Physics of the gluon mass gap

Jan M. Pawlowski; Joannis Papavassiliou; Mauricio N. Ferreira; Nicolas Wink

REVIEW 4 major objections 6 minor 104 references

Physics of the gluon mass gap

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The gluon mass gap is a physical scale: Tc ≈ c_conf mgap, and the deep infrared leaves Tc and fπ untouched.

desk verdict Useful IR-insensitivity results; the 'gluon mass gap' defined via the pole of a fitting ansatz needs a stability check before the central physical claim is sold. read the letter →

arxiv 2508.20568 v1 pith:UWLEDYRN submitted 2025-08-28 hep-ph hep-lathep-th

Mauricio N. Ferreira , Joannis Papavassiliou , Jan M. Pawlowski , Nicolas Wink This is my paper · ORCID

classification hep-phhep-lathep-th

keywords gluonmassgapSchwingermechanismLandaugaugeconfinement-deconfinementtransitionpiondecayconstantpropagatorfunctionalmethodsinfrareddecoupling

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

The paper argues that the gluon mass gap mgap, defined as the first complex pole of the Landau-gauge gluon propagator, is not a fitting artifact but a physical scale with direct observable consequences: the confinement-deconfinement temperature is linearly proportional to it, Tc ≈ c_conf mgap. The same analysis shows that both Tc and the pion decay constant fπ are insensitive to the gluon propagator's momentum dependence below the infrared inflection point, indicating that the deep infrared decouples from these observables. The paper also builds a compact fit of the gluon dressing in which all parameters belong to one of three momentum regimes (ultraviolet, Schwinger, deep infrared) and the scale is set by mgap instead of Λ_QCD. If the claims hold, the gluon mass gap becomes a genuine observable of QCD that connects confinement to the phase transition and can be used to probe the interplay between confinement and chiral symmetry breaking.

What carries the argument

The central object is the gluon mass gap mgap, defined as the real part of the first non-trivial zero of the gluon dressing Z_A in the complex plane: mgap = min{Re ω_s | ω_s ≠ 0, Z_A(-$ω_s^{2}$) = 0}, with ω_s = (1 + i γ_gap) mgap. This complex-pole condition is applied to the analytic fit Z_A,fit (equation 31), whose parameters are fixed separately in the three momentum regimes (uv, sc, ir), so that all scales are measured in units of mgap. The machinery converts a gauge-fixed correlation function into an RG-invariant observable that drives the exponential suppression of the gluon loop in the Polyakov-loop potential, and thereby sets the critical temperature.

What would settle it

Locate the physical gluon propagator's first complex-plane singularity by direct spectral reconstruction from lattice or functional data (rather than from the fitting form) and compare its real part with the mgap obtained from equations (31) and (45); the central claim fails if the two disagree beyond the fit uncertainty, or if varying the fit's mass gap changes Tc in a way inconsistent with the linear relation (48).

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Extended reading notes

Core claim

In Landau-gauge QCD, the gluon mass gap mgap — defined as the real part of the first non-trivial complex singularity of the gluon propagator, with ω_gap = (1 + i γ_gap) mgap — is proportional to the confinement-deconfinement temperature, Tc ≈ c_conf mgap, and both Tc and the pion decay constant fπ are insensitive to the momentum dependence of the gluon propagator below the infrared inflection point p^-_in (≈ 370 MeV for Yang-Mills, ≈ 390 MeV for 2+1 flavour QCD). The paper identifies three momentum regimes — ultraviolet, strongly correlated Schwinger regime, and deep infrared — and shows that the first two control these observables while the third leaves no imprint. It then constructs a fit for the gluon dressing, Z_A,fit, in which every parameter carries a physical meaning from one of the three regimes, and the only mass scale is mgap. As a corollary, the fit predicts that if mgap is increased relative to the chiral symmetry breaking scale, chiral symmetry breaking turns off and fπ vanishes beyond a critical value; if mgap is lowered, fπ saturates at a finite value f0π.

Load-bearing premise

The argument assumes that the complex-plane zero of a fitted analytic form of the gluon propagator faithfully locates the actual singularity of the full propagator; if that continuation is wrong, mgap is an artifact and the linear relation with Tc loses physical content.

Editorial extensions

If this is right

Tc is linearly proportional to the gluon mass gap, Tc ≈ c_conf mgap, making mgap a direct measure of the confinement scale rather than a mere property of a gauge-fixed correlator.
Both Tc and fπ are unchanged by any modification of the gluon propagator below the infrared inflection point, so the deep infrared carries no imprint on these two observables.
If mgap is increased relative to the chiral scale, the quark gap equation loses its non-trivial solution and fπ vanishes beyond a critical value; if mgap is decreased, fπ saturates at a finite value f0π.
The fit (31) with scale setting through mgap provides a minimal parametrisation of the gluon propagator whose parameters each correspond to one of the three momentum regimes.

Reading between the lines

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

If the linear relation Tc ≈ c_conf mgap survives under variations of the gauge group or the number of flavours, it would supply a cheap estimate of the deconfinement temperature from a single complex-plane pole computation — a test the paper does not perform.
The complex-pole definition of mgap could become a standard RG-invariant scale-setting parameter for functional computations, potentially replacing Λ_QCD in many applications.
The observed insensitivity below p^-_in means that the unresolved deep infrared, where lattice volumes are small and functional results differ, is irrelevant for Tc and fπ; these observables can therefore be computed with controlled error even while the deep infrared remains uncertain.

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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

Here's my read on Ferreira, Papavassiliou, Pawlowski, and Wink, arXiv:2508.20568.

The strongest, most durable piece is the deformation study: Tc in Yang-Mills and fπ in 2+1-flavour QCD are insensitive to changes in the gluon propagator for momenta below the infrared inflection point p−_in ≈ 370 or 390 MeV. That result is clean, explicit, and useful to anyone who wants to know which part of the gluon propagator actually matters for these observables. The three-regime decomposition of the dressing (UV, Schwinger, deep-IR) using p±_in and p_peak is also a nice organizing idea, and the fit (31) is a compact, physically motivated parametrization with mgap as the only scale.

The soft spot is the definition of mgap itself. It is extracted by solving Z_A,fit(-ω_s^2) = 0 for the complex pole of a fitting ansatz. Euclidean data fix Z_A only for positive p^2; the analytic continuation to negative x goes through logs with branch cuts, and the paper gives no test that a different but equally good fit would put the first zero in the same place. The authors admit mgap is hard to pin down, but they do not check the stability of their one value. Until that check is done, I'd call mgap a useful fit parameter rather than a measured physical scale. The linear relation Tc ≈ c_conf mgap is then less surprising: once the fit is written in terms of x = p^2/m_gap^2, single-scale dimensional analysis forces Tc ∝ mgap. The non-trivial content is the value of c_conf and the IR-insensitivity, not the proportionality itself.

The fπ part is honest about its limits, but it is not a prediction: αs is tuned to Mq(0) = 350 MeV, and the 93.2 MeV output inherits that tuning. There are also no error bars on Tc or fπ, which weakens the 'agrees with lattice' claims to agreement at face value.

So: worth a serious referee, especially in the functional-QCD community, but the referee should press for a stability analysis of the pole extraction and for error estimates. If those come out okay, the paper moves from conditional to solid. I'd bring it to a reading group.

Referee Report

4 major / 6 minor

Summary. The paper argues that the Landau-gauge gluon propagator carries a renormalisation-group-invariant mass gap mgap, defined as the real part of the first complex pole of the propagator, and proposes a compact analytic fit (31) whose only dimensionful parameter is mgap (x=p^2/m_gap^2). Using this fit, the authors compute the Yang-Mills deconfinement temperature Tc from a background-field DSE (dropping two-loop terms and using vacuum propagators) and the pion decay constant fπ from the quark gap equation with a simplified vertex. They show that both observables are insensitive to deformations of the gluon propagator for momenta below the infrared inflection point p_in^- (Figures 4a,b), and they derive a linear relation Tc≈c_conf mgap (eq. 48). They further discuss the mgap-dependence of fπ and the interplay between confinement and chiral symmetry breaking in QCD-type theories.

Significance. The paper is useful in several respects. It provides a compact, physically motivated parametrisation of the gluon dressing that reproduces lattice and fRG data in the ultraviolet and intermediate regimes, and it demonstrates convincingly that Tc and the relative value fπ/fπ(phys) are insensitive to gluon-propagator deformations below p_in^-. The infrared-insensitivity result is robust and likely to be of lasting practical value for functional studies. If the analytic-continuation step that defines mgap were validated, the relation Tc≈c_conf mgap would provide a convenient bridge between the Schwinger-mechanism scale and the deconfinement temperature. However, as the paper stands, this central step is an assumption, and the linear relation is largely an expression of the fit's single-scale nature; hence the advertised 'direct physical meaning' of mgap is not yet established.

major comments (4)

[Section IV B, eqs. (31), (45); definition (28)] The mass gap mgap is extracted as the first zero of Z_A,fit(-ω_s^2), i.e., by analytically continuing a particular Euclidean fitting ansatz to complex p^2. Euclidean lattice and fRG data constrain Z_A only on the positive real p^2 axis; the logarithms in (31c) and the branch choice for x<0 are not fixed by those data. Section V acknowledges that mgap is difficult to determine precisely, but no stability test is provided. As it stands, mgap, and hence the coefficient c_conf in (48), could be artifacts of the chosen fit rather than properties of the true gluon propagator. Please add a consistency check, for instance by extracting the pole with a second independent fit ansatz or a Padé/spectral reconstruction, and by verifying that the first zero persists under variations of the fit within the data-constrained uncertainty.
[Section IV C, eq. (48), with eqs. (31)-(32)] In Yang-Mills theory the fit is written entirely in terms of x=p^2/m_gap^2 and dimensionless parameters, and eq. (34) identifies Λ_QCD with mgap. With only one dimensionful scale in the problem, any dimensionful observable is necessarily proportional to mgap, so the relation Tc≈c_conf mgap restates dimensional analysis rather than demonstrating a dynamical connection. The nontrivial contents are the value c_conf ≈ 275/686 ≈ 0.40 obtained from the background DSE and its stability under changes of the fit parameters. The text should be reworded to present (48) as a consequence of the single-scale structure of the fit, with the computed coefficient as the quantitative result, and the claim that this 'assigns direct physical meaning' to mgap should be moderated unless the analytic-continuation issue in the previous comment is resolved.
[Section III B, eqs. (23)-(24), (27)] The value fπ = 93.2 MeV is not an independent prediction of the framework because α_s is tuned in eq. (24) so that M_q(0) = 350 MeV. The relative response f_π^±/f_π to gluon deformations, shown in Figure 4b, is well defined and is the robust message of that part of the paper. Please state explicitly in the abstract or conclusion that the absolute scale of fπ is fitted, and that only the relative insensitivity below p_in^- is claimed.
[Section III A and Section V] The Tc computation drops the two-loop terms in Figure 5 and uses vacuum propagators, and no uncertainty is quoted for Tc, fπ, or the extracted mgap. Since the coefficient c_conf in (48) derives from this DSE computation, the absence of error estimates makes it difficult to assess the significance of the agreement Tc≈275 MeV and of the linear relation. Please provide at least an estimate of the systematic error, for example by comparing one-loop and two-loop results for the potential and by estimating the thermal corrections to mgap.

minor comments (6)

[Section III A 3, text below Figure 7] The second bullet says 'For T > Tc, the minima become the maxima and vice versa'; this should read 'For T < Tc', otherwise it contradicts the first bullet and the deconfined phase at T > Tc.
[Section IV B 2] The subheading 'Deep IR regime (sc)' should read 'Deep IR regime (ir)'.
[Appendix D, eq. (D3)] The transformation law for cuv has an apparent sign and dimension inconsistency (cuv is multiplied by a dimensionless logarithm but the result is added to a dimensionless cuv); please check the formula.
[Section IV A, Figure 11] The caption refers to 'mgap from Table II', but Table II appears only in the following subsection; consider giving the numerical value in the caption or moving the figure.
[Section IV B 1, after eq. (31)] The statement that the exponentiated form of the square bracket comes from a one-loop resummation would be clearer if the renormalisation scheme and the scale of the logarithms were specified.
[Section IV B 1, eq. (34)] The proportionality Λ_QCD∝mgap is used for scale setting before it is discussed in Appendix D; consider moving or expanding that discussion to the point of first use.

Circularity Check

1 steps flagged · score 3.0 of 10

Partial circularity: the Tc∝mgap relation is built into the single-scale fit, but c_conf is computed; fπ tuning is disclosed, and no load-bearing self-citation chain is found.

self definitional [Section IV C, Eq. (48), with x(p) defined in Eq. (32) and the fit given in Eqs. (31a)-(31c)]
"We have shown in Section IV B that the gluon propagator can be written in terms of the dimensionless momentum p2/m2gap, see (32), together with fitting parameters that do not depend on m2gap. Consequently, the critical temperature is simply given by Tc≈cconfmgap"

The fit (31) depends on momentum only via x=p^2/m_gap^2, so m_gap is the only dimensionful scale entering the Yang-Mills background-field DSE (12). Any dimensionful output of that computation, including T_c, must scale linearly with m_gap; the functional form of (48) is therefore fixed by the parametrization before any dynamics is solved. The coefficient c_conf is a computed, not fitted, output, so the reduction is only partial: the relation's linear form is construction, while the numerical coefficient carries the dynamical content. The separate concern that m_gap itself comes from analytic continuation of the same ansatz via (45) is a reliability assumption rather than a circularity.

full rationale

The paper's independent content is the computation of the proportionality coefficient c_conf (via T_c≈275 MeV from propagators benchmarked against lattice data), the infrared-insensitivity demonstration for T_c and fπ, and the physically motivated fit. The fπ=93.2 MeV value is not presented as parameter-free: α_s is tuned to M_q(0)=350 MeV in Eq. (24), and the paper explicitly says the proximity to the physical fπ is expected from that tuning; this is a disclosed consistency check, not a hidden fit. Self-citations to [42,43,58] provide the method and input vertex but are benchmarked against lattice results and do not invoke an unverified uniqueness theorem. No step was found in which the central claims reduce entirely to a fitted parameter or to a self-citation chain; the main caveat is that the linear T_c-m_gap relation is a scaling consequence of the single-scale fit, with the coefficient as the actual result.

Assumptions & free parameters 25 free parameters · 6 assumptions · 1 invented entities

The central calculations carry one RGI mass scale mgap defined by a complex pole of a fitted propagator, plus eight dimensionless fit parameters per flavor set (Table II), a tuned quark-gluon coupling (24), ghost fit parameters (Table III), and hand-chosen deformation parameters (A1). Key axioms are the Schwinger mechanism, the validity of complex continuation of the fit, ΛQCD ∝ mgap, the two-loop-truncated A0-DSE, and the simplified quark-gluon vertex. These are standard within the field or stated assumptions; none is independently machine-checked.

free parameters (25)

zsat (Nf=0) = 0.245
Saturation mass ratio m_sat^2/m_gap^2 for Yang-Mills; fixed to GA(0), Table II.
zpeak (Nf=0) = 0.670
Peak height of the gluon dressing for Yang-Mills; fit in Schwinger regime, Table II.
zgh (Nf=0) = 0.036
Subleading infrared logarithmic running from ghost loop, Yang-Mills; Table II.
zuv (Nf=0) = 0.853
Amplitude of ultraviolet dressing, Yang-Mills; Table II.
cuv (Nf=0) = 0.326
Ultraviolet logarithmic coefficient, Yang-Mills; Table II.
c+ (Nf=0) = 0.074
Interface parameter between uv and sc regimes, Yang-Mills; Table II.
c- (Nf=0) = 3.71
Interface parameter for infrared ghost log decoupling, Yang-Mills; Table II.
gamma_gap (Nf=0) = 0.585
Imaginary part fraction of complex pole, solved from (45), Yang-Mills; Table II.
zsat (Nf=2+1) = 0.279
Saturation mass ratio m_sat^2/m_gap^2 for 2+1 flavor QCD; Table II.
zpeak (Nf=2+1) = 0.175
Peak height of the gluon dressing for 2+1 flavor QCD; Table II.
zgh (Nf=2+1) = 0.050
Subleading infrared logarithmic running from ghost loop, 2+1 flavor QCD; Table II.
zuv (Nf=2+1) = 0.540
Amplitude of ultraviolet dressing, 2+1 flavor QCD; Table II.
cuv (Nf=2+1) = 1.47
Ultraviolet logarithmic coefficient, 2+1 flavor QCD; Table II.
c+ (Nf=2+1) = 0.162
Interface parameter between uv and sc regimes, 2+1 flavor QCD; Table II.
c- (Nf=2+1) = 3.70
Interface parameter for infrared ghost log decoupling, 2+1 flavor QCD; Table II.
gamma_gap (Nf=2+1) = 0.399
Imaginary part fraction of complex pole, solved from (45), 2+1 flavor QCD; Table II.
alpha_s = 0.54
Strong coupling at µ = 4.3 GeV tuned to Mq(0) = 350 MeV, eq (24).
zc_ir = 0.268
Ghost propagator fit parameter, Table III.
zc_uv = 0.616
Ghost propagator fit parameter, Table III.
buv = 2.64
Ghost propagator fit parameter, Table III.
dir = 1.14 GeV^-2
Ghost propagator fit parameter, Table III.
duv = 2.59 GeV^-2
Ghost propagator fit parameter, Table III.
delta0 = 3.3 GeV^-2
Amplitude of infrared deformations in (A1), chosen by hand.
kappa = 3
Exponent of infrared deformations in (A1), chosen by hand.
nu = 0.1 to 0.5 GeV
Range of deformation scales in (A1), chosen by hand.

assumptions (6)

domain assumption The Schwinger mechanism dynamically generates a mass gap in the Landau-gauge gluon propagator through massless poles in three-gluon and ghost-gluon vertices.
Section II, citing [14-20]; underlies identification of mgap with the physical confinement scale.
ad hoc to paper The analytic continuation of the fit (31) to complex momenta faithfully represents the true gluon propagator's singularity structure, so the pole condition (45) yields the physical mgap.
Section IV B; not derived from first principles.
ad hoc to paper ΛQCD is proportional to mgap, so mgap is the only mass scale in Yang-Mills and one of two scales in QCD.
Eq (34); used to justify x = p²/mgap² and the mgap-parameterization.
domain assumption Dropping two-loop terms in the A0-DSE and using vacuum propagators is quantitatively accurate for Tc.
Section III A; checked against [43] but not against a full thermal computation in this paper.
ad hoc to paper The quark-gluon vertex can be truncated to the classical tensor plus a tuned αs while still capturing the relative response of fπ to gluon deformations.
Eqs (23)-(24), Section III B 1.
standard math The Pagels-Stokar formula (27) gives fπ from the quark propagator.
Section III B 3; standard but approximate formula.

invented entities (1)

Gluon mass gap mgap as a screening mass defined by the complex pole of the fitted gluon propagator independent evidence
purpose: Provides a single mass scale for the gluon fit and connects gluon dynamics to Tc and fπ.
Introduced in (28) and used throughout. Independent support: Tc computed from the same propagator reproduces lattice Tc ≈ 275 MeV and the Polyakov-loop gluon term decays as exp(-mgap/T) (Figure 11). It is not a new particle, but a new definitional object.

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Cite this review

Pith. "Pith review of Physics of the gluon mass gap." pith.science (2026). https://pith.science/paper/UWLEDYRN

@misc{pith2026250820568,
  author       = {Pith},
  title        = {Pith review of: Physics of the gluon mass gap},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UWLEDYRN}},
  note         = {Machine review of arXiv:2508.20568}
}

read the original abstract

It has long been known that the gluon propagator in Landau-gauge QCD exhibits a mass gap; and its emergence has been ascribed to the action of the Schwinger mechanism in the gauge sector of QCD. In the present work, we relate this property to the physical mass gap of QCD by considering two observables associated with confinement and chiral symmetry breaking, namely the confinement-deconfinement transition temperature and the pion decay constant, respectively. It turns out that the first observable is linearly proportional to the gluon mass gap, a fact that allows us to assign a direct physical meaning to this scale. Moreover, we identify three distinct momentum regimes in the gluon propagator, ultraviolet, intermediate, and deep infrared, and assess their impact on the aforementioned observables. Both observables are sensitive to the first two regions of momenta, where functional approaches essentially coincide, but are insensitive to the third, deep infrared, regime. The combined information is used for a simple fit for the gluon propagator, all of whose parameters admit a clear physical interpretation. Finally, we discuss how this fit can help us access the intertwined dynamics of confinement and chiral symmetry breaking in QCD-type theories.

Figures

Figures reproduced from arXiv: 2508.20568 by the authors.

**Figure 2.** FIG. 2: Dressing [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3: Gluon dressings and propagators (inlays) in Yang-Mills theory, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: FIG. 4: Confinement-deconfinement temperature [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5: Functional background field DSE. Full propagators are indicated by lines with grey circles, while classical [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6: Perturbative potential [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7: Contour plot of the potential [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 9.** Figure 9: FIG. 9: Quark propagator DSE. Full propagators are de [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 8.** Figure 8: FIG. 8: Polyakov potential [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 10.** Figure 10: FIG. 10: Quark mass functions, [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

**Figure 11.** Figure 11: FIG. 11: Gluon part of the Polyakov loop potential [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 12.** Figure 12: FIG. 12: Dressing 1 [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: FIG. 13: Gluon dressing for fixed Λ [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

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Works this paper leans on

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Confinement and the gluon mass gap The importance of the gluon mass gap can already by assessed at the level of a perturbative one-loop compu- tation. To that end, we evaluate the first two loops in Figure 5 using classical (tree-level) propagators, whose common scalar part, G(0) i , is given by G(0) i = 1 4π2T 2(n +νj)2 + p2 , i =A,c. (15) FIG. 6: Pertur...
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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

For constant gauge fields A0, we find ∂Veff(φ) ∂φ = 0, V eff(φ) = T V3 Γ[A0], (9) andφ(A0) is given by (C5)

Polyakov-loop effective potential in functional approaches It is left to compute the effective potential Veff of the temporal background field φ(A0), whose minima define the order parameter. For constant gauge fields A0, we find ∂Veff(φ) ∂φ = 0, V eff(φ) = T V3 Γ[A0], (9) andφ(A0) is given by (C5). Here, V3 denotes the spatial volume. Equation (9) can be ...

[2] [2]

Confinement and the gluon mass gap The importance of the gluon mass gap can already by assessed at the level of a perturbative one-loop compu- tation. To that end, we evaluate the first two loops in Figure 5 using classical (tree-level) propagators, whose common scalar part, G(0) i , is given by G(0) i = 1 4π2T 2(n +νj)2 + p2 , i =A,c. (15) FIG. 6: Pertur...

[3] [3]

Critical temperature and the gluon mass gap It is left to determine the critical temperature. The qualitative analysis above illustrates that the confinement-deconfinement phase transition is triggered by the exponential suppression of the gluon contribu- tion due to the presence of the gluon mass gap in the gluon propagator. We have performed the computa...

[4] [4]

The set of deformations used is shown in Figure 3a, and their parametrisation is shown in Appendix A

Infrared (in)sensitivity of the critical temperature We finally turn to one of the main results of this Sec- tion, and discuss the sensitivity of the critical tempera- tureTc on infrared deformations of the gluon propagator. The set of deformations used is shown in Figure 3a, and their parametrisation is shown in Appendix A. This par- ticular exercise con...

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I. C. Cloet and C. D. Roberts, Prog.Part.Nucl.Phys. 77, 1 (2014), arXiv:1310.2651 [nucl-th]

arXiv 2014

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Quark gap equation This analysis is based on the solution of the quark gap equation in Landau-gauge QCD. The quark propagator is parametrised as follows, GAB q¯q (p) =δABGq¯q(p), (21a) withA,B = 1, 2, 3 are the color indices in the fundamen- tal representation and Gq¯q(p) = 1 Zq(p)[i/p +Mq(p)]. (21b) The momentum evolution ofGq¯q(p) is determined by the q...

[7] [7]

Now we apply this same argument to the gap equation (22)

Infrared (in)sensitivity of the constituent quark mass In Section III A we have argued that the insensitivity ofTc and further observables to infrared deformations of the gluon propagator can be explained by the appear- ance of the gluon dressing 1/ZA in the loop integrals; see in particular (20) and the related discussion. Now we apply this same argument...

[8] [8]

screening mass

Infrared (in)sensitivity of the pion decay constant The two dressing functions Zq and Mq of the quark propagator are not observables themselves, as they are coefficients of a gauge-fixed correlation function. However, as discussed before, they enter into observ- ables that are defined as momentum integrals of products or ratios of correlation functions. T...