Dissecting the collinear structure of quark splitting at NNLL

Abstract

We explore the collinear limit of final-state quark splittings at order ${\alpha }_s^2$. While at general NLL level, this limit is described simply by a product of leading-order $1\to 2$ DGLAP splitting functions, at the NNLL level we need to consider $1\to 3$ splitting functions. Here, by performing suitable integrals of the triple-collinear splitting functions, we demonstrate how one may extract ${\mathcal{B}}_2^q(z)$, a differential version of the coefficient $B_2^q$ that enters the quark form factor at NNLL and governs the intensity of collinear radiation from a quark. The variable $z$ corresponds to the quark energy fraction after an initial $1\to 2$ splitting, and our results yield effective higher-order splitting functions, which may be considered as a step towards the construction of NNLL parton showers. Further, while in the limit $z\to 1$ we recover the standard soft limit results involving the CMW coupling with scale $k_t$, the $z$ dependence we obtain also motivates the extension of the notion of a physical coupling beyond the soft limit.

33 pages, 5 figures. Some typographical errors are corrected. Matches published version

References in corpus (15)

• An Introduction to PYTHIA 8.2
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Resummation of heavy jet mass and comparison to LEP data
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• Transverse-momentum resummation for heavy-quark hadroproduction
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Transverse-momentum resummation for top-quark pairs at hadron colliders
• Energy-energy correlation in electron-positron annihilation at NNLL+NNLO accuracy
• Spin correlations in final-state parton showers and jet observables
• QCD predictions for new variables to study dilepton transverse momenta at hadron colliders
• Automated NNLL+NLO Resummation for Jet-Veto Cross Sections
• Investigating top tagging with Y${}_{\text{m}}$-Splitter and N-subjettiness

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