The thrust and heavy-jet mass distributions in the two-jet region

TL;DR

The paper develops and applies Dressed Gluon Exponentiation (DGE) to thrust and heavy-jet mass distributions in the two-jet region of e+e− annihilation, combining renormalon-resummed perturbation theory with a shape-function description of non-perturbative corrections. By expressing both observables in terms of the single-jet mass distribution, it unifies hadronization effects and includes hadron-mass schemes to enable meaningful cross-observable comparisons. The thrust distribution is described well across energies when matched to NLO, while the heavy-jet mass is reliable only for ρ_H<1/6 due to kinematic phase-space limitations, which constrains extracting α_s from this observable. Importantly, fixing α_s from the thrust analysis yields consistent power corrections for both observables, supporting a renormalon-driven, hemisphere-uncorrelated shape-function picture in the peak region.

Abstract

Dressed Gluon Exponentiation (DGE) is used to calculate the thrust and the heavy-jet mass distributions in e+e- annihilation in the two-jet region. We perform a detailed analysis of power corrections, taking care of the effect of hadron masses on the measured observables. In DGE the Sudakov exponent is calculated in a renormalization-scale invariant way using renormalon resummation. Neglecting the correlation between the hemispheres in the two-jet region, we express the thrust and the heavy-jet mass distributions in terms of the single-jet mass distribution. This leads to a simple description of the hadronization corrections to both distributions in terms of a single shape function, whose general properties are deduced from renormalon ambiguities. Matching the resummed result with the available next-to-leading order calculation, we get a good description of the thrust distribution in a wide range, whereas the description of the heavy-jet mass distribution, which is more sensitive to the approximation of the phase space, is restricted to the range rho_H<1/6. This significantly limits the possibility to determine alpha_s from this observable. However, fixing alpha_s by the thrust analysis, we show that the power corrections for the two observables are in good agreement.

Figures (11)

• Figure 1: The NLO coefficient for the thrust (upper set of curves) and heavy-jet mass (lower set of curves) distributions obtained by expanding the DGE result (dashed and dotted line for the unmodified and modified log, respectively) compared to the exact result (solid line).
• Figure 2: A contour plot of the doubly differential light and heavy-jet mass cross section based on 10 million events generated with Pythia at $Q={M_{\rm Z}}$ on the parton level, using only light quarks (uds). The contours spacing is based on a logarithmic scale: the lowest contour corresponds to two events and the others are spaced by a relative factor of 5. This illustrates the available phase space and, in particular, the constraints on $\rho_L$ for $\rho_H > 1/6$.
• Figure 3: Thrust data at ${M_{\rm Z}}$ in the peak region together with shift-based fits using the range $0.05\,{M_{\rm Z}}/Q < t< 0.30$ (dashed line) in different HMS. The perturbative calculation (DGE) is also shown (dotted line).
• Figure 4: The $Q$-dependence of the shift $\lambda_1$ for a fixed $\alpha_s$ in the decay and P schemes. The lines are fits of the form $\lambda_1\bar{\Lambda} =p_1+ p_2 \ln ({Q}/{\bar{\Lambda}})$.
• Figure 5: Thrust data at ${M_{\rm Z}}$ in the decay scheme together with the best shape-function-based fit (solid line) and a shift-based fit using the range $0.06\,{M_{\rm Z}}/Q < t< 0.30$ (dashed line). The DGE perturbative calculation is also shown (dotted line).