On the cos⁡ϕhcos⁡ϕh asymmetry in electroproduction of pions in double longitudinally polarized process

We study the cos⁡ϕhcos⁡ϕh azimuthal asymmetry in double polarized semi-inclusive pion production by considering the twist-3 effects directly from a quark–quark correlator. In particular, we evaluate the role of the transverse momentum dependent distributions eL(x,kT2) and gL⊥(x,kT2) on the asymmetry. Using two different sets of spectator model results for these distributions, we predict the cos⁡ϕhcos⁡ϕh asymmetry of π+π+, π−π−, and π0π0 at the kinematic configuration available at CLAS, HERMES. Our estimate shows that the asymmetries for charged and neutral pions are sizable and could be accessed by CLAS and HERMES. We also calculate the asymmetries for charged hadrons at the kinematics of COMPASS and compare them with the experimental data. We find that the asymmetry at COMPASS in our model is small which is consistent with the COMPASS data. We also find that gL⊥ gives the dominant contribution to the cos⁡ϕhcos⁡ϕh asymmetry, while the contribution of eLeL is almost negligible.