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REVIEW 3 major objections 4 minor 46 references

Direct-photon production in inelastic and high-multiplicity proton-proton collisions at $\sqrt{s} =$ 13 TeV

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper reports the first low-transverse-momentum direct-photon signal in 13 TeV proton-proton collisions, with 3.2σ and 1.9σ significance in inelastic and high-multiplicity events, and a charged-particle-multiplicity scaling exponent…

desk verdict First low-pT direct-photon measurement in pp at 13 TeV, but 'observed in both classes' overstates a 1.9σ HM signal; the η-dominated cocktail systematics and missing closure test need attention. read the letter →

arxiv 2411.14366 v2 pith:74ZDN7TS submitted 2024-11-21 hep-ex nucl-ex

ALICE Collaboration This is my paper · ORCID
classification hep-exnucl-ex
keywords directphotonsvirtualdielectronpairsKroll-Wadaformulaproton-protoncollisionshighmultiplicitycharged-particlescalinglowtransversemomentum
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 direct photons—photons not coming from hadron decays—are produced at low transverse momentum in ordinary proton-proton collisions at 13 TeV, and that their yield grows with the number of charged particles produced. Using the virtual-photon method, it reports the first such signal at LHC energies in both inelastic and high-multiplicity event classes, with significances of 3.2σ and 1.9σ. The integrated yield in the range $1 < p_{\rm T} < 3$ GeV/$c$ rises with charged-particle multiplicity as a power law with exponent $\alpha = 1.17 \pm 0.18 (\text{stat.}) \pm 0.21 (\text{syst.})$. If correct, the result shows that high-multiplicity proton-proton collisions produce more direct photons than prompt perturbative-QCD expectations alone, opening the low-momentum window to searches for thermal radiation in small collision systems.

What carries the argument

The central object is the Kroll-Wada relation, which links the yield of real photons to the yield of dielectron pairs they internally convert into; for pair transverse momentum much larger than the pair mass, the dielectron spectrum behaves as $\sim 1/m_{ee}$. This relation supplies the shape of the virtual direct-photon component $f_{\rm dir}$ and justifies taking the direct-photon fraction $r$ measured at small non-zero mass to be the real-photon fraction in the $m_{ee} \to 0$ limit. The extraction fits the dielectron cross section with $d\sigma/dm_{ee} = r\, f_{\rm dir}(m_{ee}) + (1-r)\, f_{\rm LF}(m_{ee}) + f_{\rm HF}(m_{ee})$, where $f_{\rm LF}$ and $f_{\rm HF}$ are the light- and heavy-flavour hadronic decay templates and $r$ is the only free parameter. The crucial input is the hadronic cocktail, especially the measured $\pi^0$ and $\eta$ spectra in the same event classes, which dominates the systematic uncertainty on $r$.

What would settle it

Measure the direct-photon fraction independently from real photons (calorimeter or external conversion) in the same $1 < p_{\rm T} < 6$ GeV/$c$ range in 13 TeV proton-proton collisions and compare with the virtual-photon value; a disagreement beyond the quoted uncertainties would falsify the zero-mass extrapolation or the hadron-cocktail decomposition.

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Extended reading notes

Core claim

The paper reports the first observation at LHC energies of a low-transverse-momentum direct-photon signal in proton-proton collisions, seen in both inelastic and high-multiplicity event classes. For $1 < p_{\rm T} < 6$ GeV/$c$ at midrapidity $|\eta| < 0.8$, the fraction $r$ of direct to inclusive photons is extracted from a fit to the dielectron invariant-mass spectrum in the range $0.14 < m_{ee} < 0.35$ GeV/$c^2$, where the hadronic-decay background is dominated by $\pi^0$ and $\eta$ decays. The signal is observed with 3.2σ significance in inelastic events and 1.9σ in high-multiplicity events, and the direct-photon fraction is compatible between the two event classes. The inelastic results agree with next-to-leading-order perturbative QCD calculations within uncertainties, while in high-multiplicity events the prompt-photon predictions alone do not describe the data; the best description is obtained by scaling the inelastic prompt contribution by a factor of 3.4–6.6 and adding a calculated thermal-photon component. The integrated direct-photon yield in $1 < p_{\rm T} < 3$ GeV/$c$ increases with charged-particle multiplicity with an exponent $\alpha = 1.17 \pm 0.18 \pm 0.21$.

Load-bearing premise

The result stands on the assumption that the fit to electron-positron pairs correctly splits the spectrum into decays of ordinary particles (mostly pions and etas) plus direct photons, and that the direct-photon share found there is the same as for real, massless photons.

Editorial extensions

If this is right

  • Direct photons at low transverse momentum in proton-proton collisions can be measured with the virtual-photon method, providing a new experimental handle in a momentum region where perturbative QCD is difficult.
  • The inelastic direct-photon fraction and yield are consistent with next-to-leading-order perturbative QCD predictions within uncertainties, so conventional prompt-photon physics describes minimum-bias 13 TeV proton-proton collisions.
  • In high-multiplicity collisions, prompt-photon-only calculations fail to describe the data, so an additional direct-photon source or an enhanced prompt yield is needed.
  • The integrated direct-photon yield rises faster than linearly with charged-particle multiplicity, with $\alpha \approx 1.17$, in agreement with the trend seen in heavy-ion collisions at lower energies.
  • The direct-photon fraction itself is similar in inelastic and high-multiplicity events, meaning the multiplicity dependence appears mainly in the overall yield rather than in the fractional composition of the photon field.

Reading between the lines

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

  • If the high-multiplicity excess survives higher-statistics data, it would strengthen the case that small collision systems can produce thermal-like radiation, although the paper itself does not claim a thermal-photon observation.
  • The measured $\alpha \approx 1.17$ provides a concrete baseline for proton-lead collisions: a testable extension would be to measure the same exponent in p–Pb events, where a value between the proton-proton and lead-lead results would indicate a smooth system-size interpolation.
  • Because the $\eta$ yield carries the largest systematic uncertainty on $r$, an independent high-precision measurement of the $\eta/\pi^0$ ratio at 13 TeV, or an alternative extraction of $r$ using a different mass window, would directly sharpen the result.
  • Run 3 and Run 4 data should resolve whether the high-multiplicity excess is a momentum-independent enhancement of prompt photons or a genuinely new component, since the current signal significance in high-multiplicity events is only 1.9σ.
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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

3 major / 4 minor

Summary. This letter reports the first ALICE measurement of direct photons at low transverse momentum (1 < pT < 6 GeV/c, |η| < 0.8) in inelastic (INEL) and high-multiplicity (0–0.072% INEL) proton–proton collisions at √s = 13 TeV, using the virtual-photon method. The direct-photon fraction r is extracted by fitting the dielectron invariant-mass spectrum in 0.14 < mee < 0.35 GeV/c² with a Kroll–Wada direct-photon shape, a light-flavour hadron-decay cocktail, and a fixed heavy-flavour contribution. The paper reports significances of 3.2σ (INEL) and 1.9σ (HM), compares r and the direct-photon yield with NLO pQCD calculations, and fits the integrated 1 < pT < 3 GeV/c yield versus charged-particle multiplicity to a power law with exponent α = 1.17 ± 0.18 (stat) ± 0.21 (syst). The INEL result is found consistent with the pQCD calculations; the HM data are described only after applying empirical pT-independent scaling factors of 3.4–6.6 or 7 to the prompt-photon calculations.

Significance. The measurement is valuable: it uses the same-event-class π0 and η spectra from Ref. [47], roughly four times the statistics of the previous analysis [46], and it provides the first low-pT virtual-photon direct-photon signal in pp collisions at LHC energies. The analysis is documented with fit figures and systematic tables that allow the extraction to be followed in detail, and the use of independent meson measurements and of a one-parameter fit for r are clear strengths. If the inelastic signal holds, it offers a useful low-pT reference for pQCD and for searches for thermal radiation in small systems. However, the strength of the headline claims exceeds the current statistical evidence: the HM signal is only 1.9σ, and the quoted multiplicity-scaling result does not establish a significant super-linear increase.

major comments (3)
  1. [Abstract; Sec. 4 (Results)] The abstract and Sec. 4 state that a direct-photon signal is 'observed' in both INEL and HM event classes with significances of 3.2σ and 1.9σ. Under standard HEP conventions a 1.9σ excess is not an observation, and even 3.2σ is usually termed evidence rather than observation. The conclusion that 'the direct photon signal is seen in both event classes' therefore overstates the HM result. Please revise the abstract, Sec. 4, and the summary to use 'evidence' for the INEL class and 'hint' or 'no significant excess' for the HM class unless additional analysis can raise the HM significance.
  2. [Sec. 3 and Tables A.2/A.3] The text says that the dominant systematic uncertainty on r comes from the η cocktail parameterisation and that the η/π0 ratio uncertainty is only 2–3%, yet Tables A.2 and A.3 assign the light-flavour cocktail an uncertainty on r of 16.3–31% (INEL) and 25–30.7% (HM). Since the light-flavour template in the fit function dσ/dm_ee = r f_dir + (1−r) f_LF + f_HF is dominated by η Dalitz decays in the fitting range, a 2–3% η/π0 uncertainty cannot by itself produce the quoted LF systematic. Please state exactly which variations enter the LF systematic and provide a closure or stress test (for example, an alternative η spectral parameterisation or a fit in a mass window below the η peak) demonstrating that r is not driven by an η-template misnormalisation.
  3. [Sec. 4 and Fig. 4] The abstract claims a 'significant increase of direct-photon yield with charged-particle multiplicity' based on α = 1.17 ± 0.18 (stat) ± 0.21 (syst). With only two ALICE data points, the fit is equivalent to taking a ratio, and the combined uncertainty is sqrt(0.18² + 0.21²) ≈ 0.28; the deviation from linear scaling (α = 1) is 0.17 ± 0.28, i.e. below 1σ. The paper should either present a fit that includes additional data or explicitly state that the data are consistent with, but do not establish, a super-linear increase.
minor comments (4)
  1. [Sec. 1] The last paragraph of Sec. 1 contains a typo: 'midrapitidy' should be 'midrapidity'.
  2. [Sec. 4 and Fig. 2 (right)] The statement that the unscaled pQCD models are disfavoured by a 'p-value less than 0.1' is not accompanied by a definition of the test statistic or of how systematic uncertainties were included; please provide this information.
  3. [Fig. 4] The comparison in Fig. 4 includes data at different centre-of-mass energies and different pT integration ranges (1–3 GeV/c for the present data versus 1–5 GeV/c for several other points); this should be stated explicitly in the text to avoid over-interpreting the figure as a universal scaling.
  4. [Tables A.2 and A.3] The entries 'Normalization range' and 'Fitting range' are not self-explanatory; a sentence or footnote defining the exact variations used for those uncertainties would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the direct-photon fraction is a fitted observable, and the templates, scaling factors, and multiplicity exponent are either external inputs, acknowledged fits, or bookkeeping identities.

full rationale

The central quantity r is the single free parameter in the fit dσ/dm_ee = r f_dir + (1−r) f_LF + f_HF. The LF template is built from the independent π0/η measurements of Ref. [47] (same collaboration but a separate measurement, with its uncertainties propagated as the dominant systematic), and the HF term is fixed from a separate fit to the intermediate-mass dielectron spectrum; neither is defined in terms of r or of the direct-photon yield. Equation (1), γ_dir = γ_decay × r/(1−r), is an algebraic identity following from r = γ_dir/γ_incl and is not presented as a prediction. The HM pQCD comparisons explicitly use empirical scaling factors ('scaled by an empirical factor') rather than claiming a first-principles prediction. The multiplicity-scaling exponent α = 1.17 ± 0.18 ± 0.21 is a fit to the two measured integrated yields, so it is a derived summary, not an input renamed as a result. Self-citations to Refs. [46] and [47] provide methodology and input spectra, respectively; Ref. [47] is an independent, externally falsifiable measurement and therefore counts as real evidence under the review rules. The paper also acknowledges the limitation that the lack of HM theoretical predictions prevents conclusions on thermal radiation. The only notable concerns, namely the 1.9σ HM significance being described as an 'observed' signal and the η-template dominating the r systematic (Tables A.2/A.3), are correctness and interpretation risks rather than circularity: nothing in the derivation reduces by construction to its own inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new entities. It relies on standard QED (Kroll-Wada), completeness of the hadronic cocktail, and several empirical scaling laws for the high-multiplicity comparison. The dominant free parameters are the pT-independent scaling factors used to make pQCD match HM data and the multiplicity scaling exponent alpha.

free parameters (5)
  • Shen pQCD scaling factor for HM = 3.4-6.6 (pT-independent)
    Empirical factor applied to INEL prompt-photon calculation to describe HM data; no theoretical derivation.
  • Vogelsang pQCD scaling factor for HM = 7
    Based on PYTHIA8 HM/INEL prompt-photon ratio; used to scale INEL pQCD for comparison with HM data.
  • No-thermal pQCD scaling factor = 12
    Alternative empirical scaling used if no thermal contribution is added in the HM comparison.
  • Multiplicity scaling exponent alpha = 1.17 +/- 0.18 (stat) +/- 0.21 (syst)
    Fit to integrated direct-photon yield versus dNch/deta; central to the claim of universal scaling.
  • mT scaling ratios for eta', rho, omega relative to pi0 = 0.40 +/- 0.08, 0.87 +/- 0.17, 0.57 +/- 0.11
    Inputs to the light-flavour cocktail from Refs. [69,72,73]; chosen by hand from literature, not derived in this paper.
assumptions (6)
  • standard math The Kroll-Wada equation describes the virtual direct-photon dielectron mass shape.
    Used as the f_dir template in the fit; standard internal-conversion formula from Refs. [44,45].
  • domain assumption The dielectron spectrum in the fit range is fully described by the sum of light-flavour hadron decays, heavy-flavour decays, and virtual direct photons.
    The fit function in Section 3 assumes completeness of the cocktail; any missing source would bias the extracted r.
  • domain assumption The fraction r of virtual direct photons equals the real direct-photon fraction at m_ee -> 0.
    Central extraction method in Section 3: r = gamma_dir/gamma_incl = (gamma*_dir/gamma*_incl) at m_ee -> 0.
  • domain assumption The measured pi0 and eta transverse momentum spectra in the same event classes [47] are accurate cocktail inputs.
    The cocktail uses parameterizations of pi0 and eta from Ref. [47]; eta uncertainty dominates the systematic on r.
  • ad hoc to paper mT scaling applies to eta', rho, and omega production relative to pi0.
    In Section 3, these mesons are generated assuming mT scaling with fixed ratios; this is an empirical assumption not derived in the paper.
  • domain assumption Multiplicity scaling of J/psi and heavy-flavour yields from other measurements applies to the HM cocktail.
    For HM events, J/psi and heavy-flavour dielectron contributions are weighted by pT-dependent factors from Refs. [76] and [29]; assumes factorization of multiplicity and pT dependence.

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Pith. "Pith review of Direct-photon production in inelastic and high-multiplicity proton-proton collisions at $\sqrt{s} =$ 13 TeV." pith.science (2026). https://pith.science/paper/74ZDN7TS

@misc{pith2026241114366,
  author       = {Pith},
  title        = {Pith review of: Direct-photon production in inelastic and high-multiplicity proton-proton collisions at $\sqrts =$ 13 TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/74ZDN7TS}},
  note         = {Machine review of arXiv:2411.14366}
}
abstract

In this letter, we present the first measurement of direct photons at the transverse momentum of $ 1 < p_{\rm T} < 6$ GeV/$c$ at midrapidity $|\eta| < 0.8$ in inelastic and high-multiplicity proton--proton collisions at a centre-of-mass energy of $\sqrt{s} =$ 13 TeV. The fraction of virtual direct photons in the inclusive virtual photon spectrum is obtained from a fit to the dielectron invariant mass spectrum. In the limit of zero invariant mass, this fraction is equal to the relative contribution of real direct photons in the inclusive real photon spectrum. Contributions from decays of light-flavour neutral mesons are estimated using independent measurements in proton-proton collisions at the same energy and the same event class. For the first time at the LHC energies, a direct-photon signal is observed at low $p_{\rm T}$ in both inelastic and high-multiplicity event classes, with a significance of 3.2$\sigma$ and 1.9$\sigma$ in terms of standard deviations, correspondingly. The yield of direct photons in inelastic pp collisions is compared to perturbative QCD calculations. The integrated photon yield is studied as a function of charged-particle multiplicity and is compared to the results from other experiments and theoretical calculations. The results show a significant increase of direct-photon yield with charged-particle multiplicity.

Figures

Figures reproduced from arXiv: 2411.14366 by the authors.

Figure 1
Figure 1. Fit of the dielectron cross section as a function of mass in INEL (left) and HM (right) pp collisions in the 2 < pT,ee < 3 GeV/c interval with a three-component fit function to extract the fraction of direct photons to inclusive photons r. Statistical and systematic uncertainties of the data are displayed as vertical bars and boxes, respectively. The integrated luminosities of L MB int = 29.8±0.6 nb−1 and L HM int =… view at source ↗
Figure 2
Figure 2. Direct photon fraction r as a function of pT extracted from fits to dielectron spectra in INEL (left) and HM (right) pp collisions. Statistical and systematic uncertainties of the data are displayed as vertical bars and boxes, respectively. The results in INEL pp collisions are compared to theoretical calculations of Refs. [18] and [35]. The results from HM pp data are compared to theoretical calculations of Ref. [1… view at source ↗
Figure 3
Figure 3. Direct-photon cross section (left) and invariant differential yield (right) as a function of pT in INEL and HM pp collisions, respectively. Statistical and systematic uncertainties of the data are displayed as vertical bars and boxes, respectively. Global luminosity uncertainty of 2% is not shown in the Figure. The results in INEL pp collisions are compared to theoretical calculations from [18] and [35]. The results… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Direct photon yield at midrapidity as a function of charged-particle multiplicity dNch/dη. The results from this letter are shown as two blue markers that correspond to the measurements in INEL and HM pp collisions at √ s = 13 TeV, with the corresponding dNch/dη values…

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