Single spin asymmetry \( A _ { U L } ^ { \sin ( 3 \phi _ { h } - \phi _{ R } ) }\) in dihadron production in SIDIS

In the field of particle physics, the phenomenon of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) process has always been a significant focus. This paper focuses on the single longitudinal spin asymmetry \(A_{UL }^{\sin (3\phi _{h}-\phi _{R})}\) in the dihadron production during this process and combines the transverse-momentum-dependent dihadron fragmentation function (DiFF) \(H_1^{\perp }\) to deeply analyze its underlying mechanism. Here, the involved DiFF \(H_1^{\perp }\) is the analogue of the Collins function for single-hadron production and it describes the fragmentation of a transversely polarized quark at leading twist. Recent studies have shown that the azimuthal asymmetry signal observed by the COMPASS collaboration in the dihadron SIDIS is weak. To reveal the reason for this small signal and to study the asymmetry, we calculate the unknown T-odd DiFF \(H_1^{\perp }\) using the spectator model. The spectator model, widely used in SIDIS, describes the internal structure of hadrons and the hadronization mechanism. This model has successfully explained dihadron production in unpolarized and single-polarized processes. During the research process, while maintaining the transverse momentum dependence of the hadron pair, we employ the transverse momentum dependent(TMD) factorization framework, using this method and the model, we first simulate the asymmetry in the COMPASS energy region and compare it with experimental data. Furthermore, we predict the same asymmetry at the HERMES, expecting to provide valuable theoretical references for relevant experimental studies.