The Color-Electric Field Correlator under Gradient Flow at next-to-leading Order in Quantum Chromodynamics

Abstract

The exploration of the strong interaction by heavy-ion collisions is an important step towards a deeper understanding of nature. An experimentally and theoretically accessible probe for the details of the strong interactions are the transport properties of heavy quarks inside a quark-gluon plasma. One of the these transport coefficients is the momentum diffusion coefficient of a heavy quark. It is determined by the spectral function of an Euclidean correlator of two color-electric fields along a Polyakov loop. This purely bosonic correlator can be simulated non-perturbatively using lattice gauge theory. The correlator suffers from noise to the point where the determination of the signal is not possible. This problem can be solved by noise-reduction techniques. Luscher introduced the gradient flow procedure as an effective gauge-invariant noise-reduction technique. Gradient flow regulates the ultra-violet behavior of correlation functions hence suppressing the noise. Consequently, the renormalization properties of the gradient flowed operators are modified. In this thesis we analyze the effects of gradient flow on the color-electric field correlation function using perturbation theory in the continuum and on the lattice at next-to-leading order in the small coupling expansion, O(αₛ²). We discuss the relation between a gradient-flowed Euclidean correlator and its spectral function. From this we conclude the necessary order for taking the continuum limit first and flow time to zero limit second in lattice simulations. With a qualitative study of the correlator in lattice QED we determine the renormalization effects of the field operators at finite lattice spacing and flow time. We compute the correlation function in continuum QCD and evaluate the small separation and small flow time limits. The results obtained in this study improve the understanding of the usage of the gradient flow method in future lattice simulations of full QCD determining transport coefficients.