Distribution Amplitudes of Heavy Hadrons: Theory and Applications

The physics of heavy quarks becomes a very reach area of study thanks to an excellent operation of hadron colliders and $B$-factories and exciting results from them. Experimental data obtained allows to get some information about the heavy hadron dynamics. In this case, the models for the heavy hadron wave-functions are required to do theoretical predictions for concrete processes under study. In many cases, the light-cone description is enough to obtain theoretical estimates for heavy hadron decays. A discussion of the wave-functions of the $B$-meson and heavy bottom baryons in terms of the light-cone distribution amplitudes is given in this paper. Simple models for the distribution amplitudes are presented and their scale dependence is discussed. Moments of the distribution amplitudes which are entering the branching fractions of radiative, leptonic and semileptonic $B$-mesons decays are also briefly discussed.Comment: 17 pages, 4 figures, lecture at the Helmholtz International Summer School and Dubna International Advanced School on Theoretical Physics "Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks", JINR, Dubna, Russia, July 18--30, 201

Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds

In this note we calculate elliptic genus in various examples of twisted chiral de Rham complex on two dimensional toric compact manifolds and Calabi-Yau hypersurfaces in toric manifolds. At first the elliptic genus is calculated for the line bundle twisted chiral de Rham complex on a compact smooth toric manifold and K3 hypersurface in \mathbb{P}^{3} . Then we twist chiral de Rham complex by sheaves localized on positive codimension submanifolds in \mathbb{P}^{2} and calculate in each case the elliptic genus. In the last example the elliptic genus of chiral de Rham complex on \mathbb{P}^{2} twisted by SL(N) vector bundle with instanton number k is calculated. In all cases considered we find the infinite tower of open string oscillator contributions of the corresponding bound state of D-branes and identify directly the open string boundary conditions and D-brane charges.Comment: 14 pages, LaTex, some comments and references adde

Poisson-Lie T-duality and N=2 superconformal WZNW models on compact groups

The supersymmetric generalization of Pisson-Lie T-duality in N=2 superconformal WZNW models on the compact groups is considered. It is shown that the role of Drinfeld's doubles play the complexifications of the corresponding compact groups. These complex doubles are used to define the natural actions of the isotropic subgroups forming the doubles on the group manifolds of the N=2 superconformal WZNW models. The Poisson- Lie T-duality in N=2 superconformal U(2)-WZNW model considered in details. It is shown that this model admits Poisson-Lie symmetries with respect to the isotropic subgroups forming Drinfeld's double Gl(2,C). Poisson-Lie T-duality transformation maps this model into itself but acts nontrivialy on the space of classical solutions. Supersymmetric generalization of Poisson-Lie T-duality in N=2 superconformal WZNW models on the compact groups of higher dimensions is proposed.Comment: 12 pages, latex, misprints correcte

Supersymmetric gauged WZNW models as dressing cosets

The domain of applicability of the Poisson-Lie T-duality is enlarged to include the gauged WZNW models.Comment: 10 pages, LaTeX, reference adde

Improved η′\eta^\prime-Meson Distribution Amplitudes from Inclusive Υ(1S)→η′X\Upsilon (1S) \to \eta^\prime X Decay

We calculate the $\eta^\prime$-meson energy spectrum in the $\Upsilon (1S) \to \eta^\prime g g g \to \eta^\prime X$ decay in the leading-order perturbative QCD in the static-quark limit for the orthoquarkonium.Our principal result is the extraction of parameters of the $\eta^\prime g^* g$ effective vertex function (EVF) involving a virtual and a real gluon from the available data on the hard part of the $\eta^\prime$-meson energy spectrum. The perturbative-QCD based framework provides a good description of the available CLEO data, allowing one to constrain the lowest Gegenbauer coefficients $B^{(q)}_2$ and $B^{(g)}_2$ of the quark-antiquark and gluonic distribution amplitudes of the $\eta^\prime$-meson. The resulting constraints are combined with the existing ones on these coefficients from an analysis of the $\eta^\prime - \gamma$ transition form factor and the requirement of positivity of the EVF, yielding $B^{(q)}_2 (\mu_0^2) = -0.008 \pm 0.054$ and $B^{(g)}_2 (\mu_0^2) = 4.6 \pm 2.5$ for $\mu_0^2 = 2 GeV^2$. This reduces significantly the current uncertainty on these coefficients.Comment: 4 pages, 4 figures, use svjour.cls and svepj.clo; talk given at the International Europhysics Conference on High-Energy Physics (HEP 2003), 17-23 July 2003, Aachen, Germany. Title change

Branching Ratios for B→K∗γB \to K^* \gamma and B→ργB \to \rho \gamma Decays in Next-to-Leading Order in the Large Eneregy Effective Theory

We calculate the so-called hard spectator corrections in ${\cal O} (\alpha_s)$ in the leading-twist approximation to the decay widths for $B \to K^{*} \gamma$ and $B \to \rho \gamma$ decays and their charge conjugates, using the Large Energy Effective Theory (LEET) techniques. Combined with the hard vertex and annihilation contributions, they are used to compute the branching ratios for these decays in the next-to-leading order (NLO) in the strong coupling $\alpha_s$ and in leading power in $\Lambda_{\rm QCD}/M_B$. These corrections are found to be large, leading to the inference that the theoretical branching ratios for the decays $B \to K^* \gamma$ in the LEET approach can be reconciled with current data only for significantly lower values of the form factors than their estimates in the QCD sum rule and Lattice QCD approaches. However, the form factor related uncertainties mostly cancel in the ratios ${\cal B}(B \to \rho \gamma)/{\cal B}(B \to K^* \gamma)$ and $\Delta = (\Delta^{+0}+ \Delta^{-0})/2$, where $\Delta^{\pm 0} = \Gamma (B^\pm \to \rho^\pm \gamma)/ [2 \Gamma (B^0 (\bar B^0)\to \rho^0 \gamma)] - 1$, and hence their measurements will provide quantitative information on the standard model parameters, in particular the ratio of the CKM matrix elements $| V_{td}/V_{ts}|$ and the inner angle $\alpha$ of the CKM-unitarity triangle. We also calculate direct CP asymmetries for the decays $B^\pm \to \rho^\pm \gamma$ and $B^0/\bar B^0 \to \rho^0 \gamma$ and find, in conformity with the observations made in the existing literature, that the hard spectator contributions significantly reduce the asymmetries arising from the vertex corrections.Comment: 45 pages, 18 figures (requires amssymb and epsf); replaced with the revised versio