Soft Resummation Research Articles

Heavy quark fragmentation in e+e− collisions to NNLO+NNLL accuracy in perturbative QCD

Fragmentation of heavy quarks into heavy-flavoured hadrons receives both perturbative and non-perturbative contributions. We consider perturbative QCD corrections to heavy quark production in e+e− collisions to next-to-next-to-leading order accuracy in QCD with next-to-next-to-leading-logarithmic resummation of quasi-collinear and soft emissions. We study multiple matching schemes, and multiple regularisations of the soft resummation, and observe a significant dependence of the perturbative results on these ingredients, suggesting that NNLO+NNLL perturbative accuracy may not lead to real gains unless the interface with non-perturbative physics is properly analysed. We confirm previous evidence that D*+ experimental data from CLEO/BELLE and from LEP are not reconcilable with perturbative predictions employing standard DGLAP evolution. We extract non-perturbative contributions from e+e− experimental data for both D and B meson fragmentation. Such contributions can be used to predict heavy-quark fragmentation in other processes, e.g. DIS and proton-proton collisions.

Precision measurements of Standard Model parameters and Review of Drell-Yan and vector boson plus jets measurements with the ATLAS detector

The inclusive productions of the W and the on- or off-shell Z/γ * bosons are standard candles at hadron colliders, while the productions of light and heavy-flavour jets in association with a W or a Z boson are important processes to study quantum-chromodynamics (QCD) in multi-scale environments. The measurements of their production cross-sections integrated and differential in several variables have been measured at 7 and 8 TeV centre-of-mass energies and are compared to high-order QCD calculations and Monte Carlo simulations. These measurements have an impact on our knowledge of the parton densities of the proton, and test soft resummation effects and hard emissions for small and large momentum transfers and in multi-scale processes. Precision measurements of fundamental Standard Model parameters in Drell-Yan final states are also performed to describe the angular distributions of the decay lepton.Run-1 studies carried out by the ATLAS Collaboration are re-viewed and first LHC Run-2 results are included.

Erratum: Phenomenology of QCD threshold resummation for gluino pair production at NNLL

We examine the impact of threshold resummation for the inclusive hadronic production cross section of gluino pairs at next-to-next-to-leading-logarithmic accuracy, compared to the exact next-to-leading-order cross section and the next-to-next-to-leading-order approximation. Here, we apply formulas derived recently in the classical Mellin-space formalism. Moreover, we give the analytic input for the alternative momentum-space formalism and discuss the crucial points of the numeric implementation. We find that soft resummation keeps the hadronic cross section close to the fixed next-to-leading-order result.

The scale of soft resummation in SCET vs perturbative QCD

We summarize and extend previous results on the comparison of threshold resummation, performed using soft-collinear effective theory (SCET) in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of the SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale μs which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.

Phenomenology of QCD threshold resummation for gluino pair production at NNLL

Abstract We examine the impact of threshold resummation for the inclusive hadronic production cross section of gluino pairs at next-to-next-to-leading-logarithmic accuracy, compared to the exact next-to-leading-order cross section and the next-to-next-to-leading-order approximation. Here, we apply formulas derived recently in the classical Mellin-space formalism. Moreover, we give the analytic input for the alternative momentum-space formalism and discuss the crucial points of the numeric implementation. We find that soft resummation keeps the hadronic cross section close to the fixed next-to-leading-order result.

On Sudakov and soft resummations in QCD

In this article we extract soft distribution functions for Drell–Yan and Higgs production processes using mass factorisation theorem and the perturbative results that are known upto three loop level. We find that they are maximally non-Abelian. We show that these functions satisfy Sudakov type integro-differential equations. The formal solutions to such equations and also to the mass factorisation kernel upto four loop level are presented. Using the soft distribution function extracted from Drell–Yan production, we show how the soft plus virtual cross section for the Higgs production can be obtained. We determine the threshold resummation exponents upto three loop using the soft distribution function.

Borel resummation of soft gluon radiation and higher twists

We show that the well-known divergence of the perturbative expansion of resummed results for processes such as deep-inelastic scattering and Drell–Yan in the soft limit can be treated by Borel resummation. The divergence in the Borel inversion can be removed by the inclusion of suitable higher twist terms. This provides us with an alternative to the standard ‘minimal prescription’ for the asymptotic summation of the perturbative expansion, and it gives us some handle on the role of higher twist corrections in the soft resummation region.

Fragmentation in [formula omitted] processes

I study bottom quark fragmentation in the Standard Model Higgs decay H → b b ¯ , within the framework of perturbative fragmentation functions. I resum large collinear logarithms ln ( m H 2 / m b 2 ) in the next-to-leading logarithmic (NLL) approximation, using the DGLAP evolution equations. Soft contributions to the MS ¯ coefficient function and to the initial condition of the perturbative fragmentation function are resummed to NLL accuracy as well. The implementation of collinear and soft resummation has a relevant impact on the b energy spectrum, which exhibits a milder dependence on factorization and renormalization scales and on the Higgs mass. I present some predictions on the energy distribution of b-flavoured hadrons in Higgs decay, making use of data from LEP and SLD experiments to fit a few hadronization models. I also compare the phenomenological results yielded by a few processes recently provided with NLL collinear and soft resummations.

Soft-gluon resummation for heavy quark production in charged-current Deep Inelastic Scattering

We study soft-gluon radiation for heavy quark production in charged-current Deep Inelastic Scattering processes. We resum large- x contributions to the MS coefficient function to next-to-leading logarithmic accuracy and present results for charm quark structure functions for several values of the ratio m c / Q. The effect of soft resummation turns out to be visible, especially at small Q 2, and the results exhibit very little dependence on factorization and renormalization scales. The impact of our calculation on structure function measurements at NuTeV and HERA experiments is discussed.

Soft resummation of quark anomalous dimensions and coefficient functions in factorization

The asymptotic behaviour at large N of the MS quark anomalous dimensions is derived to all orders by assuming the all order exponentiation of soft logarithms in the quark initiated bare cross sections for deep inelastic or Drell–Yan processes, and the standard prescription for MS renormalization and factorization. The result is then used to write the MS quark coefficient functions in a form in which all terms of O(lnmN) are resummed, and illustrated by explicit LL and NLL calculations.

Angular distributions of Drell Yan pairs in the leading twist approximation

We compute the angular decay distribution of lepton pairs, integrated over the transverse momentum within the soft gluons resummation procedure. The deviations from the naive Drell-Yan model are found very small. Therefore, the phase space boundary region should provide a clear signal for higher twist contributions.