A General Effective Action for High-Density Quark Matter

Abstract

We derive a general effective action for quark matter at nonzero temperature and/or nonzero density. For this purpose, we distinguish irrelevant from relevant quark modes, as well as hard from soft gluon modes by introducing two separate cut-offs in momentum space, one for quarks, ${\Lambda }_q$, and one for gluons, ${\Lambda }_g$. We exactly integrate out irrelevant quark modes and hard gluon modes in the functional integral representation of the QCD partition function. Depending on the specific choice for ${\Lambda }_q$ and ${\Lambda }_g$, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the ``Hard Thermal Loop'' or the ``Hard Dense Loop'' action, as well as the high-density effective theory proposed by Hong and others. We then apply our effective action to review the calculation of the color-superconducting gap parameter to subleading order in weak coupling, where the strong coupling constant $g\ll 1$. In this situation, relevant quark modes are those within a layer of thickness $2{\Lambda }_q$ around the Fermi surface. The non-perturbative nature of the gap equation invalidates naive attempts to estimate the importance of the various contributions via power counting on the level of the effective action. Nevertheless, once the gap equation has been derived within a particular many-body approximation scheme, the cut-offs ${\Lambda }_q,{\Lambda }_g$ provide the means to rigorously power count different contributions to the gap equation. We recover the previous result for the QCD gap parameter for the choice $Λ_q \alt g μ\ll Λ_g \alt μ$, where $\mu$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

34 pages, 22 figures, RevTeX4, minor revisions compared to v1

References in corpus (3)

• Non-Fermi Liquid Effects in QCD at High Density
• Generalized Ward identity and gauge invariance of the color-superconducting gap
• High Density Effective Theory of QCD

Cited by in corpus (14)

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• Two lectures on color superconductivity
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• Phase space and quark mass effects in neutrino emissions in a color superconductor
• BCS-BEC crossover in a relativistic boson-fermion model beyond mean field approximation
• Absence of the London limit for the first-order phase transition to a color superconductor
• Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order
• Low Energy Dynamics in Ultradegenerate QCD Matter
• The Complex Gap in Color Superconductivity
• Treating divergence in quark matter by using energy projectors
• A massive high density effective theory
• An Abelian Ward identity and the vertex corrections to the color superconducting gap