QCD Static Force in Gradient Flow

Abstract

We compute the QCD static force and potential using gradient flow at next-to-leading order in the strong coupling. The static force is the spatial derivative of the static potential: it encodes the QCD interaction at both short and long distances. While on the one side the static force has the advantage of being free of the $O({\Lambda }_{\mathrm{QCD}})$ renormalon affecting the static potential when computed in perturbation theory, on the other side its direct lattice QCD computation suffers from poor convergence. The convergence can be improved by using gradient flow, where the gauge fields in the operator definition of a given quantity are replaced by flowed fields at flow time $t$, which effectively smear the gauge fields over a distance of order $\sqrt{t}$, while they reduce to the QCD fields in the limit $t\to 0$. Based on our next-to-leading order calculation, we explore the properties of the static force for arbitrary values of $t$, as well as in the $t\to 0$ limit, which may be useful for lattice QCD studies.

24 pages, 8 figures, 1 table

References in corpus (8)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Sector Decomposition
• Nonperturbative determination of the QCD potential at O(1/m)
• Spin-dependent potentials from lattice QCD
• ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential
• Inclusive Production of Heavy Quarkonia in pNRQCD
• The static force from generalized Wilson loops using gradient flow

Cited by in corpus (8)

• Unveiling confinement in pure gauge SU(3): flux tubes, fields, and magnetic currents
• Off-lightcone Wilson-line operators in gradient flow
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Subleading power corrections to heavy quarkonium production in QCD factorization approach
• QCD static force in gradient flow
• Non-Markovian dynamics of bottomonia in the QGP
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• One-loop matching for quark dipole operators in a gradient-flow scheme