Momentum expansions in finite-density perturbative calculations

Abstract

Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to integration order dependent results are even further pronounced in the presence of additional scales such as external momenta. This plays a noticeable role in systems featuring fermionic degrees of freedom such as cold Quantum Chromodynamics, where loop integrals are complexified by chemical potential(s). Working in the limit of vanishing temperature, we utilize novel complex-valued extensions to bubble Feynman integrals and study momentum expansions of fermionic loop integrals. The expansions are then used to illustrate the mechanisms of manifested discrepancies between orders of integration, associated with the residue theorem. Finally, we address the issues by introducing a representation avoiding the observed ambiguity and briefly overview classes of integrals insensitive to problems from external momenta.

arXiv comment54 pages, 2 figures (v3: minor modifications following referee comments)

References in corpus (24)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Evidence for quark-matter cores in massive neutron stars
• QCD and strongly coupled gauge theories: challenges and perspectives
• Cold Quark Matter
• The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
• Predictions for all processes e^+e^- -> 4 fermions + gamma
• Basics of thermal field theory -- a tutorial on perturbative computations
• The pressure of QCD at finite temperatures and chemical potentials
• NNNLO pressure of cold quark matter: leading logarithm
• Perturbative Thermal QCD: Formalism and Applications
• On the Apparent Convergence of Perturbative QCD at High Temperature
• Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma
• Cool quark matter
• Equation of State of Cold Quark Matter to $O({\alpha }_s^3\ln {\alpha }_s)$
• Angular integrals in d dimensions
• Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence
• On high-order perturbative calculations at finite density
• Augmenting the residue theorem with boundary terms in finite-density calculations
• Degenerate fermionic matter at N${}^3$LO: Quantum Electrodynamics
• Soft photon propagation in a hot and dense medium to next-to-leading order
• Quark Matter Equation of State from Perturbative QCD
• Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge
• Integrating by parts at finite density
• Particle-theory input for neutron-star physics