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Register a new userRethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation
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We introduce an infinite set of jet substructure observables, derived as projections of $N$-point energy correlators, that are both convenient for experimental studies and maintain remarkable analytic properties derived from their representations in terms of a finite number of light ray operators. We show that these observables can be computed using tracking or charge information with a simple reweighting by integer moments of non-perturbative track or fragmentation functions. Our results for the projected $N$-point correlators are analytic functions of $N$, allowing us to derive resummed results to next-to-leading logarithmic accuracy for all $N$. We analytically continue our results to non-integer values of $N$ and define a corresponding analytic continuation of the observable, which we term a $ u$-correlator, that can be measured on jets of hadrons at the LHC. This enables observables that probe the leading twist collinear dynamics of jets to be placed into a single analytic family, which we hope will lead to new insights into jet substructure.
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Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in $mathcal{N}=4$ super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In $mathcal{N}=4$, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.
With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2= 4 m^2 (threshold, where m is the quark mass) and q^2=-infty (high-energy) in a systematic way. We exemplify the method for the perturbative vector correlator at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of the Taylor expansion of the vacuum polarization function in terms of the conformal variable omega admit, for large n, an expansion in powers of 1/n (up to logarithms of n) that we can calculate exactly. This large-n expansion has a sign-alternating component given by the logarithms of the OPE, and a fixed-sign component given by the logarithms of the threshold expansion in the external momentum q^2.
We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to $mu_Bapprox 300$ MeV. For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on $N_t=$ 10, 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value $kappa = 0.0149 pm 0.0021$.
In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Pad{e} method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.
We develop an effective field theory (EFT) framework to perform an analytic calculation for energy correlator observables computed on groomed heavy-quark jets. A soft-drop grooming algorithm is applied to a jet initiated by a massive quark to minimize soft contamination effects such as pile-up and multi-parton interactions. We specifically consider the two-particle energy correlator as an initial application of this EFT framework to compute heavy quark jet substructure. We find that there are different regimes for the event shapes, depending on the size of the measured correlator observable, that require the use of different EFT formulations, in which the quark mass and grooming parameters may be relevant or not. We use the EFT to resum large logarithms in the energy correlator observable in terms of the momentum of a reconstructed heavy hadron to NLL$$ accuracy and subsequently match it to a full QCD $mathcal{O}(alpha_s)$ cross section, which we also compute. We compare our predictions to simulations in PYTHIA for $e^+e^-$ collisions. We find a good agreement with partonic simulations, as well as hadronic ones with an appropriate shape function used to describe nonperturbative effects and the heavy quark hadron decay turned off. We also predict the scaling behavior for the leading nonperturbative power correction due to hadronization. Consequently, we can give a prediction for the energy correlator distribution at the level of the reconstructed heavy hadron. This work provides a general framework for the analysis of heavy quark jet substructure observables.
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