Vladimir M. Braun

Evolution Equations for QCD String Operators

Abstract It is shown that all of the usual programs for the operator expansion can be performed in terms of string operators on the light cone; namely, the separation of contributions from large and small distances, the study of higher twist corrections and the renormalization group analysis. Evolution equations for the leading-twist QCD string operators such as g y(x)P exp (ig∫ C A μ d x μ )ψ(0) are studied in the coordinate space, which has an advantage of preserving explicitly the Lorentz and (in one-loop) conformal invariance of the theory. The solution is found, relating the two string operators in different normalization points. Its short-distance expansion reproduces conventional results for the summation of leading logs in deep inelastic scattering and evolution of hadron wave functions. The light-cone expansion of string operators provides an effective covariant technique for a separation of higher twist effects. As an illustration we calculate the twist-three and twist-four corrections for the deep inelastic scattering and confirm in this way the recent results on the renormalization of twist-three operators.

Heavy quark effective theory beyond perturbation theory: Renormalons, the pole mass and the residual mass term

We study the asymptotic behaviour of the perturbative series in the heavy quark effective theory (HQET) using the 1/Nƒ expansion. We find that this theory suffers from an ultraviolet renormalon problem, corresponding to a non-Borel-summable behaviour of perturbation series in large orders, and leading to a principal nonperturbative ambiguity in its definition. This ambiguity is related to an infrared renormalon in the pole mass and can be understood as the necessity to include the residual mass term δm in the definition of HQET, which must be considered as ambiguous (and possibly complex), and is required to cancel the ultraviolet renormalon singularity generated by the perturbative expansion. The formal status of δm is thus identical to that of condensates in the conventional short-distance expansion of correlation functions in QCD. The status of the pole mass of a heavy quark, the operator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.We study the asymptotic behaviour of the perturbative series in the heavy quark effective theory (HQET) using the 1/N f expansion. We find that this theory suffers from an ultraviolet renormalon problem, corresponding to a non-Borel-summable behaviour of perturbation series in large orders, and leading to a principal nonperturbative ambiguity in its definition. This ambiguity is related to an infrared renormalon in the pole mass and can be understood as the necessity to include the residual mass term δm in the definition of HQET, which must be considered as ambiguous (and possibly complex), and is required to cancel the ultraviolet renormalon singularity generated by the perturbative expansion. The formal status of δm is thus identical to that of conden-sates in the conventional short-distance expansion of correlation functions in QCD. The status of the pole mass of a heavy quark, the operator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.

Integrability of Three-Particle Evolution Equations in QCD

We show that Brodsky-Lepage evolution equation for the spin-3/2 baryon distribution amplitude is completely integrable and reduces to the three-particle

Exclusive semileptonic and rare B meson decays in QCD

{\mathrm{XXX}}_{s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1}

Higher twist distribution amplitudes of vector mesons in QCD: Formalism and twist 3 distributions

Heisenberg spin chain. Trajectories of the anomalous dimensions are identified and calculated using the

D* D pi and B* B pi couplings in QCD

1/N

Baryon distribution amplitudes in QCD

expansion. Extending this result, we prove integrability of the evolution equations for twist-3 quark-gluon operators in the large

Radiative decay σ+ → pγ in quantum chromodynamics

{N}_{c}

The Uses of conformal symmetry in QCD

limit.

Higher-twist distribution amplitudes of the K meson in QCD

We present the first complete results for the semileptonic and rare radiative form factors of the B meson’s weak decay into a light vector meson (r,v,K*,f) in the light-cone sum rule approach. The calculation includes radiative corrections, higher twist corrections, and SU ~3! breaking effects. The theoretical uncertainty is investigated in detail. A simple parametrization of the form factors is given in terms of three parameters each. We find that the form factors observe several relations inspired by heavy quark symmetry. @S0556-2821~98!06519-9# The challenge to understand the physics of CP violation related to the structure of the Cabibbo-Kobayashi-Maskawa ~CKM! mixing matrix in ~and beyond! the standard model is fueling an impressive experimental program for the study of B decays, both exclusive and inclusive. Abundant data in various exclusive channels are expected to arrive within the next few years from the dedicated B factories BaBar and Belle, and their potential impact on our understanding of CP violation at the electroweak scale will depend crucially on our possibility to control the effects of strong interactions. For exclusive decays with only one hadron in the final state the task is to calculate various transition form factors; it has already attracted significant attention in the literature. In this paper we present the first complete results for the exclusive semileptonic and rare radiative B decays to light vector mesons in the light-cone sum rule approach. Exclusive decays which are the principal concern of this work can be grouped as semileptonic decays Bu,d!ren, Bs!K*en, rare decays corresponding to b!s transitions which we term CKM-allowed, Bu,d!K*1g, Bu,d!K*1l 1 l 2 , Bs!f 1g, Bs!f1l 1 l 2 , and b!d transitions which we call CKM suppressed, Bd!(r,v)1g, Bd!(r,v)1l 1 l 2 , Bu !r1g, B u !r1l 1 l 2 , B s !K*1g, B s !K*1l 1 l 2 .