Abstract
We analytically compute non-global logarithms at finite Nc fully up to 4 loops and partially at 5 loops, for the hemisphere mass distribution in e+e- to di-jets to leading logarithmic accuracy. Our method of calculation relies solely on integrating the eikonal squared-amplitudes for the emission of soft energy-ordered real-virtual gluons over the appropriate phase space. We show that the series of non-global logarithms in the said distribution exhibits a pattern of exponentiation thus confirming - by means of brute force - previous findings. In the large-Nc limit, our results coincide with those recently reported in literature. A comparison of our proposed exponential form with all-orders numerical solutions is performed and the phenomenological impact of the finite-Nc corrections is discussed.
Highlights
These techniques require in many situations calculations of QCD observables which need special attention in the vicinity of the threshold limit where they become highly contaminated with perturbative large logarithms as well as non-perturbative corrections
For the majority of QCD observables and substructure techniques the only other option available is resorting to numerical simulations which are based on Monte Carlo (MC) integration methods, and which use several approximations, e.g., Herwig [16, 17], Pythia [18, 19] and Sherpa [20]
3This code will be improved, in the near future [39], into a full Mathematica package capable of analytically computing QCD eikonal amplitudes at any loop order. With these squared-amplitudes at hand, we provide in this paper a calculation of NGLs at finite Nc to single logarithmic accuracy for single-hemisphere mass distribution in e+e− → di-jets up to five-loops
Summary
Our aim in this paper is to calculate NGLs at finite Nc to single logarithmic accuracy up to the fifth order in the strong coupling αs (or equivalently up to five-loops). Our calculation is performed using QCD squared-amplitudes for the emission of energy-ordered gluons in the eikonal approximation. The latter is sufficient to capture all single logarithms αsnLn, with L being the large NGL. As stated in the introduction, we do not show explicit formulae for the said squared-amplitudes and refer the reader to our coming paper [39]. For the purpose of this paper, we do not consider the role of any jet algorithm, and postpone such work to future publications
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