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We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper provides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time.
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We show that the Heavy Quark Effective Theory is renormalizable perturbatively. We also show that there exist renormalization schemes in which the infinite quark mass limit of any QCD Green function is exactly given by the corresponding Green function of the Heavy Quark Effective Theory. All this is accomplished while preserving BRS invariance.
It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry $C(u)$ of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the ground state wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.
The scaling behavior of semileptonic form-factors in Heavy to Light transitions is studied in the Heavy Quark Effective Theory. In the case of $Hrightarrow pi e u$ it is shown that the same scaling violations affecting the heavy meson decay constant will be present in the semileptonic form-factors.
We report results from a study of heavy-baryon spectroscopy within a relativistic constituent- quark model, whose hyperfine interaction is based on Goldstone-boson-exchange dynamics. While for light-flavor constituent quarks it is now commonly accepted that the effective quark-quark interaction is (predominantly) furnished by Goldstone-boson exchange - due to spontaneous chiral-symmetry breaking of quantum chromodynamics at low energies - there is currently still much speculation about the light-heavy and heavy-heavy quark-quark interactions. With the increasing amount of experimental data on heavy-baryon spectroscopy these issues might soon be settled. Here, we show, how the relativistic constituent-quark model with Goldstone-boson-exchange hyperfine interactions can be extended to charm and bottom baryons. It is found that the same model that has previously been successful in reproducing the light and strange baryon spectra is also in line with the existing phenomenological data on heavy-baryon spectroscopy. An analogous model with one-gluon-exchange hyperfine interactions for light-heavy flavors does not achieve a similarly good performance.
We present a general study on exclusive semileptonic decays of heavy (B, D, B_s) to light (pi, rho, K, K^*) mesons in the framework of effective field theory of heavy quark. Transition matrix elements of these decays can be systematically characterized by a set of wave functions which are independent of the heavy quark mass except for the implicit scale dependence. Form factors for all these decays are calculated consistently within the effective theory framework using the light cone sum rule method at the leading order of 1/m_Q expansion. The branching ratios of these decays are evaluated, and the heavy and light flavor symmetry breaking effects are investigated. We also give comparison of our results and the predictions from other approaches, among which are the relations proposed recently in the framework of large energy effective theory.
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