Shadowing in multiparton proton–deuteron collisions

0 Physics Department, Penn State University, University Park , PA, USA 1 Department of Physics, Technion-Israel Institute of Technology , 32000 Haifa, Israel We study the screening effect for the multiparton interactions (MPI) for proton-deuteron collisions in the kinematics where one parton belonging to the deuteron has small x1, so the leading twist shadowing is present, while the second parton (x2) is involved in the interaction in the kinematics where shadowing effects are small. We find that the ratio of the shadowing and the impulse approximation terms is approximately a factor of 2 larger for MPI than for the single parton distributions. We also calculate the double parton antishadowing (DPA) contribution to the cross section due to the independent interactions of the partons of the projectile proton with two nucleons of the deuteron and find that shadowing leads to a strong reduction of the DPA effect. For example, for the resolution scale Q2 1 4 GeV2 of the interaction with parton x1 we find that shadowing reduces the DPA effect by 30 %. It is argued that in the discussed kinematics the contribution of the interference diagrams, which correspond to the interchange of partons between the proton and neutron, constitutes only a small correction to the shadowing contributions. 1 Introduction Recently there was a renewed interest in the theoretical studies of the multiparton interactions (MPI) in which at least two partons of one of the colliding particles are involved in the protonnucleus collisions [17]. To a large extent this is due to the first experimental studies of p A collisions at the LHC [811]. It was suggested in [14] that MPI would be easier to observe experimentally in p A collisions than in pp collisions since they are parametrically enhanced in the p A case by a factor A1/3 [1]. General formulas for this cross section were derived in [2] within perturbative QCD (pQCD) in the impulse approximation (that is, neglecting deviations of the a e-mail: b e-mail: nuclear parton distribution functions (pdf) from the additive sum of the nucleon pdfs). The analysis demonstrated connection of the pQCD treatment with the parton model calculation of [1] for the large A limit and uncorrelated nucleon distribution in the nucleus. The calculation of [2] employed the formalism developed in Refs. [1215], which is based on the use of the generalized double parton distributions in momentum space introduced in Ref. [12]. The calculation was done explicitly in the impulse approximation. It was argued in Refs. [57] that the impulse approximation is not a complete answer and one must include also the so-called interference diagrams, although no explicit estimates of their relative strength was performed. In Ref. [2] the arguments were presented that interference diagrams become important for small x due to the leading twist (LT) nuclear shadowing phenomenon. The main aim of the paper is to calculate explicitly the interference corrections to the impulse approximation due to the nuclear shadowing for the case of protondeuteron scattering based on the theory of the leading twist shadowing phenomena (for a recent review see [16]) which successfully predicted gluon shadowing for the coherent photoproduction of J / recently observed at the LHC [17,18]. We will focus on the limit when one of partons in the deuteron has small enough x , so that nuclear shadowing is present for the deuteron pdf while the second parton is probed in the kinematics where shadowing effects are absent. We will demonstrate that in this limit nuclear shadowing induced interference is present already on the level of diagrams where one of the nucleons is active in the amplitude and two in the conjugated amplitude (or vise versa), and that it has the same magnitude as the enhancement of MPI due to the interaction with two nucleons in the impulse approximation. In our analysis we will neglect a small effect of antishadowing in the deuteron pdfs at x 0.1 which is present due to the momentum sum rule; see the discussion in [16]. We also consider the interference for the case when just one parton of the proton is interchanged with one parton of the neutron and argue that this interference effect is much smaller than the leading twist shadowing interference. While the actual experiments are done with the heavy nuclei, we believe that the deuteron case provides a simple laboratory for the studying possible mechanisms of shadowing in four jet production processes. In the case of heavy nuclei, the combinatorics of the shadowing diagrams is much more complicated. It will be considered elsewhere. The shadowing in the multijet production differs significantly from the LT shadowing for nuclear pdfs since the two partons belonging to the projectile proton are typically located in a very small transverse area of the radius 0.5 f m. As a result they scatter off two different but very close in the impact parameter space nucleons that may be rather strongly correlated. This is especially true for the case of scattering off the deuteron which is a highly correlated system. Hence the analysis presented here can serve as the stepping stone to a discussion of similar effects for MPI with heavy nuclei. In the current experimental studies one usually starts with a trigger on a hard process of large virtualitysay a dijet with pt s larger than 50 100 GeV and one next looks for a second hard subprocess in the underlying event. Since the LT nuclear shadowing for pt 100 GeV/c is very small we will focus here on consideration of the MPI in which one of the subprocesses has large enough x or large virtuality so that the leading twist nuclear shadowing can be neglected in this case. The paper is organized as follows. In Sect. 2 we apply the general expressions relating double hard four jet cross section for the collision of hadrons A and B in terms of 2GPDs (Eq. 3) to obtain a compact expression for the double parton antishadowing contribution (DPA) taking into account the finite transverse size of the gluon GPD in the nucleon. In Sect. 3 we summarize first the theory of the LT shadowing for the deuteron pdfs and next use it to calculate the shadowing correction to the MPI rate for the case when x of one of the partons of the deuteron participating in collision is large and another is small. We demonstrate that the shadowing in the case of MPI is a factor of 2 stronger than in the case of the deuteron pdfs. At the same time an additional contribution to MPI due to the pQCD evolution induced correlations in the proton wave function reduces this enhancement. In Sect. 4 we present the numerical results. We find that the shadowing effect is smaller but of the same magnitude as DPA for modest virtualities (Q2 4 GeV2). We show explicitly that the double parton shadowing is negligible when both of the partons have large x , confirming the results of Ref. [2]. In Sect. 5 we estimate the contribution of the interference diagrams corre (...truncated)