Exact QCD evolution kernel for the twist-3 fragmentation function

Derive the exact DGLAP evolution kernel for the twist-3 T-odd quark-gluon-quark fragmentation function \(\tilde{D}_T\), thereby replacing the phenomenological assumption that \(\tilde{D}_T\) evolves in the same way as the unpolarized fragmentation function \(D_1\).

Background

The paper calculates the twist-3, naive-T-odd quark-gluon-quark fragmentation function D~T\tilde{D}_T in a diquark spectator model and uses it to predict the transverse-spin asymmetry for transversely polarized Λ\Lambda production in SIDIS. Because the model scale is substantially lower than the experimental scales relevant to the EIC and EicC, QCD evolution is required to compare the model results with phenomenological predictions.

The authors state that the exact DGLAP evolution kernel for D~T\tilde{D}_T is unavailable. Consequently, they approximate its evolution by applying the unpolarized fragmentation-function evolution of D1D_1 through the QCDNUM package. Determining the exact evolution kernel would establish a theoretically consistent scale dependence for D~T\tilde{D}_T and reduce the model dependence of the predicted asymmetry.

References

Since the exact DGLAP evolution kernel for \tilde{D}_T is not available, the present evolution effects should be regarded as a phenomenological approximation.

— The transverse-spin asymmetry $A^{\sinφ_{S_Λ}}_{UUT}$ in $Λ$ production in SIDIS within the collinear framework  (2609.08644 - Yang et al., 8 Sep 2026) in Section 2, subsection “The collinear fragmentation function \(\tilde{D}_T\) in a diquark model,” subsection “Model calculation of \(\tilde{D}_T\)”