Resummation of Next-to-Leading Nonglobal Logarithms at the LHC.

In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as nonglobal logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading nonglobal logarithms remained a challenge that we solve in this Letter using renormalization group methods in effective field theory. To achieve next-to-leading logarithmic accuracy, we implement the two-loop anomalous dimension governing the resummation of nonglobal logarithms into a large-N_{c} parton shower framework, together with one-loop matching corrections. As a first application, we study the interjet energy flow in e^{+}e^{-} annihilation into two jets. We then present, for the first time, resummed predictions at next-to-leading logarithmic accuracy for a gap-between-jets observable at hadron colliders.

Resummation of Super-Leading Logarithms.

Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called nonglobal 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 2→l scattering processes at hadron colliders and resum them in closed form.

Event-based transverse momentum resummation.

We have developed a framework for automated transverse momentum resummation for arbitrary electroweak final states based on reweighting tree-level events. It is fully differential in the kinematics of the electroweak final states, which facilitates a straightforward analysis of arbitrary observables in the small transverse momentum region. We have implemented the resummation at next-to-next-to-leading logarithmic accuracy and match to next-to-leading fixed-order results using the event generator MadGraph5_aMC@NLO. Results for Z and W boson production with leptonic decay as well as WZ production are presented. We compare to experimental measurements for the transverse momentum and the angular observable ϕ ∗ .

Effective Field Theory for Jet Processes.

Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.

Mirror movements in unilateral spastic cerebral palsy: Specific negative impact on bimanual activities of daily living.

AIM: Mirror movements are involuntary movements of the other hand during voluntary unimanual movements. Some, but not all children with unilateral spastic cerebral palsy (USCP) show this phenomenon. In this observational study, we investigated whether these mirror movements have a specific negative impact on bimanual activities of daily living. METHODS: Eighteen children (six girls; age range, 6-16 years; mean age, 12 years 1 month; SD, 3 years 3 month) with USCP, nine with and nine without mirror movements, underwent the Jebsen Taylor Hand Function Test (unimanual capacity) and the Assisting Hand Assessment (bimanual performance). In addition, we measured the time the participants needed for the completion of five activities we had identified as particularly difficult for children with mirror movements. RESULTS: Multivariate analysis demonstrated that mirror movements indeed have a specific negative impact on bimanual performance (Assisting Hand Assessment) and on the time needed for the completion of these five particularly difficult activities. This effect was independent from unimanual capacity. CONCLUSION: Functional therapies in children with USCP and mirror movements should address this phenomenon.

Automated NNLL [Formula: see text] NLO resummation for jet-veto cross sections.

In electroweak-boson production processes with a jet veto, higher-order corrections are enhanced by logarithms of the veto scale over the invariant mass of the boson system. In this paper, we resum these Sudakov logarithms at next-to-next-to-leading logarithmic accuracy and match our predictions to next-to-leading-order (NLO) fixed-order results. We perform the calculation in an automated way, for arbitrary electroweak final states and in the presence of kinematic cuts on the leptons produced in the decays of the electroweak bosons. The resummation is based on a factorization theorem for the cross sections into hard functions, which encode the virtual corrections to the boson production process, and beam functions, which describe the low-[Formula: see text] emissions collinear to the beams. The one-loop hard functions for arbitrary processes are calculated using the MadGraph5_aMC@NLO framework, while the beam functions are process independent. We perform the resummation for a variety of processes, in particular for [Formula: see text] pair production followed by leptonic decays of the [Formula: see text] bosons.

Enhanced nonperturbative effects through the collinear anomaly.

We show that nonperturbative effects are logarithmically enhanced for transverse-momentum-dependent observables such as qT spectra of electroweak bosons in hadronic collisions and jet broadening at e+ e- colliders. This enhancement arises from the collinear anomaly, a mechanism characteristic for transverse observables, which induces logarithmic dependence on the hard scale in the product of the soft and collinear matrix elements. Our analysis is based on an operator product expansion and provides, for the first time, a systematic, model-independent way to study nonperturbative effects for this class of observables. For the case of jet broadening, we relate the leading correction to the nonperturbative shift of the thrust distribution.

Resummation for W and Z production at large p{T}.

Soft-collinear effective theory is used to perform threshold resummation for W and Z production at large transverse momentum to next-to-next-to-leading logarithmic accuracy including matching to next-to-leading fixed-order results. The results agree very well with data from the Tevatron, and predictions are made for the high-p{T} spectra at the LHC. While the higher-log terms are of moderate size, their inclusion leads to a substantial reduction of the perturbative uncertainty. With these improvements, the parton distribution function uncertainties now dominate the error on the predicted cross section.

Infrared singularities of scattering amplitudes in perturbative QCD.

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of loops and legs. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory is fully determined by three functions of alpha{s}, which can be extracted from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/;{k} poles for arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.

Analysis of B(B-->Xsgamma) at next-to-next-to-leading order with a cut on photon energy.

By combining a recent estimate of the total B-->X(s)gamma branching fraction at O(alpha(s)2) with a detailed analysis of the effects of a cut E(gamma)>or=1.6 GeV on photon energy, a prediction for the partial B-->Xsgamma branching fraction at next-to-next-to-leading order in renormalization-group improved perturbation theory is obtained, in which contributions from all relevant scales are factorized. The result B(B-->Xsgamma)=(2.98+/-0.26) x 10(-4) is about 1.4 sigma lower than the experimental world average. This opens a window for significant new physics contributions in rare radiative B decays.

Threshold resummation in momentum space from effective field theory.

Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function F2(x,Q2) in the end-point region x-->1 directly in momentum space. An explicit all-order formula is derived, which expresses the short-distance coefficient function C in the convolution F2 = C multiply sign in circle phi q in terms of Wilson coefficients and anomalous dimensions defined in the effective theory. Contributions associated with the physical scales Q2 and Q2(1-x) are separated from nonperturbative hadronic physics in a transparent way. A crucial ingredient to the momentum-space resummation is the exact solution to the integro-differential evolution equation for the jet function, which is derived. The methods developed in this Letter can be applied to many other hard QCD processes.