REVIEW
Saturation models of HERA DIS data and inclusive hadron distributions in p+p collisions at the LHC
High Energy Physics - Phenomenology · Submitted 8 Nov 2010 · 70 references
Pith's verdict: Honest, useful synthesis: the multiplicity section is the real contribution, the single-inclusive part is a careful update of Levin–Rezaeian, and the authors flag their own weak points rather than hiding them.
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Referee report
The paper
The paper claims
Gluon saturation models fitted to HERA data also reproduce LHC proton-proton hadron spectra and multiplicity distributions, with the multiplicity width set by a single constant of order unity.
The reading
What carries the argument
The load-bearing object is the impact-parameter dependent dipole cross-section $dσ^{p}_{dip}/d^2 b_⊥$, fitted to HERA data in three models: IP-Sat, which eikonalizes a DGLAP-evolved gluon density over a Gaussian profile $T_p(b_⊥)$; b-CGC, which builds the impact-parameter dependence into the saturation scale $Q_S(x,b_⊥)$ itself through a Gaussian in $b$ with an $x$-dependent exponent; and NLO-BK, which solves the running-coupling Balitsky-Kovchegov equation with a factorized $b$-dependence. Fourier transforming $[1 - dσ^{p}_{dip}/d^2 b_⊥/2]^2$ against $e^{i k_⊥·r_⊥}$ converts each dipole cross-section into an unintegrated gluon distribution, which then enters the $k_⊥$-factorized inclusive gluon formula together with a second proton's distribution. The second piece of machinery is the Glasma flux-tube argument: multiparticle production at fixed impact parameter is an average over color sources, and that average produces a negative binomial whose width parameter counts flux tubes, $k ∝ Q_S^2 S_⊥$. The third piece is the convolution over impact parameter, which converts a distribution defined at fixed $b_⊥$ into the minimum-bias distribution actually measured.
Extended reading notes
Core claim
The paper's central claim is that LHC proton-proton multiplicity distributions agree with the Color Glass Condensate prediction for multiparticle production. That prediction is a negative binomial distribution, $P^{NB}_n(ḡn(b),k(b))$, whose width parameter is not free but computed as $k = ζ (N_c^2-1) Q_S^2 S_⊥ / 2π$, where $Q_S^2 S_⊥$ is the saturation scale integrated over the overlap area of the two protons and $ζ$ is a dimensionless constant of order unity. The saturation scales come from fits to HERA data in the IP-Sat and b-CGC dipole models, so the only quantity left to fix is $ζ$; the authors extract $ζ = 0.35$ for IP-Sat and $0.25$ for b-CGC, values they note are compatible with numerical Yang-Mills computations of two-gluon correlations. Convolving the fixed-impact-parameter distribution with an inelastic impact-parameter weight and normalising at the lowest energy, they compare with UA5 and ALICE data at $200$ GeV to $7$ TeV and over $|η|<0.5$ and $|η|<1$, and find good agreement for IP-Sat across all energies and rapidity cuts, and good agreement for b-CGC at $2.36$ TeV with deviations elsewhere at the highest multiplicities. The supporting claim is that the same HERA-fitted distributions, used without new parameters in the $k_⊥$-factorization formula, give reasonable single-inclusive rapidity and $p_⊥$ spectra up to $7$ TeV, with agreement improving at higher energy as expected since the high-$p_⊥$ region is where the large-$x$ extrapolation enters.
Load-bearing premise
The step that turns a distribution defined at fixed impact parameter into a measured one uses an inclusive-multiplicity weight for the inelastic probability, which the authors state is strictly not correct because the mean multiplicity and the inelastic probability are different quantities, and the alternative eikonal weight is never computed for comparison.
Editorial extensions
If this is right
- The multiplicity distribution in proton-proton collisions, including its high-multiplicity tail, is fixed by the saturation scale extracted from HERA plus one constant of order unity, so a HERA measurement constrains an LHC observable.
- Because the same flux tubes that set the multiplicity width also produce long-range rapidity correlations, the near-side ridge seen in high-multiplicity proton-proton events has a candidate microscopic explanation within the same framework.
- The extracted $ζ$ values, $0.25$ to $0.35$, sit in the range obtained from numerical solutions of the Yang-Mills equations for two colliding dense color sources, so multiplicity data can in principle be used to constrain the screening of Glasma flux tubes.
- The energy dependence of the average charged multiplicity at mid-rapidity follows the saturation scale, and the authors find the form $Q_S^2/α_S(Q_S)$ fits better than $Q_S^2$ alone for IP-Sat, while b-CGC predicts the energy dependence without fitting it.
- The average transverse momentum rises approximately linearly with the saturation scale, so $\(langle p_⊥ \rangle\) versus $\(sqrt{s}\)$ is a second, independent handle on the same scale.
Reading between the lines
- The result would be considerably sharper if the impact-parameter weight were varied: the authors use an inclusive-multiplicity weight that they themselves say is not the inelastic probability, and the eikonal alternative with a gluon-gluon cross-section is never computed, so how much of the agreement survives that substitution is untested here.
- Because the normalisation is fixed at the lowest energy and then run up, the agreement at $7$ TeV is partly a statement about the growth of $Q_S$ with energy rather than about the shape of the distribution alone; a reader wanting to isolate the flux-tube claim should look at the shape at fixed energy.
- The b-CGC model's impact-parameter dependence is tied to its $x$ dependence, and the authors find the fitted coefficient of $\(ln s\)$ in $b_{max}$ is essentially zero for that model, which suggests the model already contains something like the Gribov diffusion that IP-Sat has to insert by hand.
- If the same convolution were applied to proton-lead or lead-lead data with the corresponding nuclear saturation scales, the flux-tube counting would predict a specific broadening of the multiplicity distribution with system size, which is a check that does not require new parameters.
Original abstract
Unintegrated gluon distributions sensitive to the transverse spatial distribution of gluons in the proton are extracted from data on exclusive and diffractive final states at HERA in the dipole approach. These unintegrated gluon distributions can be used to compute inclusive hadron production in p+p collisions at the LHC. In this paper, we consider a number of saturation models with differering dynamical assumptions that give good fits to the available HERA data. We apply these models to study the rapidity and transverse momentum dependence of the LHC data up to $\sqrt{s} = 7$ TeV. We examine the sensitivity of these results to parameters that are not constrained by the HERA data and comment on similarities and differences with previous work. We compute the n-particle inclusive multiplicity distribution and show that the LHC p+p results are in agreement with predictions for multi-particle production in the Color Glass Condensate approach. This result has significant ramifications for the interpretation of multi-particle correlations in high multiplicity events at the LHC.
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
Unintegrated gluon distributions sensitive to the transverse spatial distribution of gluons in the proton are extracted from data on exclusive and diffractive final states at HERA in the dipole approach. These unintegrated gluon distributions can be used to compute inclusive hadron production in p+p collisions at the LHC. In this paper, we consider a number of saturation models with differering dynamical assumptions that give good fits to the available HERA data. We apply these models to study the rapidity and transverse momentum dependence of the LHC data up to $\sqrt{s} = 7$ TeV. We examine the sensitivity of these results to parameters that are not constrained by the HERA data and comment on similarities and differences with previous work. We compute the n-particle inclusive multiplicity distribution and show that the LHC p+p results are in agreement with predictions for multi-particle production in the Color Glass Condensate approach. This result has significant ramifications for the interpretation of multi-particle correlations in high multiplicity events at the LHC.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Unintegrated gluon distributions sensitive to the transverse spatial distribution of gluons in the proton are extracted from data on exclusive and diffractive final states at HERA in the dipole approach. | method 0.56 | 0.53 | 0.03 | asserted 1.00 |
| s1 | These unintegrated gluon distributions can be used to compute inclusive hadron production in p+p collisions at the LHC. | method 0.53 | 0.20 | 0.06 | hedged possibility 0.70 |
| s2 | In this paper, we consider a number of saturation models with differering dynamical assumptions that give good fits to the available HERA data. | method 0.60 | 0.78 | 0.03 | asserted 0.98 |
| s3 | We apply these models to study the rapidity and transverse momentum dependence of the LHC data up to $\sqrt{s} = 7$ TeV. | contribution 0.77 | 0.92 | 0.04 | asserted 0.87 |
| s4 | We examine the sensitivity of these results to parameters that are not constrained by the HERA data and comment on similarities and differences with previous work. | contribution 0.63 | 0.92 | 0.04 | asserted 0.70 |
| s5 | We compute the n-particle inclusive multiplicity distribution and show that the LHC p+p results are in agreement with predictions for multi-particle production in the Color Glass Condensate approach. | result 0.98 | 0.95 | 0.59 | asserted 1.00 |
| s6 | This result has significant ramifications for the interpretation of multi-particle correlations in high multiplicity events at the LHC. | interpretation 1.00 | 0.70 | 0.40 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v3
- 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
Figures reproduced from arXiv:1011.1895 by the authors.
References
How the literature uses it
44 arXiv papers cite this in 69 sentences
Papers citing it · 44 sentences without a confident label
Contests it 1 paper
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However, the main complication of this model is that it gives rather a large value of $Q_0^2$ (see qs) which is in sharp contradiction to the value of the saturation momentum, from all other model description of the experimental data [ref] .
CGC/saturation approach: a new impact-parameter dependent model in the next-to-leading order of perturbative QCD · Fitting $F_2$ and values of the parameters · contest 0.74
Uses its method or tool 3 papers
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The latter is computed in a $k_⊥$ factorized approximation to the CGC EFT [ref] as shown in Appendix [ref].
Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions · Results for $D$-meson and $J/ψ$ production · 0.97
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[ref] : we change $γ̅$ in T γ̅ =1 - γ_cr → 1 - γ_cr - 1/2 κ λ Y ln r^2 Q^2_sb = 0.63 - 1/2 κ λ Y ln r^2 Q^2_sb where $κ = χ”γ_cr/χ'γ_cr= 9.8$. $χγ$ is the BFKL kernel which has the foliowing form χγ = 2 ψ(1) - ψ(γ) - ψ( 1 - γ) χγ_cr/1 - γ_cr = d χγ/ d γ|_γ= γ_cr where $ψ(z) = d Γ(z)/d z$ is the Euler $ψ$-function (see Ref. [ref] formula 8.360).
A CGC/saturation approach for angular correlations in proton-proton scattering · Modification to also include DIS · 0.81
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We use two well-known impact-parameter dependent saturation models, the so-called IP-Sat [ref] and the b-CGC [ref] models which both have been very successful in phenomenological applications from HERA to the Relativistic Heavy Ion Collider (RHIC) and the LHC, see for example [ref] .
Diffractive Dijet Production in Deep Inelastic Scattering and Photon-Hadron Collisions in the Color Glass Condensate · Numerical results · 0.90
Uses its data or values 4 papers
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The quantity $k$ which characterizes the fluctuations in the saturation approach has been estimated as be [ref]
Gluon saturation in $pA$ collisions at the LHC: KLN model predictions for hadron multiplicities · Introduction · 0.94
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One important source of uncertainty is due to the non-perturbative constant[$ζ$ is constrained by numerical computations [ref] and fits to the n-particle p+p multiplicity distribution [ref] to be $ζ∼1/6$.
Evidence for BFKL and saturation dynamics from di-hadron spectra at the LHC · Introduction · 0.95
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This leaves only the parameter $ζ$, which was extracted previously by an independent $$ factorization analysis of data on $n$-particle multiplicity distributions [ref] and estimated to be $ζ=1/6$.
Energy dependence of the ridge in high multiplicity proton-proton collisions · Introduction · 0.99
Compares with it 4 papers
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The weak statement is nevertheless stronger than the one that we can make from the models of Refs. [ref] : shadowing corrections are, perhaps, needed to describe the experimental data.
CGC/saturation approach: a new impact-parameter dependent model · Conclusions · 0.93
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This formula exhibits the main features of the DIS amplitude , given in Refs. [ref] , but it is different from the interpolation procedure that have been used in numerous attempts to build a such model in Refs. [ref] .
CGC/saturation approach: an impact-parameter dependent model for diffraction production in DIS · Introduction. · 0.87
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Similar geometric scaling for inclusive hadron production at central rapidity has been observed in [ref] , where it is the differential cross section alone exhibits the geometric scaling.
Single Spin Asymmetry Scaling in the Forward Rapidity Region at RHIC · Transverse Momentum Dependent Geometric Scaling · 0.82
Cites it as support 2 papers
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Various kinematic variables exhibit scaling with the saturation scale [ref] .
Inclusive hadron distributions in p+p collisions from saturation models of HERA DIS data · Results and discussion · 0.96
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These geometrical correlations give rise [ref] to the negative binomial distribution which explains multiplicity distributions [ref] and forward-backward multiplicity correlations [ref] in hadronic collisions.
From many body wee parton dynamics to perfect fluid: a standard model for heavy ion collisions · The little bang and the Glasma · 0.96
Cites it as background 10 papers
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We can see that the interaction of the BFKL Pomeron with the proton is known from the DIS data and we have numerous attempts to describe this interaction using the Balitsky-Kovchegov parton cascade [ref] .
Soft Pomeron in the Colour Glass Condensate approach · The master equation · 0.89
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In most cases, these models include the non-perturbative $b$-behavior of the scattering amplitude and has been widely applied in what is commonly referred to as saturation models [ref] .
CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data · Introduction · 0.80
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The colour dipole model provides an unified framework to study the inclusive, exclusive, and inclusive diffractive data [ref] gathered in ep collisions and the inclusive particle production data in pp, pA, and AA collisions [ref] at small x.
Investigating saturation effects and the virtual pion in leading neutron events at HERA with the dipole model · Introduction · 0.95
What it cites · 5 sentences without a confident label
Cites as background 3 papers
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This Color Glass Condensate (CGC) [ref] description of saturated gluons is universal to hadrons and nuclei and can be tested both in deeply inelastic scattering experiments off hadrons and nuclei as well as in hadron/nuclear collisions.
The Color Glass Condensate · Introduction · 0.97
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[ref] and references therein.
Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation · The NLO-BK Model · 0.99
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The transverse diffusion of the proton, often termed Gribov diffusion [ref] , is not fully accounted for by the diffusion of the unintegrated single inclusive gluon distribution because this growth does not automatically ensure the proper growth of the inelastic cross-section.
Space-time description of the hadron interaction at high energies · Single inclusive distribution in p+p collisions · 0.82
Discussion
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