Precision Thrust Cumulant Moments at N^3LL

TL;DR

The paper advances precision thrust analyses by leveraging a full spectrum calculation that combines ${\cal O}(\alpha_s^3)$ fixed-order results, N^3LL resummation, and renormalon-free power corrections within an SCET-inspired framework. By performing a global fit to the first thrust moment, it extracts ${\alpha_s(m_Z)}$ and the leading nonperturbative parameter ${\Omega_1}$, and demonstrates that higher moments and cumulants cleanly expose subleading power corrections ${\Omega'_n}$ and related coefficients. The study shows cumulants are less sensitive to leading power corrections and thus ideal for probing higher-order nonperturbative effects, with a nonzero ${\tilde\Omega'_2}/Q^2$ extracted from $M'_2$. Overall, the work confirms consistency with previous tail analyses, improves theoretical uncertainty via renormalon subtraction, and highlights a path to characterize subleading power corrections across a broader set of event shapes.

Abstract

We consider cumulant moments (cumulants) of the thrust distribution using predictions of the full spectrum for thrust including O(alpha_s^3) fixed order results, resummation of singular N^3LL logarithmic contributions, and a class of leading power corrections in a renormalon-free scheme. From a global fit to the first thrust moment we extract the strong coupling and the leading power correction matrix element Omega_1. We obtain alpha_s(m_Z) = 0.1141 \pm (0.0004)_exp \pm (0.0014)_hadr \pm (0.0007)_pert, where the 1-sigma uncertainties are experimental, from hadronization (related to Omega_1) and perturbative, respectively, and Omega_1 = 0.372 \pm (0.044)_exp \pm (0.039)_pert GeV. The n-th thrust cumulants for n > 1 are completely insensitive to Omega_1, and therefore a good instrument for extracting information on higher order power corrections, Omega'_n/Q^n, from moment data. We find (\tilde Omega'_2)^(1/2) = 0.74 \pm (0.11)_exp \pm (0.09)_pert GeV.

Figures (16)

• Figure 1: Theoretical computations at various orders in perturbation theory for the total hadronic cross section at the Z-pole normalized to the Born-level cross section $\sigma_0$. Here the small blue points correspond to fixed order perturbation theory, green squares to resummation without renormalon subtractions, and red triangles to resummation with renormalon subtractions.
• Figure 2: Theoretical prediction for the first three moments at the Z-pole at various orders in perturbation theory. The blue circles correspond to fixed order perturbation theory (normalized with the total hadronic cross section) at ${\cal O}(\alpha_s)$, ${\cal O}(\alpha_s^2)$ and ${\cal O}(\alpha_s^3)$, green squares correspond to resummed predictions at NLL, NNLL, and N${}^3$LL normalized with the total hadronic cross section, and red triangles correspond to resummation normalized with the norm of the resummed distribution. For these plots we use $\alpha_s(m_Z)=0.114$.
• Figure 3: Theory scan for uncertainties in pure QCD with massless quarks. The panels are fixed order (top-left), resummation without the nonperturbative correction (top-right), resummation with a nonperturbative function using the $\overline{\textrm{MS}}$ scheme for $\overline\Omega_1$ (bottom-left), resummation with renormalon subtraction and a nonperturbative function in the Rgap scheme for $\Omega_1$ (bottom-right).
• Figure 4: Difference between theoretical predictions with default parameters for the first moment as function of $Q$ when varying one parameter at a time. The red solid line corresponds to varying $\Delta\alpha_s(m_Z)=\pm 0.001$ and the blue dashed lines to varying $\Delta\Omega_1=\pm 0.1$, with respect to the pure QCD best-fit values. There is a strong degeneracy of the two parameters in the region $Q>100$ GeV, which is obviously broken when considering values of $Q$ below $70$ GeV.
• Figure 5: Evolution of the best-fit values for $\alpha_s(m_Z)$ from thrust first moment fits when including various levels of improvement with respect to fixed order QCD. Only points at the right of the vertical dashed line include nonperturbative effects.