Single-spin asymmetries: The Trento conventions

Abstract

During the workshop "Transversity: New Developments in Nucleon Spin Structure" (ECT * , Trento, Italy, 14-18 June 2004), a series of recommendations was put forward by the participants concerning definitions and notations for describing effects of intrinsic transverse momentum of partons in semi-inclusive deep inelastic scattering.

Azimuthal and single spin asymmetries in hard scattering processes

“…These moments of the azimuthal asymmetries are usually indicated by A W (φ) S B S T , where S B , S T = U, L, T refer to unpolarized (U), longitudinally (L) and (for the target) transversely (T ) polarized beam, target respectively, while W (φ) refers to some appropriate φ-dependent circular function, W = 1, sin φ, cos φ, sin 2φ, etc. As a phenomenologically relevant example, A sin(φ h ±φ S ) U T is given as [73] A sin(φ h ±φ S ) U T ≡ 2 sin(φ h ± φ S ) = dφ h dφ S sin(φ h ± φ S )[dσ(φ S ) − dσ(φ S + π)] dφ h dφ S [dσ(φ S ) + dσ(φ S + π)] .…”

“…The extra π phase in the figure label keeps into account the different choice w.r.t. Trento conventions [73]. The curves are obtained from Eq.…”

“…1T [73]), and to the function ∆f a,sz/A,S T , (related to g 1T of Ref. [108]); 4) Finally, the combinations F +− ++ ±F +− −− are related to the probability of finding a transversely polarized quark respectively inside an unpolarized hadron (that is, to the Boer-Mulders function [108], ∆ N f a ↑ /A or h ⊥ 1 ) or inside a longitudinally polarized hadron (that is, to the PDF ∆f a,s T /A,S L or h ⊥ 1L [108]).…”

“…14. We take the photon and the proton colliding along the z axis with momenta q and P respectively; following the so-called "Trento conventions" [73], the leptonic plane coincides with the x-z plane. We consider the kinematic regime in which P T ≃ Λ QCD ≃ k ⊥ , where P T = |P T | is the final hadron transverse momentum.…”

“…[73]) is referred to as the Sivers function. In this first formulation the numerator of A N , see Eq.…”