^{3}.

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.

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 [

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 [

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 [

As theoretically anticipated in [

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 [

The paper is organised as follows. In Section

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:

The associated production of a particle and a Drell-Yan pair in terms of partonic degrees of freedom starts at

Example of diagram contributing to hadron production in the central fragmentation region to order

Assuming that the hadronic cross sections admit a factorisation in terms of long distance nonperturbative distributions and short distance perturbative calculable matrix elements for the partonic process

The use of fracture functions allows for particles production already to

Pictorial representation of the parton model formula (

Example of diagram contributing to

We stress, however, that our ability to consistently subtract collinear singularities in such a semi-inclusive process is a necessary but not sufficient condition for factorisation to hold in hadronic collisions. The one-loop calculation outlined above in fact does involve only the so-called active partons. It completely ignores multiple soft parton exchanges between active and spectators partons, whose effects should be accounted for in any proof of QCD factorisation. Therefore, there is no guarantee that fracture functions extracted from SIDIS can be successfully used to describe forward or backward particle production in hadronic collisions. Reversing the argument, such a comparison may instead offer new insights into nonperturbative aspects of QCD and to the breaking of factorisation.

As an application of the formalism presented in the previous sections we will consider single hard diffractive production of a Drell-Yan pair:

Diffractive processes have been intensively analysed in DIS at HERA

Diffractive parton distributions ^{2}. Since they are extracted from large rapidity gap data where the proton is not directly measured, they contain a contribution (23%) from the so-called proton dissociation contribution. In order to use dPDFs in the present context we first note that

In Figure ^{2}. The distribution shrinks as lower

(a) Double differential cross sections for the production of a Drell-Yan pair of mass ^{2}. Blue error bands represent theoretical errors estimation, as described in the text. (b) Double differential cross sections for three different invariant masses.

(a) Double differential cross sections for the production of a Drell-Yan pair at

By changing variable from ^{2} and ^{2} and for three different ^{2} and, for the diffractive case, integrated in the range

(a) Triple differential cross sections for the production of a Drell-Yan pair at ^{2}. Blue error bands represent theoretical errors estimation, as described in the text. (b) Triple differential cross sections for three different

(a) Rapidity distributions for inclusive and diffractive Drell-Yan of mass ^{2}. Blue error bands represent theoretical errors estimation, as described in the text. (b) Diffractive to inclusive Drell-Yan rapidity distributions ratio.

We wish to end this section with a brief overview of other possible applications of the proposed formalism. A completely analogous program can be performed for the associated production of forward neutron and a Drell-Yan pair,

As a third application we consider hyperon production associated with a Drell-Yan pair,

As a last application we consider the associated production of one particle and a Drell-Yan pair in the context of multiparton interactions. The latter process has already been used to investigate the contamination of the so-called underlying event [

We have briefly reviewed a perturbative approach to single particle production associated with a Drell-Yan pair in hadronic collisions. On the theoretical side we have shown that the introduction of fracture functions allows a consistent factorisation of new class of collinear singularities arising in this type of processes. The factorisation procedure coincides with the one used in DIS confirming, as expected, the universal structure of collinear singularities and supports the proposed collinear factorisation formula. On the phenomenological side we have outlined some areas in which the formalism can be fully tested. In particular, focusing on the AFTER@LHC kinematical range, we have presented numerical predictions for the single diffractive production of virtual photons. The study of such a process might improve our understanding of nonperturbative aspects of QCD and it allows one to explore in detail the nature of factorisation breaking at intermediate energies.

The author declares that there is no conflict of interests regarding the publication of this paper.