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Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions

Christoffer Flensburg, Gösta Gustafson

TL;DR

This work shows that fluctuations in BFKL evolution are large enough to extend the Good–Walker formalism to diffractive excitation across both low and high masses, providing a unified description without invoking separate triple-Regge parameters. Using the Lund dipole cascade model (DIPSY), the authors demonstrate that saturation effects in $pp$ collisions suppress fluctuations, causing diffractive excitation to be predominantly peripheral and breaking factorisation with DIS. The analysis reproduces the bare-pomeron behavior of a Regge pole with $oldsymbol{ m abla igl(oldsymbol{ m \alpha(0)=1.21, oldsymbol{ m abla \alpha' =0.2\,GeV^{-2}}igr)}$ and a nearly constant triple-pomeron coupling $oldsymbol{g_{3 ext{P}}} oughly 0.3\,GeV^{-1}$, showing consistency with triple-Regge expectations in the appropriate limit. Overall, the results unify two traditional approaches to diffraction, quantify saturation’s impact on diffractive observables, and clarify the breakdown of factorisation between DIS and $pp$ scattering.

Abstract

Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good--Walker formalism the cross section is determined by the fluctuations in the interaction. In this paper we show that by taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation by the Good--Walker mechanism. In high energy $pp$ collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and $pp$ collisions. The Dipole Cascade Model reproduces the expected triple-Regge form for the bare pomeron, and the triple-pomeron coupling is estimated.

Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions

TL;DR

This work shows that fluctuations in BFKL evolution are large enough to extend the Good–Walker formalism to diffractive excitation across both low and high masses, providing a unified description without invoking separate triple-Regge parameters. Using the Lund dipole cascade model (DIPSY), the authors demonstrate that saturation effects in collisions suppress fluctuations, causing diffractive excitation to be predominantly peripheral and breaking factorisation with DIS. The analysis reproduces the bare-pomeron behavior of a Regge pole with and a nearly constant triple-pomeron coupling , showing consistency with triple-Regge expectations in the appropriate limit. Overall, the results unify two traditional approaches to diffraction, quantify saturation’s impact on diffractive observables, and clarify the breakdown of factorisation between DIS and scattering.

Abstract

Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good--Walker formalism the cross section is determined by the fluctuations in the interaction. In this paper we show that by taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation by the Good--Walker mechanism. In high energy collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and collisions. The Dipole Cascade Model reproduces the expected triple-Regge form for the bare pomeron, and the triple-pomeron coupling is estimated.

Paper Structure

This paper contains 20 sections, 27 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The eikonal approximation and the Good--Walker formalism
  3. Eikonal approximation
  4. Good--Walker formalism
  5. What are the diffractive eigenstates?
  6. The dipole cascade model
  7. Mueller's dipole model
  8. The Lund dipole cascade model
  9. NLL effects
  10. Non-linear effects and saturation
  11. Confinement effects
  12. Initial dipole configurations
  13. Application to diffraction
  14. The nature of the fluctuations and effects of saturation
  15. $\gamma^* p$ scattering
  16. ...and 5 more sections

Figures (2)

  • Figure 1: (a) An example of a parton (or dipole) cascade evolved in rapidity. (b) The exchange of a gluon gives rise to an inelastic interaction. (c) Elastic scattering is obtained from coherent scattering of different partons in different cascades, via the exchange of two gluons. (d) Diffractive excitation is obtained when the result of the two-gluon exchange does not correspond to the coherent initial proton state. Here the dashed lines indicate virtual emissions, which are not present in the diffractive final state.
  • Figure 2: Single diffractive excitation with no final state particles in the $Y_{\mathrm{t}}$ range. The virtual target evolutions are summed on amplitude level, while the real projectile evolutions are summed on cross section level.