Resumming the Light Hemisphere Mass and Narrow Jet Broadening distributions in e^+e^- annihilation

TL;DR

This work develops a next-to-leading logarithmic (NLL) resummation of the light hemisphere mass $ρ_L$ and narrow jet broadening $B_N$ distributions in e+e- annihilation using the coherent branching formalism. It provides all-orders summation of the leading and next-to-leading infrared logarithms and incorporates non-logarithmic NLO contributions, with simple power corrections to reconcile with LEP data. The results show substantial improvements over fixed-order predictions in the small-$ρ_L$ and small-$B_N$ regions, though non-perturbative hadronisation effects remain essential for quantitative agreement. The framework lays groundwork for more precise extractions of the strong coupling and for testing QCD in four-jet-like observables by integrating dispersive hadronisation approaches.

Abstract

We present predictions of two event shape distributions, the light hemisphere mass and the narrow jet broadening, to next-to-leading logarithmic order. We apply the coherent branching formalism to resum the leading O(alphas^n L^{2n-1}) and next-to-leading O(alphas^n L^{2n-2}) infrared logarithms to all orders in the coupling constant. We include the recently calculated non-logarithmic next-to-leading order contributions. Applying simple power corrections to the resummed result gives good agreement with the available data from LEP.

Figures (6)

• Figure 1: Event pictures of (a) two-jet configurations from quark-antiquark final states and (b) three-jet configurations originating from $q \bar{q} g$ events where the gluon is the hardest parton. The cones represent coherent soft and collinear gluon emission. The thrust axis is denoted by a dashed line.
• Figure 2: The towers of infrared logarithms appearing in the four-jet event shape rates $R_L$ and $R_N$. The resummation includes the leading and next-to-leading logarithms denoted by filled squares and the complete ${\cal O}(\alpha_{s}^2,\alpha_{s}^3)$ contributions from fixed order denoted by the empty squares. All other terms are incomplete and denoted by empty circles. The black filled squares denote terms generated purely in the two-jet limit.
• Figure 3: The resummed (solid) and fixed order NLO (dashed) predictions for the light hemisphere mass distribution $\frac{\rho_L}{\sigma}\frac{d\sigma}{d\rho_L}$ at $\mu = Q = M_Z$. The resummed prediction at $\mu = Q/2$ ($\mu = 2Q$) is shown as a dotted (dot-dashed) curve.
• Figure 4: The resummed (solid) and fixed order NLO (dashed) predictions for the narrow jet broadening distribution $\frac{B_N}{\sigma}\frac{d\sigma}{dB_N}$ at $\mu = Q = M_Z$. The resummed prediction at $\mu = Q/2$ ($\mu = 2Q$) is shown as a dotted (dot-dashed) curve.
• Figure 5: The resummed prediction for the light hemisphere mass distribution $\frac{\rho_L}{\sigma}\frac{d\sigma}{d\rho_L}$ at $\mu = Q = M_Z$ modified by a non-perturbative power correction $\rho_L \to \rho_L + 1~{\rm GeV}/Q$. The resummed prediction without power correction is shown as a dashed line. For comparison, we also show the charged hadron data collected at the $Z$ resonance by the DELPHI collaboration delphi.