Valery Yundin

Numerical evaluation of virtual corrections to multi-jet production in massless QCD

We present a C++ library for the numerical evaluation of one-loop virtual corrections to multi-jet production in massless QCD. The pure gluon primitive amplitudes are evaluated using NGluon (Badger et al., (2011) [62]). A generalized unitarity reduction algorithm is used to construct arbitrary multiplicity fermion–gluon primitive amplitudes. From these basic building blocks the one-loop contribution to the squared matrix element, summed over colour and helicities, is calculated. No approximation in colour is performed. While the primitive amplitudes are given for arbitrary multiplicities, we provide the squared matrix elements only for up to 7 external partons allowing the evaluation of the five jet cross section at next-to-leading order accuracy. The library has been recently successfully applied to four jet production at next-to-leading order in QCD (Badger et al., 2012 [92]).

Update of the Binoth Les Houches Accord for a standard interface between Monte Carlo tools and one-loop programs

We present an update of the Binoth Les Houches Accord (BLHA) to standardise the interface between Monte Carlo programs and codes providing one-loop matrix elements.

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4−2ε dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop ε-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.

NLO QCD corrections to multi-jet production at the LHC with a centre-of-mass energy of s=8 TeV

Abstract We study three and four jet production in hadronic collisions at next-to-leading order accuracy in massless QCD. We cross check results previously obtained by the BlackHat Collaboration for the LHC with a centre-of-mass energy of s = 7 TeV and present new results for the LHC operating at 8 TeV. We find large negative NLO corrections reducing the leading order cross sections by about 40–50%. Furthermore we observe an important reduction of the scale uncertainty. In addition to the cross sections we also present results for differential distributions. The dynamical renormalization/factorization scale used in the calculation leads to a remarkably stable K-factor. The results presented here were obtained with the NJet package (Badger et al., 2012) [1] , a publicly available library for the evaluation of one-loop amplitudes in massless QCD.

Next-to-leading order QCD corrections to five jet production at the LHC

We present theoretical predictions for five jet production in proton-proton collisions at next-to-leading order accuracy in QCD. Inclusive as well as differential observables are studied for collision energies of 7 and 8 TeV. In general the next-to-leading order corrections stabilize the theoretical predictions with respect to scale variations. In case of the inclusive jet cross sections, we compare with experimental data where possible and find reasonable agreement. We observe that the four-to-three and five-to-four jet ratios show better perturbative convergence than the known three-to-two ratio and are promising candidates for future alpha_s measurements. Furthermore, we present a detailed analysis of uncertainties related to parton distribution functions. The full colour virtual matrix elements used in the computation were obtained with the NJet package, a publicly available library for the evaluation of one-loop amplitudes in massless QCD.

Three-loop master integrals for ladder-box diagrams with one massive leg

A bstractThe three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter ϵ = (4 − d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six. The considered integrals enter the next-to-next-to-next-to-leading order virtual corrections to scattering processes like the three-jet production mediated by vector boson decay, V* → jjj, as well as the Higgs plus one-jet production in gluon fusion, pp → Hj.

Next-to-leading order QCD corrections to di-photon production in association with up to three jets at the Large Hadron Collider

A bstractWe present the computation of next-to-leading order (NLO) QCD corrections to di-photon production in association with two or three hard jets in pp collisions at a centre-of-mass energy of 8 TeV. The inclusion of NLO corrections is shown to substantially reduce the theoretical uncertainties estimated from scale variations on total cross section predictions. We study a range of differential distributions relevant for phenomenological studies of photon pair production in association with jets at the LHC. Using an efficient computational set-up we performed a detailed study of uncertainties due to parton distribution functions. The computation of the virtual corrections is performed using new features of the C++ library NJet.

Phenomenological analysis of Higgs boson production through gluon fusion in association with jets

A bstractWe present a detailed phenomenological analysis of the production of a Standard Model Higgs boson in association with up to three jets. We consider the gluon fusion channel using an effective theory in the large top-quark mass limit. Higgs boson production in gluon fusion constitutes an irreducible background to the vector boson fusion (VBF) process; hence the precise knowledge of its characteristics is a prerequisite for any measurement in the VBF channel. The calculation is carried out at next-to-leading order (NLO) in QCD in a fully automated way by combining the two programs GoSam and Sherpa. We present numerical results for a large variety of observables for both standard cuts and VBF selection cuts. We find that for all jet multiplicities the NLO corrections are sizeable. This is particularly true in the presence of kinematic selections enhancing the VBF topology, which are based on vetoing additional jet activity. In this case, precise predictions for the background can be made using our calculation by taking the difference between the inclusive H+2 jets and the inclusive H+3 jets result.

Complete QED NLO contributions to the reaction e + e − → μ + μ − γ and their implementation in the event generator PHOKHARA

A bstractKLOE and Babar have an observed discrepancy of 2% to 5% in the invariant pion pair production cross section. These measurements are based on approximate NLO μ+μ−γ cross section predictions of the Monte Carlo event generator PHOKHARA7.0. In this article, the complete NLO radiative corrections to μ+μ−γ production are calculated and implemented in the Monte Carlo event generator PHOKHARA9.0. Numerical reliability is guaranteed by two independent approaches to the real and the virtual corrections. The novel features include the contribution of pentagon diagrams in the virtual corrections, which form a gauge-invariant set when combined with their box diagram partners. They may contribute to certain distributions at the percent level. Also the real emission was complemented with two-photon final state emission contributions not included in the generator PHOKHARA7.0. We demonstrate that the numerical influence reaches, for realistic charge-averaged experimental setups, not more than 0.1% at KLOE and 0.3% at BaBar energies. As a result, we exclude the approximations in earlier versions of PHOKHARA as origin of the observed experimental discrepancy.

One-Loop Tensor Feynman Integral Reduction with Signed Minors

We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until ve-point functions of rank ve. The numerical C++ package PJFry evaluates tensor coecients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely ecient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are dierences of external momenta. These sums may be evaluated analytically in a systematic way. The nal expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions.