Recursive parametrization of Quark flavour mixing matrices

We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of $U(n)$ and $SU(n)$ matrices developed by some of us in Refs.[2] and [3]. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix

Grand canonical partition functions for multi level para Fermi systems of any order

A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.Comment: 9 pages, latex, no figure

Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses

We obtain constraints on possible structures of mass matrices in the quark sector by using as experimental restrictions the determined values of the quark masses at the $M_Z$ energy scale, the magnitudes of the quark mixing matrix elements $V_{\rm ud}$, $V_{\rm us}$, $V_{\rm cd}$, and $V_{\rm cs}$, and the Jarlskog invariant $J(V)$. Different cases of specific mass matrices are examined in detail. The quality of the fits for the Fritzsch and Stech type mass matrices is about the same with $\chi^2/{\rm dof}=4.23/3=1.41$ and $\chi^2/{\rm dof}=9.10/4=2.28$, respectively. The fit for a simple generalization (one extra parameter) of the Fritzsch type matrices, in the physical basis, is much better with $\chi^2/{\rm dof}=1.89/4=0.47$. For comparison we also include the results using the quark masses at the 2 GeV energy scale. The fits obtained at this energy scale are similar to that at $M_Z$ energy scale, implying that our results are unaffected by the evolution of the quark masses from 2 to 91 GeV.Comment: Evolution effects include

Identities involving elementary symmetric functions

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to a hierarchy of identities for q-binomial coefficients

Mapping of non-central potentials under point canonical transformations

Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure is also exist between a class of non-central potentials. As an illustrative example, we discuss the inter-relation between the generalized Coulomb and oscillator systems.Comment: 11 pages article in LaTEX (uses standard article.sty). Please check http://www1.gantep.edu.tr/~gonul for other studies of Nuclear Physics Group at University of Gaziante

Implications of measured properties of the mixing matrix on mass matrices

It is shown how the two experimentally measurable properties of the mixing matrix V, the asymmetry Δ(V) = |V12|2 - |V21|2 of V with respect to the main diagonal and the Jarlskog invariant J(V)= Im(V11V∗12V ∗21V22), can be exploited to obtain constraints on possible structures of mass matrices in the quark sector. Specific mass matrices are examined in detail as an illustration

Nuclear deformation and neutrinoless double-β\beta decay of 94,96^{94,96}Zr, 98,100^{98,100}Mo, 104^{104}Ru, 110^{110}Pd, 128,130^{128,130}Te and 150^{150}Nd nuclei in mass mechanism

The $(\beta ^{-}\beta ^{-})_{0\nu}$ decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied in the Projected Hartree-Fock-Bogoliubov framework. In our earlier work, the reliability of HFB intrinsic wave functions participating in the $\beta ^{-}\beta ^{-}$ decay of the above mentioned nuclei has been established by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$, gyromagnetic factors $g(2^{+})$ as well as half-lives $T_{1/2}^{2\nu}$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $(\beta ^{-}\beta ^{-})_{0\nu}$ decay for the $0^{+}\to 0^{+}$ transition in the mass mechanism and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives $T_{1/2}^{0\nu}(0^{+}\to 0^{+})$ using nuclear transition matrix elements calculated with the same set of wave functions. Further, the effect of deformation on the nuclear transition matrix elements required to study the $(\beta ^{-}\beta ^{-})_{0\nu}$ decay in the mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately same magnitude in $(\beta ^{-}\beta ^{-})_{2\nu}$ and $(\beta ^{-}\beta ^{-})_{0\nu}$ decay.Comment: 15 pages, 1 figur