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

Centers and Cocenters of 00-Hecke algebras

In this paper, we give explicit descriptions of the centers and cocenters of $0$-Hecke algebras associated to finite Coxeter groups.Comment: 13 pages, a mistake in 4.2 is correcte

A Study of Some Methods for Measuring CKM CP Violating Phases

We study the influence of penguin (especially, electroweak penguin) effects on some methods of measuring the angles $\alpha$, $\beta$, and $\gamma$ in the CKM unitarity triangle. We use next-to-leading order effective Hamiltonian, and present numerical estimates based on the factorization approximation. We find that some techniques suggested in the literature, especially for $\alpha$ determination, are not workable in light of the electroweak penguin effects. Nevertheless, there are methods that would work for each angle determination. For angle $\beta$ we consider $B \rightarrow D^{+} D^{-}$ mode and estimate the penguin contamination. For angle $\gamma$ we consider a method based on SU(3) symmetry and carefully consider SU(3) breaking effects. We point out regions in the parameter space where this method could be used reliably.Comment: 25 pages (Latex), 5 PS figs (uuencoded, epsf.tex

Constraints on the phase γ\gamma and new physics from B→KπB\to K\pi Decays

Recent results from CLEO on $B\to K\pi$ indicate that the phase $\gamma$ may be substantially different from that obtained from other fit to the KM matrix elements in the Standard Model. We show that $\gamma$ extracted using $B\to K\pi, \pi\pi$ is sensitive to new physics occurring at loop level. It provides a powerful method to probe new physics in electroweak penguin interactions. Using effects due to anomalous gauge couplings as an example, we show that within the allowed ranges for these couplings information about $\gamma$ obtained from $B\to K \pi, \pi\pi$ can be very different from the Standard Model prediction.Comment: Revised version with analysis done using new data from CLEO. RevTex, 11 Pages with two figure