Two- and Three-Loop Data for Groomed Jet Mass

Abstract

We discuss the status of resummation of large logarithmic contributions to groomed event shapes of hadronic final states in electron-positron annihilation. We identify the missing ingredients needed for next-to-next-to-next-to-leading logarithmic (NNNLL) resummation of the mMDT groomed jet mass in $e^{+}{e}^{-}$ collisions: the low-scale collinear-soft constants at two-loop accuracy, $c_{S_c}^{(2)}$, and the three-loop non-cusp anomalous dimension of the global soft function, ${\gamma }_S^{(2)}$. We present a method for extracting those constants using fixed-order codes: the EVENT2 program to obtain the color coefficients of $c_{S_c}^{(2)}$, and MCCSM for extracting ${\gamma }_S^{(2)}$. We present all necessary formulae for resummation of the mMDT groomed heavy jet mass distribution at NNNLL accuracy.

Comments: 21 pages + appendices, preprint format, 5 figures; v2: added new reference to SoftServe results; v3: minor corrections, PRD version