No 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.

We study the role of purely external kinematical approximations in inclusive deep-inelastic lepton-hadron scattering within QCD factorization, and consider factorization with an exact treatment of the target hadron mass. We discuss how an observed phenomenological improvement obtained by accounting for target mass kinematics could be interpreted in terms of general properties of target structure, and argue that such an improvement implies a hierarchy of nonperturbative scales within the hadron. *

We compute the inclusive unpolarized dihadron production cross section in the far from backto-back region of e + e − annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation roughly coincide at intermediate transverse momentum. We find significant tension, within the intermediate transverse momentum region, between calculations done with existing non-perturbative TMD fragmentation functions and collinear factorization calculations if the center-of-mass energy is not extremely large. We argue that e + e − measurements are ideal for resolving this tension and exploring the large-to-small transverse momentum transition, given the typically larger hard scales ( 10 GeV) of the process as compared with similar scenarios that arise in semi-inclusive deep inelastic scattering and fixed-

We demonstrate testing QCD factorization theorems using a simple quantum field theory. Specifically we test standard collinear factorization in order to better explore deeply inelastic scattering (DIS) at lower Q and larger Bjorken x.