From Target to Projectile and Back Again: Self-Duality of High-Energy Scattering Evolution in QCD

Kovner, Alex; Lublinsky, Michael

doi:10.1103/physrevlett.94.181603

Cited by 90 publications

(178 citation statements)

References 37 publications

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“…It requires a much better understanding of the non-asymptotic behavior of the solutions of the BK equation with running (41) is the solid line. The dashed line is the approximation (42), and the dashed-dotted line corresponds to the result for a model with running coupling mean-field dynamics plus fixed coupling noise effects. We have taken here Y0 = e 2.5 ≃ 12.…”

Section: Final Resultsmentioning

confidence: 99%

“…This has led to conjecture that high-energy scattering processes in QCD may fall in the same universality class as a reaction-diffusion process [35], extending the mapping from BK to FKPP beyond the mean field approximation. The generalization of the Balitsky and JIMWLK equations including pomeron loops have been investigated 1 through various formalisms [34,[36][37][38][39][40][41][42][43][44]. For example, the QCD evolution equation with pomeron loops has been formulated in [34,38] as a Langevin equation.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotics of QCD traveling waves with fluctuations and running coupling effects

Beuf

2008

Nuclear Physics A

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Extending the Balitsky-Kovchegov (BK) equation independently to running coupling or to fluctuation effects due to pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper we study the extension of the forward BK equation, including both running coupling and fluctuations effects, extending the method developed for the fixed coupling case [1]. We derive the exact asymptotic behavior in rapidity of the probabilistic distribution of the saturation scale.

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Section: Final Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotics of QCD traveling waves with fluctuations and running coupling effects

Beuf

2008

Nuclear Physics A

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“…Moreover, the Hilbert space in the D-representation is not constrained anymore: Indeed, Eq. (3.12) can be inverted to yield 15) showing that any operator built with D is physically acceptable. Thus, as anticipated, by changing from the α to the D-representation we have eliminated all the constraints.…”

Section: Hamiltonian Theory In the D-representationmentioning

confidence: 99%

“…In analogy with Eqs. (4.1)-(4.3) we can write 15) where the gain and loss terms have now the following structure…”

Section: Master Equation For Recombinationmentioning

confidence: 99%

“…(3.11), where the duality transformation [11,15] consists in replacing 5) and then exchanging the relative ordering of the operators 9 S † and S. Note also that the splitting and merging pieces in the original Hamiltonian (3.2)-(3.4) get interchanged by this transformation: The merging piece H 2→1 , which is the same as the second line of Eq. (3.11), is dual to the expression in the second line of Eq.…”

Section: Hamiltonian In the S-representationmentioning

confidence: 99%

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On the probabilistic interpretation of the evolution equations with pomeron loops in QCD

2006

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We study some structural aspects of the evolution equations with Pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.

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JIMWLK evolution in the Gaussian approximation

Iancu

Triantafyllopoulos

2012

J. High Energ. Phys.

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We demonstrate that the Balitsky-JIMWLK equations describing the highenergy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.

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From Target to Projectile and Back Again: Self-Duality of High-Energy Scattering Evolution in QCD

Cited by 90 publications

References 37 publications

Asymptotics of QCD traveling waves with fluctuations and running coupling effects

Asymptotics of QCD traveling waves with fluctuations and running coupling effects

On the probabilistic interpretation of the evolution equations with pomeron loops in QCD

JIMWLK evolution in the Gaussian approximation

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