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Register a new userThe Sudakov radiator for jet observables and the soft physical coupling
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We present a procedure to calculate the Sudakov radiator for a generic recursive infrared and collinear (rIRC) safe observable in two-scale problems. We give closed formulae for the radiator at next-to-next-to-leading-logarithmic (NNLL) accuracy, which completes the general NNLL resummation for this class of observables in the {tt ARES} method for processes with two emitters at the Born level. As a byproduct, we define a physical coupling in the soft limit, and we provide an explicit expression for its relation to the $overline{rm MS}$ coupling up to ${cal O}(alpha_s^3)$. This physical coupling constitutes one of the ingredients for a NNLL accurate parton shower algorithm. As an application we obtain analytic NNLL results, of which several are new, for all angularities $tau_x$ defined with respect to both the thrust axis and the winner-take-all axis, and for the moments of energy-energy correlation $FC_x$ in $e^+e^-$ annihilation. For the latter observables we find that, for some values of $x$, an accurate prediction of the peak of the differential distribution requires a simultaneous resummation of the logarithmic terms originating from the two-jet limit and at the Sudakov shoulder.
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There has been recent interest in understanding the all loop structure of the subleading power soft and collinear limits, with the goal of achieving a systematic resummation of subleading power infrared logarithms. Most of this work has focused on subleading power corrections to soft gluon emission, whose form is strongly constrained by symmetries. In this paper we initiate a study of the all loop structure of soft fermion emission. In $mathcal{N}=1$ QCD we perform an operator based factorization and resummation of the associated infrared logarithms, and prove that they exponentiate into a Sudakov due to their relation to soft gluon emission. We verify this result through explicit calculation to $mathcal{O}(alpha_s^3)$. We show that in QCD, this simple Sudakov exponentiation is violated by endpoint contributions proportional to $(C_A-C_F)^n$ which contribute at leading logarithmic order. Combining our $mathcal{N}=1$ result and our calculation of the endpoint contributions to $mathcal{O}(alpha_s^3)$, we conjecture a result for the soft quark Sudakov in QCD, a new all orders function first appearing at subleading power, and give evidence for its universality. Our result, which is expressed in terms of combinations of cusp anomalous dimensions in different color representations, takes an intriguingly simple form and also exhibits interesting similarities to results for large-x logarithms in the off diagonal splitting functions.
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $htogammagamma$ decay of the Higgs boson, for which we resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order. We also briefly discuss the related $ggto h$ amplitude.
Studies of fully-reconstructed jets in heavy-ion collisions aim at extracting thermodynamical and transport properties of hot and dense QCD matter. Recently, a plethora of new jet substructure observables have been theoretically and experimentally developed that provide novel precise insights on the modifications of the parton radiation pattern induced by a QCD medium. This report, summarizing the main lines of discussion at the 5th Heavy Ion Jet Workshop and CERN TH institute Novel tools and observables for jet physics in heavy-ion collisions in 2017, presents a first attempt at outlining a strategy for isolating and identifying the relevant physical processes that are responsible for the observed medium-induced jet modifications. These studies combine theory insights, based on the Lund parton splitting map, with sophisticated jet reconstruction techniques, including grooming and background subtraction algorithms.
The Sudakov veto algorithm for generating emission and no-emission probabilities in parton showers is revisited and some reweighting techniques are suggested to improve statistics by oversampling in specific cases.
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