Renormalization group analysis of color superconductivity revisited

TL;DR

This paper revisits the analysis of color superconductivity in dense quark matter using a renormalization group approach, incorporating self-energy corrections to better understand the gap structure and compare with lattice results.

Contribution

It introduces an RG framework with self-energy corrections for analyzing the color-superconducting gap, providing clearer insight into pairing patterns and higher-order calculations.

Findings

Reproduces known weak-coupling gap results at order O(g^0)

Clarifies the angular momentum structure of pairing channels

Suggests RG as a systematic method for higher-order gap computations

Abstract

Color superconductivity in cold, dense quark matter is a key feature of the QCD phase diagram, whose present theoretical understanding relies predominantly on weak-coupling calculations. In this work, we revisit the evaluation of the color-superconducting gap using a renormalization group (RG) framework formulated in effective theory near the Fermi surface. By incorporating quark self-energy corrections into the RG equation, we reproduce the known weak-coupling results from the gap equation at the same perturbative order at $O(g^0)$. Within the RG approach, the angular momentum structure of the pairing channel becomes more transparent, allowing us to examine the size of the gap for various pairing patterns. We also compare our results with recent lattice QCD calculations at finite isospin density. Finally, we argue that the RG method potentially offers a simpler and more systematic route to higher-order computations of the gap, which are of order $O(g)$ and thus quantitatively important.