arXiv subjects
Publications and source records attributed to A. G. Grozin.
Three-loop propagator diagrams in HQET can be reduced, using integration by parts, to 8 basis integrals: 5 trivial ones, two expressible via 3F2, and one only known up to ε^0. Calculation of the heavy-quark propagator in HQET is considerably simplified by the non-abelian exponentiation theorem.
Contribution of the gluon distribution in the nucleon to the cross section for the pion diffractive dissociation into two jets has been calculated recently. In addition, we present here calculation of contribution of the quark distributions to this process. It is expected usually that the quark contributions are much smaller than the gluon one at high energies. We show that, under the conditions of the E791 experiment, the quark contributions are as significant as the gluon one, so that the total cross section exceeds several times those with only gluon contribution. Nevertheless, the distribution of jets in longitudinal momentum fractions does not change significantly and remains qualitatively the same. We compare our results with the data from the E791 experiment.
We calculate the HQET quark-gluon vertex at one loop, for arbitrary external momenta, in an arbitrary covariant gauge and space-time dimension. Relevant results and algorithms for the three-point HQET integrals are presented. We also show how one can obtain the HQET limit directly from QCD results for the quark-gluon vertex.
Extended version of lectures given at the University of Karlsruhe and at Calc-2000 school in Dubna. Properties of HQET as a field theory, methods of calculation of HQET diagrams and some simple applications are explained in detail. These lectures can be used as an additional chapter with any modern QCD textbook.
An algorithm for calculation of three-loop propagator diagrams in HQET, based on integration-by-parts recurrence relations, is constructed and implemented as a REDUCE package Grinder, and in Axiom.
Semileptonic B decays are described by the Isgur-Wise form factor to the leading order in 1/m; four new functions appear in the first order [Luke]. Values of these functions are crucial for the applicability of the whole approach to processes involving c quark. We obtain the sum rules for three subleading form factors from the QCD sum rules with finite masses by expanding to the first order in 1/m. The results respect the pattern of the first 1/m corrections established in HQET, and obey the Luke's theorem. The numerical estimates show that 1/m_c corrections are sizable but not catastrophic.
Heavy Quark Effective Theory (HQET) is a new approach to QCD problems involving a heavy quark. In the leading approximation, the heavy quark is considered as a static source of the gluon field; 1/m corrections can be systematically included in the perturbation theory. New symmetry properties not apparent in QCD appear in HQET. They are used, in particular, to obtain relations among heavy hadron form factors. HQET also simplifies lattice simulation and sum rules analysis of heavy hadrons.
We give a recurrence relation for two-loop integrals encountered in the effective field theory of an infinitely heavy quark, Q, interacting with gluons and Nl massless quarks, q, from which we obtain exact two-loop results, in any dimension and covariant gauge, for the propagator of Q and the vertex function of the heavy-light current J = Q Gamma q, at zero q momentum. The anomalous dimension of the Q field agrees with the recent result of Broadhurst, Gray and Schilcher. The anomalous dimension of the current is gamma_J = d log Z_J / d log mu = - alpha_s/pi (1 + (127 + 56 zeta(2) - 10 Nl)/72) alpha_s/pi + O(alpha_s^2)) which gives the new two-loop correction to the result of Voloshin and Shifman.
HQET currents with the quantum numbers of the ground-state baryons are discussed. One-loop anomalous dimensions are calculated, and exact one-loop matching to QCD currents is found. Two-point correlators of these currents are calculated taking into account $d\le9$ terms of the OPE. Sum rules for heavy baryons Lambda_Q and Sigma^(*)_Q are analyzed. Three-point correlators of two baryonic currents and a heavy-heavy velocity changing current are calculated with the same accuracy. The baryonic Isgur-Wise form factors are estimated from the corresponding sum rules.
We calculate the coefficients of operators with dimensions d <= 7 in the operator product expansion of correlators of q Gamma Q currents, for the effective field theory of an infinite-mass quark, Q. Exact two-loop results are obtained, with an arbitrary gauge group and spacetime dimension, for the perturbative (d=0) and quark-condensate (d=3) contributions, confirming our previous result for the anomalous dimension of the current. Leading-order results are given for light-quark operators with d=5, 6, 7 and gluon operators with d=4, 6. The existence of a perturbative correction of order 100% precludes a reliable determination of f_B from non-relativistic sum rules.
The effect of non-zero c quark mass on b quark HQET Lagrangian, up to 1/m_b level, is calculated at two loops. The results are expressed in terms of dilogarithmic functions of m_c/m_b. This calculation involves on-shell two-loop propagator-type diagrams with two different masses, m_b and m_c. A general algorithm for reducing such Feynman integrals to the basis of two nontrivial and two trivial integrals is constructed.
Matching of light-light quark currents in QCD with a heavy flavour and in the low-energy effective QCD is calculated in MSbar at two loops. Heavy-light HQET currents are similarly considered.
HQET lagrangian up to $1/m^3$ terms is discussed. Consequences of reparameterization invariance are considered. Results for the chromomagnetic interaction coefficient at two loops, and in all orders in the large--$β_1$ approximation, are presented.
The leading beta_0^(n-1) alpha_s^n terms in the Wilson coefficient and anomalous dimension of the chromomagnetic operator in the heavy-quark effective Lagrangian are summed to all orders of perturbation theory. The perturbation series for the anomalous dimension is well behaved, while that for the Wilson coefficient exhibits a divergent behaviour already in low orders, caused by a nearby infrared renormalon singularity. The resulting ambiguity is commensurate with terms of order 1/m^2 in the effective Lagrangian, whose corresponding ultraviolet renormalons are identified. An excellent approximation for the scheme-invariant Wilson coefficient at next-to-next-to-leading order in renormalization-group improved perturbation theory is obtained.
We estimate the couplings in the Heavy Hadron Chiral Theory (HHCT) lagrangian from the QCD sum rules in an external axial field. We take into account the perturbative correction to the meson correlator in the infinite mass limit. With the perturbative correction and three successive power corrections, the meson correlator in an axial field becomes one of the best known correlators. In spite of this, the corresponding sum rule is not very stable. It yields the result g_1 F^2/(380MeV)^3 = 0.1 - 0.2, where F^2 = f_M^2 m/4 = (380MeV)^3 is the central value of the heavy meson decay constant with the perturbative correction. This result is surprisingly low as compared with the constituent quark model estimate g_1 = 0.75. The sum rules for g_{2,3} following from nondiagonal Sigma-Sigma and diagonal Lambda-Sigma baryon correlators in an external axial field suggest g_{2,3} = 0.4 - 0.7, while diagonal Sigma-Sigma and nondiagonal Lambda-Sigma baryon sum rules have too large uncertainties.
We present the coefficient of the chromomagnetic interaction operator, the only unknown coefficient in the Heavy Quark Effective Theory (HQET) lagrangian up to the $1/m$ level, with the two-loop accuracy by matching scattering amplitudes of an on-shell heavy quark in an external field in full QCD and HQET, and obtain the two-loop anomalous dimension of this operator in HQET.
We review algorithmic methods for two-loop calculations in HQET, and the analogous methods for on-shell QCD, needed for matching HQET to QCD.
Although the methods of calculation of power corrections in QCD sum rules are well known, algebraic complexity rapidly grows with the increase of vacuum condensates' dimensions. Currently, state-of-the-art calculations include dimension 7 and 8 condensates. I summarize and extend algorithms of such calculations. First, I present all the formulae necessary for application of the systematic classification of bilinear quark condensates proposed earlier, and extend this method to the case of gluon condensates. Then I apply these systematic procedures to expansions of bilinear and noncollinear quark and gluon condensates in local ones, and of noncollinear condensates in bilocal ones. The formulae obtained can be used for calculation of correlators involving nonlocal condensates, and for inventing consistent anzatzs for these condensates. Finally, I briefly summarize the methods of calculation of heavy- and light-quark currents' correlators. This paper is aimed both to present new results on gluon and nonlocal condensates and to be a self-contained handbook of formulae necessary for calculation of power corrections in QCD sum rules.