REVIEW
2-soft-gluon exchange and factorization breaking
High Energy Physics - Phenomenology · Submitted 31 Aug 2007 · 13 references
Pith's verdict: A genuine two-gluon extension of the Collins-Qiu counterexample, but the load-bearing sign evaluation is asserted rather than shown.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
The paper argues that standard transverse-momentum factorization fails for unpolarized high-transverse-momentum hadron production once two soft gluons are exchanged.
The reading
What carries the argument
The calculation reduces the extra gluon attachments to eikonal factors. For one gluon the eikonal is $E(ell)=g_2/(ell^+ + iepsilon)+g_2/(-ell^+ + iepsilon)+g_1/(-ell^+ + iepsilon)=-pi i(2g_2+g_1)delta(ell^+)-mathrm{PV},g_1/ell^+$; for two gluons the product $E(ell_1)E(ell_2)^*$ produces delta-function terms that are the anomaly. The argument relies on the Glauber region, where longitudinal gluon momentum is much smaller than transverse momentum and the standard Ward identities used in factorization proofs fail. The paper checks whether the anomaly cancels between cuts and whether it vanishes after integrating over the active parton's transverse momentum.
Extended reading notes
Core claim
At two extra gluons, the eikonal factors from exchanges on opposite sides of the final-state cut contain the anomaly term $E(1)E(2)^*|{m anom}=4pi^2 g_2(g_2+g_1)delta(1^+)delta(2^+)$, while exchanges on the same side contain an anomaly of the opposite sign. The paper verifies in a scalar model that these do not cancel: $I_1(k_T)+I_2(k_T)$ is nonzero, with $I_1(0)+I_2(0)<0$, although $int d^2k_T,[I_1+I_2]=0$. Hence standard $k_T$ factorization fails for the unpolarized cross section at this order, even though collinear factorization is retained. For the single-spin asymmetry the iterated anomalous imaginary part does not yet contribute at this order, so the color-factor proposal of Refs. [6,7] is not contradicted until one more gluon is exchanged.
Load-bearing premise
The load-bearing premise is that the graphs examined in Figs. 3, 4, and 5, together with their Hermitian conjugates and all attachments of the upper gluon ends to the active partons, exhaust the leading-power contributions that could cancel the anomaly; the paper argues this from collinear and Glauber-region power counting but does not give an exhaustive graph-by-graph proof.
Editorial extensions
If this is right
- Standard transverse-momentum-dependent parton densities extracted from deep-inelastic scattering and $e^+e^-$ annihilation cannot be used universally for high-transverse-momentum hadron-pair production; process-dependent Wilson lines are required.
- Collinear factorization remains valid at this order when the active parton's transverse momentum is integrated over, so inclusive cross sections are not immediately affected.
- Resummation methods for the back-to-back region, and any observable sensitive to the detailed transverse structure of the final state, are endangered.
- The single-spin asymmetry at this order is still consistent with the proposal that factorization is restored by a process-dependent color factor in the hard scattering; a contradiction requires one more gluon exchange.
- Spectator-spectator interactions may introduce further nonfactorization, because the cancellation conditions familiar from Drell-Yan need not hold when hadrons are observed in the final state.
Reading between the lines
- If the anomaly survives all orders, a practical test would compare transverse-momentum distributions extracted from Drell-Yan or deep-inelastic scattering with those needed for dihadron production at high transverse momentum.
- Because the anomaly cancels upon integration over $k_T$, its signature is likely a redistribution in transverse-momentum shape rather than a change in the total inclusive rate.
- The same eikonal imaginary-part mechanism may affect other processes with both initial- and final-state colored partons, such as jet or photon-hadron production, and could be tested by extending the same model calculation.
Original abstract
A previous counterexample to disprove k_T-factorization for H_1+H_2 --> H_3+H_4+X is extended calculationally to one higher order in gluon exchange. The result is that, by explicit calculation, standard k_T-factorization fails for the unpolarized cross-section for the production of hadrons of high transverse momentum in hadron-hadron collisions.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
A previous counterexample to disprove k_T-factorization for H_1+H_2 --> H_3+H_4+X is extended calculationally to one higher order in gluon exchange. The result is that, by explicit calculation, standard k_T-factorization fails for the unpolarized cross-section for the production of hadrons of high transverse momentum in hadron-hadron collisions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A previous counterexample to disprove k_T-factorization for H_1+H_2 --> H_3+H_4+X is extended calculationally to one higher order in gluon exchange. | contribution 0.82 | 0.64 | 0.07 | asserted 0.96 |
| s1 | The result is that, by explicit calculation, standard k_T-factorization fails for the unpolarized cross-section for the production of hadrons of high transverse momentum in hadron-hadron collisions. | result 1.00 | 0.89 | 0.94 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Showing 5 of the paper's 6 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:0708.4410 by the authors.
References
How later papers used it
57 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 paper
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An alternative way to verify the existence of the Glauber divergence in the attachment $F$ follows the derivation in Ref. [ref] : we eikonalize the quark line with the momentum $k_1-l$ first, and focus on the imaginary piece proportional to $δ(l^-)$.
Glauber gluons in annihilation amplitudes for heavy meson decays (2021) · NLO Corrections to Fig. [ref](a) · 0.99
How the literature uses it
57 arXiv papers cite this in 125 sentences
Papers citing it · 108 sentences without a confident label
Uses its method or tool 1 paper
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An alternative way to verify the existence of the Glauber divergence in the attachment $F$ follows the derivation in Ref. [ref] : we eikonalize the quark line with the momentum $k_1-l$ first, and focus on the imaginary piece proportional to $δ(l^-)$.
Glauber gluons in annihilation amplitudes for heavy meson decays · NLO Corrections to Fig. [ref](a) · 0.99
Cites it as support 5 papers
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More importantly, however, the results in [ref] become highly relevant and show us that generally factorization is broken in di-hadron production.
TMD factorization and the gluon distribution in high energy QCD · The gluon distribution function · 0.98
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Moreover, the production of color-octet states will potentially spoil TMD factorization due to the presence of uncanceled Glauber gluons [ref] .
Proper TMD factorization for quarkonia production: $pp\to\eta_{c,b}$ as a study case · Factorization theorem for $pp→η_c,b+X$ at low $q_T$ · 0.96
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Certainly, the product $δ(l_1^+)δ(l_2^+)$ does not break the collinear factorization [ref] : it has been explicitly demonstrated [ref] that the two-loop residual soft divergence cancels, when the parton transverse momenta are integrated out.
Restoration of $k_T$ factorization for low $p_T$ hadron hadroproduction · Introduction · 0.96
Cites it as background 10 papers
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It has been known that the $k_T$ factorization of complicated QCD processes involving more than two hadrons, such as hadron hadroproduction at the transverse momentum $q_T$ [ref] , is broken by residual infrared divergences from the Glauber region.
Glauber gluons in pion-induced Drell-Yan processes · Introduction · 0.90
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The existence, factorization, and impact of a special type of infrared divergences, called Glauber gluons [ref] , on studies of two-body hadronic heavy meson decays have been explored thoroughly [ref] .
Glauber gluons in annihilation amplitudes for heavy meson decays · INTRODUCTION · 0.98
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General operator definitions, including the region $x ∼1$, and issues of lightcone singularities are discussed e.g. in [ref] and references therein.] The physical picture reflects the growth of the k$_⊥$ transmitted along the initial-state jet, and includes corrections to the collinear ordering implemented in standard showers such as and .
Three-jet DIS final states from kt-dependent parton showers · Parton showers with k$_⊥$-branching and jet correlations · 0.84
What it cites · 45 sentences without a confident label
Builds on 1 paper
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Therefore it is the purpose of this paper to lay to rest any doubts about nonfactorization by extending the counterexample of [ref] to one higher order of perturbation theory.
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions · Introduction · 1.00
Uses the method or tool of 2 papers
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The methods of [ref] enable this calculation to be done quite simply.
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions · Introduction · 0.88
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The figures in this paper were made using JaxoDraw [ref] .
JaxoDraw: A graphical user interface for drawing Feynman diagrams · Conclusions · 1.00
Compares with 7 papers
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In this section, we examine the relation between the result of nonfactorization in [ref] and the argument compatible with factorization in [ref] , which appears to encompass the model calculations in [ref] .
Asymmetric Di-jet Production in Polarized Hadronic Collisions · Comparison with CITEMARK15Z · 1.00
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In this section, we examine the relation between the result of nonfactorization in [ref] and the argument compatible with factorization in [ref] , which appears to encompass the model calculations in [ref] .
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions · Comparison with CITEMARK15Z · 1.00
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In this section, we examine the relation between the result of nonfactorization in [ref] and the argument compatible with factorization in [ref] , which appears to encompass the model calculations in [ref] .
Single Transverse-Spin Asymmetry in Hadronic Dijet Production · Comparison with CITEMARK15Z · 1.00
Cites as background 1 paper
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In [ref] , as in the present paper, “factorization” means “standard factorization”.
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions · Introduction · 0.88
Discussion
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