Abstract
We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes — a result reminiscent of a previously proposed “naive real-time formalism” for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.
Highlights
Understanding the properties of cold and dense strongly interacting matter is known to be a very challenging task
The current state-of-the-art result for the perturbative Equation of State (EoS) of zero-temperature quark matter is from a three-loop, or O(αs2), calculation that was first performed at vanishing quark masses [7,8], but later generalized to nonzero quark masses [9] and small but nonvanishing temperatures [11]
Generalization to finite density: Assume that some of the internal propagators of the graph are fermionic in the sense that they carry a chemical potential μ in the way stated in the previous section
Summary
Understanding the properties of cold and dense strongly interacting matter is known to be a very challenging task. The current state-of-the-art result for the perturbative EoS of zero-temperature quark matter is from a three-loop, or O(αs2), calculation that was first performed at vanishing quark masses [7,8], but later generalized to nonzero quark masses [9] (see [10]) and small but nonvanishing temperatures [11] Extending these zero-temperature results to higher orders, presents a considerable technical challenge. In the paper at hand, we present a new technical tool for perturbative calculations at zero temperature but finite chemical potentials that we argue enables a high-order determination of many important thermodynamic quantities. This tool is referred to as a set of “cutting rules”, which were proposed but not explicitly derived in ref. Many details of the more subtle parts of our proof have been relegated to Appendices A–C
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