New approach to the Sivers effect in the collinear twist-3 formalism

Abstract

The single-transverse spin asymmetry(SSA) for hadron production in the transversely polarized proton scattering receives major contribution from Sivers effect, which can be systematically described within the collinear twist-3 factorization framework in various processes. Conventional method in the evaluation of the Sivers effect known as pole calculation is technically quite different from non-pole calculation which is another method used in evaluating the final state twist-3 effect. In this paper, we extend the non-pole technique to the Sivers effect, and show the consistency with the conventional method through an explicit calculation of O(αs) correction in semi-inclusive deep inelastic scattering. As a result, we clarify that the conventional pole calculation is implicitly using the equation of motion and the Lorentz invariant relations whose importance became widely known in the non-pole calculation. We also clarify some technical advantages in using the new non-pole method.

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

“…As for the method of [63], they treated the l.h.s. of (31) in the same way as ours (although they did not refer to the presence of ∆H 3T term). On the other hand, they analyzed the first term in the r.h.s.…”

“…By now theoretical methods for dealing with those twist-3 effects have been developed and widely used to derive many relevant twist-3 cross section formula. Such theoretical studies include those for g 2 -structure function of the nucleon measured in deep-inelastic scattering [1,2], single spin asymmetries (SSA) for a hadron or (virtual) photon production in proton-proton (nucleus) collisions with one proton transversely polarized, p ↑ p → hX (h = π, D, γ, γ * etc) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], p ↑ A → hX [18][19][20][21][22], and semi-inclusive deep-inelastic scattering (SIDIS), ep ↑ → ehX [23][24][25][26][27][28][29][30][31][32], SSA in transversely polarized hyperon production in the unpolarized proton-proton collision, pp → Λ ↑ X [33][34][35][36][37][38] and in e + e − -collision, e + e − → Λ ↑ X [39], and the longitudinal-transverse double spin asymmetry A LT in the proton-proton collision, pp ↑ → {h, γ * } X [40][41][42]…”

Role of transverse gluon in SSA

“…Works on these aspects are ongoing. When this work is finished, it is found that in [22], a similar formula eq. ( 35) is obtained with a different method.…”

“…( 35) is obtained with a different method. Ward identity is used in [22] before pole condition is taken. The derivation and conclusion there seems more general than ours.…”

Reformulation of the twist-3 gluon Sivers effect toward the application to the heavy quarkonium production

“…We can check that each hard part has the following pole structure(See discussion around Eq. ( 47) in [29]).…”