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.
Highlights
At the Large Hadron Collider (LHC), quantum chromodynamics (QCD) has been studied at an unprecedented precision in both experiment and theory
Where we fix the number of active quarks to nf 1⁄4 5. These results enable resummation to nextto-next-to-next-to-leading logarithmic (NNNLL) accuracy for jet substructure observables for the first time, which we present in a companion paper [53]
Using numerical predictions at NLO and Next-to-next-to-leading fixed order (NNLO) accuracies, we were able to extract two-loop constants and threeloop anomalous dimensions for the mass mass drop tagger (mMDT) groomed mass factorization theorem in eþe− → hadrons events
Summary
At the Large Hadron Collider (LHC), quantum chromodynamics (QCD) has been studied at an unprecedented precision in both experiment and theory. × 1⁄2JðτRÞ ⊗ ScðτR; zcutÞ; ð1Þ where σ0 is the leading-order eþe− → qqcross section, zcut is a parameter of the mMDT/soft drop groomer, and τL, τR are the left- and right-hemisphere masses, respectively Extending this factorization theorem beyond NNLL requires the two-loop constants for each of the functions on the right, as well as their three-loop anomalous dimensions. These results enable resummation to NNNLL accuracy for jet substructure observables for the first time, which we present in a companion paper [53]. Using the mMDT constraint, the value of the hemisphere mass for such an emission is ρ ≳ 2zcut; ð16Þ and mMDT strongly affects the cross section for values of ρ smaller than this
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