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Register a new userResummation of Super-Leading Logarithms
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Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called non-global logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. This effect was discovered a long time ago, but not much is known about the higher-order behavior of these terms and their process dependence. We derive, for the first time, the all-order structure of these super-leading logarithms for generic $2to l$ scattering processes at hadron colliders and resum them in closed form.
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We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the rapidity identity operators, that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $mathcal{N}$=4 super-Yang-Mills. These logarithms can also be extracted to $mathcal{O}(alpha_s^3)$ from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawsons integral, with an argument related to the cusp anomalous dimension. We call this functional form Dawsons Sudakov. Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the $p_T$ spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.
In a previous paper we reported the discovery of super-leading logarithmic terms in a non-global QCD observable. In this short update we recalculate the first super-leading logarithmic contribution to the gaps between jets cross-section using a colour basis independent notation. This sheds light on the structure and origin of the super-leading terms and allows them to be calculated for gluon scattering processes for the first time.
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $beta$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $gammagamma^ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.
With the approaching start-up of the experiments at LHC, the urgency to quantify systematic uncertainties of the generators, used in the interpretation of the data, is becoming pressing. The PHOTOS Monte Carlo program is often used for the simulationof experimental, selection-sensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. Thanks to its complete phase-space coverage it is possible, with no approximations for any decay channel, to implement the matrix-element. The present paper will be devoted to those parts of the next-to-leading order corrections for Z decays which are normally missing in PHOTOS. The analytical form of the exact and truncated (standard) kernel used in PHOTOS will be explicitly given. The correction, being the ratio of the exact to the approximate kernel, can be activated as an optional contribution to the internal weight of PHOTOS. To calculate the weight, the information on the effective Born-level Z/gamma* couplings and even directions of the incoming beams, is needed. A universal implementation would have made the PHOTOS solution less modular and less convenient for the users. That is why, for the time being, we will keep the correcting weight as an extra option, available for special tests only. We will quantify the numerical effect of the approximation with the help of a multitude of distributions. The numerical size of the effect is in general below 0.1%; however, in some corners of the phase-space (well defined and contributing less than 0.5% to the total rate), it may reach up to about 20% of their relative size.
Differential distributions for heavy quark production depend on the heavy quark mass and other momentum scales, which can yield additional large logarithms and inhibit accurate predictions. Logarithms involving the heavy quark mass can be summed in heavy quark parton distribution functions in the ACOT factorization scheme. A second class of logarithms involving the heavy-quark transverse momentum can be summed using an extension of Collins-Soper-Sterman (CSS) formalism. We perform a systematic summation of logarithms of both types, thereby obtaining an accurate description of heavy-quark differential distributions at all energies. Our method essentially combines the ACOT and CSS approaches. As an example, we present angular distributions for bottom quarks produced in parity-conserving events at large momentum transfers Q at the ep collider HERA.
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