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Decay of a scalar condensate in two different approaches

Ayuki Kamada, Kodai Sakurai

Abstract

Decay of a scalar condensate via interactions with (quasi-)particles is of interest to many fields in physics, including cosmology. In cosmology, the decay of an inflaton condensate leads to the production of daughter particles and reheating of the Universe. In computing the decay rate, two quantum field theoretic approaches can be found in the literature: one is based on parametric resonance of mode functions of the daughter particle; another is based on the $S$-matrix of a coherent state and Feynman-diagrammatic perturbation theory. We modify the latter from the previous literature in a way that manifests what we are computing and does not include unwanted Feynman diagrams. We notice the equivalence of these two approaches and demonstrate it by explicitly computing the decay rate at lower orders in the double expansion of the amplitude of coherent oscillation (or narrow resonance) and velocity of the daughter particle.

Decay of a scalar condensate in two different approaches

Abstract

Decay of a scalar condensate via interactions with (quasi-)particles is of interest to many fields in physics, including cosmology. In cosmology, the decay of an inflaton condensate leads to the production of daughter particles and reheating of the Universe. In computing the decay rate, two quantum field theoretic approaches can be found in the literature: one is based on parametric resonance of mode functions of the daughter particle; another is based on the -matrix of a coherent state and Feynman-diagrammatic perturbation theory. We modify the latter from the previous literature in a way that manifests what we are computing and does not include unwanted Feynman diagrams. We notice the equivalence of these two approaches and demonstrate it by explicitly computing the decay rate at lower orders in the double expansion of the amplitude of coherent oscillation (or narrow resonance) and velocity of the daughter particle.

Paper Structure

This paper contains 21 sections, 111 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Review of two methods
  3. Parametric-resonance approach
  4. Feynman-diagrammatic approach
  5. Comparison of the two methods
  6. Double expansion ($\theta$ and $\beta$)
  7. Results of the parametric-resonance approach
  8. Methodology
  9. Calculation of the matrix elements of the tridiagonal matrix
  10. Analytical results with higher order terms
  11. $n_\varphi=1$
  12. $n_\varphi=2$
  13. Results of the Feynman-diagrammatic approach
  14. Evaluation of bubble diagrams
  15. $p=1$
  16. ...and 6 more sections

Figures (6)

  • Figure 1: Schematic picture of $\beta$ and $\theta$ expansions. Left panel: the case of $n_\varphi=1$. Right panel: the case of $n_\varphi=2$.
  • Figure 2: Possible cuts for the "pinched" diagram for the one of $p=2$ graphs. Diagrams 2-1 and 2-2 contribute to the $n_\varphi=1$ process, while Diagram 2-3 contributes to the $n_\varphi=2$ process.
  • Figure 3: $p=1$ diagram and possible cut contributing to $n_\varphi=1$.
  • Figure 4: $p=2$ diagrams.
  • Figure 5: $p=3$ diagrams.
  • ...and 1 more figures