NNLO interpolation grids for jet production at the LHC.

Fast interpolation-grid frameworks facilitate an efficient and flexible evaluation of higher-order predictions for any choice of parton distribution functions or value of the strong coupling α s . They constitute an essential tool for the extraction of parton distribution functions and Standard Model parameters, as well as studies of the dependence of cross sections on the renormalisation and factorisation scales. The APPLfast project provides a generic interface between the parton-level Monte Carlo generator and both the APPLgrid and the fastNLO libraries for the grid interpolation. The extension of the project to include hadron-hadron collider processes at next-to-next-to-leading order in perturbative QCD is presented, together with an application for jet production at the LHC.

Fully Differential Higgs Boson Production to Third Order in QCD.

We present the first fully differential predictions for the production cross section of a Higgs boson via the gluon fusion mechanism at next-to-next-to-next-to-leading order (N^{3}LO) in QCD perturbation theory. Differential distributions are shown for the two-photon final state produced by the decay of the Higgs boson for a realistic set of fiducial cuts. The N^{3}LO corrections exhibit complex features and are in part larger than the inclusive N^{3}LO corrections to the production cross section. Overall, we observe that the inclusion of the N^{3}LO QCD corrections significantly reduces the perturbative uncertainties and leads to a stabilization of the perturbative expansion.

Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of α s from HERA data.

The extension of interpolation-grid frameworks for perturbative QCD calculations at next-to-next-to-leading order (NNLO) is presented for deep inelastic scattering (DIS) processes. A fast and flexible evaluation of higher-order predictions for any a posteriori choice of parton distribution functions (PDFs) or value of the strong coupling constant is essential in iterative fitting procedures to extract PDFs and Standard Model parameters as well as for a detailed study of the scale dependence. The APPLfast project, described here, provides a generic interface between the parton-level Monte Carlo program NNLOjet and both the APPLgrid and fastNLO libraries for the production of interpolation grids at NNLO accuracy. Details of the interface for DIS processes are presented together with the required interpolation grids at NNLO, which are made available. They cover numerous inclusive jet measurements by the H1 and ZEUS experiments at HERA. An extraction of the strong coupling constant is performed as an application of the use of such grids and a best-fit value of α s ( M Z ) = 0.1170 ( 15 ) exp ( 25 ) th is obtained using the HERA inclusive jet cross section data.

Triple Differential Dijet Cross Section at the LHC.

The measurement of the triple-differential dijet production cross section as a function of the average transverse momentum p_{T,avg}, half the rapidity separation y^{*}, and the boost y_{b} of the two leading jets in the event enables a kinematical scan of the underlying parton momentum distributions. We compute for the first time the second-order perturbative QCD corrections to this triple-differential dijet cross section, at leading color in all partonic channels, thereby enabling precision studies with LHC dijet data. A detailed comparison with experimental CMS 8 TeV data is performed, demonstrating how the shape of this differential cross section probes the parton densities in different kinematical ranges.

Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude.

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order.

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2→3 scattering process, thereby opening up a new level of precision collider phenomenology.

Vector boson production in association with a jet at forward rapidities.

Final states with a vector boson and a hadronic jet allow one to infer the Born-level kinematics of the underlying hard scattering process, thereby probing the partonic structure of the colliding protons. At forward rapidities, the parton collisions are highly asymmetric and resolve the parton distributions at very large or very small momentum fractions, where they are less well constrained by other processes. Using theory predictions accurate to next-to-next-to-leading order (NNLO) in QCD for both W ± and Z production in association with a jet at large rapidities at the LHC, we perform a detailed phenomenological analysis of recent LHC measurements. The increased theory precision allows us to clearly identify specific kinematical regions where the description of the data is insufficient. By constructing ratios and asymmetries of these cross sections, we aim to identify possible origins of the deviations, and highlight the potential impact of the data on improved determinations of parton distributions.

Analytic Result for a Two-Loop Five-Particle Amplitude.

We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms.

Large-scale generation and analysis of filamentous fungal DNA barcodes boosts coverage for kingdom fungi and reveals thresholds for fungal species and higher taxon delimitation.

Species identification lies at the heart of biodiversity studies that has in recent years favoured DNA-based approaches. Microbial Biological Resource Centres are a rich source for diverse and high-quality reference materials in microbiology, and yet the strains preserved in these biobanks have been exploited only on a limited scale to generate DNA barcodes. As part of a project funded in the Netherlands to barcode specimens of major national biobanks, sequences of two nuclear ribosomal genetic markers, the Internal Transcribed Spaces and 5.8S gene (ITS) and the D1/D2 domain of the 26S Large Subunit (LSU), were generated as DNA barcode data for ca. 100 000 fungal strains originally assigned to ca. 17 000 species in the CBS fungal biobank maintained at the Westerdijk Fungal Biodiversity Institute, Utrecht. Using more than 24 000 DNA barcode sequences of 12 000 ex-type and manually validated filamentous fungal strains of 7 300 accepted species, the optimal identity thresholds to discriminate filamentous fungal species were predicted as 99.6 % for ITS and 99.8 % for LSU. We showed that 17 % and 18 % of the species could not be discriminated by the ITS and LSU genetic markers, respectively. Among them, ∼8 % were indistinguishable using both genetic markers. ITS has been shown to outperform LSU in filamentous fungal species discrimination with a probability of correct identification of 82 % vs. 77.6 %, and a clustering quality value of 84 % vs. 77.7 %. At higher taxonomic classifications, LSU has been shown to have a better discriminatory power than ITS. With a clustering quality value of 80 %, LSU outperformed ITS in identifying filamentous fungi at the ordinal level. At the generic level, the clustering quality values produced by both genetic markers were low, indicating the necessity for taxonomic revisions at genus level and, likely, for applying more conserved genetic markers or even whole genomes. The taxonomic thresholds predicted for filamentous fungal identification at the genus, family, order and class levels were 94.3 %, 88.5 %, 81.2 % and 80.9 % based on ITS barcodes, and 98.2 %, 96.2 %, 94.7 % and 92.7 % based on LSU barcodes. The DNA barcodes used in this study have been deposited to GenBank and will also be publicly available at the Westerdijk Institute's website as reference sequences for fungal identification, marking an unprecedented data release event in global fungal barcoding efforts to date.

Second-order QCD corrections to event shape distributions in deep inelastic scattering.

We compute the next-to-next-to-leading order (NNLO) QCD corrections to event shape distributions and their mean values in deep inelastic lepton-nucleon scattering. The magnitude and shape of the corrections varies considerably between different variables. The corrections reduce the renormalization and factorization scale uncertainty of the predictions. Using a dispersive model to describe non-perturbative power corrections, we compare the NNLO QCD predictions with data from the H1 and ZEUS experiments. The newly derived corrections improve the theory description of the distributions and of their mean values.

Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD.

Hard processes in diffractive deep-inelastic scattering can be described by a factorisation into parton-level subprocesses and diffractive parton distributions. In this framework, cross sections for inclusive dijet production in diffractive deep-inelastic electron-proton scattering (DIS) are computed to next-to-next-to-leading order (NNLO) QCD accuracy and compared to a comprehensive selection of data. Predictions for the total cross sections, 40 single-differential and four double-differential distributions for six measurements at HERA by the H1 and ZEUS collaborations are calculated. In the studied kinematical range, the NNLO corrections are found to be sizeable and positive. The NNLO predictions typically exceed the data, while the kinematical shape of the data is described better at NNLO than at next-to-leading order (NLO). A significant reduction of the scale uncertainty is achieved in comparison to NLO predictions. Our results use the currently available NLO diffractive parton distributions, and the discrepancy in normalisation highlights the need for a consistent determination of these distributions at NNLO accuracy.

Next-to-Next-to-Leading-Order QCD Corrections to the Transverse Momentum Distribution of Weak Gauge Bosons.

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 W boson mass extraction. To fully exploit the potential of the LHC data, we compute the second-order [next-to-next-to-leading-order (NNLO)] QCD corrections to the inclusive-p_{T}^{W} spectrum as well as to the ratios of spectra for W^{-}/W^{+} and Z/W. We find that the inclusion of NNLO QCD corrections considerably improves the theoretical description of the experimental CMS data and results in a substantial reduction of the residual scale uncertainties.

Precise Predictions for Dijet Production at the LHC.

We present the calculation of dijet production, doubly differential in dijet mass m_{jj} and rapidity difference |y^{*}|, at leading color in all partonic channels at next-to-next-to-leading order (NNLO) in perturbative QCD. We consider the long-standing problems associated with scale choice for dijet production at next-to-leading order (NLO) and investigate the impact of including the NNLO contribution. We find that the NNLO theory provides reliable predictions, even when using scale choices that display pathological behavior at NLO. We choose the dijet invariant mass as the theoretical scale on the grounds of perturbative convergence and residual scale variation and compare the predictions to the ATLAS 7 TeV 4.5 fb^{-1} data.

Determination of the strong coupling constant α s ( m Z ) in next-to-next-to-leading order QCD using H1 jet cross section measurements: H1 Collaboration.

The strong coupling constant α s is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic ep scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of α s ( m Z ) at the Z-boson mass m Z are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be α s ( m Z ) = 0.1157 ( 20 ) exp ( 29 ) th . Complementary, α s ( m Z ) is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value α s ( m Z ) = 0.1142 ( 28 ) tot obtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations.

Precise predictions for V + jets dark matter backgrounds.

High-energy jets recoiling against missing transverse energy (MET) are powerful probes of dark matter at the LHC. Searches based on large MET signatures require a precise control of the Z ( ν ν ¯ ) +  jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by Z ( ℓ + ℓ - ) +  jet, W ( ℓ ν ) +  jet and γ +  jet production, and extrapolating to the Z ( ν ν ¯ ) +  jet background by means of precise theoretical predictions. In this context, recent advances in perturbative calculations open the door to significant sensitivity improvements in dark matter searches. In this spirit, we present a combination of state-of-the-art calculations for all relevant V +  jets processes, including throughout NNLO QCD corrections and NLO electroweak corrections supplemented by Sudakov logarithms at two loops. Predictions at parton level are provided together with detailed recommendations for their usage in experimental analyses based on the reweighting of Monte Carlo samples. Particular attention is devoted to the estimate of theoretical uncertainties in the framework of dark matter searches, where subtle aspects such as correlations across different V +  jet processes play a key role. The anticipated theoretical uncertainty in the Z ( ν ν ¯ ) +  jet background is at the few percent level up to the TeV range.

Precise QCD Predictions for the Production of a Z Boson in Association with a Hadronic Jet.

We compute the cross section and differential distributions for the production of a Z boson in association with a hadronic jet to next-to-next-to-leading order (NNLO) in perturbative QCD, including the leptonic decay of the Z boson. We present numerical results for the transverse momentum and rapidity distributions of both the Z boson and the associated jet at the LHC. We find that the NNLO corrections increase the NLO predictions by approximately 1% and significantly reduce the scale variation uncertainty.

Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116, 062001 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.062001.

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD.

Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.

W+ W- production at hadron colliders in next to next to leading order QCD.

Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell W+ W- production that include, for the first time, QCD effects up to next to next to leading order in perturbation theory. As compared to next to leading order, the inclusive W+ W- cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the W+ W- cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free W+ W- production in the four and five flavor number schemes, we demonstrate that top-quark resonances can be separated from the inclusive W+ W- cross section without a significant loss of theoretical precision.

Precise QCD predictions for the production of a photon pair in association with two jets.

We compute the cross section for the production of a high-mass photon pair in association with two hadronic jets to next-to-leading order in quantum chromodynamics. Our results allow us for the first time to reliably predict the absolute normalization of this process and demonstrate that the shape of important kinematical distributions is modified by higher-order effects. The perturbative corrections will be an important ingredient in precision studies of Higgs boson properties from its production in association with two jets.