Measuring |V_{td} / V_{ub}| through B -> M \nu \bar\nu (M=\pi,K,\rho,K^*) decays

We propose a new method for precise determination of |V_{td} / V_{ub}| from the ratios of branching ratios BR(B -> \rho \nu \bar \nu ) / BR(B ->\rho l \nu ) and BR(B -> \pi \nu \bar \nu ) / BR(B -> \pi l \nu ). These ratios depend only on the ratio of the Cabibbo-Kobayashi-Maskawa (CKM) elements |V_{td} / V_{ub}|$ with little theoretical uncertainty, when very small isospin breaking effects are neglected. As is well known, |V_{td} / V_{ub}| equals to (\sin \gamma) / (\sin \beta) for the CKM version of CP-violation within the Standard Model. We also give in detail analytical and numerical results on the differential decay width d\Gamma(B -> K^* \nu \bar \nu ) / dq^2 and the ratio of the differential rates dBR(B -> \rho \nu \bar \nu )/dq^2 / dBR(B -> K^* \nu \bar \nu )/dq^2 as well as BR(B -> \rho \nu \bar \nu ) / BR(B -> K^* \nu \bar \nu) and BR(B -> \pi \nu \bar \nu ) / BR(B -> K \nu \bar \nu).Comment: LaTeX with 2 figures, 12 page

Quantisation of derived Lagrangians

We investigate quantisations of line bundles $\mathcal{L}$ on derived Lagrangians $X$ over $0$-shifted symplectic derived Artin $N$-stacks $Y$. In our derived setting, a deformation quantisation consists of a curved $A_{\infty}$ deformation of the structure sheaf $\mathcal{O}_{Y}$, equipped with a curved $A_{\infty}$ morphism to the ring of differential operators on $\mathcal{L}$; for line bundles on smooth Lagrangian subvarieties of smooth symplectic algebraic varieties, this simplifies to deforming $(\mathcal{L}, \mathcal{O}_{Y})$ to a DQ module over a DQ algebroid. For each choice of formality isomorphism between the $E_2$ and $P_2$ operads, we construct a map from the space of non-degenerate quantisations to power series with coefficients in relative cohomology groups of the respective de Rham complexes. When $\mathcal{L}$ is a square root of the dualising line bundle, this leads to an equivalence between even power series and certain anti-involutive quantisations, ensuring that the deformation quantisations always exist for such line bundles. This gives rise to a likely candidate for the new type of Fukaya category, of algebraic Lagrangians, envisaged by Behrend and Fantechi. We also sketch a generalisation of these quantisation results to Lagrangians on higher $n$-shifted symplectic derived stacks.Comment: 53 pp; v2 minor additions and refs updated; v3 expanded generally, with some new material in final sectio

Demonstration of the double Q^2-rescaling model

In this paper we have demonstrated the double Q^2-rescaling model (DQ^2RM) of parton distribution functions of nucleon bounded in nucleus. With different x-region of l-A deep inelastic scattering process we take different approach: in high x-region (0.1\le x\le 0.7) we use the distorted QCD vacuum model which resulted from topologically multi -connected domain vacuum structure of nucleus; in low x-region (10^{-4}\le x\le10^{-3}) we adopt the Glauber (Mueller) multi- scattering formula for gluon coherently rescattering in nucleus. From these two approach we justified the rescaling parton distribution functions in bound nucleon are in agreement well with those we got from DQ^2RM, thus the validity for this phenomenologically model are demonstrated.Comment: 19 page, RevTex, 5 figures in postscrip

Minimal fqf^q-martingale measures for exponential L\'evy processes

Let $L$ be a multidimensional L\'evy process under $P$ in its own filtration. The $f^q$-minimal martingale measure $Q_q$ is defined as that equivalent local martingale measure for $\mathcal {E}(L)$ which minimizes the $f^q$-divergence $E[(dQ/dP)^q]$ for fixed $q\in(-\infty,0)\cup(1,\infty)$. We give necessary and sufficient conditions for the existence of $Q_q$ and an explicit formula for its density. For $q=2$, we relate the sufficient conditions to the structure condition and discuss when the former are also necessary. Moreover, we show that $Q_q$ converges for $q\searrow1$ in entropy to the minimal entropy martingale measure.Comment: Published in at http://dx.doi.org/10.1214/07-AAP439 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Universality and m_X cut effects in B -> Xs l+ l-

The most precise comparison between theory and experiment for the B -> Xs l+ l- rate is in the low q^2 region, but the hadronic uncertainties associated with an experimentally required cut on m_X potentially spoil the search for new physics in these decays. We show that a 10-30% reduction of d\Gamma(B -> Xs l+ l-) / dq^2 due to the m_X cut can be accurately computed using the B -> X_s gamma shape function. The effect is universal for all short distance contributions in the limit m_X^2 << m_B^2, and this universality is spoiled neither by realistic values of the m_X cut nor by alpha_s corrections. Both the differential decay rate and forward-backward asymmetry with an m_X cut are computed.Comment: 5 pages, journal versio

Lattice Study of the Decay B^0-bar -> rho^+ l^- nu_l-bar: Model-Independent Determination of |V_{ub}|

We present results of a lattice computation of the vector and axial-vector current matrix elements relevant for the semileptonic decay B^0-bar -> rho^+ l^- nu_l-bar. The computations are performed in the quenched approximation of lattice QCD on a 24^3 x 48 lattice at beta = 6.2, using an O(a) improved fermionic action. Our principal result is for the differential decay rate, dGamma/dq^2, for the decay B^0-bar -> rho^+ l^- nu_l-bar in a region beyond the charm threshold, allowing a model-independent extraction of |V_{ub}| from experimental measurements. Heavy quark symmetry relations between radiative and semileptonic decays of B-bar mesons into light vector mesons are also discussed.Comment: 22 pages LaTeX-209 (dependent on settings in a4.sty), 23 PostScript figures included with epsf.sty. Complete PostScript file including figures available at http://wwwhep.phys.soton.ac.uk/hepwww/papers/shep9518

Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table