dorsal/arxiv
View SchemaA General Effective Action for High-Density Quark Matter
| Authors | Philipp T. Reuter, Qun Wang, Dirk H. Rischke |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0405079 |
| URL | https://arxiv.org/abs/nucl-th/0405079 |
| DOI | 10.1103/PhysRevD.70.114029 10.1103/PhysRevD.71.099901 |
| Journal | Phys.Rev.D70:114029,2004; Erratum-ibid.D71:099901,2005 |
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 $\Lambda_q \alt g \mu \ll \Lambda_g \alt \mu$, where $\mu$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.
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"abstract": "We derive a general effective action for quark matter at nonzero temperature\nand/or nonzero density. For this purpose, we distinguish irrelevant from\nrelevant quark modes, as well as hard from soft gluon modes by introducing two\nseparate cut-offs in momentum space, one for quarks, $\\Lambda_q$, and one for\ngluons, $\\Lambda_g$. We exactly integrate out irrelevant quark modes and hard\ngluon modes in the functional integral representation of the QCD partition\nfunction. Depending on the specific choice for $\\Lambda_q$ and $\\Lambda_g$, the\nresulting effective action contains well-known effective actions for hot and/or\ndense quark matter, for instance the ``Hard Thermal Loop\u0027\u0027 or the ``Hard Dense\nLoop\u0027\u0027 action, as well as the high-density effective theory proposed by Hong\nand others. We then apply our effective action to review the calculation of the\ncolor-superconducting gap parameter to subleading order in weak coupling, where\nthe strong coupling constant $g \\ll 1$. In this situation, relevant quark modes\nare those within a layer of thickness $2 \\Lambda_q$ around the Fermi surface.\nThe non-perturbative nature of the gap equation invalidates naive attempts to\nestimate the importance of the various contributions via power counting on the\nlevel of the effective action. Nevertheless, once the gap equation has been\nderived within a particular many-body approximation scheme, the cut-offs\n$\\Lambda_q, \\Lambda_g$ provide the means to rigorously power count different\ncontributions to the gap equation. We recover the previous result for the QCD\ngap parameter for the choice $\\Lambda_q \\alt g \\mu \\ll \\Lambda_g \\alt \\mu$,\nwhere $\\mu$ is the quark chemical potential. We also point out how to improve\nthis result beyond subleading order in weak coupling.",
"arxiv_id": "nucl-th/0405079",
"authors": [
"Philipp T. Reuter",
"Qun Wang",
"Dirk H. Rischke"
],
"categories": [
"nucl-th",
"cond-mat.supr-con",
"hep-ph"
],
"doi": "10.1103/PhysRevD.70.114029 10.1103/PhysRevD.71.099901",
"journal_ref": "Phys.Rev.D70:114029,2004; Erratum-ibid.D71:099901,2005",
"title": "A General Effective Action for High-Density Quark Matter",
"url": "https://arxiv.org/abs/nucl-th/0405079"
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