Equilibrium and non-equilibrium hard thermal loop resummation in the real time formalism

Carrington, M. E.; Hou, Defu; Thoma, Markus H.

doi:10.1007/s100520050412

Cited by 29 publications

(40 citation statements)

References 23 publications

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“…This quantity has been computed for vanishing velocity in [25] and we find that The scalar quantity u u Å s has a simple interpretation in the comoving frame, where it turns out to be given by Å s 00 . Then we have that…”

Section: The Static Potential Of Muonic Hydrogen In the Range T ) 1=rmentioning

confidence: 91%

“…This frame has been successfully used in the past, for example, in [24]. Studying a bound state in a moving thermal bath is akin to studying a bound state in nonequilibrium field theory [25]; in that case the Bose-Einstein or Fermi-Dirac distribution functions are substituted by a general distribution, which in our case will be the boosted Bose-Einstein or Fermi-Dirac distribution functions reported in Eq. (1).…”

Section: General Frameworkmentioning

confidence: 99%

“…In the expression above, fðk 0 ; TÞ is the distribution function of the longitudinal photons in the thermal bath. However, the last relation does not hold for a bound state moving through a thermal bath [25], and must be substituted by the following one: …”

Section: The Static Potential Of Muonic Hydrogen In the Range T ) 1=rmentioning

confidence: 99%

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Nonrelativistic bound states in a moving thermal bath

2011

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We study the propagation of nonrelativistic bound states moving at constant velocity across a homogeneous thermal bath and we develop the effective field theory which is relevant in various dynamical regimes. We consider values of the velocity of the bound state ranging from moderate to highly relativistic and temperatures at all relevant scales smaller than the mass of the particles that form the bound state. In particular, we consider two distinct temperature regimes, corresponding to temperatures smaller or higher than the typical momentum transfer in the bound state. For temperatures smaller or of the order of the typical momentum transfer, we restrict our analysis to the simplest system, a hydrogenlike atom. We build the effective theory for this system first considering moderate values of the velocity and then the relativistic case. For large values of the velocity of the bound state, the separation of scales is such that the corresponding effective theory resembles the soft collinear effective theory (SCET). For temperatures larger than the typical momentum transfer we also consider muonic hydrogen propagating in a plasma which contains photons and massless electrons and positrons, so that the system resembles very much a heavy quarkonium in a thermal medium of deconfined quarks and gluons. We study the behavior of the real and imaginary part of the static two-body potential, for various velocities of the bound state, in the hard thermal loop approximation. We find that Landau damping ceases to be the relevant mechanism for dissociation from a certain critical velocity on, in favor of screening. Our results are relevant for understanding how the properties of heavy quarkonia states produced in the initial fusion of partons in the relativistic collision of heavy ions are affected by the presence of an equilibrated quark-gluon plasma.

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Section: The Static Potential Of Muonic Hydrogen In the Range T ) 1=rmentioning

confidence: 91%

Section: General Frameworkmentioning

confidence: 99%

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Nonrelativistic bound states in a moving thermal bath

2011

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“…The corresponding results at vanishing chemical potential µ have already been obtained before; see, for example, ref. [14,[36][37][38]. Here, we recompute the gluon self energies at finite chemical potential by keeping track of the quark distribution function f + F (k) and the anti quark distribution function f − F (k) explicitly during the calculation.…”

Section: A Gluon Self Energies In the Real Time Formalismmentioning

confidence: 99%

Bulk viscous corrections to screening and damping in QCD at high temperatures

Dumitru

Yun

et al. 2017

J. High Energ. Phys.

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Non-equilibrium corrections to the distribution functions of quarks and gluons in a hot and dense QCD medium modify the "hard thermal loops" (HTL). The HTLs determine the retarded, advanced, and symmetric (time-ordered) propagators for gluons with soft momenta as well as the Debye screening and Landau damping mass scales. We compute such corrections to a thermal as well as to a non-thermal fixed point. The screening and damping mass scales are sensitive to the bulk pressure and hence to (pseudo-) critical dynamical scaling of the bulk viscosity in the vicinity of a second-order critical point. This could be reflected in the properties of quarkonium bound states in the deconfined phase and in the dynamics of soft gluon fields.

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“…Several authors have pointed out that the calculations using the CTP formulation in terms of the standard form of free propagators in eqs. (7.1) or those obtained by the replacement of the distribution functions by the nonequilibrium ones, lead to pinch singularities [30,31,[60][61][62][63][64][65][66].…”

Section: Secular Terms Vs Pinch Singularitiesmentioning

confidence: 99%

Dynamical renormalization group approach to quantum kinetics in scalar and gauge theories

2000

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We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solution of this equation of motion reveals secular terms that grow in time; the dynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. This method allows us to include consistently medium effects via resummations akin to hard thermal loops but away from equilibrium. A close relationship between this approach and the renormalization group in Euclidean field theory is established. In particular, coarse graining, stationary solutions, the relaxation time approximation, and relaxation rates have a natural parallel as irrelevant operators, fixed points, linearization, and stability exponents in the Euclidean renormalization group, respectively. We used this method to study the relaxation in a cool gas of pions and sigma mesons in the O(4) chiral linear sigma model. We obtain in the relaxation time approximation the pion and sigma meson relaxation rates. We also find that in the large momentum limit emission and absorption of massless pions result in a threshold infrared divergence in the sigma meson relaxation rate and lead to a crossover behavior in relaxation. We then study the relaxation of charged quasiparticles in scalar quantum electrodynamics ͑SQED͒. We begin with a gauge invariant description of the distribution function and implement the hard thermal loop resummation for longitudinal and transverse photons as well as for the scalars. While longitudinal, Debye-screened photons lead to purely exponential relaxation, and transverse photons, only dynamically screened by Landau damping, lead to anomalous ͑nonexponential͒ relaxation, thus leading to a crossover between two different relaxational regimes. We emphasize that infrared divergent damping rates are indicative of nonexponential relaxation and the dynamical renormalization group reveals the correct relaxation directly in real time. Furthermore the relaxational time scales for charged quasiparticles are similar to those found in QCD in a self-consistent HTL resummation. Finally we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establish a direct correspondence between pinch singularities and secular terms in time-dependent perturbation theory. We argue that this method is particularly well suited to study quantum kinetics and transport in gauge theories.

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Equilibrium and non-equilibrium hard thermal loop resummation in the real time formalism

Cited by 29 publications

References 23 publications

Nonrelativistic bound states in a moving thermal bath

Nonrelativistic bound states in a moving thermal bath

Bulk viscous corrections to screening and damping in QCD at high temperatures

Dynamical renormalization group approach to quantum kinetics in scalar and gauge theories

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