NNLO QCD Research Articles

Bottom-quark production at hadron colliders: fully differential predictions in NNLO QCD

We report on the first fully differential calculation of the next-to-next-to-leading-order (NNLO) QCD radiative corrections to the production of bottom-quark pairs at hadron colliders. The calculation is performed by using the qT subtraction formalism to handle and cancel infrared singularities in real and virtual contributions. The computation is implemented in the Matrix framework, thereby allowing us to efficiently compute arbitrary infrared-safe observables in the four-flavour scheme. We present selected predictions for bottom-quark production at the Tevatron and at the LHC at different collider energies, and we perform some comparisons with available experimental results. We find that the NNLO corrections are sizeable, typically of the order of 25–35%, and they lead to a significant reduction of the perturbative uncertainties. Therefore, their inclusion is crucial for an accurate theoretical description of this process.

Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO

Within the framework of local analytic sector subtraction, we present the full analytic integration of double-real and real-virtual local infrared counterterms that enter NNLO QCD computations with any number of massless final-state partons. We show that a careful choice of phase-space mappings leads to simple analytic results, including non-singular terms, that can be obtained with conventional integration techniques.

Triphoton production at hadron colliders in NNLO QCD

We present next-to-next-to-leading-order (NNLO) QCD corrections to the production of three isolated photons in hadronic collisions at the fully differential level. We employ qT subtraction within Matrix and an efficient implementation of analytic two-loop amplitudes in the leading-colour approximation to achieve the first on-the-fly calculation for this process at NNLO accuracy. Numerical results are presented for proton–proton collisions at energies ranging from 7 TeV to 100 TeV. We find full agreement with the 8 TeV results of Ref. [1] and confirm that NNLO corrections are indispensable to describe ATLAS 8 TeV data. In addition, we demonstrate the significance of NNLO corrections for future precision studies of triphoton production at higher collision energies.

Anatomy of inclusive [formula omitted] production at hadron colliders

In LHC searches for new and rare phenomena the top-associated channel pp→tt‾W±+X is a challenging background that multilepton analyses must overcome. Motivated by sustained measurements of enhanced rates of same-sign and multi-lepton final states, we reexamine the importance of higher jet multiplicities in pp→tt‾W±+X that enter at O(αs3α) and O(αs4α), i.e., that contribute at NLO and NNLO in QCD in inclusive tt‾W± production. Using fixed-order computations, we estimate that a mixture of real and virtual corrections at O(αs4α) in well-defined regions of phase space can arguably increase the total tt‾W± rate at NLO by at least 10%−14%. However, by using non-unitary NLO multi-jet matching, we estimate that these same corrections are at most 10%−12%, and at the same time exhibit the enhanced jet multiplicities that are slightly favored by data. This seeming incongruity suggests a need for the full NNLO result. We comment on implications for the tt‾Z process.

Three-body non-leptonic heavy-to-heavy B decays at NNLO in QCD

Exclusive non-leptonic two-body decays of B mesons have been studied extensively in the past two decades within the framework of factorization. However, the exploration of the corresponding three-body case has only started recently, in part motivated by new data. We consider here the simplest non-leptonic three-body B decays from the point of view of factorization, namely heavy-to-heavy transitions. We provide a careful derivation of the SCET/QCDF factorized amplitudes to NNLO in αs, and discuss the numerical impact of NLO and NNLO corrections. We then study the narrow-width limit, showing that the three-body amplitude reproduces analytically the known quasi-two-body decay amplitudes, and compute finite-width corrections. Finally, we discuss certain observables that are sensitive to perturbative NLO and NNLO corrections and to higher Gegenbauer moments of the dimeson LCDAs. This is the first study of non-leptonic three-body B decays to NNLO in QCD.

Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD

We present a local subtraction scheme for computing next-to-next-to-leading order QCD corrections to the production of a massive quark-antiquark pair from a colourless initial state. The subtraction terms are built following the CoLoRFulNNLO method and refined in such a way that their integration gives rise to compact, fully analytic expressions. All ingredients necessary for a numerical implementation of our subtraction scheme are provided in detail. As an example, we calculate the fully differential decay rate of the Standard Model Higgs boson to massive bottom quarks at next-to-next-to-leading order accuracy in perturbative QCD.

Precise predictions for double-Higgs production via vector-boson fusion

Theoretical predictions with next-to-next-to-leading order (NNLO) QCD accuracy combined with the next-to-leading order (NLO) electroweak (EW) corrections are presented for differential observables of the double-Higgs production process via vector-boson fusion. While the QCD corrections were previously known, the EW ones are computed here for the first time. The numerical results are obtained for a realistic experimental set-up at the LHC and are presented in the form of fiducial cross sections and differential distributions. Within this setup we find that the VBF approximation employed in the NNLO QCD correction is accurate at the sub-percent level. We find that the NLO EW corrections within the fiducial volume are -,6.1%, making them of almost the same order as the NLO QCD corrections. In some kinematic regions they can grow as large as -,30% making them the dominant radiative corrections. When the EW corrections are combined with the NNLO QCD corrections we find a total correction of -,14.8%. The results presented here thus comprise the state-of-the-art theoretical predicition for the double-Higgs production via vector-boson fusion, which will be of value to the high-luminosity programme at the LHC.

Phenomenology of NNLO jet production at the LHC and its impact on parton distributions

We present a systematic investigation of jet production at hadron colliders from a phenomenological point of view, with the dual aim of providing a validation of theoretical calculations and guidance to future determinations of parton distributions (PDFs). We account for all available inclusive jet and dijet production measurements from ATLAS and CMS at 7 and 8 TeV by including them in a global PDF determination, and comparing to theoretical predictions at NNLO QCD supplemented by electroweak (EW) corrections. We assess the compatibility of the PDFs, specifically the gluon, obtained before and after inclusion of the jet data. We compare the single-inclusive jet and dijet observables in terms of perturbative behaviour upon inclusion of QCD and EW corrections, impact on the PDFs, and global fit quality. In the single-inclusive case, we also investigate the role played by different scale choices and the stability of the results upon changes in modelling of the correlated experimental systematics.

Varepsilon '/varepsilon in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio varepsilon '/varepsilon in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the octet approximation for lowest-lying mesons and a very recent estimate in the nonet scheme that takes into account the contribution of eta _0. We find (varepsilon '/varepsilon )^{(8)}_text {SM} = (17.4 pm 6.1) times 10^{-4} and (varepsilon '/varepsilon )^{(9)}_text {SM} = (13.9 pm 5.2) times 10^{-4}, respectively. Despite a very good agreement with the measured value (varepsilon '/varepsilon )_text {exp} = (16.6 pm 2.3) times 10^{-4}, the large error in (varepsilon '/varepsilon )_text {SM} still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for (varepsilon '/varepsilon )_text {BSM} valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters B_6^{(1/2)}(mu ) and B_8^{(3/2)}(mu ) at the mu -scales used by the RBC-UKQCD collaboration and at lower scales mathcal {O}(1, text {GeV}) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for (varepsilon '/varepsilon )_text {SM} in terms of these parameters and hat{Omega }_text {eff} that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the mathcal {O}(alpha _{text {em}}) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at mathcal {O}(alpha _{text {em}}) in the present analyses of varepsilon '/varepsilon .

Bottom quark mass effects in associated WH production with the H→bb¯ decay through NNLO QCD

We present a computation of NNLO QCD corrections to the production of a Higgs boson in association with a $W$ boson at the LHC followed by the decay of the Higgs boson to a $b\bar{b}$ pair. At variance with previous NNLO QCD studies of the same process, we treat $b$ quarks as massive. An important advantage of working with massive $b$ quarks is that it makes the use of flavor jet algorithms unnecessary and allows us to employ conventional jet algorithms to define $b$ jets. We compare NNLO QCD descriptions of the associated $WH(b\bar{b})$ production with massive and massless $b$ quarks and also contrast them with the results provided by parton showers. We find ${\cal O}(5\%)$ differences in fiducial cross sections computed with massless and massive $b$ quarks. We also observe that much larger differences between massless and massive results, as well as between fixed-order and parton-shower results, can arise in selected kinematic distributions.

Towards overline{B}to {X}_sgamma at the NNLO in QCD without interpolation in mc

Strengthening constraints on new physics from the overline{B}to {X}_sgamma branching ratio requires improving accuracy in the measurements and the Standard Model predictions. To match the expected Belle-II accuracy, Next-to-Next-to-Leading Order (NNLO) QCD corrections must be calculated without the so-far employed interpolation in the charm- quark mass mc. In the process of evaluating such corrections at the physical value of mc, we have finalized the part coming from diagrams with closed fermion loops on the gluon lines that contribute to the interference of the current-current and photonic dipole operators. We confirm several published results for corrections of this type, and supplement them with a previously uncalculated piece. Taking into account the recently improved estimates of non-perturbative contributions, we find ℬsγ = (3.40±0.17)×10−4 and Rγ≡ {mathrm{mathcal{B}}}_{left(s+dright)gamma }/{mathrm{mathcal{B}}}_{cmathrm{ell}overline{v}} = (3.35 ± 0.16) × 10−3 for Eγ> 1.6 GeV in the decaying meson rest frame.

Mixed scalar-pseudoscalar Higgs boson production through next-to-next-to-leading order at the LHC

We study the production of a mixed scalar-pseudoscalar Higgs boson in gluon fusion at the LHC, through next-to-next-to-leading order (NNLO) in QCD. We obtain fully differential results, including the decay of the Higgs boson to two charged lepton pairs. We discuss the impact of the interference between the scalar and pseudoscalar states. We also show differential distributions for several kinematic variables whose shape is sensitive to the parity of the Higgs boson, and assess the impact of the NNLO QCD corrections on these shapes.

MiNNLOPS: a new method to match NNLO QCD to parton showers

We present a novel method to combine QCD calculations at next-to-next-to-leading order (NNLO) with parton shower (PS) simulations, that can be applied to the production of heavy systems in hadronic collisions, such as colour singlets or a toverline{t} pair. The NNLO corrections are included by connecting the MiNLO′ method with transverse- momentum resummation, and they are calculated at generation time without any additional reweighting, making the algorithm considerably efficient. Moreover, the combination of different jet multiplicities does not require any unphysical merging scale, and the matching preserves the structure of the leading logarithmic corrections of the Monte Carlo simulation for parton showers ordered in transverse momentum. We present proof-of-concept applications to hadronic Higgs production and the Drell-Yan process at the LHC.

Isolated photon and photon+jet production at NNLO QCD accuracy

We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to isolated photon and photon-plus-jet production, and discuss how the experimental hadron-level photon definition and isolation criteria can be approximated in the theoretical parton-level calculation. The NNLO corrections lead to a considerable reduction of the theory uncertainty on the predictions, typically to less than five per cent, and enable an improved description of experimental measurements from ATLAS and CMS.

The Optimal Strategy for ε ′/ε in the SM: 2019

Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio ε ′/ε in the Standard Model. In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ε ′/ε, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An important role play also the isospin-breaking and QED effects, which presently are best known from chiral perturbation theory, albeit still with a significant error. Finally, it is essential to include NNLO QCD corrections in order to reduce unphysical renormalization scheme and scale dependences present at the NLO level. Here µ c in m c (µ c ) in the case of QCD penguin contributions and µ t in m t (µ t ) in the case of electroweak penguin contributions play the most important roles. Presently the error on ε ′/ε is dominated by the uncertainties in the QCDP parameter and the isospin-breaking parameter . We present a table illustrating this.

Triple Higgs production at hadron colliders at NNLO in QCD

In this work we analyse the triple Higgs boson production cross section at hadron colliders via gluon fusion, and present for the first time the full set of QCD NNLO corrections in the heavy top limit. In order to account for finite top mass effects we perform two different reweighting procedures, and study the dependence of the result on the choice of the approximation. Combining the most accurate predictions available to date, we present the following result for the total NNLO cross section for triple Higgs boson production at a 100 TeV collider: {sigma}_{mathrm{NNLO}}={5.56}_{-6%}^{+5%} ± 20% fb, where the first uncertainty is an estimate for higher order effects from scale variations, while the last one is an estimate for the missing finite top mass effects.

NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production

We present the first combination of NNLO QCD and NLO EW corrections for vector-boson pair production at the LHC. We consider all final states with two, three and four charged leptons, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Detailed predictions are discussed for three representative channels corresponding to W+W−, W±Z and Z Z production. Both QCD and EW corrections are very significant, and the details of their combination can play a crucial role to achieve the level of precision demanded by experimental analyses. In this context we point out nontrivial issues that arise at large transverse momenta, where the EW corrections are strongly enhanced by Sudakov logarithms and the QCD corrections can feature so-called giant K -factors. Our calculations have been carried out in the Matrix+OpenLoops framework and can be extended to the production of an arbitrary colour singlet in hadronic collisions, provided that the required two-loop QCD amplitudes are available. Combined NNLO QCD and NLO EW predictions for the full set of massive diboson processes will be made publicly available in the next release of Matrix and will be instrumental in advancing precision diboson studies and new-physics searches at the LHC and future hadron colliders.

NNLO QCD corrections to three-photon production at the LHC

We compute the NNLO QCD corrections to three-photon production at the LHC. This is the first NNLO QCD calculation for a 2 → 3 process. Our calculation is exact, except for the scale-independent part of the two-loop finite remainder which is included in the leading color approximation. We estimate the size of the missing two-loop corrections and find them to be phenomenologically negligible. We compare our predictions with available 8 TeV measurement from the ATLAS collaboration. We find that the inclusion of the NNLO corrections eliminates the existing significant discrepancy with respect to NLO QCD predictions, paving the way for precision phenomenology in this process.

Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme

We present analytic results that describe fully-differential NNLO QCD corrections to deep-inelastic scattering processes within the nested soft-collinear subtraction scheme. This is the last building block required for the application of this scheme to computations of NNLO QCD corrections to arbitrary processes at hadron colliders.

Nested Soft–Collinear Subtractions in NNLO QCD Computations

Nested Soft–Collinear Subtractions in NNLO QCD Computations