Collins Effect in Single Spin Asymmetries of the p ↑ p → πX Process

We investigate the Collins effect in single spin asymmetries (SSAs) of the pp→ πX process, by taking into account the transverse momentum dependence of the microscopic sub-process cross sections, with the transverse momentum in the Collins function integrated over. We find that the asymmetries due to the Collins effect can only explain the available data at best qualitatively, by using our choices of quark distributions in the quark-diquark model and a pQCD-based analysis, together with several options of the Collins function. Our results indicate the necessity to take into account contributions from other effects such as the Sivers effect or twist-3 contributions. PACS. 13.75.Cs – 13.85.Ni – 13.87.Fh – 13.88.+e a Deceased on June 11, 2004. 2 Bo-Qiang Ma et al.: Collins Effect in Single Spin Asymmetries of the pp→ πX Process Single spin asymmetries in hadronic reactions have become an active research topic recently since they may help us to uncover the transverse quark structure of the nucleon. Experimentally, there are data on meson electroproduction asymmetries in semi-inclusive deep inelastic scattering [1,2,3], whose most common explanation is to relate them to the transversity distribution of the quarks in the hadron [4,5], convoluted with a transverse momentum dependent fragmentation function [6,7,8,9,10], i.e., the Collins function [6,11]. The Collins function, which gives the distributions for a transversely polarized quark to fragment into an unpolarized hadron with non-zero transverse momentum, has aroused great interest recently since a chiral-odd structure function can be accessible together with another chiral-odd distribution/fragmentation function. Large single spin asymmetries (SSA) in pp → πX have been also observed by the E704 Group at Fermilab [12]. Anselmino, Boglione and Murgia [13] tried to reproduce the experimental data using a parametrization of the Collins fragmentation function, with several assumptions and in a generalized factorization scheme at the parton level. Notice that the Collins function obtained in Ref. [13] is different from the original Collins parametrization [6]. Other mechanisms such as the Sivers effect [14,15,16,17], and twist-3 contributions [18,19,20], have been also proposed. Very recently, Bourrely and Soffer [21] pointed out that the SSA observed several years ago at FNAL by the experiment E704 [12] and the recent result observed at BNL-RHIC by STAR [22] are due to different phenomena. It is thus important to check whether a calculation with more detailed microscopic dynamics taken into account, and with also proper constraints on the Collins function, can indeed explain the single spin asymmetries in pp → πX . We will show in the following that the Collins effect in single spin asymmetries (SSAs) of the pp → πX process can only explain the available experimental data at best qualitatively, but we have not been able to explain the magnitude of the data at large xF by using several options of the Collins function and with our choices of the quark distributions in the quark-diquark model and a pQCD-based analysis. In our analysis, we work within the same simplified planar configuration of Ref. [13], using several options of Collins function with a Gaussian-type transverse momentum dependence, together with our choices of quark distributions. Notice also that measurements of SSAs in weak interaction processes can distinguish between different QCD mechanisms [16]. We first focus on the formalism of description of single spin asymmetries at the parton level. For the inclusive production of a hadron C from the hadron A and hadron B collision process