Power Counting and β Function in NRQCD
نویسنده
چکیده
A computation of the NRQCD β 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 homogenëıty of dimensional regularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order Mv2 decouple from the theory. Suggested PACS numbers: 12.38.Bx, 12.39.Hg, 12.39.Jh, 11.10.Gh. Suggested
منابع مشابه
Power Counting in Dimensionally Regularized NRQCD
We present a scheme for calculating in NRQCD with consistent power counting in the heavy quark velocity v. As an example, we perform the systematic matching of an external current onto NRQCD at subleading order in v, a calculation relevant for the process ee → hadrons near threshold. Consistent velocity power counting in dimensional regularization is achieved by including two distinct gluon fie...
متن کاملThe Soft Régime and β Function of NRQCD
Progress towards a complete velocity power counting in non-relativistic effective field theories, especially NRQCD, is motivated and summarised. Talk presented at the “Euroconference QCD ’98” in Montpellier, France, 2nd – 8th July 1998 (to appear in Nucl. Phys. B(Proc. Suppl.)), and at the conference “Quark Confinement and the Hadron Spectrum III” at TJNL, Newport News, USA, 8th – 12th June 199...
متن کاملPower Counting and Effective Field Theory for Charmonium
We hypothesize that the correct power counting for charmonia is in the parameter ΛQCD/mc, but is not based purely on dimensional analysis (as is HQET). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of NRQCD. In particular, we show that while ΛQCD/mc power counting preserves the empirically verified predictions of spin sym...
متن کاملNRQCD, Effective Field Theories and Potential Models
The study of the heavy quark–antiquark system is an old topic (see [1] for earlier references). Here we will concentrate on recent developments based on effective field theories. For large enough masses, these systems can be considered to be non-relativistic (NR) and are then characterized by, at least, three widely separated scales: hard (the mass m, of the heavy quarks), soft (the relative mo...
متن کاملHadronic quarkonium decays at order v
We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M4 in the heavy-quark mass expansion, which includes center of mass operators, and at order αs in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order 1/M6 and at order αs that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at or...
متن کامل