The hyperfine splitting in QCD mesonic screening masses at asymptotically large temperatures

TL;DR

This paper analytically calculates the hyperfine splitting in QCD mesonic screening masses at very high temperatures using a dimensionally-reduced effective theory, providing insights for interpreting lattice QCD data.

Contribution

It presents the first $O(g^4)$ analytic calculation of hyperfine splitting in high-temperature QCD screening masses, aiding the understanding of non-perturbative effects.

Findings

Analytic $O(g^4)$ result for hyperfine splitting.

Comparison with lattice data shows higher order effects are significant.

Results help interpret non-perturbative lattice QCD data at high temperatures.

Abstract

We determine the hyperfine splitting in the QCD flavour non-singlet mesonic screening masses at asymptotically large temperatures. The analytic calculation is carried out in the dimensionally-reduced effective theory where the first non-zero contribution is of $O(g^4)$ in the QCD coupling constant $g$. Apart for its own theoretical interest, this result provides instrumental information to interpret and to parameterize non-perturbative data that are being produced at very high temperatures by numerical simulations of lattice QCD. Indeed, the comparison with existing non-perturbative results shows that higher order (non-perturbative) contributions in $g$ are needed to explain the data up to the highest temperatures explored, which is of the order of the electroweak scale.