Differential cross sections for high energy elastic hadron-hadron scattering in nonperturbative QCD

Berger, E. R.; Nachtmann, Otto

doi:10.1007/s100520050420

Cited by 16 publications

(48 citation statements)

References 17 publications

(53 reference statements)

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“…(2.22), corresponding to Pomeron exchange, has been already evaluated in the eikonal formalism [5,6,8,10,11], and it has been investigated in many papers [12,13,14,15,16,18,19,20,21,22]. The main building block is the truncatedconnected fermion propagator in an external field, which can be easily evaluated in an eikonal approximation using the path-integral representation described in the previous section.…”

Section: Pomeron Exchangementioning

confidence: 99%

“…Exploiting the invariance of W u i under translations along the longitudinal coordinate parallel to u i (which, strictly speaking, holds in the limit of infinite length), and the invariance of the expectation value under translations, we can rewrite this integral as 8) and changing variables to z Q , zq → z Q , z 1 = zq − z Q and zQ, z q → zQ, z 2 = z q − zQ, we obtain…”

Section: Pomeron Exchangementioning

confidence: 99%

“…Another, more physical reason, is that for large distances one expects the impact-parameter amplitude to vanish, since it corresponds to a process where the mesons undergoing the scattering process are very far away: since at large distances the Wilson loop correlator is expected to factorise, the impact-parameter amplitude could vanish only if the Wilson loop expectation value were 1 independently of its size. 8 To understand the origin of the problem, one can consider the amplitude for an isolated stable meson to remain unchanged. According to the LSZ approach, in and out state should coincide in this case, namely, considering for definiteness…”

Section: Pomeron Exchangementioning

confidence: 99%

“…where the trace is over colour indices, and where we have introduced the phases 8) and the compact notation…”

Section: Reggeon Exchangementioning

confidence: 99%

“…This approach is based on the description of the interacting hadrons in terms of partons, which together with the LSZ reduction formulas [3,4], and the eikonal approximation for propagators in an external field, leads to the Wilson-loop formalism for soft high energy scattering [5,6,7,8,9,10,11]. The resulting expressions for the scattering amplitudes have been investigated by means of various nonperturbative techniques, including the Stochastic Vacuum Model [5,6,8,10,11,12], the Instanton Liquid Model [13,14], the AdS/CFT correspondence for non-confining [15,16,17] and confining [18,19,20] backgrounds, and Lattice Gauge Theory [21,14,22], taking advantage, in most cases, of the analytic continuation of the amplitudes in Euclidean space [23,24,25,26,27,28,29]. These works are concerned with the leading behaviour of the elastic scattering amplitudes at high energy, and so non-vacuum Reggeon-exchange contributions are neglected from the onset.…”

Section: Introductionmentioning

confidence: 99%

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Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Giordano

2012

J. High Energ. Phys.

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We derive a nonperturbative expression for the non-vacuum, qq-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qq dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.

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Section: Pomeron Exchangementioning

confidence: 99%

Section: Pomeron Exchangementioning

confidence: 99%

Section: Pomeron Exchangementioning

confidence: 99%

“…where the trace is over colour indices, and where we have introduced the phases 8) and the compact notation…”

Section: Reggeon Exchangementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Giordano

2012

J. High Energ. Phys.

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Soft and hard Pomeron in the structure function of the proton at low x and low $Q^2$

1999

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We study inclusive electroproduction on the proton at low x and low Q 2 using a soft and a hard Pomeron. The contribution of the soft Pomeron is based on the Stochastic Vacuum Model, in which a nonperturbative dipole-dipole cross section can be calculated by means of a gauge invariant gluon field strength correlator. To model the hard Pomeron exchange we phenomenologically extend the leading order evolution of a power-behaved structure function, F 2 ∝ x −λ , proposed by López and Ynduráin. This extension allows to consider both the case Q 2 = 0 and the region of higher Q 2 on the basis of the same parametrization. A good simultaneous fit to the data on F 2 and on the cross section σ γp of real photoproduction is obtained for λ = 0.37. With four parameters we achieve a χ 2 /d.o.f. = 0.98 for 222 data points. In addition, we use our model of the inclusive γ * p interaction to compute the longitudinal structure function F L .

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On the loop–loop scattering amplitudes in Abelian and non-Abelian gauge theories

Meggiolaro

2005

Nuclear Physics B

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The high-energy elastic scattering amplitude of two colour-singlet qq pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finitness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with N c colours, but stopping to the order O(g 4 ) in perturbation theory. In connection with the above-mentioned IR finitness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections.

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Differential cross sections for high energy elastic hadron-hadron scattering in nonperturbative QCD

Cited by 16 publications

References 17 publications

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Soft and hard Pomeron in the structure function of the proton at low x and low $Q^2$

On the loop–loop scattering amplitudes in Abelian and non-Abelian gauge theories

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