Quark-quark double scattering and modified (anti-)quark fragmentation functions in nuclei

Quark-quark double scattering in eA DIS and its contribution to quark and antiquark fragmentation functions are investigated with the generalized factorization of the relevant twist-four processes in pQCD. It is shown that the resulting modifications to quark and anti-quark fragmentation functions are different. While the numerical size of these effects cannot be determined from pQCD, the structure of our result leads to a number of qualitative predictions for the relative size of the effect for different hadrons. These qualitative predictions agree with the multiplicity ratios for positive and negative hadrons as observed by HERMES. Multiple scattering in a nuclear medium is a key process to understand how hard processes are modified in nuclei. Detailed experimental information, which is available for such diverse reactions as electron-nucleus collisions (e+ A) in fixed target kinematics and hadron-nucleus collisions (h+A) and nucleusnucleus collisions (A+A) at RHIC or LHC is confronted by highly advanced theoretical descriptions [1,2,3,4,5,6]. Still, however, a truly comprehensive and reliable description of all phenomena has not been reached. In this contribution we discuss one element which should be contained in such an ultimate theoretical description. We analyse [7] quark-quark double scattering in nuclei and consider the nuclear effects on the quark and anti-quark fragmentation functions (FF), using the generalized factorization theory by LQS [8] in perturbative QCD. We find that quark-quark double scattering will give different corrections to quark and anti-quark FF, and obtain qualitative predictions which are in agreement with quite remarkable observation by the HERMES Collaboration [9]. In general, there are two different kinds of double scattering with nuclear enPreprint submitted to Elsevier Science 9 February 2008 Fig. 1. Two typical diagrams for quark-quark double scattering with three possible cuts, central(C), left(L) and right(R): (a) lowest-order of quark-quark rescattering; (b)next-to-leading order quark-quark rescattering. hancement in eA DIS: quark-gluon double scattering and quark-quark double scattering. Quark-gluon double scattering gives the dominant contribution to the leading quark energy loss and has been studied in detailed [3,4,10], while quark-quark double scattering may mixes quark and gluon fragmentation functions and therefore gives rise to new nuclear effects, as pointed out by Wang and Guo [3]. This is illustrated in Fig. 1(a). For the central-cut diagram, the final parton is a gluon fragmenting into the hadron considered. For the leftcut or right-cut diagrams, however, the final fragmenting parton is a quark. Therefore, adding up the contributions of these three cut diagrams we will get a mixture of quark and gluon fragmentation functions. Moreover, we can see from the central cut of diagram (a) that the quark jet is converted into a gluon jet by annihilation with an anti-quark in the nucleus, which provides a mechanism to change the jet flavor [11]. For quark-quark double scattering, there are three cut diagrams in leadingorder as shown in Fig. 1(a), and 46 cut diagrams in next-to-leading order, see Fig. 1(b) [7]. By summing all these contributions and including virtual corrections we can rewrite the semi-inclusive tensor in terms of a modified fragmentation function taking into account quark-quark double scattering: