Renormalization group scaling in nonrelativistic QCD

Abstract

We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed in which a subtraction velocity nu is used rather than a subtraction scale mu. We derive a novel renormalization group equation in velocity space which can be used to sum logarithms of v in the effective theory. We apply our method to several examples. In particular we show that our formulation correctly reproduces the two-loop anomalous dimension of the heavy quark production current near threshold.Comment: (27 pages, revtex

Mesonic screening masses at high temperature and finite density

“…This works well in the case of a single heavy quark, but, as discussed in [28], will run into problems in NRQCD at two-loop level. We will in this paper follow [28] in keeping the p 2 ⊥ /2p 0 term resummed into the propagator.…”

“…This works well in the case of a single heavy quark, but, as discussed in [28], will run into problems in NRQCD at two-loop level. We will in this paper follow [28] in keeping the p 2 ⊥ /2p 0 term resummed into the propagator. This also means that we have to use the multipole expansion, which in practice means that the gluons are not allowed to transfer transverse momentum to quarks.…”

Heavy pair production currents with general quantum numbers in dimensionally regularized nonrelativistic QCD

“…The matching is carried out at the hard scale ν = 1 and the theory is evolved to ν ∼ v ∼ α s of order of the relative velocity of the two-body system for computations of matrix elements. The running properly sums logarithms of the momentum and the energy scale at the same time [11,12,13,14] and is referred to as the velocity renormalization group (VRG) [11]. Within dimensional regularization the powers of µ ǫ S and µ ǫ U multiplying the operators of the Lagrangian are uniquely determined by the v counting and the dimension of the operators in d = 4 − 2ǫ dimensions.…”

“…[11] is was pointed out that for dynamical heavy quarkonium systems the dispersive correlation between ultrasoft energy and soft momentum scales, E ∼ p 2 /m, can be implemented systematically at the field theoretic level by matching to the proper EFT directly at the hard scale µ ∼ m (one-step matching). The EFT, called vNRQCD ("velocity" NRQCD) has a strict power counting in v. It contains soft and ultrasoft degrees of freedom as well as soft and ultrasoft renormalization scales, µ S and µ U .…”

Heavy quark pair production near threshold with potential non-relativistic QCD

“…Inclusive electromagnetic decays of heavy quarkonium have been computed to NLL [26,23] and for the spin-zero, spin-one ratio to NNLL [27]. In the case of top-quark pair production a renormalization-group improved (RGI) calculation is available [28,29], using a somewhat different approach, referred to as vNRQCD [30] (in this theory, soft degrees of freedom are kept dynamical and the matching from QCD to vNRQCD is carried out directly). However, so far, there is no RGI calculation of heavy-quark pair production within the conventional pNRQCD approach.…”