A supersymmetric resolution of the anomaly in charmless nonleptonic BB-decays

We examine the large branching ratio for the process $B\to \eta^{\prime} K$ from the standpoint of R parity violating supersymmetry. We have given all possible $R_p$ violating contributions to $B\to \eta^{\prime} K$ amplitudes. We find that only two pairs of $\lambda^{\prime}$-type $R_p$ violating couplings can solve this problem after satisfying all other experimental bounds. We also analyze those modes where these couplings can appear, {\em e.g.}, $B^\pm \to \pi^{\pm}K^0$, $B^{\pm,0} \to K^{*\pm,0} \eta^{(\prime)}$, $B^{\pm} \to\phi K^{\pm}$ etc., and predict their branching ratios. Further, one of these two pairs of couplings is found to lower the branching ratio of $B^{\pm}\to\phi K^\pm$, thereby allowing larger $\xi\equiv{1\over N_c}$. This allows us to fit $B^{\pm}\to \omega K^{\pm}$ and $B^{\pm}\to \omega \pi^{\pm}$, which could not be done in the SM framework.Comment: 12 pages, 5 figure

Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure

A statistical model with a standard Gamma distribution

We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $\lambda$. We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard Gamma distribution. The model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity $\lambda$. Alternatively, from the nature of the equilibrium distribution, we show that the model can also be interpreted as a perfect gas at an effective temperature $T(\lambda)$, where particles exchange energy in a space with an effective dimension $D(\lambda)$.Comment: 5 pages, including 4 figures. Uses REVTeX styl

A Curious Truncation of N=4 Yang-Mills

The coupling constant dependence of correlation functions of BPS operators in N=4 Yang-Mills can be expressed in terms of integrated correlation functions. We approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the AdS/CFT correspondence. We conjecture that this truncation becomes exact in the large N and large 't Hooft coupling limit.Comment: 10 pages, LaTeX; additional comments, added reference

Two-loop neutrino masses with large R-parity violating interactions in supersymmetry

We attempt to reconcile large trilinear R-parity violating interactions in a supersymmetric (SUSY) theory with the observed pattern of neutrino masses and mixing. We show that, with a restricted number of such interaction terms with the $\lambda'$-type couplings in the range (0.1-1.0), it is possible to forbid one-loop contributions to the neutrino mass matrix. This is illustrated with the help of a `working example' where an econnomic choice of SUSY parameters is made, with three non-vanishing and `large' R-parity violating terms in the superpotential. The two-loop contributions in such a case can not only generate the masses in the requisite order but can also lead us to specific allowed regions of the parameter space.Comment: Revised version, 25 pages, 16 figure

Constraining Scalar Leptoquarks from the K and B Sectors

Upper bounds at the weak scale are obtained for all $\lambda_{ij}\lambda_{im}$ type product couplings of the scalar leptoquark model which may affect K-K(bar), B_d-B_d(bar), and B_s-B_s(bar)$ mixing, as well as leptonic and semileptonic K and B decays. Constraints are obtained for both real and imaginary parts of the couplings. We also discuss the role of leptoquarks in explaining the anomalously large CP-violating phase in B_s-B_s(bar) mixing.Comment: 16 pages, 5 figures, more constraints analyzed, added a number of reference

Interpolating Action for Strings and Membranes - a Study of Symmetries in the Constrained Hamiltonian Approach

A master action for bosonic strings and membranes, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The role of the gauge symmetries vis-\`{a}-vis reparametrization symmetries of the various actions is analyzed by a constrained Hamiltonian approach. This analysis reveals the difference between strings and higher branes, which is essentially tied to a degree of freedom count. The cosmological term for membranes follows naturally in this scheme. The conncetion of our aproach with the Arnowitt--Deser--Misner representation in general relativity is illuminated.Comment: LaTex, 23 pages; discussion on ADM representation included and new references adde