Traveling wave fronts and the transition to saturation

R. Peschanski; S. Munier

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Traveling wave fronts and the transition to saturation

S. Munier, R. Peschanski

High Energy Physics - Phenomenology · Submitted 31 Oct 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.17 · mentions code or data availability 0.02.

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We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves.	method 0.63	0.84	0.11	asserted 0.88
s1	In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave.	result 0.77	0.93	0.80	asserted 1.00
s2	Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum.	result 0.80	0.94	0.10	asserted 1.00
s3	The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.	result 0.78	0.90	0.16	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from proof or derivation 0.91.

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The paper

Original abstract

We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.

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References

Forward citations

Cited by 20 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Summing large Pomeron loops in the saturation region: dipole-nucleus collision beyond nonlinear equations
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After summing large Pomeron loops, the dipole-nucleus amplitude has the same energy dependence as dipole-dipole scattering, limiting the BK equation to z' below roughly 2 sqrt(kappa c) A^{1/6}.
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Evolving the NLO BK equation in target rapidity rather than projectile rapidity removes the large scheme dependence that plagued earlier collinear resummations and yields a stable, resummable evolution equation.

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Solving The High Energy Evolution Equation Including Running Coupling Corrections
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Restoring the previously neglected subtraction term reconciles the Balitsky and Kovchegov-Weigert running-coupling kernels and yields a full numerical BK solution whose scaling function has anomalous dimension about 0.85.
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Homotopy solutions to BFKL Pomeron evolution equations in nuclear DIS produce multiplicity distributions of produced gluons.
Dipole-dipole scattering: summing large Pomeron loops in non-linear evolution with leading twist kernel
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In a leading-twist kernel, matching the BK solution to fan-diagram series yields KNO multiplicity distributions and gluon entropy S_E = ln(xG) for dipole-nucleus and dipole-dipole scattering.
Summing large Pomeron loops in the saturation region: nucleus-nucleus collision
hep-ph 2025-06 conditional novelty 5.0 of 10

The nucleus-nucleus scattering amplitude deep in the saturation region reduces to the single nucleon-nucleon term and therefore has the same energy dependence as dipole-dipole scattering.
Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation
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Including impact parameter in the small-x nonlinear evolution equation makes the solution sensitive to kinematical cuts that are invisible in the impact-parameter-independent approximation.
Single Inclusive Hadron Production at RHIC and the LHC from the Color Glass Condensate
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A running-coupling BK gluon distribution, with two parameters fitted to RHIC forward data, describes p+p and d+Au hadron spectra and predicts roughly factor-two suppression of forward hadrons in p+Pb at the LHC.
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The authors derive a traveling-wave solution to the diffusive-approximation BK equation, match it to CT14 gluon distributions, and extract a saturation scale Q_s^2 proportional to (1/x)^0.386.
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How the literature uses it

40 arXiv papers cite this in 70 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 56 sentences without a confident label

Builds on it 1 paper

As shown in [ref] the dispersion in the final saturation scales are caused by fluctuations in the low density tail of the initial condition and can be realized by averaging over the initial saturation momenta drawn from a Gaussian distribution in the logarithm of the saturation scale, [equation] Our treatment extends the work of [ref] to include fluctuations in both nucleons in which case the event averaging can be performed according to [equation] where the two saturations scale $Q_o,1^2$ and $Q_o,2^2$, fluctuate event-by-event around the mean saturation scales $o,1$ and $o,2$ respectively.

Probing proton fluctuations with asymmetric rapidity correlations · Rapidity distribution in proton-proton collisions · 0.95

Uses its method or tool 1 paper

Namely, we expand $f(x,Y)$ as an infinite series in powers of $Y^-1/2$ multiplied by diffusive scaling functions $G_n$ [ref] : [equation] Using this expansion and solving order by order for the functions $G_n$ with appropriate boundary conditions, we can fix the asymptotic development of $ρ̇_s$.

Transverse momentum broadening from NLL BFKL to all orders in pQCD · Revisiting the fixed coupling problem · 0.99

Compares with it 3 papers

Another remarkable feature of our result is that the asymptotic expansion for $lnq̂_s(Y)$ appears to be extremely similar to that of $lnQ_s^2(Y)$ (the saturation momentum for a large nucleus, or `shockwave'), as computed in [ref] .

Running coupling effects in the evolution of jet quenching · Introduction · 1.00
The solution in this work is similar to the traveling wave front introduced by Munier and Peschanski [ref] .

An Analytical Solution of the Balitsky-Kovchegov Equation with the Homogeneous Balance Method · Discussions and summary · 1.00
It is also interesting to compare with the universal asymptotic expansion of the saturation scale in the case of small-$x$ evolution (see [ref] ).

Transverse momentum broadening from NLL BFKL to all orders in pQCD · Running coupling effects and all-order result for the saturation momentum · 0.99

Cites it as background 7 papers

The idea of intrinsic fluctuations of the saturation momentum goes back to Ref. [ref] , which extended a correspondence between high-energy QCD and the reaction-diffusion problem that was originally identified in Ref. [ref] at the level of mean field approximation.

Intrinsic Fluctuations of the Proton Saturation Momentum Scale in High Multiplicity p+p Collisions · Additional Sources of Fluctuations · 0.95
It is well known that in spite of intensive work [ref] , the problem of summation of the Pomeron loops has not been solved.

Summing large Pomeron loops in the saturation region: dipole-nucleus collision beyond nonlinear equations · Introduction · 0.88
However, in spite of intensive work [ref] , this problem has not been solved.

Summing large Pomeron loops in the saturation region: amplitude and multiplicity distributions for dipole-dipole scattering · Introduction · 0.91

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