The inclusive decay B --> X_u l nu is of much interest because of its potential to constrain the CKM element |V_ub|. Experimental cuts required to suppress charm background restrict measurements of this decay to the shape-function region, where the hadronic final state carries a large energy but only a moderate invariant mass. In this kinematic region, the differential decay distributions satisfy a factorization formula of the form $H \cdot J \otimes S$, where S is the non-perturbative shape function, and the object $H \cdot J$ is a perturbatively calculable hard-scattering kernel. In this paper we present the calculation of the hard function H at next-to-next-to-leading order (NNLO) in perturbation theory. Combined with the known NNLO result for the jet function J, this completes the perturbative part of the NNLO calculation for this process.
We present the next-to-next-to-leading order (NNLO) QCD corrections to dijet production in the purely gluonic channel retaining the full dependence on the number of colours. The sub-leading colour contribution in this channel first appears at NNLO and, as expected, increases the NNLO correction by around 10% and exhibits a pT dependence, rising from 8% at low pT to 15% at high pT . The present calculation demonstrates the utility of the antenna subtraction method for computing the full colour NNLO corrections to dijet production at the Large Hadron Collider.
This talk expands on recently published results for the factorising next-to-next-to-leading order (NNLO) QCD corrections to Higgs boson production in the vector boson fusion (VBF) channel. The calculation is fully differential in the kinematics of the Higgs boson and the final state jets and is implemented in the NNLOJET framework for computing higher-order QCD corrections. We find the NNLO corrections to be limited in magnitude to about $\pm 5$\% with a weak kinematical dependence in the transverse momenta and rapidity separation of the two tagging jets.
We discuss interplay between the high-twist (HT) terms in the operator-product expansion and the next-to-next-to-leading-order (NNLO) QCD corrections to the deep-inelastic-scattering structure functions in analysis of the high-precision data for charged leptons. Under account of the NNLO corrections the observed HT terms change within their experimental errors only and do not vanish in the NNLO.
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.
We present results for the $Z$-boson and $W$-boson transverse momentum ($p_T$) distributions for large $p_T$ at LHC and Tevatron energies. We calculate complete next-to-leading-order (NLO) QCD corrections as well as soft-gluon corrections at next-to-next-to-leading-order (NNLO) to the differential cross section. The NNLO soft-gluon contributions are derived from next-to-next-to-leading-logarithm (NNLL) resummation at two loops. We find enhancements of the $p_T$ distributions and reductions of the scale dependence when the NNLO corrections are included.
For processes involving structure functions and/or fragmentation functions, arguments that there is a part that dominates the NLO corrections are briefly reviewed. The arguments are tested against more recent NLO and in particular NNLO calculations.
We present partial results on NLO and NNLO QCD, and NLO electroweak corrections to polarized top quark decays. In parallel we derive positivity bounds for the polarized structure functions in polarized top quark decays and check them against the perturbative corrections to the structure functions.
We give an overview of our calculation of the next-to-next-to-leading order (NNLO) QCD corrections to W + jet production in hadronic collisions. Phenomenological results for multiple differential distributions are compared to CMS data for 8 TeV proton-proton collisions. We further discuss the application of the calculation to the transverse momentum spectrum of inclusive W boson production, again accompanied by a comparison to 8 TeV CMS data. In both cases, the inclusion of NNLO QCD effects give an improved agreement between theory and data with considerably reduced scale uncertainties with re…
I present a master formula for the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections for any process in hadron-hadron and lepton-hadron colliders. The formula is derived from a unified threshold resummation formalism. Applications to various QCD processes are discussed.
We calculate the cross section of the process e^+e^- \to t\bar t near threshold by resumming Coulomb-like terms with next-to-next-to-leading (NNLO) accuracy. The nonrelativistic Green function formalism and the method of ``direct matching'' are used. The NNLO correction turns out to be large, of the same size as the NLO correction. It changes the position and the normalization of the 1S-peak. The obtained results are compared with results existing in the literature.
We present a fully-differential calculation of the NNLO QCD corrections to the t-channel mechanism for producing single top quarks at the LHC. We work in the structure function approximation, computing QCD corrections to the light- and heavy-quark lines separately and neglecting the dynamical cross-talk between the two. The neglected contribution, which appears at NNLO for the first time, is color-suppressed and is expected to be sub-dominant. Within this approximation, we find that, for the total cross section, NNLO QCD corrections are in the few percent range and, therefore, are comparable t…
We report on the status of the perturbative calculation in the QCD factorization framework to charmless hadronic B meson decays and present a compilation of available NNLO results.
The recent evaluation of the parametrically dominant next-to-next-to-leading order corrections to four-fermion production near the W-pair threshold in the framework of unstable-particle effective theory is briefly summarized.
In this contribution we consider NNLO real radiation corrections to the total cross section for Higgs boson pair production in gluon fusion. Special emphasis is put on the cross check of the asymptotic expansion in the inverse top quark mass.
For the GLS and Bjorken DIS sum rules we compare fixed-order NNLO perturbative QCD estimates, and all-orders resummed estimates, with the available data, in order to assess the reliability of fixed-order perturbation theory at rather small Q^2 values. Fits are also performed for non-perturbative power corrections using a recently proposed model.
The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. To aid the effort, the theoretical formulation for the fixed order NNLO QED corrections are described and the virtual NNLO leptonic corrections are calculated with complete mass effects.
We report work on the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculation for event shape variables in electron-positron annihilation. The correction of the combined NLLA+NNLO computation in the three-jet region, relevant for precision phenomenology, is small compared with pure NNLO or NLLA+NLO.
The calculation of partial decay rates in B --> X_u l nu decays at next-to-next-to-leading order (NNLO) in alpha_s and to leading order in 1/m_b is described. New results for the hard function are combined with known results for the jet function and shape-function moments in a numerical analysis which explores the impact of the NNLO corrections on partial decay rates and the determination of |V_{ub}|.
Recent developements in the calculation of the NNLO QCD corrections to the charm quark mass dependent matrix elements in B -> X_s gamma are reported. Special emphasis is put on the new results of the virtual O(alpha_s^2) fermionic contribution to these matrix elements [1].
We report first results on the calculation of NNLO corrections to event shape distributions in electron-positron annhilation. The corrections are sizeable for all variables, however their magnitude is substantially different for different observables. We observe that inclusion of the NNLO corrections yields a considerably better agreement between theory and experimental data both in shape and normalisation of the event shape distributions.
In this talk we present the calculation of next-to-next-to-leading order (NNLO) QCD corrections to dijet production and related observables at hadron colliders in the purely gluonic channel. Results for this channel are obtained keeping all orders of $N_C$ in the colour expansion. We show that the NNLO correction significantly reduces the scale uncertainty compared to next-to-leading order (NLO). We present the NNLO double-differential single jet inclusive cross section where jets are reconstructed using the anti-$k_T$ jet algorithm and show the dependence on the jet resolution parameter $R$.
We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors $N_l$. While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles ca…
In this talk we report work on the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculations for event shape distributions in electron-positron annihilation. Furthermore we present preliminary results on the determination of the strong coupling constant obtained using NLLA+NNLO predictions and ALEPH data.
The paper discusses the two-loop (NNLO) electroweak radiative corrections to the parity-violating Moller scattering asymmetry induced by insertions to boxes of electron and neutrino mass operators (fermion self-energies), vertex functions and boson self-energies. The results will be relevant to the ultra-precise 11 GeV MOLLER experiment planned at the Jefferson Laboratory, which will measure the weak charge of the electron and search for new physics. The numerical estimations for the NNLO contribution to the cross section asymmetry are presented.
We report on several methodologically different NNLO determinations of the strong coupling constant from event shapes and related observables in e+e- annihilation. The event shape distributions are analyzed within a combined framework of NNLO and NNLA resummation. We also investigate the role of hadronisation corrections, using both Monte Carlo generator predictions and analytic models to parametrise non-perturbative power corrections.
Precision studies of QCD at electron-positron colliders are based on measurements of event shapes and jet rates. To match the high experimental accuracy, theoretical predictions to next-to-next-to-leading order (NNLO) in QCD are needed for a reliable interpretation of the data. We report the first calculation of NNLO corrections O(alpha_s^3) to three-jet production and related event shapes, and discuss their phenomenological impact.
This article gives the perturbative NNLO results for the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable. In addition the NNLO results for the jet rates corresponding to the Durham, Geneva, Jade-E0 and Cambridge jet algorithms are presented.
We determine the NNLO electroweak correction to the $e^+ e^-\to b\bar{b}W^+W^- X$ production cross section near the top-pair production threshold. The calculation includes non-resonant production of the final state as well as electroweak effects in resonant top anti-top pair production with non-relativistic resummation, and elevates the theoretical prediction to NNNLO QCD plus NNLO electroweak accuracy. We then study the impact of the new contributions on the top-pair threshold scan at a future lepton collider.
We review recent progress in the perturbative calculations for semileptonic and hadronic B meson decays with an emphasis on the phenomenological implications of the next-to-next-to-leading order (NNLO) corrections. Specifically, we consider CP-averaged branching ratios of tree-dominated B -> pi pi/pi rho/rho rho decays and the inclusive determination of |V_ub| from B -> X_u l nu.
We discuss the next-to-next-to-leading order (NNLO) corrections to the total cross section for (pseudo-) scalar Higgs boson production. The computation is carried out in the effective Lagrangian approach which emerges from the standard model by taking the limit $m_t \to \infty$ where $m_t$ denotes the mass of the top quark.
We present a preliminary strategy for modeling multidimensional distributions through neural networks. We study the efficiency of the proposed strategy by considering as input data the two-dimensional next-to-next leading order (NNLO) jet k-factors distribution for the ATLAS 7 TeV 2011 data. We then validate the neural network model in terms of interpolation and prediction quality by comparing its results to alternative models.
This article gives the perturbative NNLO results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable.
We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced a…
I present applications of a master formula for next-to-next-to-leading order soft and virtual QCD corrections to various electroweak, Higgs, and supersymmetric processes. They include Drell-Yan and charged Higgs production, single-top production in flavor-changing neutral-current processes, and squark and gluino production.
We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B -> X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO co…
The strong coupling constant is a fundamental parameter of nature. It can be extracted from experiments measuring three-jet events in electron-positron annihilation. For this extraction precise theoretical calculations for jet rates and event shapes are needed. In this talk I will discuss the NNLO calculation for these observables.
We compute the next-to-next-to-leading order (NNLO) QCD corrections to the six most important event shape variables related to three-particle final states in electron-positron annihilation. The corrections are sizeable for all variables, however their magnitude is substantially different for different observables. We observe that the NNLO corrections yield a considerably better agreement between theory and experimental data both in shape and normalisation of the event shape distributions. The renormalisation scale dependence of the theoretical prediction is substantially reduced compared to th…
We describe the status of the calculation of the branching ratio for the decay \bar B^0 --> D^+ pi^- to NNLO in QCD factorization. Here, we present the result for the colour-singlet hard-scattering kernel. The calculation has been performed using multi-loop techniques like Laporta's reduction to master integrals, and Mellin-Barnes representations and differential equations for evaluating the latter.
We study the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculation for event shape distributions in electron-positron annihilation. The resulting theoretical predictions combine all precision QCD knowledge on the distributions, and are theoretically reliable over an extended kinematical range. Compared to previously available matched NLLA+NLO and fixed order NNLO results, we observe that the effects of the combined NLLA+NNLO are small in the three-jet region, relevant for precision physics.
We compute the NNLO QCD corrections for the hadroproduction of a pair of off-shell photons in the limit of a large number of quark flavors. We perform a reduction of the two-loop amplitude to master integrals and calculate the latter analytically as a Laurent series in the dimensional regulator using modern integration methods. Real radiation corrections are evaluated numerically with a direct subtraction of infrared limits which we cast in a simple factorized form. The results presented here constitute a gauge invariant part of the full NNLO corrections but are not necessarily dominant. We vi…
We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B -> pi pi. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quar…
We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic (NNLL) accuracy, including the two-loop hard factor. The approximate NNLO terms are obtained by expansion of the resummed expression. They include all terms in Mellin space that are logarithmically enhanced at threshold, or that are constant. In terms of the customary SIDIS variables $x$ and $z$ they include all double distributions (that is, "plus" dis…
The contributions of virtual corrections and soft gluon emission to the inclusive Higgs production cross section pp -> H + X are computed at next-to-next-to-leading order in the heavy top quark limit. We show that this part of the total cross section is well behaved in the sense of perturbative convergence, with the NNLO corrections amounting to an enhancement of the NLO cross section by \sim 5% for LHC and 10-20% for the Tevatron. We compare our results with an existing estimate of the full NNLO effects and argue that an analytic evaluation of the hard scattering contributions is needed.
Current status of the NNLO QCD corrections to B -> X_s gamma is reviewed. The calculations include three-loop matching conditions, four-loop anomalous dimensions as well as two- and three-loop on-shell amplitudes. Certain parts of the three-loop matrix elements are found by interpolation in the charm quark mass between the large-beta_0 approximation in the m_c=0 case and the complete result in the m_c >> m_b/2 case.
The top-quark mass can be determined with very high precision from a scan of the total $e^+e^-\to b\bar{b}W^+W^-X$ cross section near the top-pair production threshold. We present the full calculation of electroweak and non-resonant corrections to this process at NNLO. We discuss the size of the new contributions and estimate the theory uncertainty on the top-quark mass in the PS mass scheme.
We consider QCD corrections to Higgs boson production through gluon-gluon fusion in hadron collisions. Using the recently evaluated two-loop amplitude for this process and the corresponding factorization formulae for soft-gluon bremsstrahlung at O(alpha_s^2), we compute the soft and virtual contributions to the NNLO cross section. We also discuss soft-gluon resummation at next-to-next-to-leading logarithmic accuracy. Numerical results for Higgs boson production at the LHC are presented.
We discuss the motivation for making predictions for jet cross sections at next-to-next-to-leading order. We describe the theoretical ingredients needed for such a calculation and briefly review the progress in the field.
We compute the next-to-next-to-leading order (NNLO) QCD corrections to the decay $t(\uparrow) \to X_b +W^+$ of a polarized top quark. The spin-momentum correlation in this quasi two-body decay is described by the polar angle distribution $\mathrm{d}Γ/\mathrm{d}\cosθ_P=\fracΓ{2}(1+P_t\, α_P\, \cosθ_P)$ where $P_t$ is the polarization of the top quark and $α_P$ denotes the asymmetry parameter of the decay. For the latter we find $α^{\mathrm{NNLO}}_P=0.3792\pm 0.0037$.
I report on a numerical program, which can be used to calculate any infrared safe three-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The results are compared to a recent calculation by another group. Numerical differences in three colour factors are discussed and explained.
The transverse momentum spectra of weak gauge bosons and their ratios probe the underlying dynamics and are crucial in testing our understanding of the Standard Model. They are an essential ingredient in precision measurements, such as the $\mathrm{W}$-boson mass extraction. To fully exploit the potential of the LHC data, we compute the second-order (NNLO) QCD corrections to the inclusive-$p_\mathrm{T}^\mathrm{W}$ spectrum as well as to the ratios of spectra for $\mathrm{W}^-/\mathrm{W}^+$ and $\mathrm{Z}/\mathrm{W}$. We find that the inclusion of NNLO QCD corrections considerably improves the…
We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear…
I report on a numerical program, which can be used to calculate any infra-red safe two-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The calculation is based on the subtraction method. The result for the two-jet cross section is compared to the literature.
We present the O(as^4) virtual QCD corrections to unlike-quark and like-quark scattering due to the interference of one-loop amplitudes with one-loop amplitudes. The structure of the infrared divergences agrees with that predicted by Catani. The results are expressed in an analytic form so that the relevant expressions for crossed scattering processes can be obtained in a straightforward manner. The one-loop contributions presented here, together with the interference of tree with two-loop amplitudes given recently, complete the 2 to 2 virtual QCD corrections at NNLO for the massless quark sca…
We report on the calculation of NNLO corrections to the 3-jet cross section and related event shape distributions in electron-positron annihilation. The corrections are sizable for all variables, however the magnitude of the corrections is substantially different for different observables. We observe that inclusion of the NNLO corrections yields a considerably better agreement between theory and experimental data both in shape and normalization of the event shape distributions in the region where the perturbative result is expected to hold. A new extraction of $α_{s}$ using the event shape var…
We present a complete next to next to leading order QCD corrections to the resonant sneutrino and charged slepton production cross sections at hadronic colliders such as the Tevatron and the Large Hadron Collider within the context of $R$-parity violating supersymmetric model. We have demonstrated the role of these corrections in reducing uncertainties resulting from renormalisation and factorisation scales and thereby making our predictions reliable. We have incorporated soft gluon effects at $N^3LO$ level in order to study the stability of our results under perturbation. The NNLO corrections…
We outline the computational details to obtain mixed EW-QCD corrections to on-shell production of a single vector boson at the LHC at two-loop level. We use the method of differential equation to obtain the pure virtual, real-virtual and double-real master integrals. Finally, we obtain the ${\cal O}(αα_s)$ corrections to the total partonic cross section of the process $q \bar{q} \rightarrow Z + X$.
We discuss the result with full mass dependence for the virtual NNLO QCD corrections to the W boson pair production in the quark-anti-quark annihilation channel. We also report on our progress regarding the treatment of the double-real radiative corrections which, along with the virtual-real corrections, are the other two necessary ingredients for a theoretical prediction of the total cross section for W+ W- production to NNLO accuracy.
We provide an exact calculation of next-to-next-to-leading order (NNLO) massive corrections to Bhabha scattering in QED, relevant for precision luminosity monitoring at meson factories. Using realistic reference event selections, exact numerical results for leptonic and hadronic corrections are given and compared with the corresponding approximate predictions of the event generator BabaYaga@NLO. It is shown that the NNLO massive corrections are necessary for luminosity measurements with per mille precision. At the same time they are found to be well accounted for in the generator at an accurac…
