Non-global logarithms in jet and isolation cone cross sections

TL;DR

The authors derive a first-principles parton-shower equation from an EFT factorization to resum non-global logarithms in jet- and isolation-cone cross sections, and implement it in a MC interfaced with a tree-level generator to achieve LL resummation in the large-$N_c$ limit. They apply the framework to gap-between-jet and photon-isolation observables, comparing with fixed-order results and LHC data, and show that naive exponentiation can fail for small veto regions due to enhanced non-global contributions. The work clarifies the ingredients required for subleading resummation and highlights the significance of non-global effects for precision predictions, while outlining clear future directions such as including subleading logs, momentum-conservation effects, and going beyond large-$N_c$. Overall, this provides a systematic, RG-based approach to improve resummations for non-global observables in collider phenomenology.

Abstract

Starting from a factorization theorem in effective field theory, we derive a parton-shower equation for the resummation of non-global logarithms. We have implemented this shower and interfaced it with a tree-level event generator to obtain an automated framework to resum the leading logarithm of non-global observables in the large-$N_c$ limit. Using this setup, we compute gap fractions for dijet processes and isolation cone cross sections relevant for photon production. We compare our results with fixed-order computations and LHC measurements. We find that naive exponentiation is often not adequate, especially when the vetoed region is small, since non-global contributions are enhanced due to their dependence on the veto-region size. Since our parton shower is derived from first principles and based on renormalization-group evolution, it is clear what ingredients will have to be included to perform resummations at subleading logarithmic accuracy in the future.

Figures (13)

• Figure 1: The relation between shower time $t$, hard scale $\mu_h$ and soft scale $\mu_s$. We stop the lines in the plot when $\mu_s$ reaches $1\,{\rm GeV}$.
• Figure 2: The action of the operator $\bm{R}_m$ on an amplitude with $m$ legs in the large-$N_c$ limit. The double and single lines represent gluons and quarks, respectively.
• Figure 3: Left: Two-loop global and non-global coefficients as a function of the gap size $\Delta y$. Right: Comparison of the LL resummation and fixed-order results up to four loops, for $\Delta y=1$.
• Figure 4: Definition of the gap region for a dijet system in the rapidity and azimuthal plane, as used by ATLAS Aad:2011jz. If a jet with transverse momentum larger than $Q_0$ is radiated into the gray region, the event is vetoed. The two dashed red lines indicate the boundary of the approximated veto region used in Hatta:2013qj.
• Figure 5: The gap fraction as a function of the jet transverse momentum $\overline{p}_T$ (left plot) and the gap energy $Q_0$ (right plot). The red line shows the LL result for the gap fraction; the error band is obtained from scale variation. The ATLAS data is plotted in blue.