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By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.
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We develop the theoretical framework needed to study the distribution of hadrons with general polarization inside jets, with and without transverse momentum measured with respect to the standard jet axis. The key development in this paper, referred to as polarized jet fragmentation functions, opens up new opportunities to study both collinear and transverse momentum dependent (TMD) fragmentation functions. As two examples of the developed framework, we study longitudinally polarized collinear $Lambda$ and transversely polarized TMD $Lambda$ production inside jets in both $pp$ and $ep$ collisions. We find that both observables have high potential in constraining spin-dependent fragmentation functions with sizeable asymmetries predicted, in particular, at the future Electron-Ion Collider.
In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of $Lambda_{QCD}$, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than $Lambda_{QCD}$ but much smaller than $Q$ which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.
The target fragmentation region of semi-inclusive deep inelastic scattering is described at leading twist, taking beam and target polarizations into account. The formalism of polarized and transverse-momentum dependent fracture functions is developed and the observables for some specific processes are presented.
We study the production of a large-pT photon in association with a jet in proton-proton collisions. We examine the sensitivity of the jet rapidity distribution to the gluon distribution function in the proton. We then assess the sensitivity of various photon + jet correlation observables to the photon fragmentation functions. We argue that RHIC data on photon-jet correlations can be used to constrain the photon fragmentation functions in a region which was barely accessible in LEP experiments.
Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside $Z$-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction $z_h$ of the jet carried by the hadron and the transverse momentum $j_perp$ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate $z_h$ region. For $j_perp$-dependence, we suggest binning in both $z_h$ and $j_perp$, which would lead to a more direct probing of TMD fragmentation functions.
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