document: An OPE of VQCD(r) was developed in [3]. In this and the next paragraph, we review the content of that paper relevant to our analysis. Within this framework, short-distance contributions are contained in the potentials, which are in fact the Wilson coefficients, while non-perturbative contributions are contained in the matrix elements that are organized in multipole expansion in r→ at r≪ΛQCD−1. The following relation was derived: (16)VQCD(r)=VS(r)+δEUS(r),(17)δEUS=−ig2TFNC∫0∞dte−iΔV(r)t×〈r→⋅E→a(t)φadj(t,0)abr→⋅E→b(0)〉+O(r3). VS(r) denotes the singlet potential. δEUS(r) denotes the non-perturbative contribution to the QCD potential, which starts at O(ΛQCD3r2) in the multipole expansion. ΔV(r)=VO(r)−VS(r) denotes the difference between the octet and singlet potentials; see [3] for details. Intuitively VS(r) corresponds to VUV(r;μf) and δEUS(r) to VIR(r;μf). We adopt dimensional regularization in our analysis; we also refer to hard cutoff schemes when discussing conceptual aspects.
extractive_keyphrases: dimensional regularization hard cutoff schemes multipole expansion ope qcd potential
abstractive_keyphrases: vqcd(r)