Next-to-leading order calculation of three-jet observables in hadron-hadron collision

TL;DR

This work presents a next-to-leading order calculation of three-jet observables in hadron-hadron collisions using a modified Catani-Seymour dipole subtraction framework with an $\alpha$-cut to improve numerical stability. The authors implement a Monte Carlo program, validate it with cross-checks, and provide NLO predictions for inclusive and exclusive three-jet cross sections, Dalitz energy-fraction variables, and transverse-plane event shapes, using LHAPDF inputs and multiple jet algorithms. They show that NLO reduces scale uncertainties and improves the reliability of predictions, while highlighting regions with large logarithms that require all-order resummation or matching to NLL. The work advances precision QCD phenomenology for jet final states and informs experimental analyses of strong coupling and PDFs, with opportunities for further refinement through resummation and phenomenological studies of subjet structure.

Abstract

The production of the three jets in hadron-hardon collision is the first more complex process which allow us to define a branch of variables in order to do more precise measurement of the strong coupling and the parton distribution function of the proton. This process is also suitable for studying the geometrical properties of the hadronic final state at hadron colliders. This requires next-to-leading order prediction of the three-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient details. We use a the dipole method to construct Monte Carlo program for calculating three-jet observables at next-to-leading order accuracy. We present a theoretical prediction for inclusive and exclusive cross section and for some relevant event shape variables like transverse thrust, transverse jet broadening and Et3 variable.

Figures (9)

• Figure 1: The fix order QCD predictions for the inclusive three-jet differential cross sections of the transverse momentum of the leading jet obtained using the inclusive $k_\perp$ and midcone algorithms. The bands indicate the theoretical uncertainty due to the variation of the scales $x_{R,F}$ between $0.5$ and $2$. The grey band is the leading order and the dark grey band is the next-to-leading order. The inset figures show the $K$ factor and its scale dependence. The solid line represents the $x_{R,F} = 1$ scale choice.
• Figure 2: The scale dependence of the total 3-jet cross sections.
• Figure 3: Next-to-leading order perturbative prediction for normalised double differential distribution ($1/\sigma d\sigma/dX_1dX_2$) of the energy fraction variables $X_1$ and $X_2$ using the midcone and inclusive $k_{\perp}$ algorithm.
• Figure 4: The energy fraction distribution of the leading ($X_1$) and second leading ($X_2$) jets. The upper figure is result with the inclusive $k_\perp$ algorithm and the lower figures shows the midcone result.
• Figure 5: Distribution of the $E_{t3}$ event shape variable at LO an NLO level. The bands indicate the theoretical uncertainty due to the variation of the scales $x_{R,F}$ between $0.5$ and $2$. The grey band is the leading order and the black band is the next-to-leading order. The inset figure shows the $K$ factor and its scale dependence. The solid line represents the $x_{R,F} = 1$ scale choice.