Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism

Wu, Bin; Kovchegov, Yuri V.

doi:10.1007/jhep03(2018)158

Title: Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism

Abstract

We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function G^{aμ, bν}₂₂ due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to G^{aμ, bν}₂₂ coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τ_Z gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τ_Z >> 1/Qs and τ - τ_Z >> 1/Qs (with Qs the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ - τ_Z >> τ_Z >> 1/Qs we end up with a result very different from kinetic theory and consistent with a picture of “free-streaming” particles. Due to the approximations made,more »« less

Authors:

Wu, Bin ^[1]; Kovchegov, Yuri V. ^[1]

The Ohio State Univ., Columbus, OH (United States). Dept. of Physics

Publication Date:: Mon Mar 26 00:00:00 EDT 2018

Research Org.:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1506450

Grant/Contract Number:: SC0004286

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Perturbative QCD; Quark-Gluon Plasma

Citation Formats


                    Wu, Bin, and Kovchegov, Yuri V. Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep03(2018)158.

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                    Wu, Bin, & Kovchegov, Yuri V. Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism.  United States.  https://doi.org/10.1007/jhep03(2018)158

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                    Wu, Bin, and Kovchegov, Yuri V. Mon .  
"Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism".  United States.  https://doi.org/10.1007/jhep03(2018)158.  https://www.osti.gov/servlets/purl/1506450.

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@article{osti_1506450,

  title        = {Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism},

  author       = {Wu, Bin and Kovchegov, Yuri V.},

  abstractNote = {We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function Gaμ, bν22 due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to Gaμ, bν22 coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τZ gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τZ >> 1/Qs and τ - τZ >> 1/Qs (with Qs the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ - τZ >> τZ >> 1/Qs we end up with a result very different from kinetic theory and consistent with a picture of “free-streaming” particles. Due to the approximations made, our calculation is too coarse to indicate whether the region (i) or (ii) is the correct one: to resolve this controversy, we shall present a detailed diagrammatic calculation of the rescattering correction in the φ4 theory in the second paper of this duplex.},

  doi          = {10.1007/jhep03(2018)158},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2018,

  place        = {United States},

  year         = {Mon Mar 26 00:00:00 EDT 2018},

  month        = {Mon Mar 26 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

Quantum corrections to the classical statistical approximation for the expanding quantum field
journal, January 2019

Leonidov, A. V.; Radovskaya, A. A.
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Cougoulic, Florian; Kovchegov, Yuri V.
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Title: Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism

Abstract

Citation Formats

Color Glass Condensate in Schwinger–Keldysh QCD journal, January 2014

Initial Energy Density of Gluons Produced in Very-High-Energy Nuclear Collisions journal, May 2000

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Collinear singularities and running coupling corrections to gluon production in CGC journal, July 2008

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Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions journal, October 2013

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The Color Glass Condensate journal, November 2010

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From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory journal, May 1996

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Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC text, January 2007

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Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions journal, October 2013

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Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies journal, September 1999

The quark–gluon plasma: collective dynamics and hard thermal loops journal, March 2002

Effective kinetic theory for high temperature gauge theories journal, January 2003

Introduction to Nonequilibrium Quantum Field Theory conference, January 2004

Quantum corrections to the classical statistical approximation for the expanding quantum field journal, January 2019

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Helicity-dependent extension of the McLerran-Venugopalan model text, January 2020

Color Glass Condensate in Schwinger–Keldysh QCD
journal, January 2014

Initial Energy Density of Gluons Produced in Very-High-Energy Nuclear Collisions
journal, May 2000

Equilibrium and nonequilibrium formalisms made unified
journal, February 1985

Collinear singularities and running coupling corrections to gluon production in CGC
journal, July 2008

High energy factorization in nucleus-nucleus collisions. II. Multigluon correlations
journal, September 2008

Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution
journal, February 2016

The Boltzmann Equation in Classical Yang-Mills Theory
text, January 2014

Quantum Chromodynamics at High Energy
book, September 2012

$n$ -particle irreducible effective action techniques for gauge theories
journal, November 2004

Real- and imaginary-time field theory at finite temperature and density
journal, January 1987

Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions
journal, October 2013

Properties of the Boltzmann equation in the classical approximation
text, January 2014

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015

The Color Glass Condensate
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Production of gluons in the classical field model for heavy ion collisions
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Small-x behavior and parton saturation: A QCD model
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On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
journal, March 2004

Pressure Isotropization in High Energy Heavy Ion Collisions
journal, December 2013

“Bottom-up” thermalization in heavy ion collisions
journal, March 2001

Energy density of the glasma
journal, November 2006

Initial fields and instabilities in the classical model of relativistic heavy-ion collisions
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Green’s function in the color field of a large nucleus
journal, August 1994

Probing a color glass condensate in high energy heavy ion collisions
journal, January 2003

2PI effective action and gauge dependence identities
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From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
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Lattice worldline representation of correlators in a background field
journal, June 2015

Brownian Motion of a Quantum Oscillator
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Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations
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Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC
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Finite-temperature quantum field theory in Minkowski space
journal, January 1984

Can thermalization in heavy ion collisions be described by QCD diagrams?
journal, December 2005

Quantum corrections to the Weizsäcker-Williams gluon distribution function at small x
journal, January 1996

The Boltzmann equation for gluons at early times after a heavy ion collision
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Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus
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The Boltzmann equation in classical Yang–Mills theory
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Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions
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Classical gluon radiation in ultrarelativistic nucleus-nucleus collisions
journal, August 1997

Gluon distribution functions for very large nuclei at small transverse momentum
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