Studies of Azimuthal Modulations in Two Hadron Fragmentation of a Transversely Polarised Quark

Abstract: We study the azimuthal modulations of dihadron fragmentation functions (DiFFs) of a transversely polarised quark using an NJL-jet based model that incorporates the Collins effect for single hadron emission. The DiFFs are extracted as Monte Carlo (MC) averages of corresponding multiplicities using their probabilistic interpretation. To simplify the model and highlight the possible mechanisms that create this modulation, we choose the elementary Collins function to be proportional to the elementary unpolarised fragmentation and a constant probability ($P_{SF}$) for the quark to flip its spin after a single hadron emission. Moreover, as a leading order calculation, only one of the produced hadrons in the decay chain of the quark is produced with elementary Collins modulation. We calculate the dependence of the polarised DiFFs on various angles such as the azimuthal angle of the single hadron and the angle of the two hadron production plane $\varphi_R$ for several values of $P_{SF}$. We observe that the polarised DiFFs for oppositely charged pion pairs exhibit a $\sin(\varphi_R)$ modulation. This effect is induced purely via the elementary Collins effect and persists even when the quark completely depolarises after a single hadron emission ($P_{SF}=0.5$). Moreover, similar sine modulations are present in the distribution of pion pairs with respect to the azimuthal angle of their total transverse momentum, $\varphi_T$.