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Scalar field damping at high temperatures
High Energy Physics - Phenomenology · Submitted 27 May 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For an interaction with another scalar field we obtain a simple relation between the damping coefficient and the bulk viscosity, so that one can make use of known results for the latter.
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The abstract, sentence by sentence
The motion of a scalar field that interacts with a hot plasma, like the inflaton during reheating, is damped, which is a dissipative process. At high temperatures the damping can be described by a local term in the effective equation of motion. The damping coefficient is sensitive to multiple scattering. In the loop expansion its computation would require an all-order resummation. Instead we solve an effective Boltzmann equation, similarly to the computation of transport coefficients. For an interaction with another scalar field we obtain a simple relation between the damping coefficient and the bulk viscosity, so that one can make use of known results for the latter. The numerical prefactor of the damping coefficient turns out to be rather large, of order $ 10 ^ 4 $.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The motion of a scalar field that interacts with a hot plasma, like the inflaton during reheating, is damped, which is a dissipative process. | background 1.00 | 0.10 | 0.19 | asserted 1.00 |
| s1 | At high temperatures the damping can be described by a local term in the effective equation of motion. | background 0.87 | 0.18 | 0.11 | asserted 0.85 |
| s2 | The damping coefficient is sensitive to multiple scattering. | background 0.59 | 0.27 | 0.08 | asserted 1.00 |
| s3 | In the loop expansion its computation would require an all-order resummation. | background 0.66 | 0.16 | 0.04 | asserted 0.79 |
| s4 | Instead we solve an effective Boltzmann equation, similarly to the computation of transport coefficients. | method 0.98 | 0.87 | 0.09 | asserted 1.00 |
| s5 | For an interaction with another scalar field we obtain a simple relation between the damping coefficient and the bulk viscosity, so that one can make use of known results for the latter. | result 0.92 | 0.87 | 0.30 | asserted 0.99 |
| s6 | The numerical prefactor of the damping coefficient turns out to be rather large, of order $ 10 ^ 4 $. | result 1.00 | 0.91 | 0.25 | asserted 0.99 |
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The paper
Original abstract
The motion of a scalar field that interacts with a hot plasma, like the inflaton during reheating, is damped, which is a dissipative process. At high temperatures the damping can be described by a local term in the effective equation of motion. The damping coefficient is sensitive to multiple scattering. In the loop expansion its computation would require an all-order resummation. Instead we solve an effective Boltzmann equation, similarly to the computation of transport coefficients. For an interaction with another scalar field we obtain a simple relation between the damping coefficient and the bulk viscosity, so that one can make use of known results for the latter. The numerical prefactor of the damping coefficient turns out to be rather large, of order $ 10 ^ 4 $.
Human review
References
How the literature uses it
5 arXiv papers cite this in 9 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 1 paper
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In particular, it is known that in computing correlation functions in the zero-momentum, zero-frequency limit, e.g., in studying hydrodynamic transport coefficients [ref] or damping coefficients in the slow-roll regime or at very high temperatures [ref] , resummation of an infinity set of diagrams is required.
Fate of homogeneous $\mathbb{Z}_2$-symmetric scalar condensates · Conclusion and discussion · 0.90
What it cites · 34 sentences without a confident label
Contests 5 papers
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[ The damping coefficients computed in Refs. [ref] are of the same form as in Ref. [ref] . ] This approximation, however, does not give the correct result for the bulk viscosity in scalar theory [ref] .
From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory · Introduction · contest 0.83
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[ The damping coefficients computed in Refs. [ref] are of the same form as in Ref. [ref] . ] This approximation, however, does not give the correct result for the bulk viscosity in scalar theory [ref] .
Microphysical Approach to Nonequilibrium Dynamics of Quantum Fields · Introduction · contest 0.83
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[ The damping coefficients computed in Refs. [ref] are of the same form as in Ref. [ref] . ] This approximation, however, does not give the correct result for the bulk viscosity in scalar theory [ref] .
Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory · Introduction · contest 0.83
Builds on 1 paper
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This extends a result [ref] which was obtained for a scalar field with derivative interaction.
Moduli decay in the hot early Universe · Conclusion · 0.99
Uses the method or tool of 2 papers
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Here we carefully treat the collision term as well as thermal effects by employing the effective Boltzmann equations which were used to perturbatively compute bulk viscosities in scalar theories [ref] ,
Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory · Introduction · 0.99
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Here we carefully treat the collision term as well as thermal effects by employing the effective Boltzmann equations which were used to perturbatively compute bulk viscosities in scalar theories [ref] ,
From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory · Introduction · 0.99
Uses data or values from 1 paper
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The effective mass for the $$ particles is given by [equation] Inserting Eq. ([ref]) into Eq. ([ref]) we obtain the damping coefficient [equation] with the remarkably large numerical prefactor [equation] In the temperature range $T ≫m /g ^ 2$ the form ([ref]) and thus Eq. ([ref]) remain valid when a cubic self-interaction is included in ([ref]), while in the intermediate regime $m ≪T ≪m/g ^ 2$ the bulk viscosity depends nontrivially on the relative strengths of cubic and quartic $χ$ self-couplings [ref] .
Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory · Damping coefficient and bulk viscosity · 0.85
Cites as background 5 papers
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Let us now recall some properties of the bulk viscosity, as described, e.g., in Ref. [ref] .
The Bulk Viscosity of High-Temperature QCD · Damping coefficient and bulk viscosity · 0.99
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Similar complications arise in the computation of transport coefficients, such as bulk viscosity, which can be written as the zero-momentum zero-frequency limit of a stress-tensor correlation function [ref] .
Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory · Introduction · 0.97
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Similar complications arise in the computation of transport coefficients, such as bulk viscosity, which can be written as the zero-momentum zero-frequency limit of a stress-tensor correlation function [ref] .
From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory · Introduction · 0.97
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