The Lund String Fragmentation Model, widely used in Monte Carlo generators of jets, is extended to include the quark spin as a full quantum-mechanical degree of freedom, described by Pauli spinors. Such a model is needed to describe consistently the azimuthal asymmetries in jets from polarized quarks, like the Collins effect, di-hadron asymmetry and jet handedness.
The model is formulated in terms of quark propagators and quark-meson-quark vertices which are combinations of Pauli matrices. The basic assumption is that, when a string breaks, the created q-qbar pair is in the 3P0 state. This is implemented by a quark propagator proportional to mu+sigma_z sigma.k_T, where mu is a complex mass parameter. The model has been recently translated in a recursive Monte Carlo code for pseudoscalar meson production.
The introduction of vector mesons needed to complete the model requires a special recipe accounting for the entanglement between the spins of the meson and of the left-over quark. The longitudinal and transverse mesons are coupled to the quark line with two independent complex, constants G_L and G_T.
The expected properties are chiefly:
- Collins asymmetries of the same size but opposite signs for pi+ and pi-,
- di-hadron asymmetry linked to the Collins one,
- generation of jet handedness,
- vector mesons have Collins asymmetries whose signs depend on their linear polarizations,
- vector mesons can be generated with oblique (i.e., between transverse and longitudinal) polarizations. This is a new source of di-hadron asymmetry.
The main theoretical aspects of the model are presented in this talk, while the results of MC simulations and their comparison with existing data are the subject of a different dedicated talk (A. Kerbizi).