Abstract
We present results for SCET and bHQET matching coefficients and jet functions in the large-β0 limit. Our computations exactly predict all terms of the form {alpha}_s^{n+1}{n}_f^n for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to mathcal{O}left({alpha}_s^4right) . 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 αs 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 Hm 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-β0 approximation (MSR, RS and two versions of the jet mass), work out their μ- 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.
Highlights
In the LHC era, the scientific interest in jet physics has experienced a significant boost
One can show within factorization theorems derived the context of Soft-Collinear Effective Theory (SCET) [2,3,4,5,6] that the soft function can be re-factorized in a partonic part and a non-perturbative shape function, see refs. [10, 12, 13], whose first moment encompasses in a single parameter the leading hadronization effects in the tail of the distribution
In this article we investigate non-perturbative corrections coming from the remaining pieces of the SCET and a boosted version of Heavy Quark Effective Theory [26,27,28,29,30] factorization theorems, which are associated to different physical scales
Summary
In the LHC era, the scientific interest in jet physics has experienced a significant boost. One can investigate power corrections through so-called renormalons, that is, the asymptotic behavior of the associated perturbative series This approach was applied to the soft function appearing in the factorized cross section for the doubly differential hemisphere mass distribution (which can be projected onto thrust and heavy jet mass in a straightforward manner) in ref. [18, 21] only the asymptotic behavior of the soft function was computed, which does not exactly reproduce the terms leading in 1/β0 at low orders) To carry out these computations we generalize the procedure presented in ref. The closed form for the renormalized series can be written as the sum of a μ-independent inverse-Borel integral, where all ambiguities are confined, plus other μdependent terms with finite convergence radius The former depends explicitly on ΛQCD, the non-perturbative QCD scale.
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