CP-violating phases in the other eight different schemes. We check the dependence of these mixing angles on the CP-violating phases in different phase schemes. The dependence of QLC and SC relations on the CP phase in the other eight schemes is recognized and then analyzed, suggesting that measurements on CP-violating phases of the lepton sector are crucial to the explicit forms of QLC and SC in different schemes.
Inspired by a new relation $theta_{13}^{rm PMNS}={theta_C}/{sqrt{2}}$ observed from the relatively large $theta_{13}^{rm PMNS}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the PMNS matrix are all related to the Wolfenstein parameter $lambda$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $lambda$, A, and a Dirac CP-violating phase $delta$. Such parametrizations for the PMNS matrix have the same explicitly hierarchical structure as the Wolfenstein parametrization for the CKM matrix in the quark mixing, and the bimaximal mixing pattern is deduced at the leading order. We also discuss implications of these phenomenological relations in parametrizations.
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 $delta_{rm CP}$.
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.
We reexamine the quark-lepton complementarity (QLC) in nine angle-phase parametrizations with the latest result of a large lepton mixing angle $vartheta_{13}$ from the T2K, MINOS and Double Chooz experiments. We find that there are still two QLC relations satisfied in P1, P4 and P6 parametrizations, whereas only one QLC relation holds in P2, P3, P5 and P9 parametrizations separately. We also work out the corresponding reparametrization-invariant forms of the QLC relations and check the resulting expressions with the experimental data. The results can be viewed as a check of the validity of the QLC relations, as well as a new perspective into the issue of seeking for the connection between quarks and leptons.
With the latest results of a large mixing angle $theta_{13}$ for neutrinos by the T2K, MINOS and Double Chooz experiments, we find that the self-complementarity (SC) relations agree with the data in some angle-phase parametrizations of the lepton mixing matrix. There are three kinds of self-complementarity relations: (1) $vartheta_i+vartheta_j=vartheta_k=45^circ$; (2) $vartheta_i+vartheta_j=vartheta_k$; (3) $vartheta_i+vartheta_j=45^circ$ (where $i$, $j$, $k$ denote the mixing angles in the angle-phase parametrizations). We present a detailed study on the self-complementarity relations in nine different angle-phase parametrizations, and also examine the explicit expressions in reparametrization-invariant form, as well as their deviations from global fit. These self-complementarity relations may lead to new perspective on the mixing pattern of neutrinos.
We re-evaluate neutrino mixing patterns according to the latest T2K result for a larger mixing angle $theta_{13}$, and find that the PMNS mixing matrix has larger deviations from bimaximal (BM) and tribimaximal (TB) mixing patterns than previously expected. We also find that several schemes connecting PMNS and CKM mixing matrices can accommodate the latest T2K result nicely. As necessary updates to former works, we make new triminimal expansions of PMNS mixing matrix based on BM and TB mixing patterns. We also propose a new mixing pattern with a self-complementary relation between the mixing angles $theta_{12}^{ u} + theta_{13}^{ u} simeq 45^circ$, and find such a new mixing pattern in leading order can provide a rather good description of the data.
