Abstract
Within the framework of perturbative quantum chromodynamics we derive the evolution equations for transverse momentum dependent distributions and apply them to the case of semi-inclusive deep inelastic scattering. The evolution equations encode the perturbative component of transverse momentum generated by collinear parton branchings. The current fragmentation is described via transverse momentum dependent parton densities and fragmentation functions. Target fragmentation instead is described via fracture functions. We present, to leading logarithmic accuracy, the corresponding semi-inclusive deep inelastic scattering cross-section, which applies to the entire phase space of the detected hadron. Some phenomenological implications and further developments are briefly outlined.
Highlights
The predictivity of perturbative Quantum Chromodynamics relies upon the factorization of hadronic cross-sections into perturbative process dependent coefficient functions, universal perturbative evolution equations and non-perturbative process independent densities [1]
In this work we have extended ordinary distributions to include transverse degrees of freedom both in the current and in the target fragmentation region of semi-inclusive deep inelastic lepton-hadron scattering (DIS)
As long as a factorization theorem holds for transverse momentum dependent fracture functions, the semiinclusive cross-sections are predictable on the whole phase space of the detected hadrons
Summary
The predictivity of perturbative Quantum Chromodynamics (pQCD) relies upon the factorization of hadronic cross-sections into perturbative process dependent coefficient functions, universal perturbative evolution equations and non-perturbative process independent densities [1]. In semi-inclusive Deep Inelastic Scattering (SIDIS) processes, at variance with inclusive DIS, one hadron is detected in the final state, l + P → l + h + X In this case, on the contrary, an accurate theoretical description has not yet been developed. Within the usual pQCD-improved parton model approach to SIDIS [7, 8], one deals only with current fragmented hadrons Another distinct issue enters the perturbative description. First we derive transverse momentum dependent (TMD) evolution equations which enter SIDIS cross-sections in the current fragmentation region. We extend this treatment to distributions in the target fragmentation region via fracture functions. As a result of these generalization, the combined SIDIS cross section is presented descibing hadron production on the whole phase space
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