Continuum extrapolation of the gradient-flowed color-magnetic correlator at $1.5\,T_c$

Abstract

In a recently published work we employ gradient flow on the lattice to extract the leading contribution of the heavy quark momentum diffusion coefficient in the heavy quark limit from calculations of a well-known two-point function of color-electric field operators. In this article we want to report the progress of calculating the recently derived color-magnetic correlator that encodes a finite mass correction to this transport coefficient. The calculations we present here are based on the same ensemble of quenched gauge configurations at 1.5 𝑇 𝑐 that we previously used for the color-electric correlator.

Heavy quark diffusion coefficient with gradient flow

“…Our main result is summarized in Eqs. ( 32), (33) and (34). Our results for κ E agree with the previous determinations [22,33,51] within the estimated uncertainties.…”

“…( 32), (33) and (34). Our results for κ E agree with the previous determinations [22,33,51] within the estimated uncertainties. The value of κ B obtained by us agrees with the very recent result obtained using multilevel algorithm and non-perturbative renormalization based on Schrödinger functional [26].…”

“…The limit to zero flow time has to be taken after the continuum limit to avoid the large discretization effects at small flow times. Also, it is argued in [33,43] that the inversion of spectral function via Eq. ( 5) is mathematically well-defined only at zero flow time limit.…”

“…Also, preliminary measurements of the chromomagnetic correlator required for κ B have been performed with the gradient flow and presented in conference proceedings by two groups using gradient flow [33,34].…”

Heavy quarks at finite temperature

“…( 11) is related to the O ( / ℎ ) corrections to . Preliminary results of the first such calculations have been reported at this conference [31,32]. The imaginary part in Eq.…”