From Non-interacting to Interacting Picture of Quark Gluon Plasma in presence of magnetic field and its fluid property

Ankita Mishra; Jayanta Dey; Sabyasachi Ghosh; Sarthak Satapathy; Souvik Paul

REVIEW 3 major objections 4 minor 2 cited by

From Non-interacting to Interacting Picture of Quark Gluon Plasma in presence of magnetic field and its fluid property

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper attempts to map lattice-QCD thermodynamics and quark condensate data at finite temperature and magnetic field onto a quasi-particle parametrization, then claims that magnetic field and QCD interaction are the two dominant…

desk verdict Useful heuristic extension of the authors' B=0 quasi-particle mapping to finite B, but a 4/3 normalization error in the shear-viscosity expression undermines the reported suppression percentages. read the letter →

arxiv 1908.04335 v2 pith:WVFKSMYB submitted 2019-08-12 hep-ph nucl-th

Jayanta Dey , Sarthak Satapathy , Ankita Mishra , Souvik Paul , Sabyasachi Ghosh This is my paper · ORCID

classification hep-phnucl-th

keywords quark-gluonplasmamagneticfieldshearviscosityelectricalconductivityquasi-particlemodellatticeQCDthermodynamicsinversecatalysisrelaxationtimeapproximation

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

This paper tries to establish that the quark-gluon plasma's interaction and its exposure to a magnetic field can both be captured by a small set of temperature- and field-dependent quasi-particle parameters, and that those same parameters control the plasma's fluid response. Concretely, it claims that interaction and magnetic field are the two dominant sources that reduce the shear viscosity and electrical conductivity of QGP, with interaction alone cutting $\eta$ by 50% to 98.5% and $\sigma$ by 30% to 90% over the temperature range considered. The motivation is practical: once the parameters are fitted to lattice QCD thermodynamics, the model gives quick analytical estimates of any phenomenological quantity in a magnetized, interacting QGP without a full microscopic transport calculation.

What carries the argument

The load-bearing mechanism is the fitted set of quasi-particle parameters $g(T,B)$, $f_E(T,B)$, $f_k(T,B)$, and $v_{\rm av}(T,B)$, defined so that average energy and momentum are $E_{\rm av}=3T f_E$ and $k_{\rm av}=3T f_k$ with $k_{\rm av}=v_{\rm av}E_{\rm av}$. These parameters map the non-interacting massless Stefan-Boltzmann picture onto the interacting lattice picture by matching pressure, energy density, entropy density, and a number density built from the lattice quark condensate via $M=(M_N/3)\langle\bar q q\rangle$. Eq. (31) then carries these parameters into the transport coefficients, multiplying the massless $\eta$ and $\sigma$ by the interaction factors and by the magnetic denominators, so the equilibrium fit directly determines how much transport is suppressed in the magnetized plasma.

What would settle it

A direct lattice calculation of the total number density $n/T^3$ at finite $B$ would settle the mapping without the condensate proxy: if the $g(T,B)$ extracted from the condensate differs from the one obtained directly from $n$, the transport chain collapses. A second check is to test the magnetic-field functional form itself: for fixed $T$, $\eta_\perp$ should fall as $1/[1+(\tau_c/\tau_B)^2]$ and $\eta_\parallel$ as $1/[1+4(\tau_c/\tau_B)^2]$ when $B$ is varied, which a kinetic simulation can verify.

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Extended reading notes

Core claim

The paper's central claim is that the same factors used to map lattice QCD thermodynamics—a degeneracy factor $g(T,B)$, average energy $E_{\rm av}=3T f_E(T,B)$, average momentum $k_{\rm av}=3T f_k(T,B)$ and average velocity $v_{\rm av}=f_k/f_E$—can be inserted into kinetic-theory expressions for the shear viscosity and electrical conductivity. In the resulting formulas, Eqs. (31), interaction enters as multiplicative factors $v_{\rm av}^2 f_k^2 g$ for $\eta$ and $v_{\rm av}^2 g$ for $\sigma$, while the magnetic field enters through the denominators $1/[1+(\tau_c/\tau_B)^2]$ and $1/[1+4(\tau_c/\tau_B)^2]$, where $\tau_B=E_{\rm av}/(qB)$ is the inverse synchrotron frequency. The two suppression mechanisms act independently: the magnetic field shortens the effective relaxation time, and the interaction shrinks the thermodynamic phase space. With both included, the anisotropic components satisfy $\eta_\parallel>\eta_\perp$ and $\sigma_\parallel>\sigma_\perp$, all suppressed relative to the free massless values.

Load-bearing premise

The entire suppression chain rests on treating the lattice quark condensate as a constituent quark mass through $M=(M_N/3)\langle\bar q q\rangle$ and then requiring the resulting number density to equal $g(T,B)\times 5.23\,T^3$; if that linear proxy misrepresents the finite-$B$ lattice data, every reported reduction of $\eta$ and $\sigma$ changes.

Editorial extensions

If this is right

Heavy-ion fluid simulations that take the model at face value should use strongly reduced, anisotropic viscosities and conductivities, especially near the transition temperature where suppression is largest.
The inequality $\eta_\parallel>\eta_\perp$ and $\sigma_\parallel>\sigma_\perp$ means charge and momentum transport are faster along the magnetic field than across it, so magneto-hydrodynamic descriptions require separate longitudinal and transverse coefficients rather than one scalar value.
Because the suppression grows with magnetic field strength, the model predicts that the plasma's fluid behavior becomes more dissipative in the direction transverse to the field at large $eB$.
The same $T,B$-dependent parameters can be reused to estimate other QGP observables—strangeness enhancement, thermal dilepton and photon rates, heavy-quark diffusion, jet quenching—giving quick non-perturbative approximations.

Reading between the lines

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

If the condensate-to-mass proxy is trustworthy, then $g(T,B)$ can be read as an effective number of available degrees of freedom; a natural cross-check would be to extract $g(T,B)$ from the lattice entropy density alone and compare it with the value obtained from the condensate route.
Since the paper leaves $\tau_c$ free, one could turn its $\eta/s$ curves into a prediction for a temperature-dependent $\tau_c(T,B)$ by fixing $\eta/s$ near the KSS bound, a concrete input that magneto-hydrodynamic simulations could test.
The authors note that inverse magnetic catalysis is faint in $\eta$ and $\sigma$ because the thermal distribution suppresses the mass effect; the natural place to look for the IMC signal is the interaction measure $\epsilon-3P$ or the bulk viscosity, where a peak shift with $eB$ should appear.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know before you read it. First, it does something new: it takes the same group's B=0 quasi-particle mapping of LQCD thermodynamics, extends it to finite B, and then feeds the fitted g(T,B), v_av(T,B), and f_k(T,B) into RTA transport expressions for shear viscosity and electrical conductivity. Second, the shear-viscosity formula has a normalization bug. With all interaction factors set to 1, Eq. (29) gives 3/(5π^2)(g_g+g_Q) τ_c T^4, while the non-interacting baseline Eq. (23) is 4/(5π^2)(g_g+g_Q) τ_c T^4. The paper says Eq. (29) reduces to Eq. (23); it does not. The source is the replacement of ⟨k^2⟩=12T^2 by (k_av)^2=9T^2. This affects η_parallel, η_perp, and η/s, so the ratios in Fig. 3 are not a clean interaction-suppression factor. The electrical-conductivity expression does reduce correctly, so the flaw is specific to shear viscosity.

What the paper does well: the parametric mapping of the finite-B LQCD thermodynamics is transparent and honest. The authors state the limitations themselves: the condensate-to-mass conversion M=(M_N/3)⟨q̄q⟩ is a heuristic guided by an NJL gap equation, Landau quantization is neglected, and the model is meant only for order-of-magnitude estimates. The appendix gives a self-contained derivation of the anisotropic transport coefficients in RTA. The comparison with HRG and NJL results is useful context.

The soft spots beyond the normalization issue: the weakest link is the chain from LQCD condensate to a constituent mass to a number density, which then fixes g(T,B) that later controls transport suppression. This is acknowledged as heuristic, but it means the quantitative reductions are essentially propagated from the fit rather than independently predicted. The relaxation time τ_c is a free parameter, so absolute values of η/s are not predictions; only the ratios of interacting to non-interacting values carry the model's message, and those are distorted by the 4/3 error. There are also no error bars on the LQCD fits, which matters for claims about 50-98% reductions.

The qualitative conclusion—both magnetic field and interaction suppress transport coefficients—is likely robust, since g<1, v_av<1 and the magnetic denominators all act in the same direction. But the specific percentages should not be quoted until the normalization is fixed.

Who is this for? Heavy-ion phenomenologists who need quick analytic estimates of magnetized QGP transport inputs for MHD simulations. It deserves a serious referee; the idea is useful and the problems are addressable. I would send it to review with a request to fix the normalization, add error estimates, and clarify the strong-field domain of validity.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes a quasi-particle model of the quark-gluon plasma in a finite magnetic field, in which the interaction is encoded through temperature- and magnetic-field-dependent factors: an effective degeneracy factor g(T,B), an average-energy rescaling f_E(T,B), an average-momentum rescaling f_k(T,B), and an average velocity v_av(T,B). These factors are tuned so that the model reproduces LQCD results for the number density, pressure, energy density, and entropy density at eB = 0, 0.2, and 0.4 GeV^2. The tuned factors are then inserted into relaxation-time-approximation expressions for the shear viscosity and electrical conductivity, producing parallel and perpendicular components in a magnetic field. The paper's central quantitative claim is that both the magnetic field and the QCD interaction are dominant sources of reduction of these transport coefficients, with reported reductions of 50-98.5% for shear viscosity and 30-90% for electrical conductivity in the temperature range studied.

Significance. If the central claim survived scrutiny, the paper would offer a simple, analytic way to translate LQCD-matched thermodynamics into anisotropic transport coefficients for magnetized QGP, which could be useful for magnetohydrodynamic simulations and for quick phenomenological estimates. The authors are transparent about the heuristic nature of the model, and they compare their results with HRG and NJL estimates, which helps place the work in context. However, the quantitative claim is currently weakened by a normalization mismatch in the shear-viscosity expression and by the fact that the transport suppression is largely inherited from the fitted thermodynamic factors rather than emerging from an independent transport calculation. The paper therefore has value as a rough parametric tool, but its headline percentages and the statement that interaction is a 'dominating source' need to be reformulated or supported by additional analysis.

major comments (3)

[§3, Eqs. (23), (25), (29), and Fig. 3] The claim that Eq. (29) reduces to the non-interacting baseline Eq. (23) is not correct for shear viscosity. Setting v_av = f_k = g = 1 in Eq. (29) gives η = (g_g + g_Q) 3 T^4 / (5π^2) τ_c, whereas Eq. (23) gives η = (g_g + g_Q) 4 T^4 / (5π^2) τ_c. The discrepancy is a factor 3/4 and originates from replacing the second moment ⟨k^2⟩ = 12T^2 with k_av^2 = (3T)^2 in the k^4/E^2 weight. Because Eq. (31) multiplies η_parallel, η_perp, and hence η/s by the same prefactor, the 'Int./Non-Int.' ratios in the lower panels of Fig. 3 do not isolate the interaction effect; they contain a spurious normalization factor. The quoted 50-98.5% reductions are therefore not trustworthy until this normalization is corrected.
[§2, Eqs. (14), (18), (20) and §3, Eqs. (29), (31)] The factors g(T,B), v_av(T,B), and f_k(T,B) are obtained by requiring that Eqs. (14) and (20) reproduce n_LQCD, P_LQCD, and ε_LQCD point by point. Inserting these same fitted functions into Eqs. (29) and (31) means that the reported suppression of η and σ relative to the Stefan-Boltzmann limits is largely a restatement of the fitted suppression of the thermodynamic quantities. The abstract's statement that 'magnetic field and interaction both are two dominating sources' reducing transport coefficients is therefore, at present, partly a consequence of the construction rather than a falsifiable prediction of the transport calculation. The authors should either demonstrate that some feature of the result is not determined by the fitted factors (for example, the specific interplay between the τ_B denominators and the f_k, v_av factors) or explicitly reframe the claim as an estimate inherited from LQCD-matched thermodynamics.
[§2, Eqs. (13)-(14)] The conversion from the LQCD quark condensate to a constituent quark mass, M(T,B) = (M_N/3)⟨q̄q⟩_T, is a heuristic assumption motivated only by analogy to an NJL gap equation with zero current quark mass. No normalization of the condensate or derivation of the factor M_N/3 is provided. This relation determines g(T,B) through Eq. (14), and g(T,B) enters every transport coefficient in Eq. (31), so the quantitative reductions reported in the paper hinge on this assumption. The authors should test the sensitivity of their results to this choice, for example by varying the proportionality constant over a range typical of NJL/PNJL models, and should state clearly that the condensate-to-mass mapping is an unvalidated assumption rather than a QCD-derived relation.

minor comments (4)

[§3.2] The sentence 'Eav(T, B = 0) < 1' is dimensionally inconsistent; the text should say E_av(T, B = 0) < 3T, as is stated correctly for k_av.
[§3.1] The reference 'as shown in the right panel of Fig. (2)' appears to point to the wrong figure; the comparison with HRG and NJL results is displayed in Fig. (4), not Fig. (2).
[Fig. 3 caption and legend] The notation η1, η2, σ0 is used without explicit identification with η_parallel, η_perp, and σ_parallel/σ_perp from Eq. (31); the caption should define these symbols to avoid confusion.
[General presentation] There are several typographical errors, including 'coppied' in §2 and 'Completely vanished' in the Summary; the manuscript would benefit from a careful proofreading pass.

Circularity Check

1 steps flagged · score 6.0 of 10

The interaction-driven suppression of eta and sigma is the LQCD thermodynamic fit carried into transport by construction, so the central 'interaction reduces transport' claim is partly circular; the magnetic-field suppression is independent.

fitted input called prediction [Sec. 3, Eqs. (20), (29), and Abstract]
"P_LQCD = v_av^2 f_E g × 5.23T^4; ǫ_LQCD = f_E g × 15.69T^4; ... σ = [v_av^2(T)g(T)] g_Q T^2/(9π^2) τ_c Σ_f q_f^2. ... magnetic field and interaction both are two dominating sources, for which the values of transport coefficients can be reduced."

Combining Eq. (20) gives v_av^2 g = P_LQCD/(f_E × 5.23T^4) = 3P_LQCD/ǫ_LQCD, since ǫ_LQCD = f_E g × 15.69T^4. Inserting this into Eq. (29) yields σ_int/σ_free = 3P_LQCD/ǫ_LQCD. Thus the conductivity suppression displayed as an interaction effect is exactly the lattice pressure-to-energy ratio already fitted into the model; it is the input thermodynamic fit, not an independent transport prediction. The shear-viscosity suppression factor v_av^2 f_k^2 g is likewise the same set of fitted parameters g, v_av, and f_k coming from Eqs. (14), (18), and (20), so the qualitative statement that interaction reduces η and σ is forced by the construction of the quasi-particle factors. The magnetic-field denominators in Eq.

full rationale

The one genuine circular step is the interaction-suppression of transport. The paper fits g, f_E, and v_av pointwise to LQCD thermodynamics in Eqs. (14), (18), and (20), and then Eq. (29) multiplies the free transport coefficients by products of those same fitted factors. Algebraically, the conductivity ratio becomes exactly 3P_LQCD/ǫ_LQCD, so the abstract's statement that interaction reduces the transport coefficients is a restatement of the lattice equation of state rather than a transport-derived result. However, the magnetic-field dependence is not circular: the denominators 1/[1+(τ_c/τ_B)^2] follow from the RTA Boltzmann-equation solution in the appendix and would be present independently of the LQCD fit. The self-citation to Ref. [66] is also not load-bearing in a circular way, because the present paper refits the parameters to LQCD data rather than relying solely on that earlier work. A separate internal inconsistency—Eq. (29) with v_av=f_k=g=1 gives a coefficient 3/(5π^2) instead of Eq. (23)'s 4/(5π^2), so the stated reduction to the non-interacting limit is not exact—is a correctness problem rather than a circularity and is not scored here. Overall, the central interaction-reduction claim is partly circular by construction, while the magnetic-field part retains independent content.

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

The central claim rests on a chain of choices: LQCD thermodynamics and the quark condensate are encoded into three rescaling factors applied to massless ideal-gas formulas; the condensate is converted to a constituent mass through a linear heuristic; transport is evaluated in relaxation-time approximation with a magnetic time scale and without Landau quantization; and the same fitted factors are then inserted into the transport formulas. Because the factors are tuned to the very quantities the model is designed to reproduce, the output transport reductions partly inherit the fit. There are no new physical entities, but there are four fit or free parameters and four physical assumptions.

free parameters (4)

g(T,B): effective degeneracy factor = pointwise function of T and B, approximately 0.1 to 1 in Fig. 2
Fixed by requiring g(T,B) times 5.23 T^3 to equal n_LQCD, where n_LQCD is computed from the LQCD quark condensate via Eq. (13). No functional form or uncertainty is given.
fE(T,B): average energy rescaling = pointwise function, with E_av/3T roughly 0.8 to 2.4 in Fig. 2
Tuned to reproduce the LQCD energy density through epsilon_LQCD = fE times g times 15.69 T^4 in Eq. (20).
vav(T,B): average velocity = pointwise function, approximately 0.2 to 1 in Fig. 2
Tuned to reproduce the LQCD pressure through P_LQCD = vav^2 times fE times g times 5.23 T^4 in Eq. (20). The momentum rescaling fk is then derived as fk = fE times vav in Eq. (17).
tau_c: relaxation time = free parameter; set to 5 fm in the numerical plots
Not fitted to data, but it sets the absolute scale of eta and sigma. Transport results are shown normalized by tau_c or for tau_c = 5 fm, so comparisons with data require an independent determination of tau_c.

assumptions (4)

domain assumption LQCD thermodynamics in a magnetic field can be represented as a massless ideal gas with rescaled degeneracy, average energy, and average velocity factors.
Equations (14), (18), and (20) define the interacting picture by multiplying massless ideal-gas expressions by g(T,B), fE(T,B), and vav(T,B). This is the central quasiparticle mapping.
ad hoc to paper The LQCD quark condensate maps linearly to a constituent quark mass via M = (M_N/3) times the condensate.
Invoked after Eq. (12) and used in Eq. (13) to obtain n_LQCD. The relation is described as guided by an NJL gap equation with zero current quark mass, but no derivation from QCD is provided.
domain assumption Magnetic-field transport is captured by the relaxation time approximation with tau_B = E_av/(qB) and the standard denominators 1/(1+(tau_c/tau_B)^2), with Landau quantization neglected.
The appendix, Eqs. (48)-(58) and (69)-(76), derives the magnetic field modifications in this way. The neglect of Landau levels is acknowledged in Sec. 3.2 as a demerit.
domain assumption In a magnetic field, the relevant thermodynamic pressure is the longitudinal pressure P_z, so s = (epsilon + P_z)/T holds.
Equation (19) states this relation and it is used to connect the finite-B LQCD data to the fitted thermodynamic quantities.

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Pith. "Pith review of From Non-interacting to Interacting Picture of Quark Gluon Plasma in presence of magnetic field and its fluid property." pith.science (2026). https://pith.science/paper/WVFKSMYB

@misc{pith2026190804335,
  author       = {Pith},
  title        = {Pith review of: From Non-interacting to Interacting Picture of Quark Gluon Plasma in presence of magnetic field and its fluid property},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WVFKSMYB}},
  note         = {Machine review of arXiv:1908.04335}
}

read the original abstract

We have attempted to build a parametric based simplified and analytical model to map the interaction of quarks and gluons in presence of magnetic field, which has been constrained by quark condensate and thermodynamical quantities like pressure, energy density etc., obtained from the calculation of lattice quantum chromodynamics. To fulfill that mapping, we have assumed a parametric temperature and magnetic field dependent degeneracy factor, average energy, momentum and velocity of quarks and gluons. Implementing this QCD interaction in calculation of transport coefficient at finite magnetic field, we have noticed that magnetic field and interaction both are two dominating sources, for which the values of transport coefficients can be reduced. Though the methodology is not so robust, but with the help of its simple parametric expressions, one can get a quick rough estimation of any phenomenological quantity, influenced by temperature and magnetic field dependent QCD interaction.

Figures

Figures reproduced from arXiv: 1908.04335 by the authors.

**Figure 1.** Constituent quark mass M (left) and normalized total number density nLQCD/T 3 vs temperature T at different magnetic field. The estimations are based on LQCD quark condensate data [5]. ǫLQCD data but not nLQCD data. Using their quark condensate (hqq¯ iT ) data, we can go with rough estimate of constitute quark mass as M ≈ MN 3 hqq¯ iT , with nucleon mass MN = 0.940 GeV. Reader can recognize the idea is guided from g… view at source ↗

**Figure 2.** LQCD data of pressure (black circles), energy density (r [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Left-upper: T dependence of η (dotted line), η1(eB = 0.2GeV2 ) (solid line) and η2(eB = 0.2GeV2 ) (dash line) for their non-interacting and interacting cases. Left-lower: Ratio of interaction to non-interaction values of η, η1 and η2 at different magnetic fields. Right-upper: T dependence of σ, σ0(eB = 0.2GeV2 ) for their non-interacting and interacting cases. Right-lower: Ratio of interaction to non-interaction val… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Left: Comparing our estimation (black solid line) of entropy [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: Viscosities to entropy density ratio for non-interacting a [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]

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