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The spectral reconstruction problem for thermal photon and dilepton rates

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper claims that recombining transverse and longitudinal vector spectral functions into a single estimator, $\rho_H = 2(\rho_T - \rho_L)$, makes the thermal photon production rate in hot QCD extractable from lattice QCD data.

desk verdict A clear proceedings summary of published lattice work, but no new results; the claim that the improved estimator makes the photon rate tractable is not established by the material presented. read the letter →

arxiv 2508.08770 v1 pith:VWS34IST submitted 2025-08-12 hep-ph

Anthony Francis This is my paper
classification hep-ph
keywords thermalphotonratelatticeQCDspectralreconstructioninverseproblemquark-gluonplasmadileptonimprovedestimatorBackus-Gilbertmethod
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Thermal photons and dileptons escape the quark-gluon plasma with little rescattering, so their rates carry direct information about every stage of a heavy-ion collision. Lattice QCD can only access Euclidean-time correlators, and the production rates live in spectral functions that require solving an ill-conditioned inverse problem. This paper argues that a specific recombination of the transverse and longitudinal vector spectral functions, $\rho_H(\omega,k)=2(\rho_T-\rho_L)$, which vanishes at zero temperature and obeys a sum rule, makes the photon-rate version of that problem tractable. It demonstrates the point by applying three independent reconstruction strategies — $\chi^2$ fits, Backus-Gilbert, and Gaussian process regression — to the same quenched and 2+1 dynamical QCD data and reading off an effective diffusion coefficient at the light cone. The result is a lattice estimate of the photon production rate that can be compared with perturbation theory and with earlier dynamical QCD determinations.

What carries the argument

The central object is the improved estimator $\rho_H(\omega,k)=2(\rho_T(\omega,k)-\rho_L(\omega,k))$, a combination of the transverse and longitudinal thermal vector spectral functions. It carries the argument because it vanishes at $T=0$, decays as $1/\omega^4$ at large $\omega$, obeys the sum rule $\int_0^\infty d\omega\, \omega\,\rho_H(\omega)=0$, and equals the photon rate at the light cone. The paper combines it with the 'master function' view of reconstruction $\mathcal{F}[G, C_G] = (\boldsymbol{\rho}, C_\rho)$ and with three complementary strategies so that the light-cone value is constrained by the data.

What would settle it

Split the Euclidean time extent of the same correlator into two independent halves and reconstruct $\rho_H(\omega=k,k)$ from each; if the two light-cone values move apart by more than the quoted errors, the data are not pinning the result. Alternatively, repeat the dynamical QCD analysis at $N_\tau = 48$ and $64$ at fixed temperature: if $D_{\rm eff}(k)$ leaves the envelope spanned by the three strategies in Fig. 5, the estimator has not made the problem tractable.

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Extended reading notes

Core claim

The central claim is that the inverse problem for the photon rate, which a direct three-parameter fit leaves with a flat $\chi^2$ landscape and no stable global minimum, becomes tractable when the target is changed from the trace $-\rho^\mu_{\ \mu}$ to the combination $\rho_H = 2(\rho_T - \rho_L)$. Current conservation makes $\rho_L$ vanish at light-like kinematics, Lorentz symmetry makes $\rho_H$ vanish at $T=0$, and at large $\omega$ it falls as $1/\omega^4$, so the estimator isolates genuine thermal effects and admits a perturbative benchmark. Evaluating $\rho_H$ at $\omega=k$ then gives the photon production rate directly. Applying $\chi^2$ fits, Backus-Gilbert, and Gaussian process regr

Load-bearing premise

The whole determination rests on the assumption that the reconstructed light-cone value $\rho_H(\omega = k, k)$ is fixed by the lattice data themselves, rather than being inherited from the prior or Ansatz of whichever reconstruction method is used.

Editorial extensions

If this is right

  • Thermal photon production from the QGP is now accessible to lattice QCD estimation, not just perturbative modeling, giving theory input for the photon excess measured in heavy-ion collisions.
  • The three-strategy agreement on $D_{\rm eff}(k)$ provides a systematic envelope for the photon rate, making a robust comparison with perturbation theory possible.
  • The same estimator logic that worked for photons and heavy-quark diffusion suggests other kinematic combinations of spectral functions could be designed for other transport observables.
  • In quenched QCD the continuum-extrapolated results match perturbation theory at large momenta, while the dynamical QCD results show larger deviations, motivating a continuum study of the dynamical case.
  • Comparisons with earlier $n_f=2$ results are favorable, so the improved estimator does not contradict previous determinations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the light-cone value is indeed robust, the lattice $D_{\rm eff}(k)$ can be fed directly into heavy-ion phenomenology; a persistent mismatch with the measured direct-photon excess at $p_T \sim 1$–$2$ GeV would point to non-thermal sources (e.g., pre-equilibrium photons) rather than to QCD thermodynamics.
  • Because the flat $\chi^2$ landscape is only shifted, not eliminated, by the improved estimator, averaging over reconstruction strategies gives a systematic envelope but not a proof of unbiasedness; future ultra-precise correlators may still reshuffle the central value.
  • The $\rho_H$ construction might generalize: any observable that can be written as a spectral combination vanishing at $T=0$ or at a kinematic boundary could get its own 'improved estimator,' making otherwise intractable inverse problems approachable.
  • A direct testable extension is to compute $\rho_H$ in lattice perturbation theory at finite lattice spacing and compare to the quenched data before continuum extrapolation, isolating cut-off effects from thermal physics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This manuscript is a conference-proceedings contribution that reviews the inverse problem of extracting real-time spectral functions from Euclidean lattice correlators and presents recent results on the thermal photon rate. After discussing ill-conditioning and three reconstruction strategies (data-focused, model-augmented, and smeared-estimator approaches), it introduces the improved estimator rho_H = 2(rho_T - rho_L) (Eq. 17) and reports lattice estimates of an effective diffusion coefficient D_eff(k) (Eq. 19) in quenched and 2+1-flavor QCD (Figs. 4-6). The central claim is that this improved estimator makes photon-rate reconstruction tractable and yields data-driven results at the light cone.

Significance. The manuscript is a clearly written overview of the spectral reconstruction problem, with an accurate description of the ill-conditioned inverse Laplace transform and a useful taxonomy of strategies. The improved-estimator idea is theoretically motivated, and the paper honestly notes some limitations (flat chi^2 landscape, lack of continuum extrapolation in the dynamical case, strong data-set correlations). If the companion paper [39] demonstrates controlled systematics, this direction could be important for lattice determinations of the photon emissivity. However, the standalone evidence presented here for the central 'tractable' claim is thin, and the numerical results are not self-contained.

major comments (4)
  1. [Sec. 5.2, Eqs. (17)-(19), Fig. 5] The central claim that the improved estimator rho_H = 2(rho_T - rho_L) makes photon-rate reconstruction tractable is not established by the evidence shown. At the light cone, current conservation forces rho_L(omega=k,k)=0, so D_eff in Eq. (19) is simply 2 rho_T(k,k)/(2 chi_q k): the estimator adds no new information at the point of interest. The ill-conditioning illustrated by the flat chi^2 landscape (Fig. 2) is a property of the kernel and remains. Section 5.2 combines chi^2 fits, Backus-Gilbert (Eq. 18), and Gaussian-process regression, but no method-by-method breakdown or systematic variation of reconstruction priors is shown; all three methods encode the same perturbative UV and sum-rule constraints, so the agreement in Fig. 5 may reflect shared priors rather than data. Please provide synthetic-data tests, the BG resolution function at omega=k, and a comparison with substantially di
  2. [Sec. 5.2, dynamical QCD paragraph] The 2+1-flavor results are at a single lattice spacing (a^{-1}=7.04 GeV) and are not continuum extrapolated; the text itself states that 'a further study after taking the continuum limit is desirable to clarify this issue.' Figure 4 also shows a non-negligible discrepancy between G_H and perturbation theory in the dynamical case. Given these caveats, the dynamical-QCD D_eff values in Figs. 5 and 6 should be explicitly marked as preliminary. The abstract and conclusions present the dynamical-QCD results as 'recent results' without this qualification, which overstates their robustness.
  3. [Eq. (15) vs. Eq. (17)] The parameterization in Eq. (15) appears internally inconsistent. With rho_L defined as in Eq. (14), current conservation gives rho_L = (omega^2/k^2 - 1) rho_00, and the trace combination is -rho_mu^mu = -2 rho_T - rho_L, not 2 rho_T + rho_L. Consequently rho_H = 2(rho_T - rho_L) corresponds to lambda = -2, not lambda = 2, in the parameterization of Eq. (15). Please correct the signs or explicitly state the chosen convention; as written, the relation between the estimator and the photon production rate is obscured.
  4. [Sec. 5.2, general] The numerical results are not self-contained: all ensembles, error budgets, and reconstruction details are said to reside in [39]. No tables of G_H, covariance matrices, or method-by-method D_eff values are given, so Figs. 4-6 cannot be independently checked from this manuscript. A proceedings contribution may legitimately summarize a published paper, but then it should say so explicitly and avoid presenting Figs. 5-6 as new results in this document. If the paper is meant to stand alone, the essential reconstruction parameters and a breakdown by method are required.
minor comments (4)
  1. [Eq. (20)] Please verify the prefactor: combining Eq. (19) with the photon-rate formula appears to give a factor 1/(2 pi^2) rather than 1/pi^2, and the role of the flavor-charge sum sum Q_i^2 should be clarified relative to chi_q.
  2. [Figs. 4-6] The error bars are not defined. Please state whether they are statistical only or include systematic uncertainties from the reconstruction.
  3. [Eq. (11)] The chi^2 expression is not written in full; it is missing the squared residual and the covariance normalization. A reader trying to follow the flat-landscape argument needs the explicit form.
  4. [General] There are several typographical issues: 'strongcosh-behavior' in Sec. 3, inconsistent spacing in displayed equations, and a missing reference for the 'recent overview' in Sec. 1 (only [21] is cited later).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the improved estimator is an exact linear combination, and the photon-rate result rests on lattice data, perturbation-theory benchmarks, and transparent reconstruction priors rather than on a self-referential fit or a self-citation chain.

full rationale

The paper's central move is introducing rho_H = 2(rho_T - rho_L) (Eq. 17) and reading the photon rate off D_eff(k) = rho_H(omega=k,k)/(2 chi_q k) (Eq. 19). At the light cone, current conservation forces rho_L(k,k)=0, so rho_H(k,k)=2 rho_T(k,k); the estimator therefore does not manufacture new information at the point of interest. However, this is an exact identity, not a fitted parameter renamed as a prediction, and the paper does not use it to claim that light-cone information is somehow newly present in the data. The tractability claim is about the reconstruction problem being 'more doable' through a better-conditioned Euclidean channel, a technical assertion sourced to an external method paper [42]. The quoted caveats—the flat chi^2 landscape (Fig. 2), the method-independent ill-conditioning, the need for a continuum limit in dynamical QCD, and the possibility that the consistent picture could change with more precise data—are explicitly acknowledged in the text. The actual results in Fig. 5 are compared against independent perturbative calculations [43] and other lattice determinations [44,45], so they are externally falsifiable rather than justified solely by self-citation. Even though the proceedings reports the author's collaboration's HotQCD results, that is ordinary scientific reporting, not load-bearing self-citation. The concern that shared priors and Ansatze could influence Fig. 5 is a legitimate systematic-uncertainty issue, but the paper does not disguise it as a first-principles derivation; it states the opposite: 'the aim is to enable the study of the different systematics in all approaches.' Accordingly, no step in the derivation reduces by construction to its own inputs, and the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims of this proceedings rest on standard QFT/lattice relations and on the analysis of [39], which is not included in this paper. The lambda=2 estimator introduces no new physical entity; it is a combination of existing spectral components. The main model dependence enters through reconstruction priors and fit Ansatze, listed as free parameters.

free parameters (4)
  • Fit parameters of chi-squared Ansatz (transport peak, Breit-Wigner, asymptotic tail)
    Used in Strategy II fits; the final D_eff values depend on the fitted values.
  • Polynomial and Pade Ansatz parameters
    Two sets of Ansatz functions described in Section 5.2; parameters are fit to lattice data.
  • Rescaling scale omega0 in Backus-Gilbert method (Eq. 18)
    Hand-chosen scale in f(omega,k) = (omega0/omega)^4 tanh(omega/omega0)^5.
  • Gaussian process hyperparameters (kernel correlation length, etc.)
    Assumed for the simultaneous (omega,k) reconstruction with continuity as the only constraint.
assumptions (5)
  • standard math Spectral representation of Euclidean correlators (Eq. 9)
    Stated in Section 2; the inverse problem is defined by this relation.
  • standard math Current conservation: omega^2 rho_00 = k_i k_j rho_ij
    Used in Section 5.2 to show rho_L vanishes at light-like kinematics and to define rho_H.
  • domain assumption Spectral function positivity (where needed for MEM/GP)
    Invoked in Strategy II/III descriptions, e.g., MEM naturally encodes positivity.
  • domain assumption Perturbative NLO+LPMLO thermal photon rate is a valid benchmark
    Used in Section 5.2 to compare lattice results against perturbation theory.
  • domain assumption Lattice ensembles from [39] are sufficiently close to the continuum/thermodynamic limit for the quenched conclusions
    The quenched results are continuum extrapolated; the dynamical results are stated as needing further study.

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Pith. "Pith review of The spectral reconstruction problem for thermal photon and dilepton rates." pith.science (2026). https://pith.science/paper/VWS34IST

@misc{pith2026250808770,
  author       = {Pith},
  title        = {Pith review of: The spectral reconstruction problem for thermal photon and dilepton rates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VWS34IST}},
  note         = {Machine review of arXiv:2508.08770}
}
read the original abstract

Thermal photon and dilepton rates are important probes for understanding the quark-gluon plasma and QCD at high temperatures. As a consequence there is a strong interest to determine them using lattice QCD calculations. However, this is made difficult as they are related to thermal spectral functions that are not directly accessible through lattice calculations. Instead they are indirectly obtainable through performing an inverse Laplace-type transformation of Euclidean time lattice correlation functions. In this talk we will present recent results in dynamical QCD with a focus on advancements in determining the photon production rate via spectral reconstruction from lattice data.

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Forward citations

Cited by 1 Pith paper

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    A proceedings review covering prompt, pre-equilibrium, thermal, and hadronic photon/dilepton sources, with the open tension between v2 data and lattice rate estimates.

Reference graph

Works this paper leans on

45 extracted references · 5 canonical work pages · cited by 1 Pith paper

  1. [39]

    HotQCDcollaboration, Lattice QCD estimates of thermal photon production from the QGP, Phys. Rev. D110 (2024) 054518 [2403.11647]

    arXiv 2024

  2. [42]

    M. Cè, T. Harris, H.B. Meyer, A. Steinberg and A. Toniato,Rate of photon production in the quark-gluon plasma from lattice QCD,Phys. Rev. D102 (2020) 091501 [2001.03368]

    arXiv 2020

  3. [1]

    Hansen, H.B

    M.T. Hansen, H.B. Meyer and D. Robaina,From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD,Phys. Rev. D 96 (2017) 094513 [1704.08993]

    arXiv 2017

  4. [2]

    Extended Twisted Mass collaboration, Inclusive Hadronic Decay Rate of the𝜏 Lepton from Lattice QCD: The u� s Flavor Channel and the Cabibbo Angle, Phys. Rev. Lett.132 (2024) 261901 [2403.05404]

    arXiv 2024

  5. [3]

    Fukaya, S

    H. Fukaya, S. Hashimoto, T. Kaneko and H. Ohki,Towards fully nonperturbative computations of inelasticℓ𝑁 scattering cross sections from lattice QCD,Phys. Rev. D102 (2020) 114516 [2010.01253]

    arXiv 2020

  6. [4]

    Gambino and S

    P. Gambino and S. Hashimoto,Inclusive Semileptonic Decays from Lattice QCD,Phys. Rev. Lett. 125(2020) 032001 [2005.13730]

    arXiv 2020

  7. [5]

    HadStruccollaboration,Towards unpolarized GPDs from pseudo-distributions, JHEP 08 (2024) 162 [2405.10304]

    arXiv 2024

  8. [6]

    Meyer,A Calculation of the bulk viscosity in SU(3) gluodynamics,Phys

    H.B. Meyer,A Calculation of the bulk viscosity in SU(3) gluodynamics,Phys. Rev. Lett.100 (2008) 162001 [0710.3717]

    arXiv 2008

Show all 45 references
  1. [7]

    Meyer,A Calculation of the shear viscosity in SU(3) gluodynamics, Phys

    H.B. Meyer,A Calculation of the shear viscosity in SU(3) gluodynamics, Phys. Rev. D76 (2007) 101701 [0704.1801]

    2007 arXiv

  2. [8]

    Altenkort, A.M

    L. Altenkort, A.M. Eller, A. Francis, O. Kaczmarek, L. Mazur, G.D. Moore et al.,Viscosity of pure-glue QCD from the lattice, Phys. Rev. D108 (2023) 014503 [2211.08230]

    2023 arXiv

  3. [9]

    Aarts, C

    G. Aarts, C. Allton, J. Foley, S. Hands and S. Kim,Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD, Phys. Rev. Lett.99(2007) 022002 [hep-lat/0703008]. 10 The spectral reconstruction problem for thermal photon and dilepton rates...

    2007 arXiv

  4. [10]

    H.T. Ding, A. Francis, O. Kaczmarek, F. Karsch, E. Laermann and W. Soeldner,Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD, Phys. Rev. D83(2011) 034504 [1012.4963]

    2011 arXiv

  5. [11]

    Amato, G

    A. Amato, G. Aarts, C. Allton, P. Giudice, S. Hands and J.-I. Skullerud,Electrical conductivity of the quark-gluon plasma across the deconfinement transition, Phys. Rev. Lett. 111 (2013) 172001 [1307.6763]

    2013 arXiv

  6. [12]

    Aarts, C

    G. Aarts, C. Allton, A. Amato, P. Giudice, S. Hands and J.-I. Skullerud,Electrical conductivity and charge diffusion in thermal QCD from the lattice, JHEP 02(2015) 186 [1412.6411]

    2015 arXiv

  7. [13]

    Aarts and A

    G. Aarts and A. Nikolaev,Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD,Eur. Phys. J. A57 (2021) 118 [2008.12326]

    2021 arXiv

  8. [14]

    Caron-Huot, M

    S. Caron-Huot, M. Laine and G.D. Moore,A Way to estimate the heavy quark thermalization rate from the lattice,JHEP 04(2009) 053 [0901.1195]

    2009 arXiv

  9. [15]

    Banerjee, S

    D. Banerjee, S. Datta, R. Gavai and P. Majumdar,Heavy Quark Momentum Diffusion Coefficient from Lattice QCD,Phys. Rev. D85(2012) 014510 [1109.5738]

    2012 arXiv

  10. [16]

    Francis, O

    A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus and H. Ohno,Nonperturbative estimate of the heavy quark momentum diffusion coefficient, Phys. Rev. D92(2015) 116003 [1508.04543]

    2015 arXiv

  11. [17]

    Altenkort, A.M

    L. Altenkort, A.M. Eller, O. Kaczmarek, L. Mazur, G.D. Moore and H.-T. Shu,Heavy quark momentum diffusion from the lattice using gradient flow, Phys. Rev. D103 (2021) 014511 [2009.13553]

    2021 arXiv

  12. [18]

    HotQCDcollaboration,HeavyQuarkDiffusionfrom2+1FlavorLatticeQCDwith320MeV Pion Mass,Phys. Rev. Lett.130 (2023) 231902 [2302.08501]

    2023 arXiv

  13. [19]

    Ghiglieri, O

    J. Ghiglieri, O. Kaczmarek, M. Laine and F. Meyer,Lattice constraints on the thermal photon rate, Phys. Rev. D94(2016) 016005 [1604.07544]

    2016 arXiv

  14. [20]

    Brandt, A

    B.B. Brandt, A. Francis, T. Harris, H.B. Meyer and A. Steinberg,An estimate for the thermal photon rate from lattice QCD, EPJ Web Conf.175 (2018) 07044 [1710.07050]

    2018 arXiv

  15. [21]

    Kaczmarek and H.-T

    O. Kaczmarek and H.-T. Shu,Spectral and Transport Properties from Lattice QCD,Lect. Notes Phys.999 (2022) 307 [2206.14676]

    2022 arXiv

  16. [22]

    PHENIXcollaboration, Detailed measurement of the𝑒+𝑒− pair continuum in𝑝+𝑝 and Au+Au collisions at√𝑠𝑁𝑁 = 200 GeV and implications for direct photon production,Phys. Rev. C81(2010) 034911 [0912.0244]

    2010 arXiv

  17. [23]

    Fleuret,Recent relativistic heavy ion collider results on photon, dilepton and heavy quarks, Pramana 72(2009) 23

    F. Fleuret,Recent relativistic heavy ion collider results on photon, dilepton and heavy quarks, Pramana 72(2009) 23

    2009

  18. [24]

    Lattice@CERN 2024

    Probing the photon emissivity of thermal QCD matter on the lattice byHarvey Meyer, CERN workshop 2024, “Lattice@CERN 2024.”

    2024

  19. [25]

    Karpie, K

    J. Karpie, K. Orginos, A. Rothkopf and S. Zafeiropoulos,Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks,JHEP 04(2019) 057 [1901.05408]

    2019 arXiv

  20. [26]

    Extended Twisted Mass Collaboration (ETMC) collaboration, Probing the Energy-Smeared R Ratio Using Lattice QCD,Phys. Rev. Lett.130 (2023) 241901 [2212.08467]

    2023 arXiv

  21. [27]

    J. Hadamard,Sur les problèmes aux dérivés partielles et leur signification physique, 11 The spectral reconstruction problem for thermal photon and dilepton rates Anthony Francis Princeton University Bulletin13(1902) 49

    1902

  22. [28]

    Cuniberti, E

    G. Cuniberti, E. De Micheli and G.A. Viano,Reconstructing the thermal Green functions at real times from those at imaginary times, Commun. Math. Phys.216 (2001) 59 [cond-mat/0109175]

    2001 arXiv

  23. [29]

    Meyer,Transport Properties of the Quark-Gluon Plasma: A Lattice QCD Perspective, Eur

    H.B. Meyer,Transport Properties of the Quark-Gluon Plasma: A Lattice QCD Perspective, Eur. Phys. J. A47(2011) 86 [1104.3708]

    2011 arXiv

  24. [30]

    Itou and Y

    E. Itou and Y. Nagai,Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions, JHEP 07(2020) 007 [2004.02426]

    2020 arXiv

  25. [31]

    Kades, J.M

    L. Kades, J.M. Pawlowski, A. Rothkopf, M. Scherzer, J.M. Urban, S.J. Wetzel et al.,Spectral Reconstruction with Deep Neural Networks,Phys. Rev. D102(2020) 096001 [1905.04305]

    2020 arXiv

  26. [32]

    Horak, J.M

    J. Horak, J.M. Pawlowski, J. Rodríguez-Quintero, J. Turnwald, J.M. Urban, N. Wink et al., Reconstructing QCD spectral functions with Gaussian processes,Phys. Rev. D105(2022) 036014 [2107.13464]

    2022 arXiv

  27. [33]

    H.-T. Ding, O. Kaczmarek, S. Mukherjee, H. Ohno and H.T. Shu,Stochastic reconstructions of spectral functions: Application to lattice QCD,Phys. Rev. D97(2018) 094503 [1712.03341]

    2018 arXiv

  28. [34]

    Asakawa, T

    M. Asakawa, T. Hatsuda and Y. Nakahara,Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys.46(2001) 459 [hep-lat/0011040]

    2001 arXiv

  29. [35]

    Burnier and A

    Y. Burnier and A. Rothkopf,Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories,Phys. Rev. Lett.111 (2013) 182003 [1307.6106]

    2013 arXiv

  30. [36]

    Backus and F

    G. Backus and F. Gilbert,The Resolving Power of Gross Earth Data,Geophys. J. Int.16 (1968) 169

    1968

  31. [37]

    Hansen, A

    M. Hansen, A. Lupo and N. Tantalo,Extraction of spectral densities from lattice correlators, Phys. Rev. D99 (2019) 094508 [1903.06476]

    2019 arXiv

  32. [38]

    H.-T. Ding, O. Kaczmarek and F. Meyer,Thermal dilepton rates and electrical conductivity of the QGP from the lattice, Phys. Rev. D94 (2016) 034504 [1604.06712]

    2016 arXiv

  33. [40]

    Brandt, A

    B.B. Brandt, A. Francis, H.B. Meyer and H. Wittig,Thermal Correlators in the \rho\ channel of two-flavor QCD, JHEP 03(2013) 100 [1212.4200]

    2013 arXiv

  34. [41]

    Brandt, A

    B.B. Brandt, A. Francis, B. Jäger and H.B. Meyer,Charge transport and vector meson dissociation across the thermal phase transition in lattice QCD with two light quark flavors, Phys. Rev. D93 (2016) 054510 [1512.07249]

    2016 arXiv

  35. [43]

    Jackson and M

    G. Jackson and M. Laine,Testing thermal photon and dilepton rates,JHEP 11 (2019) 144 [1910.09567]

    2019 arXiv

  36. [44]

    M. Cè, T. Harris, A. Krasniqi, H.B. Meyer and C. Török,Photon emissivity of the quark-gluon plasma: A lattice QCD analysis of the transverse channel,Phys. Rev. D106 (2022) 054501 [2205.02821]

    2022 arXiv

  37. [45]

    M.Cè, T.Harris, A.Krasniqi, H.B.MeyerandC.Török, Probingthephotonemissivityofthe quark-gluon plasma without an inverse problem in lattice QCD, Phys. Rev. D109 (2024) 014507 [2309.09884]. 12

    2024 arXiv

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