Factorization for azimuthal asymmetries in SIDIS at next-to-leading power

Abstract

Differential measurements of the semi-inclusive deep inelastic scattering (SIDIS) process with polarized beams provide important information on the three-dimensional structure of hadrons. Among the various observables are azimuthal asymmetries that start at subleading power, and which give access to novel transverse momentum dependent distributions (TMDs). Theoretical predictions for these distributions are currently based on the parton model rather than a rigorous factorization based analysis. Working under the assumption that leading power Glauber interactions do not spoil factorization at this order, we use the Soft Collinear Effective Theory to derive a complete factorization formula for power suppressed hard scattering effects in SIDIS. This yields generalized definitions of the TMDs that depend on two longitudinal momentum fractions (one of them only relevant beyond tree level), and a complete proof that only the same leading power soft function appears and can be absorbed into the TMD distributions at this order. We also show that perturbative corrections can be accounted for with only one new hard coefficient. Factorization formulae are given for all spin dependent structure functions which start at next-to-leading power. Prospects for improved subleading power predictions that include resummation are discussed.

Definition and evolution of transverse momentum dependent distribution of twist-three

“…This is a natural consequence of the NLP TMD factorization theory being at its earlier stage of development. The first convincing studies appeared only recently [6][7][8][9][10]. Further progress in this direction requires the systematization of knowledge about TMD distributions of twist-three, which we present in this paper.…”

“…The same consideration gives rise to the partonic interpretation for correlators, as the probability of emission (for x > 0) and absorption (for x < 0) of partons in the 5 In works [10,38], an alternative two-variable notation is used with x being the (positive) momentum fraction of a single parton, and ξ being imbalance of momentum fractions in the quark-gluon pair. Such as,…”

“…Here, however, one faces another complication. Many physical observables, such as cross-sections of Drell-Yan and SIDIS processes [7,9,10], quasi-TMD distributions [45], etc. contain integrals with an additional singularity at x 2 = 0.…”

Factorization for quasi-TMD distributions of sub-leading power

“…• The rapidity divergences of TMD operator and Ψ-functions are canceled by the soft factor S(y) (3.8). At LP and NLP the soft factor is ordinary TMD soft factor [32]. The cancellation of rapidity divergences for NLP operators has been demonstrated explicitly at NLO in ref.…”

“…The first steps were made in ref. [27], but the systematic development started almost twenty years later [28][29][30][31][32][33]. Still, many aspects of the NLP TMD factorization beyond leading perturbative order (LO) are mysterious.…”