Power Counting and βFunction in NRQCD

Abstract

A computation of the NRQCD $\beta$ function both in the Lorentz gauge family and in the Coulomb gauge to one loop order endorses a velocity power counting scheme for dimensionally regularised NRQCD. In addition to the ultrasoft scale represented by bremsstrahlung gluons and the potential scale with Coulomb gluons and on-shell quarks, a soft régime is identified in which energies and momenta are of order $Mv$, gluons are on shell and the quark propagator becomes static. The instantaneous gluon propagator has a non-zero vacuum polarisation only because of contributions from this régime, irrespective of the gauge chosen. Rules are derived which allow one to read up from a given graph whether it is zero because of the homogene{\ia}ty of dimensional regularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order $M{v}^2$ decouple from the theory.

41 pages, LaTeX2e, uses feynmp to generate 122 drawings in 10 figures, 4 tables and 45 graphs in equations; necessary METAPOST-files included. Major re-organisation and clarifications, adding discussion of βfunction in Coulomb gauge and detailed treatment of non-Abelian vertex corrections. Version to appear in Nucl. Phys. B

References in corpus (13)

• Asymptotic expansion of Feynman integrals near threshold
• Two-loop QCD corrections to the heavy quark pair production cross section in e+e- annihilation near the threshold
• Potential NRQED: The Positronium Case
• Effective Field Theory and Matching in Non-Relativistic Gauge Theories
• Top Quark Pair Production at Threshold: Complete Next-to-next-to-leading Order Relativistic Corrections
• Power Counting in Dimensionally Regularized NRQCD
• Renormalization Group Scaling of the 1/m^2 HQET Lagrangian
• Threshold Expansion and Dimensionally Regularised NRQCD
• The Single Photon Annihilation Contributions to the Positronium Hyperfine Splitting to Order $m_e{\alpha }^6$
• The Perturbative QCD Potential and the ttbar Threshold
• Some aspects of the quark-antiquark Wilson loop formalism in the NRQCD framework
• First study of $B\to \pi$ semileptonic decay form factors using NRQCD
• New results on heavy hadron spectroscopy with NRQCD

Cited by in corpus (13)

• Effective field theories for heavy quarkonium
• Ultrasoft Renormalization in Non-Relativistic QCD
• The Running Coulomb Potential and Lamb Shift in QCD
• Pions in the Pionless Effective Field Theory
• Renormalization of $NN$ scattering: contact potential
• B\to πϕin SM and MSSM
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Large Strong Phases and CP Violation in the Annihilation Processes ${\bar{B}}^0\to K^{+}{K}^{-}$, $K^{\ast \pm }{K}^{\mp }$, $K^{\ast +}{K}^{\ast -}$
• Decay b -> (c\bar{c}) s in the leading logarithm approximation
• Search for new physics from $B\to \pi \varphi$
• Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory
• Renormalization group analysis of electromagnetic properties of the deuteron
• The Soft Régime and βFunction of NRQCD