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Register a new userTop Jets in the Peak Region: Factorization Analysis with NLL Resummation
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We consider top-quarks produced at large energy in e+e- collisions, and address the question of what top-mass can be measured from reconstruction. The production process is characterized by well separated scales: the center-of-mass energy, Q, the top mass, m, the top decay width, Gamma_t, and also LambdaQCD; scales which can be disentangled with effective theory methods. In particular we show how the mass measurement depends on the way in which soft radiation is treated, and that this can shift the mass peak by an amount of order Q LambdaQCD/m. We sum large logs for Q >> m >> Gamma_t > LambdaQCD and demonstrate that the renormalization group ties together the jet and soft interactions below the scale m. Necessary conditions for the invariant mass spectrum to be protected from large logs are formulated. Results for the cross-section are presented at next-to-leading order with next-to-leading-log resummation, for invariant masses in the peak region and the tail region. Using our results we also predict the thrust distribution for massive quark jets at NLL order for large thrust. We demonstrate that soft radiation can be precisely controlled using data on massless jet production, and that in principle, a short distance mass parameter can be measured using jets with precision better than LambdaQCD.
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We present results for the 2-jettiness differential distribution for boosted top quark pairs produced in $e^+e^-$ collisions in the peak region accounting for QCD large-logarithm resummation at next-to-next-to-next-to-leading logarithmic (N$^3$LL) order and fixed-order corrections to matrix elements at next-to-next-to-leading order (NNLO) calculated in the framework of soft-collinear effective theory and boosted heavy quark effective theory. Electroweak and finite-width effects are included at leading order. We study the perturbative convergence of the cross section in the pole and MSR mass schemes, with and without soft gap subtractions. We find that there is a partial cancellation between the pole mass and soft function renormalons. When renormalon subtractions concerning the top mass and the soft function are implemented, the perturbative uncertainties are, however, systematically smaller and an improvement in the stability of the peak position is observed. We find that the top MSR mass may be determined with perturbative uncertainties well below $100$,MeV from the peak position of the 2-jettiness distribution. This result has important applications for Monte Carlo top quark mass calibrations.
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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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