ΔMs/ΔMd\Delta M_s/\Delta M_d, sin⁡2β\sin 2\beta and the angle γ\gamma in the Presence of New ΔF=2\Delta F=2 Operators

We present formulae for the mass differences $\Delta M_d$ and $\Delta M_s$ in the \BBds systems and for the CP violation parameter $\epsilon$ which are valid in minimal flavour violation models giving rise to new four-fermion $\Delta F=2$ operators. Short distance contributions to $\Delta M_s$, $\Delta M_d$ and $\epsilon$ are parameterized by three {\it real} functions $F^s_{tt}$, $F^d_{tt}$ and $F^\epsilon_{tt}$, respectively ($F^s_{tt} = F^d_{tt} = F^\epsilon_{tt}$ holds only if the Standard Model $(V-A) \otimes (V-A)$ operators dominate). We present simple strategies involving the ratio $\Delta M_s/\Delta M_d$, $\sin2\beta$ and $\gamma$ that allow to search for the effects of the new operators. We point out that their sizable contributions to the ratio $\Delta M_s/\Delta M_d$ would in principle allow $\gamma$ to be larger than $90^\circ$. Constraints on the functions $F^i_{tt}$ imposed by the present (and future) experimental data are also discussed. As an example we show that for large $\tan\bar\beta\equiv v_2/v_1$ and $H^+$ not too heavy, $F^s_{tt}$ in the MSSM with heavy sparticles can be substantially smaller than in the SM due the charged Higgs box contributions and in particular due to the growing like $\tan^4\bar\beta$ contribution of the double penguin diagrams involving neutral Higgs boson exchanges. As a result the bounds on the function $F^s_{tt}$ can be violated which allows to exclude large mixing of stops. In this scenario the range of $\sin2\beta$ following from $\epsilon$ and $\Delta M_d$ is identical to the SM ones ($0.5<\sin 2\beta<0.8$). On the other hand $\gamma$ following from $\Delta M_s/\Delta M_d$ is lower.Comment: 39 pages, 13 figures, uses axodraw.sty. V2: new BaBar and Belle results on \sin2\beta incorporated; some explanations of the details of calculation of \tan^4\bar\beta terms adde

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made

Non-minimally coupled f(R) Cosmology

We investigate the consequences of non-minimal gravitational coupling to matter and study how it differs from the case of minimal coupling by choosing certain simple forms for the nature of coupling, The values of the parameters are specified at $z=0$ (present epoch) and the equations are evolved backwards to calculate the evolution of cosmological parameters. We find that the Hubble parameter evolves more slowly in non-minimal coupling case as compared to the minimal coupling case. In both the cases, the universe accelerates around present time, and enters the decelerating regime in the past. Using the latest Union2 dataset for supernova Type Ia observations as well as the data for baryon acoustic oscillation (BAO) from SDSS observations, we constraint the parameters of Linder exponential model in the two different approaches. We find that there is a upper bound on model parameter in minimal coupling. But for non-minimal coupling case, there is range of allowed values for the model parameter.Comment: 7 pages, Latex style, 8 eps figure