QCD potential atO(1/m)

Abstract

Within an effective field theory framework, we obtain an expression for the next-to-leading term in the 1/m expansion of the singlet QQ QCD potential in terms of Wilson loops, which holds beyond perturbation theory. The ambiguities in the definition of the QCD potential beyond leading order in 1/m are discussed and a specific expression for the 1/m potential is given. We explicitly evaluate this expression at one loop and compare the outcome with the existing perturbative results. On general grounds we show that for quenched QED and fully Abelian-like models this expression exactly vanishes.

Heavy quarkonium and nonrelativistic effective field theories

“…A detailed description of the procedure can be found in [3,9,7,13]. Here we just state the main results and briefly discuss how they are obtained.…”

“…[14], the two-loop one in Ref. [15] and the three-loop leading-log in [6]. The β n are the coefficients of the beta function and the values of a 1 and a 2 can be found in Ref.…”

“…The one-loop leading-log dependence on ln µr is obtained in [13] (see also [17]). By taking into account the NRQCD matching coefficients (c D , c F ...; see [2,11] for its values at one loop) in the vertices when matching to pNRQCD, one obtains the leading-log dependence on ln mr plus also some finite pieces.…”

“…The last years have witnessed important progress in the theoretical understanding of heavy-quark-antiquark systems near threshold through the use of effective field theories [1][2][3][4][5][6][7] (see also [8][9][10] for related work in QED). The key point relies on the fact that, since the quark velocity v is a small quantity, v ≪ 1, a hierarchy of widely separated scales: m ≫ mv ≫ mv 2 ... is produced in these systems, where m is the heavy quark mass (hard scale), mv the soft scale and mv 2 the ultrasoft scale.…”

“…The integration of degrees of freedom is done in practice through a matching procedure (see [2,11,9,7] for details). The matching from QCD to NRQCD can always be done perturbatively since, by definition of heavy quark, m ≫ Λ QCD [2,11].…”