On the thermal sunset diagram for scalar field theories

Abstract

We study the so-called `` sunset diagram'', which is one of two-loop self-energy diagrams, for scalar field theories at finite temperature. For this purpose, we first find the complete expression of the bubble diagram, the one-loop subdiagram of the sunset diagram, for arbitrary momentum. We calculate the temperature independent part and dependent part of the sunset diagram separately. For the former, we obtain the discontinuous part first and the finite continuous part next using a twice-subtracted dispersion relation. For the latter, we express it as a one-dimensional integral in terms of the bubble diagram. We also study the structure of the discontinuous part of the sunset diagram. Physical processes, which are responsible for it, are identified. Processes due to the scattering with particles in the heat bath exist only at finite temperature and generate discontinuity for arbitrary momentum, which is a remarkable feature of the two-loop diagrams at finite temperature. As an application of our result, we study the effect of the diagram on the spectral function of the sigma meson at finite temperature in the linear sigma model, which was obtained at one-loop order previously. At high temperature where the decay $\sigma \to \pi \pi$ is forbidden, sigma acquires a finite width of the order of $10\mathrm{MeV}$ while within the one-loop calculation its width vanishes. At low temperature, the spectrum does not deviate much from that at one-loop order. Possible consequences with including other two-loop diagrams are discussed.

30 pages

References in corpus (7)

• The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
• Optimized Perturbation Theory at Finite Temperature
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• Screened Perturbation Theory to Three Loops
• On the evaluation of sunset-type Feynman diagrams
• The Massive Thermal Basketball Diagram
• A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space

Cited by in corpus (10)

• Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory
• Polyakov loop modeling for hot QCD
• Thermal Field Theory in real-time formalism: concepts and applications for particle decays
• Failure of Perturbation Theory Near Horizons: the Rindler Example
• Laurent series expansion of sunrise-type diagrams using configuration space techniques
• Effect of pion thermal width on the sigma spectrum
• Quantum decoherence of gravitational waves
• Shear Viscosity in Weakly Coupled N-Component Scalar Field Theories
• Lectures on configuration space methods for sunrise-type diagrams
• Microscopic identification of dissipative modes in relativistic field theories