Hadron Fragmentation Inside Jets in Hadronic Collisions

TL;DR

This work develops an analytical NLO QCD framework for hadron production inside jets in hadronic collisions by exploiting the Narrow Jet Approximation and universal jet functions. The approach expresses jet- and jet-plus-hadron cross sections in terms of single-inclusive parton cross sections with additional jet- and semi-inclusive jet functions, preserving the universality of fragmentation functions. It demonstrates close agreement with prior numerical results and provides detailed phenomenology for LHC and RHIC, showing strong sensitivity to gluon fragmentation, especially through the $z_h$-dependent observables. The paper also discusses resummation prospects at large $z_h$ and outlines potential extensions to spin phenomena and photon fragmentation within this jet-function formalism.

Abstract

We present an analytical next-to-leading order QCD calculation of the partonic cross sections for the process $pp\rightarrow ({\text{jet}} \,h)X$, for which a specific hadron is observed inside a fully reconstructed jet. In order to obtain the analytical results, we assume the jet to be relatively narrow. We show that the results can be cast into a simple and systematic form based on suitable universal jet functions for the process. We confirm the validity of our calculation by comparing to previous results in the literature for which the next-to-leading order cross section was treated entirely numerically by Monte-Carlo integration techniques. We present phenomenological results for experiments at the LHC and at RHIC. These suggest that $pp\rightarrow ({\text{jet}} \,h)X$ should enable very sensitive probes of fragmentation functions, especially of the one for gluons.

Figures (9)

• Figure 1: Sketch of the production of an observed hadron inside a jet, described in terms of the jet functions $j_{c\rightarrow e}$ and $\tilde{j}_{e\rightarrow c'}$ (see text).
• Figure 2: Comparison of our results in the NJA to the ones of Arleo:2013tya for LHC kinematics.
• Figure 3: LO (dashed) and NLO (solid) cross sections for $pp\rightarrow (\text{jet} \,\pi)X$ for ALICE conditions, as functions of pion $p_T$. The bands show the scale dependence of the cross section for variations of the scale between $p_T^\text{jet} / 2$ (upper end of bands) and $2 p_T^\text{jet}$ (lower end of bands). The factorization and renormalization scales have all been set equal and varied simultaneously.
• Figure 4: Same as in Fig. \ref{['diff_pthad']}, but as function of $z_h$. As before the solid bands show the scale uncertainty. The hatched band displays the uncertainty of the cross section related to the fragmentation functions. This band is only reliable up to $z_h=0.65$ and extrapolated beyond (see text).
• Figure 5: Normalized quark (solid) and gluon (dashed) contributions to the cross section differential in $z_h$ for the kinematic conditions chosen for Fig. \ref{['diff_zh']}. We show results for DSS07 dss07 and DSS14 dss14 fragmentation functions.