What are the low- Q and large- x boundaries of collinear QCD factorization theorems?

Abstract

Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, Q ∼ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable x bj is large, x bj 0.5, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. We use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-Q and large-x bj physics.

Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production

“…The reliability of the theoretical description of SIDIS at low Q 2 has been recently discussed in refs. [39,40].…”

What are the low-Q and large-x boundaries of collinear QCD factorization theorems?

“…The unintegrated structure function k T F 1 for x bj = 0.6 and Q = 2 GeV (top row) and Q = 20 GeV (bottom row), for different values of m q and m s calculated using both the exact expressions (solid red curves) and the canonical collinear factorization approximation (dashed blue curves). The choices of m s are to fix k 2 at the values discussed in [1]. At the higher Q value the collinear calculation is almost indistinguishable from the exact, while at the lower Q value the exact calculation diverges as it approaches the kinematical upper limit of k T .…”

“…The momenta on the various legs are as indicated. [1] approximations of standard collinear factorization. For details of the calculations, see [1] 3.…”

Parton distributions and cos2ϕh asymmetry induced by anomalous photon-quark coupling

“…[26], the Sivers function resulting from this Pauli coupling is successfully calculated by the correlator in terms of gauge links, adopting the same instanton model as ours and the quark wave functions from the MIT bag model. A rigorous proof of the TMD factorization theorem with regard to the Pauli couplings would follow the framework recently proposed within the scalar diquark model in our interested kinematical range and is waiting for future exploration [41].…”