In pursuit of Pomeron loops: The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation and the Wess-Zumino term

Kovner, Alex; Lublinsky, Michael

doi:10.1103/physrevd.71.085004

Cited by 106 publications

(194 citation statements)

References 40 publications

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“…Such an approximation is no longer valid in the dilute regime, however. Thus it has been proposed that the introduction of the Wess-Zumino term can handle this issue [14,15] whose necessity is also understandable from the gauge invariance of the source terms [16]. In later discussions we will clarify that under the eikonal approximation it is the gauge variant density of states which plays an equivalent role as the Wess-Zumino term in the sense as discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Once we recall our results (14) and (21) for the explicit form of the determinant, we can easily deduce from the definition (2) the alternative representation of the source terms,…”

Section: Manifestly Gauge Invariant Formmentioning

confidence: 99%

“…It is also instructive to reexpress the results in a form similar to (14) that is convenient for later discussions. By using sin 2 (T ga) = 1 2 (1 − cos(2T ga)) and expanding its inverse in terms of cos(2T ga) one may write the determinant (not the inverse) as…”

Section: B Adjoint Representationmentioning

confidence: 99%

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Gauge-invariant source terms in QCD

Fukushima

2006

Nuclear Physics A

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We discuss how to implement the source terms in Quantum Chromodynamics (QCD) respecting gauge invariance and noncommutativity of color charge density operators. We start with decomposing the generating functional of QCD into constituents projected to have specified color charge density. We demonstrate that such a projection leads to the gauge invariant source terms consisting of a naive form accompanied by the density of states which cancels the gauge dependence. We then illustrate that this form is equivalently rewritten into a manifestly gauge invariant expression in terms of the Wilson line. We confirm that noncommutativity of color charge density operators is fulfilled in both representations of the source terms. We point out that our results are useful particularly to consider the problems of the quantum evolution in high energy QCD.

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Section: Introductionmentioning

confidence: 99%

“…Once we recall our results (14) and (21) for the explicit form of the determinant, we can easily deduce from the definition (2) the alternative representation of the source terms,…”

Section: Manifestly Gauge Invariant Formmentioning

confidence: 99%

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Gauge-invariant source terms in QCD

Fukushima

2006

Nuclear Physics A

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“…When the projectile is dilute (the color charge density is small), while the target is dense the appropriate limit is the KLWMIJ Hamiltonian [48] H KLW M IJ = α s 2π 2 x,y,z K xyz J a L (x)J a L (y) + J a R (x)J a R (y) − 2J a L (x)R ab (z)J b R (y) (2.6) with the kernel K x,y;z = (x − z) i (y − z) i (x − z) 2 (y − z) 2 (2.7)…”

Section: Jhep04(2014)075mentioning

confidence: 99%

“…Nevertheless, the H RFT derived in [1] reduces to the two known limits -JIMWLK [39][40][41][42][43][44][45][46][47] and KLWMIJ [48] -in the approximation of a dilute target or dilute projectile respectively. We have argued that it adequately takes into account the Pomeron loops in the situation of scattering of two dilute objects at very high energy.…”

Section: Introductionmentioning

confidence: 99%

Reggeon field theory for large Pomeron loops

Altinoluk

Kovner

Levin

et al. 2014

J. High Energ. Phys.

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Abstract:We analyze the range of applicability of the high energy Reggeon Field Theory H RFT derived in [1]. We show that this theory is valid as long as at any intermediate value of rapidity η throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of η the dilute object could be the projectile, while at others it could be the target, so that H RFT does not reduce to either H JIM W LK or H KLW M IJ . When both objects are dense, corrections to the evolution not accounted for in [1] become important. The same limitation applies to other approaches to high energy evolution available today, such as for example [2,3] and [4][5][6]. We also show that, in its regime of applicability H RFT can be simplified. We derive the simpler version of H RFT and in the large N c limit rewrite it in terms of the Reggeon creation and annihilation operators. The resulting H RFT is explicitly self dual and provides the generalization of the Pomeron calculus developed in [4-6] by including higher Reggeons in the evolution. It is applicable for description of 'large' Pomeron loops, namely Reggeon graphs where all the splittings occur close in rapidity to one dilute object (projectile), while all the merging close to the other one (target). Additionally we derive, in the same regime expressions for single and double inclusive gluon production (where the gluons are not separated by a large rapidity interval) in terms of the Reggeon degrees of freedom.

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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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In pursuit of Pomeron loops: The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation and the Wess-Zumino term

Cited by 106 publications

References 40 publications

Gauge-invariant source terms in QCD

Gauge-invariant source terms in QCD

Reggeon field theory for large Pomeron loops

JIMWLK evolution in the Gaussian approximation

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