Towards massless and massive event shapes in the large-${\beta }_0$ limit

Abstract

We present results for SCET and bHQET matching coefficients and jet functions in the large-${\beta }_0$ limit. Our computations exactly predict all terms of the form ${\alpha }_s^{n+1}{n}_f^n$ for any $n\ge 0$, and we find full agreement with the coefficients computed in the full theory up to $\mathcal{O}({\alpha }_s^4)$. We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of ${\alpha }_s$ using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable $u$ we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown $u=1/2$ renormalon in the bHQET hard factor $H_m$ that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-${\beta }_0$ approximation (MSR, RS and two versions of the jet mass), work out their $\mu$- and $R$-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

60 pages + appendices, 19 figures, 6 tables. Added references, fixed typos, matches published version

References in corpus (13)

• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Quark and gluon form factors to three loops
• Jets from Massive Unstable Particles: Top-Mass Determination
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Designing Gapped Soft Functions for Jet Production
• Infrared Renormalization Group Flow for Heavy Quark Masses
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Top Quark Mass Calibration for Monte Carlo Event Generators
• Two-loop Jet-Function and Jet-Mass for Top Quarks
• On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass
• Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N${}^3$LO

Cited by in corpus (6)

• Linear power corrections to $e^{+}{e}^{-}$ shape variables in the three-jet region
• Anomalous Dimensions from Soft Regge Constants
• Mathematical Aspects of the Asymptotic Expansion in Contour Improved Perturbation Theory for Hadronic Tau Decays
• Precision $e^{+}{e}^{-}$ Hemisphere Masses in the Dijet Region with Power Corrections
• Three-loop jet function for boosted heavy quarks
• Renormalon effect of quasi-PDF in gradient flow formalism