Rigorous fit to the peak region of the thrust distribution

Abstract

We continue the work of Abbate et al. in [1], in which a factorization formula for the thrust distribution in electron-positron collisions was developed in the framework of soft-collinear effective theory. We extend the analysis of thrust to the peak region of the distribution, in which a nonperturbative soft function encoding the effects of large-angle soft gluon radiation plays a significant role. We write the soft function as an infinite sum of basis functions and use a truncated version in our calculations, allowing us to fit for the basis coefficients ci with all available thrust data from center-of-mass energies Q = 35 to 207 GeV. To characterize the soft function independently of a particular parameterization, we present fit results for its cumulant moments, denoted [Omega]1, up to i = 4. We compute experimental uncertainties from the fits and theory uncertainties using a random scan in the space of the undetermined parameters of the theory. Our approach significantly improves the fit in the peak region, reducing the minimum X2/d.o.f. value from to 5.29 using the best fit form the tail region without fitting basis functions, to 1.23 using five basis functions. We find [Omega]1 = 0.387 ± (0.003)exp ±(0.026)pert GeV, indicating that the peak region determines [Omega] with considerably more precision than the tail. For the second cumulant moment, we find [Omega]'2 = 0.032 ± (0.002)exp ± (0.011)pert GeV2 . We also estimate the third and fourth cumulant moments, obtaining [Omega]'3 = [3.5 ± (0.7)expt ±(2.3)pert] x 10- GeV 3 and [Omega]'4 = [-0.7 ± (3 .8)exp ± (11.9)pert] X 10-4 GeV4.