Benedikt Biedermann

NGluon: A package to calculate one-loop multi-gluon amplitudes

Abstract We present a computer library for the numerical evaluation of colour-ordered n -gluon amplitudes at one-loop order in pure Yang–Mills theory. The library uses the recently developed technique of generalised unitarity . Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments. Program summary Program title: NGluon Catalogue identifier: AEIZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIZ_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU Public License No. of lines in distributed program, including test data, etc.: 30 677 No. of bytes in distributed program, including test data, etc.: 334 896 Distribution format: tar.gz Programming language: C++ Computer: Any computer platform supported by the GNU compiler suite. Operating system: No specific requirements – tested on Scientific Linux 5.2. RAM: Depending on the complexity, for realistic applications like 10 gluon production in double precision below 10 MB. Classification: 11.5 External routines: QCDLoop ( http://qcdloop.fnal.gov/ ), qd ( http://crd.lbl.gov/~dhbailey/mpdist/ ) Nature of problem: Evaluation of next-to-leading order corrections for gluon scattering amplitudes in pure gauge theory. Solution method: Purely numerical approach based on tree amplitudes obtained via Berends–Giele recursion combined with unitarity method. Restrictions: Running in double precision the number of gluons should not exceed 14. Running time: Depending on the number of external gluons between less than a millisecond (4 gluons) up to a 1 s (14 gluons) per phase space point.

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.

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.

Electroweak Corrections to pp→μ^{+}μ^{-}e^{+}e^{-}+X at the LHC: A Higgs Boson Background Study.

The first complete calculation of the next-to-leading-order electroweak corrections to four-lepton production at the LHC is presented, where all off-shell effects of intermediate Z bosons and photons are taken into account. Focusing on the mixed final state μ^{+}μ^{-}e^{+}e^{-}, we study differential cross sections that are particularly interesting for Higgs boson analyses. The electroweak corrections are divided into photonic and purely weak corrections. The former exhibit patterns familiar from similar W- or Z-boson production processes with very large radiative tails near resonances and kinematical shoulders. The weak corrections are of the generic size of 5% and show interesting variations, in particular, a sign change between the regions of resonant Z-pair production and the Higgs signal.

Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC

A bstractWe present a state-of-the-art calculation of the next-to-leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into μ+μ−e+e− or μ+μ−μ+μ− final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of ∼ −5% and reach several −10% in the high-energy tails of distributions. Comparing the results for μ+μ−e+e− and μ+μ−μ+μ− final states, we find significant differences mainly in distributions that are sensitive to the μ+μ− pairing in the μ+μ−μ+μ− final state. Differences between μ+μ−e+e− and μ+μ−μ+μ− channels due to interferences of equal-flavour leptons in the final state can reach up to 10% in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.

Next-to-leading-order electroweak corrections to pp → W + W − → 4 leptons at the LHC

A bstractWe present results of the first calculation of next-to-leading-order electroweak corrections to W-boson pair production at the LHC that fully takes into account leptonic W-boson decays and off-shell effects. Employing realistic event selections, we discuss the corrections in situations that are typical for the study of W-boson pairs as a signal process or of Higgs-boson decays H → WW∗, to which W-boson pair production represents an irreducible background. In particular, we compare the full off-shell results, obtained treating the W-boson resonances in the complex-mass scheme, to previous results in the so-called double-pole approximation, which is based on an expansion of the loop amplitudes about the W resonance poles. At small and intermediate scales, i.e. in particular in angular and rapidity distributions, the two approaches show the expected agreement at the level of fractions of a percent, but larger differences appear in the TeV range. For transverse-momentum distributions, the differences can even exceed the 10% level in the TeV range where “background diagrams” with one instead of two resonant W bosons gain in importance because of recoil effects.

Large Electroweak Corrections to Vector-Boson Scattering at the Large Hadron Collider

For the first time full next-to-leading-order electroweak corrections to off-shell vector-boson scattering are presented. The computation features the complete matrix elements, including all nonresonant and off-shell contributions, to the electroweak process pp→μ^{+}ν_{μ}e^{+}ν_{e}jj and is fully differential. We find surprisingly large corrections, reaching -16% for the fiducial cross section, as an intrinsic feature of the vector-boson-scattering processes. We elucidate the origin of these large electroweak corrections upon using the double-pole approximation and the effective vector-boson approximation along with leading-logarithmic corrections.

Complete NLO corrections to W+W+ scattering and its irreducible background at the LHC

A bstractThe process pp → μ+νμe+νejj receives several contributions of different orders in the strong and electroweak coupling constants. Using appropriate event selections, this process is dominated by vector-boson scattering (VBS) and has recently been measured at the LHC. It is thus of prime importance to estimate precisely each contribution. In this article we compute for the first time the full NLO QCD and electroweak corrections to VBS and its irreducible background processes with realistic experimental cuts. We do not rely on approximations but use complete amplitudes involving two different orders at tree level and three different orders at one-loop level. Since we take into account all interferences, at NLO level the corrections to the VBS process and to the QCD-induced irreducible background process contribute at the same orders. Hence the two processes cannot be unambiguously distinguished, and all contributions to the μ+νμe+νejj final state should be preferably measured together.