We explore a novel approach to compute the force between a static quark-antiquark pair with the gradient flow algorithm on the lattice. The approach is based on inserting a chromoelectric field in a Wilson loop. The renormalization issues, associated with the finite size of the chromoelectric field on the lattice, can be solved with the use of gradient flow. We compare numerical results for the flowed static potential to our previous measurement of the same observable without a gradient flow.

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The heavy quark diffusion coefficient is encoded in the spectral functions of the chromoelectric and the chromomagnetic correlators that are calculable on the lattice. We study the chromoelectric and the chromomagnetic correlator in the deconfined phase of SU(3) gauge theory using Symanzik flow at two temperatures 1.5T c and 10000T c , with T c being the phase transition temperature. To control the lattice discretization errors and perform the continuum limit we use several temporal lattice extents N t = 16, 20, 24 and 28. We observe that the flow time dependence of the chromomagnetic correlator is quite different from chromoelectric correlator most likely due to the anomalous dimension of the former as has been pointed out recently in the literature.

The heavy quark diffusion coefficient is encoded in the spectral functions of the chromoelectric and the chromomagnetic correlators that are calculable on the lattice. We study the chromoelectric and the chromomagnetic correlator in the deconfined phase of SU(3) gauge theory using Symanzik flow at two temperatures 1.5𝑇 𝑐 and 10000𝑇 𝑐 , with 𝑇 𝑐 being the phase transition temperature. To control the lattice discretization errors and perform the continuum limit we use several temporal lattice extents 𝑁 𝑡 = 16, 20, 24 and 28. We observe that the flow time dependence of the chromomagnetic correlator is quite different from chromoelectric correlator most likely due to the anomalous dimension of the former as has been pointed out recently in the literature.

We calculate chromo-electric and chromo-magnetic correlators in quenched QCD at 1.5Tc and 10 4 Tc with the aim to estimate the heavy quark diffusion coefficient at leading order in the inverse heavy quark mass expansion, κE, as well as the coefficient of first mass suppressed correction, κB. We use gradient flow for noise reduction. At 1.5Tc we obtain: 1.70 ≤ κE/T 3 ≤ 3.12 and 1.23 < κB/T 3 < 2.74. The latter implies that the mass suppressed effects in the heavy quark diffusion coefficient are 20% for bottom quarks and 34% for charm quark at this temperature.