A Precise Determination of $\alpha_s$ from the Heavy Jet Mass Distribution

Abstract

A global fit for $\alpha_s(m_Z)$ is performed on available $e^+e^-$ data for the heavy jet mass distribution. The state-of-the-art theory prediction includes $\mathcal{O}(\alpha_s^3)$ fixed-order results, N$^3$LL$^\prime$ dijet resummation, N$^2$LL Sudakov shoulder resummation, and a first-principles treatment of power corrections in the dijet region. Theoretical correlations are incorporated through a flat random-scan covariance matrix. The global fit results in $0.1148^{+ 0.0015}_{-0.0022}$, compatible with similar determinations from thrust and $C$-parameter. Dijet resummation is essential for a robust fit, as it engenders insensitivity to the fit-range lower cutoff; without resummation the fit-range sensitivity is overwhelming. In addition, we find evidence for a negative power correction in the trijet region if and only if Sudakov shoulder resummation is included.