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

Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in Weyl semimetals with tilted energy dispersion

Ruderman-Kittel-Kasuya-Yosida (RKKY) is an essential long range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance ($\mathrm{R}$) between them. We have investigated the RKKY interaction between two magnetic impurities in both time-reversal and inversion symmetry broken Weyl semimetals (WSMs) where the energy dispersion is tilted in momentum space and the momentum of the conduction electron is locked with the pseudo-spin. Two important features are revealed, firstly, at the small tilt limit, we show that the RKKY coupling varies quadratically with the tilt parameter and strikingly, at large separation distance $\mathrm{R}$, the coupling decays as $1/\mathrm{R}$ compared to the conventional of $1/\mathrm{R}^{3}$ dependence exhibited by WSMs with non-tilted dispersion. The slower decay by two orders i.e. ($1/\mathrm{R}$ as opposed to $1/\mathrm{R}^{3}$) of the RKKY coupling is significant for maintaining long range RKKY coupling. Secondly, the RKKY coupling exhibits an anisotropy with respect to the angle between the tilt direction ($\mathbf{w}$) and the separation direction $\mathbf{R}$ unlike the case of non-tilted WSMs which exhibit isotropic RKKY coupling. Consequently, the RKKY coupling in tilted WSMs alternately favours ferromagnetic and anti-ferromagnetic orders and vice-versa with the change of the angle. Our results are derived analytically and verified by numerical calculations based on realistic parameter values

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

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

2SLS Versus 2SRI: Appropriate Methods for Rare Outcomes and/or Rare Exposures

This study used Monte Carlo simulations to examine the ability of the two-stage least squares (2SLS) estimator and two-stage residual inclusion (2SRI) estimators with varying forms of residuals to estimate the local average and population average treatment effect parameters in models with binary outcome, endogenous binary treatment, and single binary instrument. The rarity of the outcome and the treatment was varied across simulation scenarios. Results showed that 2SLS generated consistent estimates of the local average treatment effects (LATE) and biased estimates of the average treatment effects (ATE) across all scenarios. 2SRI approaches, in general, produced biased estimates of both LATE and ATE under all scenarios. 2SRI using generalized residuals minimized the bias in ATE estimates. Use of 2SLS and 2SRI is illustrated in an empirical application estimating the effects of long-term care insurance on a variety of binary health care utilization outcomes among the near-elderly using the Health and Retirement Study