The Nambu–Jona-Lasinio jet model is extended to accommodate hadronization of a transversely polarized quark in order to explore the Collins effect within a multihadron emission framework. This is accomplished by calculating the polarized quark spin flip probabilities after a pseudoscalar hadron emission and the elementary Collins functions. The model is then used to calculate the number densities of the hadrons produced in the polarized quark’s decay chain. The full Collins fragmentation function is extracted from the sine modulation of the polarized number densities with respect to the polar angle between the initial quark’s spin and hadron’s transverse momentum. Two cases are studied here. First, a toy model for elementary Collins function is used to study the features of the transversely polarized quark-jet model. Second, a full model calculation of transverse momentum dependent pion and kaon Collins functions is presented. The remarkable feature of our model is that the $1/2$ moments of the favored Collins fragmentation functions are positive and peak at large values of $z$ but decrease and oscillate at small values of $z$. The $1/2$ moments of the unfavored Collins functions have comparable magnitude and opposite sign to the favored functions, vanish at large $z$ and peak at small values of $z$. This feature is observed for both the toy model and full calculation and can therefore be attributed to the quark-jet picture of hadronization. Moreover, the transverse momentum dependencies of the model Collins functions differ significantly from the Gaussian form widely used in the empirical parametrizations. Finally, a naïve interpretation of the Schäfer-Teryaev sum rule is proven not to hold in our model, where the transverse momentum conservation is explicitly enforced. This is attributed to the sizable average transverse momentum of the remnant quark that needs to be accounted for to satisfy the transverse momentum sum-rule.

• Received 29 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.034025