Resummation of jet mass with and without a jet veto

TL;DR

The paper addresses the challenge of resumming jet-mass distributions in multi-jet events, where fixed-order calculations fail near the peak due to multiple scales. It develops an inclusive observable (asymmetric thrust) that can be resummed to NNLL, and introduces a small-R refactorization framework for exclusive dijet masses with a jet veto, enabling improved agreement with QCD predictions. Through heuristic arguments and phenomenological tests, the authors show that refactorizing the soft function at small R captures essential logarithmic structures and supports NNLL predictions, offering a viable path for precise jet-substructure calculations. Non-global logarithms are acknowledged but treated as subleading in the regimes analyzed, with suggestions for further refinement via full soft-function computations.

Abstract

Calculating the distribution of jet masses in high-energy collisions is challenging because fixed-order perturbation theory breaks down near the peak region, and because multiple scales complicate the resummation. To avoid using a jet veto, one can consider inclusive observables, in which every particle is in a jet. We demonstrate that calculating the mass of the hardest jet in multijet events can be problematic, and we give an example of an inclusive observable, asymmetric thrust, which can be resummed to next-to-next-to-leading logarithmic accuracy. Exclusive observables with out-of-jet regions are more complicated. Even for e+e- dijet events at energy Q, to calculate the mass m of jets of size R, one must impose a veto on the energy omega of extra jets to force dijet kinematics; then there are both log m/Q and log m/omega singularities. To proceed, we suggest a refactorization of the soft function in the small R limit. To justify this refactorization, we show that the expansion of the resummed distribution is in excellent agreement with fixed order. This motivates considering the expansion around small R as a useful handle on producing phenomenologically useful resummed jet mass distributions. The strong evidence we give for refactorization at small R is independent of non-global logarithms, which are not the subject of this paper.

Figures (7)

• Figure 1: Difference between QCD and SCET for the sum $\tau_{A_1}\frac{\text{d}\sigma}{\text{d} \tau_{A_1}}+ \tau_{A_2}\frac{\text{d}\sigma}{\text{d} \tau_{A_2}}$ at order $\alpha_s^2$. That the difference vanishes at very small $\tau_A$ (left side), shows that SCET reproduces all of the large logs of this distribution up to NNLL.
• Figure 2: Difference between QCD and SCET for $\tau_{A_1} \frac{\text{d}\sigma}{\text{d} \tau_{A_1}}$ at order $\alpha_s^2$ for a variety of jet sizes.
• Figure 3: The allowed kinematic region for $e^+ e^- \to q \bar{q} g$ in variables $u, t$. In the yellow regions, $Y_{ij}$, the Cambridge/Aachem requirements have been met and partons $i,j$ have been clustered. The green region corresponds to $E_3 < \omega$. In this plot, $R = 0.4$ and $\omega = 0.15 Q$.
• Figure 4: Difference between QCD and SCET for the $(\alpha_s/4\pi)^2$ coefficient of $\tau_\omega \frac{\text{d} \sigma}{\text{d} \tau_\omega}$ for the different color structures. After using non-Abelian exponentiation (NAE) the $C_F$ curve should go to zero at small $\tau_\omega$, up to power corrections in $\omega$.
• Figure 5: The difference between coefficient of $\alpha_s^2$ in $\text{d} \sigma/\text{d} \ln \tau_\omega$ in full QCD and in SCET for $R=0.1$ and $\omega=0.0001 Q$ after refactorization, but not including the $\Gamma_1$ piece.