The Weyl group of the fine grading of sl(n,C)sl(n,\mathbb{C}) associated with tensor product of generalized Pauli matrices

We consider the fine grading of sl(n,\mb C) induced by tensor product of generalized Pauli matrices in the paper. Based on the classification of maximal diagonalizable subgroups of PGL(n,\mb C) by Havlicek, Patera and Pelantova, we prove that any finite maximal diagonalizable subgroup $K$ of PGL(n,\mb C) is a symplectic abelian group and its Weyl group, which describes the symmetry of the fine grading induced by the action of $K$, is just the isometry group of the symplectic abelian group $K$. For a finite symplectic abelian group, it is also proved that its isometry group is always generated by the transvections contained in it

Consequences of R-Parity violating interactions for anomalies in Bˉ→D(∗)τνˉ\bar B\to D^{(*)} \tau \bar \nu and b→sμ+μ−b\to s \mu^+\mu^-

We investigate the possibility of explaining the enhancement in semileptonic decays of $\bar B \to D^{(*)} \tau \bar \nu$, the anomalies induced by $b\to s\mu^+\mu^-$ in $\bar B\to (K, K^*, \phi)\mu^+\mu^-$ and violation of lepton universality in $R_K = Br(\bar B\to K \mu^+\mu^-)/Br(\bar B\to K e^+e^-)$ within the framework of R-parity violating (RPV) MSSM. Exchange of down type right-handed squark coupled to quarks and leptons yield interactions which are similar to leptoquark induced interactions that have been proposed to explain the $\bar B \to D^{(*)} \tau \bar \nu$ by tree level interactions and $b\to s \mu^+\mu^-$ anomalies by loop induced interactions, simultaneously. However, the Yukawa couplings in such theories have severe constraints from other rare processes in $B$ and $D$ decays. Although this interaction can provide a viable solution to $R(D^{(*)})$ anomaly, we show that with the severe constraint from $\bar B \to K \nu \bar \nu$, it is impossible to solve the anomalies in $b\to s \mu^+\mu^-$ process simultaneously.Comment: RevTex, 13 pages, three figures. In our earlier version, we had neglected a contribution to C^{NP}_9 and obtained erroneous conclusions which we have corrected them in this versio

Triple Neutral Gauge Boson Couplings in Noncommutative Standard Model

It has been shown recently that the triple neutral gauge boson couplings are not uniquely determined in noncommutative extension of the Standard Model (NCSM). Depending on specific schemes used, the couplings are different and may even be zero. To distinguish different realizations of the NCSM, additional information either from theoretical or experimental considerations is needed. In this paper we show that these couplings can be uniquely determined from considerations of unification of electroweak and strong interactions. Using SU(5) as the underlying theory and integrating out the heavy degrees of freedom, we obtain unique non-zero new triple $\gamma\gamma\gamma$, $\gamma \gamma Z$, $\gamma ZZ$, $ZZZ$, $\gamma GG$, $ZGG$ and $GGG$ couplings at the leading order in the NCSM. We also briefly discuss experimental implications.Comment: 8 pages, Latex, no figur