Twist-3 fragmentation effects for $A_{LT}$ in light hadron production from proton-proton collisions

We compute the contribution from the twist-3 fragmentation function for light hadron production in collisions between transversely and longitudinally polarized protons, i.e., $p^{\uparrow }\vec{p}\to hX$, which can cause a double-spin asymmetry (DSA) $A_{LT}$. This is a na"ive T-even twist-3 observable that we analyze in collinear factorization using both Feynman gauge and lightcone gauge as well as give a general proof of color gauge invariance. So far only twist-3 effects in the transversely polarized proton have been studied for $A_{LT}$ in $p^{\uparrow }\vec{p}\to hX$. However, there are indications that the na"ive T-odd transverse single-spin asymmetry (SSA) $A_N$ in $p^{\uparrow }p\to hX$ is dominated not by such distribution effects but rather by a fragmentation mechanism. Therefore, one may expect similarly that the fragmentation contribution is important for $A_{LT}$. Given possible plans at RHIC to measure this observable, it is timely to provide a calculation of this term.