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## A relation between screening masses and real-time rates

### Citations

46 |
Free energy of QCD at high temperature, Phys. Rev. D 53
- Braaten, Nieto
- 1996
(Show Context)
Citation Context ...) 1.09(7) 2.8(2) 3.1(3) 0.61(2) 0.91(4) Table 1: The effective gauge coupling, mass parameter, and ρ-parameter (cf. eq. (7.8)) for the different sectors, according to the 2-loop computations in refs. =-=[30, 31]-=-. The two temperatures correspond to T = 254(4) MeV and T = 338(5) MeV, respectively, for Nf = 2 QCD. The errors are based on variations of the renormalization scale. T/ΛMS = 0.82(5) T/ΛMS = 1.09(7) n... |

31 |
Vier combinatorische Probleme
- Schröder
(Show Context)
Citation Context ...∑ {pn} e−|pn|r−|pn−kn|r Pα(|pn|) , (3.3) where {pn} denotes a fermionic Matsubara frequency and Pα is a polynomial of degree α ∈ {0, 1, 2}. The sums can be carried out in analytic form, cf. e.g. ref. =-=[17]-=-. Denoting r̄ ≡ 2πTr , kn 2πT = n , (3.4) we obtain (here i, j ∈ {1, 2, 3}) − r 2G (kn) 00 (r) NcT 3e−|kn|r = |n| 6 + |n|3 3 + |n|2 r̄ + |n| r̄2 + |n| r̄ sinh r̄ + cosh r̄ r̄ sinh2 r̄ + 1 r̄2 sinh r̄ ... |

31 | Two-loop QCD gauge coupling at high temperatures
- Laine, Schröder
(Show Context)
Citation Context ...) 1.09(7) 2.8(2) 3.1(3) 0.61(2) 0.91(4) Table 1: The effective gauge coupling, mass parameter, and ρ-parameter (cf. eq. (7.8)) for the different sectors, according to the 2-loop computations in refs. =-=[30, 31]-=-. The two temperatures correspond to T = 254(4) MeV and T = 338(5) MeV, respectively, for Nf = 2 QCD. The errors are based on variations of the renormalization scale. T/ΛMS = 0.82(5) T/ΛMS = 1.09(7) n... |

31 |
Speeding up lattice QCD simulations with clover-improved Wilson fermions, Nucl. Phys. B659
- Hasenbusch, Jansen
- 2003
(Show Context)
Citation Context ...on, with fermions implemented via the O(a) improved Wilson discretization with a non-perturbatively determined clover coefficient csw [33]. The configurations were generated with the MP-HMC algorithm =-=[34, 35]-=- employing the implementation of ref. [36] based on Lüscher’s DD-HMC package [37]. Spatial correlation functions were computed on two ensembles, using the same discretization and masses as in the sea... |

29 |
Infrared Problem in Thermodynamics of the Yang-Mills Gas,” Phys
- Linde
- 1980
(Show Context)
Citation Context ...computed in a power series in g. It is a consequence of the momentum scales as mentioned above that odd powers and logarithms of g appear [2, 3] and that some of the coefficients are non-perturbative =-=[4]-=-. It is also commonly believed that the series converges slowly unless g is extremely small, a problem often associated with the dynamics of the intermediate scale gT . (ii) In an effective theory app... |

28 |
High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics,” Phys
- Appelquist, Pisarski
- 1981
(Show Context)
Citation Context ...s also commonly believed that the series converges slowly unless g is extremely small, a problem often associated with the dynamics of the intermediate scale gT . (ii) In an effective theory approach =-=[5, 6]-=-, only the “hardest” scale is treated perturbatively. It is “integrated out” in order to derive an effective low-energy description for the “soft” scales gT and g2T/π. The dynamics of the low-energy m... |

25 | The strange quark mass and Lambda parameter of two flavor
- Fritzsch, Knechtli, et al.
- 2012
(Show Context)
Citation Context ...ice simulations 8.1. Basic setup For a non-perturbative crosscheck we make use of lattice simulations in two-flavour QCD, with physical parameters corresponding to ΛMS = 310(20) MeV and mpi ≈ 270 MeV =-=[28]-=-. Lattices of spatial size N3s = 64 3 and lattice spacing a = 0.0486(4)(5) fm are considered. The thermal ensembles have temporal extents Nτ = 16, 12, corresponding to the temperatures T = 254(4) MeV ... |

24 | Further results on O(a) improved lattice QCD to one-loop order of perturbation theory, Nucl. Phys
- Sint, Weisz
- 1997
(Show Context)
Citation Context ...n-perturbative value ZV(g 2 0) = 0.768(5) at 6/g 2 0 = 5.50 [41]. We have not included O(a) contributions from the improvement term proportional to the derivative of the antisymmetric tensor operator =-=[42, 43]-=-, nor a quark-mass dependent improvement of the form 1 + bV(g 2 0)amq [43]. Both should be included to ensure a smooth scaling behaviour as the continuum limit is taken, however our present study conc... |

23 |
Static correlation lengths in QCD at high temperatures and finite densities,” Nucl. Phys. B 586 (2000) 443 [arXiv:hep-ph/0004060]; A. Hart and O. Philipsen, “The spectrum of the three-dimensional adjoint Higgs model and hot SU(2) gauge theory
- Hart, Laine, et al.
- 1999
(Show Context)
Citation Context ...or the study of these observables. For screening masses related to flavour-singlet (gluonic) states, this approach leads to a good description of thermal QCD down to temperatures of a few hundred MeV =-=[8]-=-. Recently it has been proposed to apply the same approach to jet quenching [9], and indeed first simulation results exist already [10]. Nevertheless, it may be questioned with every observable how ac... |

20 | Transport Properties of the Quark-Gluon Plasma – A Lattice QCD Perspective,” [arXiv:1104.3708 [hep-lat
- Meyer
(Show Context)
Citation Context ...tions are carried out in the imaginary-time formalism. If real-time observables are to be considered, an analytic continuation is required, which in practice is ill-controlled (for a review, see ref. =-=[7]-=-). There are many phenomenologically interesting observables in thermal QCD, notably screening masses and real-time rates such as the photon and dilepton production rates from the plasma, or the rate ... |

20 |
Speeding up the hybrid Monte Carlo algorithm for dynamical fermions
- Hasenbusch
(Show Context)
Citation Context ...on, with fermions implemented via the O(a) improved Wilson discretization with a non-perturbatively determined clover coefficient csw [33]. The configurations were generated with the MP-HMC algorithm =-=[34, 35]-=- employing the implementation of ref. [36] based on Lüscher’s DD-HMC package [37]. Spatial correlation functions were computed on two ensembles, using the same discretization and masses as in the sea... |

20 |
Chiral symmetry and o(a) improvement in lattice qcd
- Luscher, Sint, et al.
- 1996
(Show Context)
Citation Context ...n-perturbative value ZV(g 2 0) = 0.768(5) at 6/g 2 0 = 5.50 [41]. We have not included O(a) contributions from the improvement term proportional to the derivative of the antisymmetric tensor operator =-=[42, 43]-=-, nor a quark-mass dependent improvement of the form 1 + bV(g 2 0)amq [43]. Both should be included to ensure a smooth scaling behaviour as the continuum limit is taken, however our present study conc... |

19 |
Quantum Chromodynamics At High Temperature
- Kapusta
- 1979
(Show Context)
Citation Context ...ays: (i) In a strict weak-coupling expansion, observables are computed in a power series in g. It is a consequence of the momentum scales as mentioned above that odd powers and logarithms of g appear =-=[2, 3]-=- and that some of the coefficients are non-perturbative [4]. It is also commonly believed that the series converges slowly unless g is extremely small, a problem often associated with the dynamics of ... |

18 |
second order phase transitions in gauge theories at finite temperature
- Ginsparg, “First
- 1980
(Show Context)
Citation Context ...s also commonly believed that the series converges slowly unless g is extremely small, a problem often associated with the dynamics of the intermediate scale gT . (ii) In an effective theory approach =-=[5, 6]-=-, only the “hardest” scale is treated perturbatively. It is “integrated out” in order to derive an effective low-energy description for the “soft” scales gT and g2T/π. The dynamics of the low-energy m... |

18 |
Simple effective Lagrangian for hard thermal loops, Phys
- Braaten, Pisarski
- 1992
(Show Context)
Citation Context ...ed, the mass and vertex corrections induced by the non-zero modes can be extracted from computations which are essentially equivalent to the derivation of the Hard Thermal Loop (HTL) effective action =-=[21, 22]-=-. The reason is that the assumptions needed in the computations are K2 ≪ (πT )2, P 2 ≪ (πT )2, (K−P )2 ≪ (πT )2, which as we have argued are true in our situation as well. The graphs to be considered ... |

16 |
Non-perturbative renormalization of the axial current with dynamical Wilson fermions, JHEP 0507
- Morte, Hoffmann, et al.
- 2005
(Show Context)
Citation Context ...ref. [40]). Correspondingly the bare vector correlators were renormalized using G(kn)µν (z) = ZV(g 2 0)G (kn)bare µν (z) , (B.6) with the non-perturbative value ZV(g 2 0) = 0.768(5) at 6/g 2 0 = 5.50 =-=[41]-=-. We have not included O(a) contributions from the improvement term proportional to the derivative of the antisymmetric tensor operator [42, 43], nor a quark-mass dependent improvement of the form 1 +... |

15 | Three-loop free energy for high-temperature QED and QCD with fermions, Phys
- Arnold, Zhai
- 1995
(Show Context)
Citation Context ...ators by G(kn)µν (r) ≡ ∫ 1/T 0 dτ eiknτ 〈 (ψ̄γµψ)(τ, r)(ψ̄γνψ)(0) 〉 c , r ≡ (x, z) . (3.1) The correlators can be computed with the mixed coordinate space-momentum space techniques introduced in ref. =-=[16]-=-. In coordinate space, spatial propagators have the form ∫ d3p (2π)3 eip·r p2n + p 2 = e−|pn|r 4πr , r ≡ |r| . (3.2) Subsequently one is faced with sums of the type ∑ {pn} e−|pn|r−|pn−kn|r Pα(|pn|) , ... |

13 |
Comparison of the mass preconditioned HMC and the DD-HMC algorithm for two-flavour
- Marinkovic, Schaefer
(Show Context)
Citation Context ...roved Wilson discretization with a non-perturbatively determined clover coefficient csw [33]. The configurations were generated with the MP-HMC algorithm [34, 35] employing the implementation of ref. =-=[36]-=- based on Lüscher’s DD-HMC package [37]. Spatial correlation functions were computed on two ensembles, using the same discretization and masses as in the sea sector. The first ensemble, with a spatia... |

12 |
Landau-Pomeranchuk-Migdal resummation for dilepton production
- Aurenche, Gelis, et al.
(Show Context)
Citation Context ...on production, lead to G (kn) L (k3) = k2n + k 2 3 k23 G (kn) 00 (k3) . (2.5) It is therefore sufficient to compute G (kn) 00 , whose analysis turns out to be simpler than that of G (kn) 33 (cf. ref. =-=[11]-=-). Apart from G (kn) 00 , we also consider the transverse part G (kn) T (k3) ≡ 2∑ i=1 G (kn) ii (k3) , (2.6) which is not constrained by Ward identities. Given that we have chosen a particular directi... |

9 | Reconstructing the thermal Green functions at real times from those at imaginary times
- Cuniberti, Micheli, et al.
(Show Context)
Citation Context ...D (cf. e.g. refs. [9]– [11]). On a general level, this observation is consistent with the statement that only non-zero Matsubara modes play a role in analytic continuation from imaginary to real time =-=[32]-=-. Apart from computing screening masses with an effective theory, we have also measured them with large-scale lattice Monte Carlo simulations in two-flavour QCD at temperatures of about 250 MeV and 34... |

7 |
The next term in the thermodynamic potential of QCD. Phys
- Toimela
- 1983
(Show Context)
Citation Context ...ays: (i) In a strict weak-coupling expansion, observables are computed in a power series in g. It is a consequence of the momentum scales as mentioned above that odd powers and logarithms of g appear =-=[2, 3]-=- and that some of the coefficients are non-perturbative [4]. It is also commonly believed that the series converges slowly unless g is extremely small, a problem often associated with the dynamics of ... |

7 |
Spatial dependence of the finite temperature meson correlation function, Z. Phys. A 347
- Florkowski, Friman
- 1994
(Show Context)
Citation Context ... are exponentially suppressed at r̄ ≫ 1; however they are relevant for n = 0 in which case the other terms disappear. (For n = 0 a similar expression for the pseudoscalar correlator was given in ref. =-=[18]-=-. NLO corrections could be worked out with the techniques introduced in ref. [19].) Let us now take the transverse averages ∫ x . The powerlike terms can be integrated in terms of the exponential inte... |

7 |
Next-to-leading order thermal photon production in a weakly coupled quark-gluon plasma
- Ghiglieri, Hong, et al.
(Show Context)
Citation Context ...odes, as defined in the text (cf. eqs. (7.11), (7.14)). The potential of eq. (7.6) agrees with the one derived and computed up toO(α3/2s ) in ref. [9]. A coordinate space expression was given in ref. =-=[25]-=-. The potential has been measured within a dimensionally reduced effective field theory (EQCD) in ref. [10]; we make use of the “cold” (T ≈ 400 MeV) β = 16 data set.6 At short distances, a polynomial ... |

6 |
O(g) plasma effects in jet quenching, Phys
- Caron-Huot
- 2009
(Show Context)
Citation Context ...let (gluonic) states, this approach leads to a good description of thermal QCD down to temperatures of a few hundred MeV [8]. Recently it has been proposed to apply the same approach to jet quenching =-=[9]-=-, and indeed first simulation results exist already [10]. Nevertheless, it may be questioned with every observable how accurate the effective theory approach really is; certainly it breaks down at tem... |

6 |
The Effective Action of Hard Thermal
- Taylor, Wong
- 1990
(Show Context)
Citation Context ...ed, the mass and vertex corrections induced by the non-zero modes can be extracted from computations which are essentially equivalent to the derivation of the Hard Thermal Loop (HTL) effective action =-=[21, 22]-=-. The reason is that the assumptions needed in the computations are K2 ≪ (πT )2, P 2 ≪ (πT )2, (K−P )2 ≪ (πT )2, which as we have argued are true in our situation as well. The graphs to be considered ... |

5 |
Intermediate distance correlators
- Laine, Vepsäläinen, et al.
- 2010
(Show Context)
Citation Context ...hich case the other terms disappear. (For n = 0 a similar expression for the pseudoscalar correlator was given in ref. [18]. NLO corrections could be worked out with the techniques introduced in ref. =-=[19]-=-.) Let us now take the transverse averages ∫ x . The powerlike terms can be integrated in terms of the exponential integral E1(z) ≡ ∫ ∞ z dt e−t t z≫1≈ e −z z ( 1− 1 z + 2 z2 + . . . ) , (3.7) 4 yield... |

5 |
Effective fermion masses of O(gT ) in high-temperature gauge theories with exact chiral invariance, Phys
- Weldon
- 1982
(Show Context)
Citation Context .... (5.4) Consider the dispersion relation following from eq. (5.4). It is known that in Minkowskian space-time the dispersion relation of the “particle branch” reads p0 = p+m2∞/(2p)+..., where p = |p| =-=[23]-=-. Continuing the frequency to imaginary time, this corresponds to p2n+ p23+p2⊥ = −m2∞. Solving for p3 with a fixed pn yields ± ip3 = pn + m 2 ∞ 2pn + p2⊥ 2pn + ... . (5.5) From here a “rest mass” can ... |

4 | A lattice study of the jet quenching parameter - Panero, Rummukainen, et al. |

4 | Mesonic correlation lengths - Laine, Vepsalainen - 2004 |

3 |
Towards understanding thermal jet quenching via lattice simulations
- Laine, Rothkopf
- 2014
(Show Context)
Citation Context ...timating the potential at distances larger than those for which measurements exist, we fit the 5 largest distances (yg2E > 2.5) to the confining form σy + µ + γ y which describes the asymptotics well =-=[27]-=-.7 We express the screening masses as “energies”, Efull =Mcm + g2ECF 2π Ê , (7.7) and define the dimensionless quantities ȳ ≡ mEy , ρ ≡ g 2 ECFMr πm2E , (7.8) where Mr is the reduced mass (cf. eqs. ... |

2 |
et al. [QCDSF-UKQCD Collaboration], Non-perturbative renormalization and improvement of the local vector current for quenched and unquenched Wilson fermions, Phys
- Bakeyev
(Show Context)
Citation Context ...el). The shaded bands represent the fitted results with the corresponding ground state masses. The local (non-conserved) vector current J lµ requires a finite renormalization factor ZV (cf. e.g. ref. =-=[40]-=-). Correspondingly the bare vector correlators were renormalized using G(kn)µν (z) = ZV(g 2 0)G (kn)bare µν (z) , (B.6) with the non-perturbative value ZV(g 2 0) = 0.768(5) at 6/g 2 0 = 5.50 [41]. We ... |

1 |
Antiscreening of the Ampere force
- Brandt, Francis, et al.
- 2014
(Show Context)
Citation Context ...ening masses are equal in this approximation: m = 2πT + cg2NcT/(2π), where c is a small positive coefficient whose value depends on the number of dynamical fermions. Numerical measurements (cf. refs. =-=[13, 14, 15]-=- and references therein) have detected discrepancies with respect to this prediction, particularly for the scalar and pseudoscalar channels where the results are clearly below 2πT . Here we extend the... |

1 | The thermodynamic and the continuum limit of meson screening masses
- Kaczmarek, Laermann, et al.
(Show Context)
Citation Context ...ening masses are equal in this approximation: m = 2πT + cg2NcT/(2π), where c is a small positive coefficient whose value depends on the number of dynamical fermions. Numerical measurements (cf. refs. =-=[13, 14, 15]-=- and references therein) have detected discrepancies with respect to this prediction, particularly for the scalar and pseudoscalar channels where the results are clearly below 2πT . Here we extend the... |

1 |
UV Suppression by Smearing and Screening Correlators
- Gupta, Karthik
(Show Context)
Citation Context ...ening masses are equal in this approximation: m = 2πT + cg2NcT/(2π), where c is a small positive coefficient whose value depends on the number of dynamical fermions. Numerical measurements (cf. refs. =-=[13, 14, 15]-=- and references therein) have detected discrepancies with respect to this prediction, particularly for the scalar and pseudoscalar channels where the results are clearly below 2πT . Here we extend the... |

1 | The Dimensionally reduced effective theory for quarks in high temperature
- Huang, Lissia
- 1996
(Show Context)
Citation Context ... µ (x, z) . (4.4) The idea of the effective approach is dimensional reduction, i.e. keeping only the Matsubara zero modes of the SU(3) gauge fields in the covariant derivatives Dµ = ∂µ−igAµ (cf. ref. =-=[20]-=-). At tree-level, this means that we replace the original action through SQCD → S0 ≡ ∫ 1/T 0 dτ ∫ x,z ψ̄ γµD (n=0) µ ψ . (4.5) Making use of the representation of Dirac matrices in eq. (2.7) and denot... |

1 | QCD thermodynamics with O(a) improved Wilson fermions at Nf
- Brandt, Francis, et al.
(Show Context)
Citation Context ...corresponding to the temperatures T = 254(4) MeV and T = 338(5) MeV, respectively. (In terms of the pseudocritical temperature of the QCD crossover these amount to T/Tc ≃ 1.2 and T/Tc ≃ 1.6 at Nf = 2 =-=[29]-=-.) Further details concerning the lattice setup and measurements are given in appendix B. For a comparison with the results of the previous sections, the parameters of the effective theory need to be ... |

1 |
et al. [ALPHA Collaboration], O(a) improvement of lattice QCD with two flavors of Wilson quarks
- Jansen
- 1998
(Show Context)
Citation Context ...ations Our simulations are based on the standard Wilson gauge action, with fermions implemented via the O(a) improved Wilson discretization with a non-perturbatively determined clover coefficient csw =-=[33]-=-. The configurations were generated with the MP-HMC algorithm [34, 35] employing the implementation of ref. [36] based on Lüscher’s DD-HMC package [37]. Spatial correlation functions were computed on... |

1 |
web page DD-HMC algorithm for two-flavour lattice QCD, http://luscher.web.cern.ch/luscher/DD-HMC/index.html
- Lüscher
(Show Context)
Citation Context ...erturbatively determined clover coefficient csw [33]. The configurations were generated with the MP-HMC algorithm [34, 35] employing the implementation of ref. [36] based on Lüscher’s DD-HMC package =-=[37]-=-. Spatial correlation functions were computed on two ensembles, using the same discretization and masses as in the sea sector. The first ensemble, with a spatial size N3s = 64 3 and a temporal extent ... |

1 | Two-flavour lattice QCD correlation functions in the deconfinement transition region, PoS ConfinementX
- Brandt, Francis, et al.
- 2012
(Show Context)
Citation Context ...ensemble, with a spatial size N3s = 64 3 and a temporal extent of Nτ = 16, consisted of 313 independent configurations. It was first presented in ref. [38] and has subsequently been analyzed in refs. =-=[13, 39]-=-. The second ensemble is newly generated, and has 262 configurations on an Nτ × N3s = 12 × 643 lattice. Both ensembles were generated at fixed bare parameters, corresponding to a lattice spacing a = 0... |