Advances in High Energy Physics

Volume 2015, Article ID 652062, 9 pages

http://dx.doi.org/10.1155/2015/652062

## Studies of Backward Particle Production with a Fixed-Target Experiment Using the LHC Beams

IFPA, Université de Liège, Allée du 6 Août, 4000 Liège, Belgium

Received 19 March 2015; Revised 28 May 2015; Accepted 17 June 2015

Academic Editor: Jean-Philippe Lansberg

Copyright © 2015 Federico Alberto Ceccopieri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The foreseen capability to cover the far backward region at a Fixed-Target Experiment using the LHC beams allows one to explore the dynamics of the target fragmentation in hadronic collisions. In this report we briefly outline the required theoretical framework and discuss a number of studies of forward and backward particle production. By comparing this knowledge with the one accumulated in Deep Inelastic Scattering on target fragmentation, the basic concept of QCD factorisation could be investigated in detail.

#### 1. Introduction

In hadronic collisions a portion of the produced particle spectrum is characterised by hadrons carrying a sizeable fraction of the available centre-of-mass energy, the so-called leading particle effect. It is phenomenologically observed that for such hadrons their valence-parton composition is almost or totally conserved with respect to the one of initial-state hadrons [1]. In collisions, for example, protons, neutrons, and lambdas show a significant leading particle effect. For such processes, the production cross section peaks at very small transverse momenta with respect to the collision axis, a regime where perturbative techniques cannot be applied, giving insight into nonperturbative aspects of QCD dynamics in high energy collisions.

Quite interestingly, the leading particle effect has been observed in Semi-Inclusive Deep Inelastic Scattering (SIDIS). At variance with the hadronic processes mentioned above, such a process naturally involves a large momentum transfer. The presence of a hard scale enables the derivation of a dedicated factorisation theorem [2–5] which ensures that QCD factorisation holds for backward particle production in DIS. The relevant cross sections can then be factorised into perturbatively calculable short distance cross sections and new distributions, fracture functions, which simultaneously encode information both on the interacting parton and on the spectator fragmentation into the observed hadron. Despite of being nonperturbative in nature, their scale dependence can be calculated within perturbative QCD [6]. The factorisation theorem [2–5] guarantees that fracture functions are universal distributions, at least in the context of SIDIS.

Detailed experimental studies of hard diffraction at HERA have shown to support the hypothesis of QCD factorisation and evolution inherent the fracture function formalism. Furthermore, they led to a quite accurate knowledge of diffractive parton distributions [7–11], a special case of fracture functions in the very backward kinematic limit. For particles other than protons, proton-to-neutron fracture functions have been extracted from a pQCD analysis of forward neutron production in DIS in [12]. A set of proton-to-lambda fracture functions has been obtained by performing a combined pQCD fit to a variety of semi-inclusive DIS lambda production data in [13].

As theoretically anticipated in [2–4, 14, 15] and experimentally observed in hard diffraction in collisions at Tevatron [16, 17], QCD factorisation is violated for fracture functions in hadronic collisions. On general grounds, it might be expected, in fact, that the dynamics of target-remnants hadronisation is affected by the coloured environment resulting from the scattering in a rather different way with respect to the Deep Inelastic Scattering case.

Nonetheless, the tools mentioned above allow us to investigate quantitatively particle production mechanisms in the very backward and forward regions, to test the concept of factorisation at the heart of QCD, and to study the dependencies of factorisation breaking upon the species and the kinematics of the selected final state particle.

This physics program could be successfully carried on at a Fixed-Target Experiment using the LHC beams [18]. Novel experimental techniques are, in fact, available to extract beam-halo protons or heavy ions from LHC beams without affecting LHC performances. Such a resulting beam would be then impinged on a high-density and/or long-length fixed target, guaranteeing high luminosities. Furthermore, most importantly for the physics program to be discussed here, the entire backward hemisphere (in the centre-of-mass system of the collision) would be accessible with standard experimental techniques allowing high precision studies of the target fragmentation. Although measurements of particle production in the very forward region (close to the beam axis) might be challenging experimentally due to the high particle densities and large energy flow, the installation of dedicated detectors, like forward neutron calorimeters and/or proton taggers, could further broaden the physics program outlined above giving access to the beam fragmentation region.

The paper is organised as follows. In Section 2 we first give a brief theoretical introduction on the fracture functions formalism and to higher order corrections to the semi-inclusive Drell-Yan process. In Section 3 we outline different analyses which could be performed at AFTER@LHC with special focus on single hard diffraction. In Section 4 we summarise our results.

#### 2. Collinear Factorisation Formula

Fracture functions, originally introduced in DIS, do depend on a large momentum transfer. Therefore, in order to use them in hadronic collisions, a hard process must be selected. We consider here the semi-inclusive version of the Drell-Yan process:in which one hadron is measured in the final state together with a Drell-Yan pair. In such a process the high invariant mass of the lepton pair, , allows the applicability of perturbative QCD, while the detected hadron can be used, without any phase space restriction, as a local probe to investigate particle production mechanisms.

The associated production of a particle and a Drell-Yan pair in terms of partonic degrees of freedom starts at . One of the contributing diagrams is depicted in Figure 1.