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arXiv · 2508.19222

Classification of color superconductivity by one-gluon exchange helicity amplitudes and renormalization group equations

Yuki Fujimoto
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Abstract

Quark matter at high baryon density exhibits diverse pairing patterns classified by color, flavor, and angular momentum quantum numbers. We compute one-gluon exchange (OGE) helicity amplitudes and introduce a nonrelativistic classification of the pairing channel, justified by the channel decomposition in a Lorentz-noninvariant medium and the decoupling of renormalization group flows at leading order. We find the new attractive channel in OGE; the medium effects can render the vacuum-repulsive color $\boldsymbol{6}$ channel attractive in the spin-triplet sector. For color $\boldsymbol{\bar{3}}$ with antisymmetric flavor, the dominant pairing is ${}^1S_0$, while for symmetric flavor the same-helicity $^1P_1$ prevails over $^3S_1$, revising the conventional single-flavor picture. With a mismatch of the Fermi momenta, $^1S_0$ channel, leading to color-flavor locked or two-flavor color superconductor, remains most stable when the separation is small, and the color-spin locked pairing becomes favored as the mismatch gets large. We suggest there are possible quark-hadron continuity in certain cases as expected in the literature.

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Yuki Fujimoto. 2025-08-26. Classification of color superconductivity by one-gluon exchange helicity amplitudes and renormalization group equations. https://arxiv.org/abs/2508.19222

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