arXiv subjects

Philipp T. Reuter

Publications and source records attributed to Philipp T. Reuter.

4 recordsLinked to original sources

arXiv2007

A massive high density effective theory

We derive an effective theory for dense, cold and massive quark matter. To this end, we employ a general effective action formalism where antiquarks and quarks far from the Fermi surface, as well as hard gluons, are integrated out explicitly. We show that the resulting effective action depends crucially on the projectors used to separate quarks from antiquarks. If one neglects the quark masses in these projectors, the Feynman rules of the effective theory involve quark mass insertions which connect quark with antiquark propagators. Including the quark masses into these projectors, mass insertions do not appear and the Feynman rules are identical to those found in the zero-mass limit.

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arXiv2006

The Complex Gap in Color Superconductivity

We solve the gap equation for color-superconducting quark matter in the 2SC phase, including both the energy and the momentum dependence of the gap, ϕ=ϕ(k_0,\vk). For that purpose a complex Ansatz for ϕis made. The calculations are performed within an effective theory for cold and dense quark matter. The solution of the complex gap equation is valid to subleading order in the strong coupling constant g and in the limit of zero temperature. We find that, for momenta sufficiently close to the Fermi surface and for small energies, the dominant contribution to the imaginary part of $ϕ$ arises from Landau-damped magnetic gluons. Further away from the Fermi surface and for larger energies the other gluon sectors have to be included into Imϕ. We confirm that Im$ ϕ$ contributes a correction of order g to the prefactor of ϕfor on-shell quasiquarks sufficiently close to the Fermi surface, whereas further away from the Fermi surface Imϕand Reϕare of the same order. Finally, we discuss the relevance of Imϕfor the damping of quasiquark excitations.

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arXiv2006

A General Effective Action for Quark Matter and its Application to Color Superconductivity

I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate choices for the projection operators one recovers various well-known effective theories such as the Hard Thermal Loop/ Hard Dense Loop Effective Theories as well as the High Density Effective Theory by Hong and Schaefer. I then apply the effective theory to cold and dense quark matter and show how it can be utilized to simplify the weak-coupling solution of the color-superconducting gap equation. In general, one considers as relevant quark degrees of freedom those within a thin layer of width 2 Lambda_q around the Fermi surface and as relevant gluon degrees of freedom those with 3-momenta less than Lambda_gl. It turns out that it is necessary to choose Lambda_q << Lambda_gl, i.e., scattering of quarks along the Fermi surface is the dominant process. Moreover, this special choice of the two cutoff parameters Lambda_q and Lambda_gl facilitates the power-counting of the numerous contributions in the gap-equation. In addition, it is demonstrated that both the energy and the momentum dependence of the gap function has to be treated self-consistently in order to determine the imaginary part of the gap function. For quarks close to the Fermi surface the imaginary part is calculated explicitly and shown to be of sub-subleading order in the gap equation.

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arXiv2004

A General Effective Action for High-Density Quark Matter

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, $Λ_q$, and one for gluons, $Λ_g$. 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 $Λ_q$ and $Λ_g$, 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 $2 Λ_q$ 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 $Λ_q, Λ_g$ 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 $μ$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

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