Abstract
We construct a language for identifying kinematical regions of transversely differential semi-inclusive deep inelastic scattering (SIDIS) cross sections with particular underlying partonic pictures, especially in the regions of moderate to low Q where sensitiv- ity to kinematical effects becomes non-trivial. These partonic pictures map to power law expansions whose leading contributions ultimately lead to well-known QCD factorization theorems. In order to establish the consistency of a particular observable in SIDIS process with an estimate of the appropriate underlying partonic picture, we introduce new quan- titative criteria expressed in terms of various ratios of partonic and hadronic momentum degrees of freedom. We propose how to use these criteria in phenomenology and provide a web tool which allows visualization of these ratios for any chosen kinematic configuration.
Highlights
We construct a language for identifying kinematical regions of transversely differential semi-inclusive deep inelastic scattering (SIDIS) cross sections with particular underlying partonic pictures, especially in the regions of moderate to low Q where sensitivity to kinematical effects becomes non-trivial
For example, refs. [8, 15, 17] there has been a large number of studies on unpolarized SIDIS cross sections [33,34,35,36,37,38,39]
Integrating SIDIS into such a program demands a clear language for identifying kinematical regions with particular underlying partonic pictures, especially in regions of moderate to low Q where sensitivity to kinematical effects outside the usual very high energy limit becomes non-trivial
Summary
We consider the process: lepton(l) + proton(P ) → lepton(l ) + Hadron(PB) + X. A sketch is shown in figure 1.4 The proton has momentum P , the virtual photon has momentum q, the produced hadron has momentum PB, and the incoming and scattered leptons have momenta l and l respectively. The variable xN is the kinematical variable usually called Nachtmann-x It is often labeled by a ξ in the literature, but for us ξ will label a partonic momentum fraction, so we use xN instead; with the subscripts on xN and xBj distinguishing between Bjorken and Nachtmann x-variables. We treat the final state B momentum in terms of the light-cone momentum fraction zN, eq (2.3), variable and relate it to the transverse momentum of the photon. In order to do this it is important to be able to express the final state momentum in both the photon and hadron frames
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