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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.
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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.
We present a novel global QCD analysis of charged $D^{*}$-meson fragmentation functions at next-to-leading order accuracy. This is achieved by making use of the available data for single-inclusive $D^{*}$-meson production in electron-positron annihilation, hadron-hadron collisions, and, for the first time, in-jet fragmentation in proton-proton scattering. It is shown how to include all relevant processes efficiently and without approximations within the Mellin moment technique, specifically for the in-jet fragmentation cross section. The presented technical framework is generic and can be straightforwardly applied to future analyses of fragmentation functions for other hadron species, as soon as more in-jet fragmentation data become available. We choose to work within the Zero Mass Variable Flavor Number Scheme which is applicable for sufficiently high energies and transverse momenta. The obtained optimum set of parton-to-$D^{*}$ fragmentation functions is accompanied by Hessian uncertainty sets which allow one to propagate hadronization uncertainties to other processes of interest.
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
The nature of a jets fragmentation in heavy-ion collisions has the potential to cast light on the mechanism of jet quenching. However the presence of the huge underlying event complicates the reconstruction of the jet fragmentation function as a function of the momentum fraction z of hadrons in the jet. Here we propose the use of moments of the fragmentation function. These quantities appear to be as sensitive to quenching modifications as the fragmentation function directly in z. We show that they are amenable to background subtraction using the same jet-area based techniques proposed in the past for jet p_ts. Furthermore, complications due to correlations between background-fluctuation contributions to the jets p_t and to its particle content are easily corrected for.
We demonstrate that spontaneous transverse polarization of Lambda baryon ($Lambda$) production in $e^+e^-$ annihilation can be described using the transverse momentum dependent polarizing fragmentation functions (TMD PFFs). Using a simple Gaussian model, we perform an extraction of the TMD PFFs by fitting the BELLE collaborations recent measurement of the $Lambda$ transverse polarization in back-to-back $Lambda+h$ production in $e^+ e^-$ collisions, $e^{-} + e^{+} rightarrow Lambda^{uparrow}+h+X$. We find that this simple model accurately describes the experimental data for $Lambda$ production associated with pions and kaons, and we are able to determine TMD PFFs for different quark flavors. We use these newly extracted TMD PFFs to make predictions for the transverse polarization of $Lambda$ produced in semi-inclusive deep inelastic scattering at a future electron-ion collider, and find that such a polarization is around $10%$ and should be measurable.
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