Lattice study of a magnetic contribution to heavy quark momentum diffusion

Abstract

Heavy quarks placed within a hot QCD medium undergo Brownian motion, characterized by specific transport coefficients. Their determination can be simplified by expanding them in T/M, where T is the temperature and M is a heavy quark mass. The leading term in the expansion originates from the colour-electric part of a Lorentz force, whereas the next-to-leading order involves the colour-magnetic part. We measure a colour-magnetic 2-point correlator in quenched QCD at T ∼ (1.2 − 2.0)Tc. Employing multilevel techniques and non-perturbative renormalization, a good signal is obtained, and its continuum extrapolation can be estimated. Modelling the shape of the corresponding spectral function, we subsequently extract the momentum diffusion coefficient, κ. For charm (bottom) quarks, the magnetic contribution adds ∼ 30% (10%) to the electric one. The same increases apply also to the drag coefficient, η. As an aside, the colour-magnetic spectral function is computed at NLO.

Heavy quark diffusion coefficient with gradient flow

“…This result is well in agreement with the recent result [12], that got 1.0 ≤ 𝜅 B /𝑇 3 ≤ 2.1. The current data is not accurate enough to determine 𝜅 B at 𝑇 = 10 4 𝑇 𝑐 .…”

“…Similarly to our preceding multilevel study [11], we extract 𝜅 E and 𝜅 B using Eq. ( 2) and modeling the spectral function 𝜌(𝜔) using the UV and IR behaviors motivated by the perturbation theory [12,24]:…”

“…where ℎ 0 is a constant and 𝛾 0 = 3/(8𝜋 2 ) is the anomalous dimension of the chromo-magnetic field [12]. Using the NLO result from Ref.…”

“…Heavy quark diffusion coefficient with gradient flow Viljami Leino Banerjee 2012 [9] Francis 2015 [10] Altenkort 2021 [18] Brambilla 2020 [11] Banerjee 2022a [12] Banerjee 2022b [13] Brambilla 2022 [20] Figure 5: Our result of 𝜅 E (Grey diamond) compared to existing lattice results.…”

“…The diffusion coefficients 𝜅 E,B have been studied on the lattice within this approach in pure gauge theory [8][9][10][11][12][13], using the multilevel algorithm [14]. Recently, the gradient flow algorithm [15,16] has been found to be useful for this quantity due to its renormalization properties and because it can be extended to theories with dynamical fermions more easily than multilevel simulations.…”