Twist-3 effect from the longitudinally polarized proton for A in hadron production from pp collisions

Abstract

We compute the contribution from the longitudinally polarized proton to the twist-3 doublespin asymmetry A LT in inclusive (light) hadron production from proton-proton collisions, i.e., p ↑ p → h X. We show that using the relevant QCD equation-of-motion relation and Lorentz invariance relation allows one to eliminate the twist-3 quark-gluon correlator (associated with the longitudinally polarized proton) in favor of one-variable twist-3 quark distributions and the (twist-2) transversity parton density. Including this result with the twist-3 pieces associated with the transversely polarized proton and unpolarized final-state hadron (which have already been calculated in the literature), we now have the complete leading-order cross section for this process.1 Data from RHIC is on tape for AN in prompt photon production and several predictions exist for this asymmetry within collinear factorization [34,37,39].2 ALT in ep collisions is also an interesting twist-3 asymmetry and has been studied in Refs. [46][47][48].

Color entanglement like effect in collinear twist-3 factorization

“…Second, it is worthwhile to make effort to study the properties of the gluon distribution G 4 at moderate or large x, such as its scale evolution, behavior in some models. Finally, though we tend to believe that the conventional collinear twist-3 formulation of T-even observables [27][28][29][30][31] and fragmentation effects [32][33][34][35][36][37][38][39] are not affected by color entanglement effect, it would be nice to verify this point by explicit calculations.…”

Exact relations for twist-3 gluon distribution and fragmentation functions from operator identities

“…The relation (51) is the FF version of (15). We can also derive another relation from (44). Following a similar step from (19) to (20), we obtain the following relation.…”

Transverse spin observables in hard-scattering hadronic processes within collinear factorization

“…However, the landscape of A LT observables goes well beyond this simple process. Extensive work has been performed on longitudinal-transverse DSAs in the Drell-Yan process; [69][70][71][72] in inclusive lepton production from W -boson decay in proton-proton scattering; 31 for jet production 73 and pion production 74 in leptonnucleon collisions; and for direct photon production, 75 jet/pion production, [76][77][78] and D-meson production 79 in proton-proton collisions.…”

“…62,63 3) Longitudinal-transverse DSAs can provide complimentary, yet equally important, information as SSAs on the quark-gluon structure of hadrons. The main analytical results have been calculated, [76][77][78] although more work is needed on the phenomenology. No experiments at RHIC have ever measured this asymmetry.…”