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.

Extraction of the higher-twist parton distribution $e(x)$ from CLAS data

“…However for such PDFs, a scale of Q = 1 GeV belongs to the extrapolation region. On the other hand, theoretical efforts towards the understanding of TMD factorization of twist-3 will stimulate progress in the TMD sector [59,60] Complementary to the phenomenological studies, the lattice QCD efforts on evaluating charges and quasi/pseudo-PDFs have been extremely fruitful in the past years, with the premise that knowledge from both the phenomenological and the lattice side could be bridge for twist-3 PDF in a near future [18,61].…”

Factorization connecting continuum & lattice TMDs

“…However, the perturbative quasito-Collins matching coefficient C q is only known at one-loop, except for certain logarithmic terms constrained by its RGE, see section 3.2.2. Recently there has been renewed interest JHEP04(2022)178 in TMDs at subleading power, with for example a derivation of the necessary form of the factorization formula for polarized SIDIS at subleading power [82,83]. Finding continuumto-lattice factorization formulas for subleading power TMDs would be interesting.…”

T-odd proton-helicity asymmetry in semi-inclusive DIS in perturbative QCD

“…At this point, however, one cannot decide whether this matching is really quantitative in the sense that not just the overall power counting matches, but also the full combination of hard-scattering coefficients, parton distributions and fragmentation functions. Currently, despite enormous progress in recent years [49][50][51][52][53][54][55][56][57][58], the high-transverse-momentum tails of TMDs are not understood at a sufficient level to obtain definitive results for A U L , especially in the case of the fragmentation correlators. Clearly, it will be very interesting to explore this issue more deeply in the future, also in the light of TMD factorization theorems extending beyond leading twist proposed recently [55,57].…”

“…Currently, despite enormous progress in recent years [49][50][51][52][53][54][55][56][57][58], the high-transverse-momentum tails of TMDs are not understood at a sufficient level to obtain definitive results for A U L , especially in the case of the fragmentation correlators. Clearly, it will be very interesting to explore this issue more deeply in the future, also in the light of TMD factorization theorems extending beyond leading twist proposed recently [55,57].…”

“…In this context also the T-odd beam-spin asymmetry A LU is interesting [16,17,47,48], for which the initial lepton is polarized, and we will briefly discuss this asymmetry as well. We note that additional insights into the matching of TMDs to perturbative calculations have become available in recent years [49][50][51][52][53][54][55][56][57][58].…”