Subjet Rates in Hadron Collider Jets

TL;DR

The paper develops a perturbative QCD framework to predict subjet rates inside jets produced in hadron collisions using the inclusive k_T algorithm. It introduces a generating-function approach to perform a combined resummation of leading and next-to-leading logarithms of the subjet resolution y_cut, incorporating both final-state and initial-state radiation, and then matches the resummed results to exact fixed-order calculations. Threshold behavior is carefully treated to ensure physically sensible predictions across the y_cut range, with numerical studies demonstrating stable predictions for up to four subjets under realistic collider conditions. The findings reveal that initial-state radiation is essential for accurate predictions and that quark and gluon jets show a striking universality with respect to production mechanism when defined inclusively, though event-level cuts can introduce sensitivity to the hard scattering. The work provides a robust framework for comparing hadron-collider jet substructure to data and highlights areas where higher-order corrections may still be important.

Abstract

We calculate the subjet rates for jets produced in hadron collisions. The kt algorithm is used to define the jets and allows the theoretical calculation to sum both the leading and next-to-leading logarithms in the resolution variable, ycut. We also ensure that our calculation matches exactly the leading order in alpha_s result and has sensible behaviour near thresholds.

Figures (22)

• Figure 1: Quark subjet rates in the NLLA (dotted), with the inclusion of $Q_0$-suppressed terms (dashed) and with shifted thresholds (solid). Also shown is the sum of all subjet rates ($n \le 4$). Final state radiation only.
• Figure 2: Gluon subjet rates in the NLLA (dotted), with the inclusion of $Q_0$-suppressed terms (dashed) and with shifted thresholds (solid). Also shown is the sum of all subjet rates ($n \le 4$). Final state radiation only.
• Figure 3: Comparison of $(R_2-\Delta_2)_q$ computed in the NLLA (dashed) with that computed after including threshold modifications (solid).
• Figure 4: Comparison of $(R_2-\Delta_2)_g$ computed in the NLLA (dashed) with that computed after including threshold modifications (solid).
• Figure 5: One subjet rate: comparison of leading order (dotted), LLA (dashed), matched NLLA (solid) and matched NLLA with threshold modifications (green).