Search

We study the production of a Higgs boson in association with a bottom-quark pair ($b \bar b H$) at hadron colliders. Our calculation is performed in the four-flavour scheme with massive bottom quarks. This work presents the first computation of next-to-next-to-leading-order (NNLO) QCD corrections to this process, and we combine them with all-order radiative corrections from a parton shower simulation (NNLO+PS). The calculation is exact, except for the two-loop amplitude, which is evaluated in the small quark mass expansion, which is an excellent approximation for bottom quarks at LHC energies. For the NNLO+PS matching, we employ the MiNNLO$_{\rm PS}$ method for heavy-quark plus colour-singlet production within the POWHEG framework. We present an extensive phenomenological analysis both at the inclusive level and considering bottom jets using flavour-tagging algorithms. By comparing four-flavour and five-flavour scheme predictions at NNLO+PS, we find that the NNLO corrections in the four-flavour scheme resolve the long-standing tension between the two schemes. Finally, we show that our NNLO+PS predictions also have important implications on modelling the $b\bar b H$ background in Higgs-pair measurements., Comment: 51 pages, 14 figures, 3 tables

The photon parton distribution function (PDF) of the proton is crucial for precise comparisons of LHC cross sections with theoretical predictions. However, it was previously affected by very large uncertainties of around ${\cal O}(100\%)$ or dependent upon phenomenologically inspired models. In the paper~\cite{Manohar:2016nzj}, we demonstrated how the photon PDF could be determined using the proton structure functions $F_2$ and $F_L$ measured in electron--proton scattering experiments. We provided an explicit formula for the PDF, which can be systematically improved order by order in perturbation theory. We obtained a photon PDF with errors $\lesssim 2$\% for $10^{-4} < x < 0.1$. Here, we recall the underlying idea and method used to obtain this result, as well as the progress made since then., Comment: Conference proceedings of the 2nd International Conference of Basics Science, 13 pages , 6 figures

We present next-to-next-to-leading-order (NNLO) QCD corrections for Higgs production through bottom-quark annihilation (\bbH{}) matched to parton showers (NNLO+PS) using the \minnlo{} technique. The \minnlo{} method is adapted for the extra scale dependence due to the Yukawa coupling renormalized in the $\overline{\rm MS}$ scheme. The computation has been carried out in the five flavour scheme (5FS) neglecting the bottom mass. Results are compared against fixed-order predictions at NNLO and resummed predictions at next-to-next-to-leading-logarithmic (NNLL) accuracy. We also present preliminary results within the four-flavour scheme (4FS) setup, reaching a new level of precision in the massive scheme., Comment: 5 pages, 2 figures, to appear in the proceedings of the 31st International Workshop on Deep Inelastic Scattering (DIS2024), 8-12 April 2024, Grenoble, France

We extend the recently presented, fully exclusive, next-to-leading-order accurate event generator for the simulation of massless neutral- and charged-current deep inelastic scattering (DIS) to the case of incoming neutrinos. The generator can be used to study neutrino-nucleon interactions at (ultra) high energies, and is relevant for a range of fixed-target collider experiments and large-volume neutrino detectors, investigating atmospheric and astrophysical neutrinos. The matching with multi-purpose event generators such as PYTHIA 8 is performed with the POWHEG method, and accounts for parton showering and non-perturbative effects such as hadronization. This makes it possible to investigate higher-order perturbative corrections to realistic observables, such as the distribution of charged particles. To illustrate the capabilities of the code we provide predictions for several differential distributions in fixed-target collisions for neutrino energies up to 1 PeV., Comment: 16 pages. Code available from https://powhegbox.mib.infn.it/

We here report on the progress of the HHH Workshop, that took place in Dubrovnik in July 2023. After the discovery of a particle that complies with the properties of the Higgs boson of the Standard Model, all SM parameters are in principle determined. However, in order to verify or falsify the model, the full form of the potential has to be determined. This includes the measurement of the triple and quartic scalar couplings. We here report on ongoing progress of measurements for multi scalar final states, with an emphasis on three SM-like scalar bosons at 125 GeV, but also mentioning other options. We discuss both experimental progress and challenges as well as theoretical studies and models that can enhance such rates with respect to the SM predictions., Comment: 117 pages, 56 figures; Whitepaper resulting from HHH Workshop in Dubrovnik 2023, https://indico.cern.ch/event/1232581/; v2: small typos corrected

We consider Higgs production through bottom-quark annihilation at hadron colliders and we calculate next-to-next-to-leading-order (NNLO) corrections in QCD perturbation theory matched to parton showers (NNLO+PS). To this end, we have adapted the MINNLO$_{\text{PS}}$ method to account for the extra scale dependence induced by an overall Yukawa coupling that is $\overline{\rm MS}$ renormalized. We compare our results against state-of-the-art fixed-order predictions at NNLO as well as resummed predictions at next-to-next-to-leading-logarithmic (NNLL) accuracy., Comment: 24 pages, 7 figures, 1 table

We present a new formulation of the MINNLO method to match NNLO QCD calculations with parton showers by using jettiness as a resummation variable. The full derivation for colour-singlet processes is presented using $0$-jettiness starting from the NNLL$^\prime$ resummation formula. We show phenomenological results for Drell-Yan and Higgs-boson production at the LHC and compare our predictions to ATLAS and CMS data. Differences to the original MINNLO formulation using the transverse momentum of the colour singlet as resummation variable are discussed. We further present a comparison of MINNLO predictions with GENEVA. Finally, we extend the formulation of the MINNLO method to 1-jettiness which is applicable to processes with a colour singlet plus one jet in the final state., Comment: 51 pages, 8 figures

This article is part of the "Review of Particle Physics" by the Particle Data Group and reviews the current status of quantum chromodynamics and the strong coupling constant $\alpha_s$. The latest updates as of August 2023 are included., Comment: 42 pages plus references, 5 figures; this submission corresponds to the 2023 update of the QCD review of the Particle Data Group (PDG) that has been made public online here: https://pdg.lbl.gov/2023/reviews/contents_sports.html The publication within the "Review of Particle Physics" by PDG is scheduled for 2024

The Higgs boson, which was discovered at CERN in 2012, stands out as a remarkable elementary particle with distinct characteristics. Unlike any other observed particle, it possesses zero spin within the Standard Model (SM) of particle physics. Theoretical predictions had anticipated the existence of this scalar boson, postulating its interaction with the $W$ and $Z$ bosons as well as through Yukawa interactions with fermions. Furthermore the Higgs boson can interact with itself, commonly referred to as the Higgs self-interaction. In this review, the current state of experimental and theoretical investigations of Higgs boson production at the LHC and the ongoing efforts to unravel its properties are described, and an up-to-date assessment of our understanding of the Higgs sector of the SM is provided. In addition, potential links between the Higgs boson and significant unresolved questions within the realm of particle physics are presented., Comment: 23 pages, 9 figures, Contribution to The Particle-Gravity Frontier in Philosophical Transactions A, based on the 2022 Humboldt Kolleg in Kitzbuehel; v2 includes additional references

We present a calculation of inclusive diboson (WZ, ZZ, WW) processes at the LHC in the presence of intermediate polarised weak bosons decaying leptonically, matching next-to-leading-order accuracy in QCD with parton-shower effects. Starting from recent developments in polarised-boson simulation based on the helicity selection at the amplitude level, we have carried out the implementation in the POWHEG-BOX-RES framework, and validated it against independent fixed-order calculations. A phenomenological analysis in realistic LHC setups, as well as a comparison with recent ATLAS measurements, are presented., Comment: 34 pages, 8 tables, 28 figures

We present a new event generator for the simulation of both neutral- and charged-current deep inelastic scattering (DIS) at next-to-leading order in QCD matched to parton showers using the POWHEG method. Our implementation builds on the existing POWHEG BOX framework originally designed for hadron-hadron collisions, supplemented by considerable extensions to account for the genuinely different kinematics inherent to lepton-hadron collisions. In particular, we present new momentum mappings that conserve the special kinematics found in DIS, which we use to modify the POWHEG BOX implementation of the Frixione-Kunszt-Signer subtraction mechanism. We compare our predictions to fixed-order and resummed predictions, as well as to data from the HERA ep collider. Finally we study a few representative distributions for the upcoming Electron Ion Collider., Comment: 54 pages, 25 figures, code obtainable from svn://powhegbox.mib.infn.it/trunk/User-Processes-RES/DIS

The production of B hadrons is among the most abundant fundamental QCD processes measured at the LHC. We present for the first time predictions for this process accurate to next-to-next-to-leading order in QCD perturbation theory by simulating bottom-quark pair production at this accuracy matched to parton showers. Our novel results are in good agreement with experimental data for the production of different types of B hadrons from ATLAS, CMS and LHCb at 7 TeV and/or 13 TeV, including various fiducial cross sections as well as single- and double-differential distributions, and 13 TeV/7 TeV cross-section ratios., Comment: 16 pages, 7 figures, 1 table

In this work we study the impact of recent findings regarding non-perturbative corrections in the three-jet region to $e^+e^-$ hadronic observables, by performing a simultaneous fit of the strong coupling constant $\alpha_s$ and the non-perturbative parameter $\alpha_0$. We extend the calculation of these power corrections, already known for thrust and C-parameter, to other $e^+e^-$ hadronic observables. We find that for some observables the non-perturbative corrections are reasonably well behaved in the two-jet limit, while for others they have a more problematic behaviour. If one limits the fit to the three-jet region and to the well-behaved observables, one finds in general very good results, with the extracted value of $\alpha_s$ agreeing well with the world average. This is the case in particular for the thrust and $C$-parameter for which notably small values of $\alpha_s$ have been reported when non-perturbative corrections have been computed using analytic methods. Furthermore, the more problematic variables are also well described provided one stays far enough from the two-jet limit, while in this same region they cannot be described using the traditional implementation of power-corrections based on two-jet kinematics., Comment: 38 pages, 9 figures

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed., Comment: Invited volume for the EJPC; 567 pages if text/figures and 4783 references occupying about 160 additional pages. arXiv abstract abridged, for the complete abstract please see the full text

Recent progress in calculating lepton density functions inside the proton and simulating lepton showers laid the foundations for precision studies of resonant leptoquark production at hadron colliders. Direct quark-lepton fusion into a leptoquark is a novel production channel at the LHC that has the potential to probe a unique parameter space for large masses and couplings. In this work, we build the first Monte Carlo event generator for a full-fledged simulation of this process at NLO for production, followed by a subsequent decay using the POWHEG method and matching to the parton showers utilizing HERWIG. The code can handle all scalar leptoquark models with renormalisable quark-lepton interactions. We then comprehensively study the differential distributions, including higher-order effects, and asses the corresponding theoretical uncertainties. We also quantify the impact of the improved predictions on the projected (HL-)LHC sensitivities and initiate the first exploration of the potential at the FCC-hh. Our work paves the way toward performing LHC searches using this channel., Comment: 33 pages, 7 figures, 3 tables

We consider $W^\pm Z$ production in hadronic collisions and present high-precision predictions in QCD and electroweak (EW) perturbation theory matched to parton showers. To this end, we match next-to-next-to-leading order QCD corrections to parton showers using the MiNNLO$_{\rm PS}$ method and consistently combine them with next-to-leading order EW corrections matched to parton showers. This is the first time such accuracy in the event generation is achieved for any collider process, and we study in detail the impact of different choices in the combination of QCD and EW corrections as well as QCD and QED showers. Spin correlations, interferences and off-shell effects are retained by considering the full leptonic processes $pp \to \ell^+\ell^-\ell'^\pm \nu_\ell'$ with $\ell'\neq\ell$ and $\ell'=\ell$ without approximations, and the matching to QED radiation is performed preserving the resonance structure of the process. We find that NNLO QCD predictions including QCD and QED shower effects provide a very good approximation in the bulk-region of the phase space, while EW effects become increasingly important in the high-energy tails of kinematic distributions. Our default predictions are in excellent agreement with recent ATLAS data., Comment: 32 pages, 8 figures

The discovery of the Higgs boson, ten years ago, was a milestone that opened the door to the study of a new sector of fundamental physical interactions. We review the role of the Higgs field in the Standard Model of particle physics and explain its impact on the world around us. We summarize the insights into Higgs physics revealed so far by ten years of work, discuss what remains to be determined, and outline potential connections of the Higgs sector with unsolved mysteries of particle physics., Comment: 16 pages, 5 figures, invited Nature perspective article

We consider associated $Zh$ production with $Z \to \ell^+ \ell^-$ and $h \to b \bar b$ decays in hadronic collisions. In the framework of the Standard Model effective field theory (SMEFT) we calculate the QCD corrections to this process and achieve next-to-next-to-leading order plus parton shower (NNLO$+$PS) accuracy using the MiNNLO$_{\rm PS}$ method. This precision is obtained for a subset of six SMEFT operators, including the corrections from effective Yukawa- and chromomagnetic dipole-type interactions. Missing higher-order QCD effects associated with the considered dimension-six operators are estimated to have a relative numerical impact of less than a percent on the total rate once existing experimental limits on the relevant Wilson coefficients are taken into account. We provide a dedicated Monte Carlo (MC) code that evaluates the NNLO SMEFT corrections on-the-fly in the event generation. This MC generator is used to study the numerical impact of NNLO$+$PS corrections on the kinematic distributions in $pp \to Zh \to \ell^+ \ell^- b \bar b$ production employing simple SMEFT benchmark scenarios. We identify the invariant mass $m_{b \bar b}$ of the two $b$-tagged jets as well as the three-invariant jet mass $m_{b \bar b j}$ as particularly interesting observables to study SMEFT effects. These distributions receive contributions that change both their normalisation and shape with the latter modifications depending on the exact jet definition. To our knowledge SMEFT effects of this type have so far not been discussed in the literature. The presented MC generator can also serve as a starting point to obtain NNLO$+$PS accuracy for a suitable enlarged set of effective operators in the future., Comment: 32 pages, 7 figures; v2: matches version accepted for publication in JHEP

We summarize the current status and near future prospects for next-to-next-to-leading order calculations matched to parton shower based on the MiNNLO$_{\rm PS}$ method. We give a theoretical overview, illustrate selected results for $ZZ\to 4\ell$ and top-pair production processes at the LHC, and provide an outlook of the future challenges., Comment: Contribution to Snowmass 2022

We consider the production of a pair of heavy quarks and illustrate the derivation of the MiNNLO method to match next-to-next-to-leading order calculations with parton showers (NNLO+PS) for this class of processes. As a first application, we construct an event generator for the fully differential simulation of hadronic top-quark pair production at NNLO+PS and discuss all details of its implementation in a parton shower Monte Carlo framework. We present new phenomenological results for the Large Hadron Collider obtained by including the tree-level decays of the top quarks, while accounting for spin-correlation effects. A comprehensive comparison to LHC measurements shows an excellent description of experimental data across multiple hadronic and leptonic particle-level observables. The computer code is available for download within the POWHEG-BOX., Comment: 55 pages, 12 figures

We consider the Higgsstrahlung process in hadronic collisions and present the computation of next-to-next-to-leading order predictions matched to parton showers for both production and $H\to b\bar{b}$ decay employing the MiNNLO$_{\rm PS}$ method. We present predictions for $ZH$ and $W^{\pm}H$ production including spin correlations and off-shell effects by calculating the full processes $pp \to \ell^+\ell^-H \to \ell^+\ell^-b\bar{b}$, $pp \to \nu_\ell\bar\nu_\ell H \to \nu_\ell\bar\nu_\ell b\bar{b}$ and $pp \to \ell^\pm \nu_\ell H \to \ell^\pm \nu_\ell b\bar{b}$ in the narrow-width approximation for the Higgs boson. For the $W^{\pm}H$ process, NNLO+PS accuracy in production and decay is achieved for the first time. Our calculations are validated against earlier simulations in the NNLOPS approach that includes NNLO corrections via multi-differential reweighting. The new MiNNLO$_{\rm PS}$ generators for these processes, which evaluate NNLO corrections on-the-fly in the event generation, will supersede those earlier calculations. Our predictions are in good agreement with recent measurements of the Higgsstrahlung cross sections., Comment: 37 pages, 8 figures, 4 tables

We study a few basic photon- and lepton-initiated processes at the LHC which can be computed using the recently developed photon and lepton parton densities. First, we consider the production of a massive scalar particle initiated by lepton-antilepton annihilation and photon-photon fusion as representative examples of searches of exotic particles. Then we study lepton-lepton scattering, since this Standard-Model process may be observable at the LHC. We examine these processes at leading and next-to-leading order and, using the POWHEG method, we match our calculations to parton shower programs that implement the required lepton or photon initial-states. We assess the typical size of cross-sections and their uncertainties and discuss the preferred choices for the factorization scale. These processes can also be computed starting directly from the lepto-production hadronic tensor, leading to a result where some collinear-enhanced QED corrections are missing, but all strong corrections are included. Thus, we are in the unique position to perform a comparison of results obtained via the factorization approach to a calculation that does not have strong corrections. This is particularly relevant in the case of lepton-scattering, that is more abundant at lower energies where it is affected by larger strong corrections. We thus compute this process also with the hadronic-tensor method, and compare the results with those obtained with POWHEG. Finally, for some lepton-lepton scattering processes, we compare the size of the signal to the main quark-induced background, which is double Drell-Yan production, and outline a preliminary search strategy to enhance the signal to background ratio., Comment: 35 pages, 28 figures

The measurement of the triple gauge couplings (TGCs) is a central part of diboson studies at the LHC. In this letter we consider the $Z\gamma$ process and include anomalous TGCs (aTGCs) in the event generation at next-to-next-to-leading order QCD accuracy (NNLO+PS) within the MiNNLO$_{\rm PS}$ framework. While our implementation is fully general and applies to both $Z\to \ell^+\ell^-$ and $Z\to \nu\bar\nu$ decays, we focus here on the $\nu\bar\nu\gamma$ final state. After validation of our simulation of $\nu\bar\nu\gamma$ events, for which NNLO+PS accuracy is achieved for the first time, the effects of aTGCs on various distributions are studied. Moreover, we show the relevance of NNLO+PS accuracy for the $\nu\bar\nu\gamma$ background to photon plus missing energy signatures in dark-matter searches, and we compare MiNNLO$_{\rm PS}$ predictions for $\nu\bar\nu\gamma$ production to recent 13 TeV data., Comment: 17 pages, 5 figures, 3 tables

We consider $ZZ$ production in hadronic collisions and present state-of-the-art predictions in QCD perturbation theory matched to parton showers. Next-to-next-to-leading order corrections to the quark-initiated channel are combined with parton showers using the MiNNLO$_{\text{PS}}$ method, while next-to-leading order corrections to the loop-induced gluon fusion channel are matched using the POWHEG method. Their combination, dubbed nNNLO+PS, constitutes the best theoretical description of $ZZ$ events to date. Spin correlations, interferences and off-shell effects are included by calculating the full process $pp \to \ell^+\ell^-\ell^{(\prime)+}\ell^{(\prime)-}$. We show the crucial impact of higher-order corrections for both quark- and gluon-initiated processes as well as the relevance of the parton shower in certain kinematical regimes. Our predictions are in very good agreement with recent LHC data., Comment: 32 pages, 7 figures, 2 tables

We consider $W^+W^-$ production in hadronic collisions and present the computation of next-to-next-to-leading order accurate predictions consistently matched to parton showers (NNLO+PS) using the MiNNLO$_{\rm PS}$ method. Spin correlations, interferences and off-shell effects are included by calculating the full process $pp \to e^+\nu_e \mu^-\bar{\nu}_\mu$. This is the first NNLO+PS calculation for $W^+W^-$ production that does not require an a-posteriori multi-differential reweighting. The evaluation time of the two-loop contribution has been reduced by more than one order of magnitude through a four-dimensional cubic spline interpolation. We find good agreement with the inclusive and fiducial cross sections measured by ATLAS and CMS. Both NNLO corrections and matching to parton showers are important for an accurate simulation of the $W^+W^-$ signal, and their matching provides the best description of fully exclusive $W^+W^-$ events to date., Comment: 45 pages, 12 figures, 2 tables

The production of top-quark pairs in hadronic collisions is among the most important reactions in modern particle physics phenomenology and constitutes an instrumental avenue to study the properties of the heaviest quark observed in nature. The analysis of this process at the Large Hadron Collider relies heavily on Monte Carlo simulations of the final state events, whose accuracy is challenged by the outstanding precision of experimental measurements. In this letter we present the first matched computation of top-quark pair production at next-to-next-to-leading order in QCD with all-order radiative corrections as implemented via parton-shower simulations. Besides its intrinsic relevance for LHC phenomenology, this work also establishes an important step towards the simulation of other hadronic processes with colour charges in the final state., Comment: Journal version

We consider $Z \gamma$ production in hadronic collisions and present the first computation of next-to-next-to-leading order accurate predictions consistently matched to parton showers (NNLO+PS). Spin correlations, interferences and off-shell effects are included by calculating the full process $pp\to\ell^+\ell^-\gamma$. We extend the recently developed MiNNLO$_{\rm PS}$ method to genuine $2\to 2$ hard scattering processes at the LHC, which paves the way for NNLO+PS simulations of all diboson processes. This is the first $2\to2$ NNLO+PS calculation that does not require an a-posteriori multi-differential reweighting. We find that both NNLO corrections and matching to parton showers are crucial for an accurate simulation of the $Z \gamma$ process. Our predictions are in very good agreement with recent ATLAS data., Comment: 42 pages, 10 figures, 2 tables

As is the case for all light coloured Standard Model particles, also photons and charged leptons appear as constituents in ultrarelativistic hadron beams, and admit a parton density function (PDF). It has been shown recently that the photon PDF can be given in terms of the structure functions and form factors for electron-proton scattering. The same holds for lepton PDFs. In the present work we set up a calculation of the lepton PDFs at next-to-leading order, using the same data input needed in the photon case. A precise knowledge of the lepton densities allows us to study lepton-initiated processes even at a hadron collider, with all possible combinations of same-charge, opposite-charge, same-flavour, different-flavour leptons and leptons-quarks, most of which cannot be realized in any other foreseeable experiment. The lepton densities in the proton are extremely small, so that their contribution to Standard Model processes is generally shadowed by processes initiated by coloured partons. We will show, however, that there are cases where these processes can be relevant, giving rise to rare Standard Model signatures and to new production channels, that can enlarge the discovery potential of New Physics at the LHC and future high energy colliders with hadrons in the initial state., Comment: 43 pages, 14 figures. In V2 we have included a class of subleading O(alpha^2) contributions to the lepton PDFs and motivated this choice. Data in the LHAPDF files have been updated accordingly (see info file). V2 is identical to the published version

Processes commonly studied at the Large Hadron Collider (LHC) are induced by quarks and gluons inside the protons of the LHC beams. In this letter we demonstrate that, since protons also contain leptons, it is possible to target lepton-induced processes at the LHC as well. In particular, by picking a lepton from one beam and a quark from the other beam, we present for the first time a comprehensive analysis of resonant single leptoquark (LQ) production at a hadron collider. In the case of minimal scalar LQs, we derive novel bounds that arise from the LHC Run II considering all possible flavour combinations of an electron or a muon and an up ($u$), a down ($d$), a strange or a charm quark. For the flavour combinations with a $u$ or a $d$ quark, the obtained limits represent the most stringent constraints to date on LQs of this type. The prospects of our method at future LHC runs are also explored. Given the discovery reach of the proposed LQ signature, we argue that dedicated resonance searches in final states featuring a single light lepton and a single light-flavour jet should be added to the exotics search canon of both the ATLAS and the CMS collaboration., Comment: 7 pages, 4 figures, v2: extended version of the manuscript that has been accepted for publication by PRL

We present an event generator that describes the Higgs boson decay into $b$-quarks at next-to-next-to-leading-order (NNLO) in QCD and allows for a consistent matching to parton shower. For this purpose, we work within the POWHEG framework and employ the MINLO method to produce an NNLO-accurate H$\to\! b\bar{b}$ event sample which can further be interfaced with a generic Higgs boson production mode. The resulting events, that combine Higgs production and decay, can be matched to parton shower by means of a vetoed shower. As an example, we present a short phenomenological study for associated Higgs production (HZ) and vector boson fusion (VBF) processes. We release the source code that was used to obtain these results as an $\text{h_bbg}$ user process in POWHEG-BOX-V2. We also provide tools that enable interfacing the decay events with events for an arbitrary Higgs production mode and subsequent matching of the combined Les Houches (LH) events with a parton shower., Comment: 28 pages, 8 figures. Few changes: improved few sentences throughout the paper, added references, added 1 plot in section 2.1, added 2 plots (1 figure) in section 4.2, removed fixed-order results from HZ plots, added one appendix. Now it matches the version published in JHEP (HZ plots rebinned on arxiv version)

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 $t\bar{t}$ pair. The NNLO corrections are included by connecting the MiNLO$^\prime$ 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., Comment: Fixed sign typo in Eq. (4.24)

We present state-of-the-art extractions of the strong coupling based on N$^3$LO+NNLL accurate predictions for the two-jet rate in the Durham clustering algorithm at $e^+e^-$ collisions, as well as a simultaneous fit of the two- and three-jet rates taking into account correlations between the two observables. The fits are performed on a large range of data sets collected at LEP and PETRA colliders, with energies spanning from $35$ GeV to $207$ GeV. Owing to the high accuracy of the predictions used, the perturbative uncertainty is considerably smaller than that due to hadronization. Our best determination at the $Z$ mass is $\alpha_s(M_Z) = 0.11881 \pm 0.00063(exp.) \pm 0.00101(hadr.) \pm 0.00045(ren.) \pm 0.00034(res.)$, which is in agreement with the latest world average and has a comparable total uncertainty., Comment: 36 pages,13 figures, 5 tables

We present a next-to-leading order accurate simulation of t-channel single-top plus jet production matched to parton showers via the POWHEG method. The calculation underlying the simulation is enhanced with a process-specific implementation of the multi-scale improved NLO (MINLO) method, such that it gives physical predictions all through phase space, including regions where the jet additional to the t-channel single-top process is unresolved. We further describe a tuning procedure for the MINLO Sudakov form factor, fitting the coefficient of the first subleading term in its exponent using an artificial neural-network. The latter tuning, implemented as a straightforward event-by-event reweighting, renders the MINLO simulation NLO accurate for t-channel single-top observables, in addition to those of the analogous single-top plus jet process., Comment: 39 pages, 10 figures; v2: minor changes, version accepted for publication in JHEP

We present novel predictions for the production of $W^+W^-$ pairs in hadron collisions that are next-to-next-to-leading order accurate and consistently matched to a parton shower (NNLOPS). All diagrams that lead to the process $pp\to e^- \bar \nu_e\;\mu^+\nu_\mu+X$ are taken into account, thereby including spin correlations and off-shell effects. For the first time full NNLOPS accuracy is achieved for a $2\to 4$ process. We find good agreement, at the 1$\sigma$ level, with the $W^+W^-$ rates measured by ATLAS and CMS. The importance of NNLOPS predictions is evident from differential distributions sensitive to soft-gluon effects and from the large impact ($10$% and more) of including next-to-next-to-leading order corrections on top of MiNLO. We define a charge asymmetry for the $W$ bosons and the leptons in $W^+W^-$ production at the LHC, which is sensitive to the $W$ polarizations and hence can be used as a probe of new physics., Comment: 40 pages, 11 figures, 3 tables

The European School of High-Energy Physics is intended to give young physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. These proceedings contain lecture notes on the theory of the Weak interaction and Higgs physics, flavour physics and CP violation, neutrinos, theories beyond the Standard Model, physics at the LHC Run-2 and beyond, practical statistics for high-energy physicists, and cosmology and dark matter., Comment: 7 lectures, 312 pages, published as CERN Yellow Report a this url: https://e-publishing.cern.ch/index.php/CYRSP/issue/view/45

We present a next-to-next-to-leading order (NNLO) accurate description of associated HZ production, followed by the Higgs boson decay into a pair of $b$-quarks treated at next-to-leading order (NLO), consistently matched to a parton shower (PS). The matching is achieved by performing reweighting of the $\texttt{HZJ-MiNLO}$ events, using multi-dimensional distributions that are fully-differential in the HZ Born kinematics, to the NNLO results obtained by using the $\texttt{MCFM-8.0}$ fixed-order calculation. Additionally we include the $gg\to\rm{HZ}$ contribution to the discussed process that appears at the $\mathcal{O}(\alpha_s^2)$. We present phenomenological results obtained for 13 TeV hadronic collisions., Comment: 30 pages, 15 figures

Vector-boson scattering processes are of great importance for the current run-II and future runs of the Large Hadron Collider. The presence of triple and quartic gauge couplings in the process gives access to the gauge sector of the Standard Model (SM) and possible new-physics contributions there. To test any new-physics hypothesis, sound knowledge of the SM contributions is necessary, with a precision which at least matches the experimental uncertainties of existing and forthcoming measurements. In this article we present a detailed study of the vector-boson scattering process with two positively-charged leptons and missing transverse momentum in the final state. In particular, we first carry out a systematic comparison of the various approximations that are usually performed for this kind of process against the complete calculation, at LO and NLO QCD accuracy. Such a study is performed both in the usual fiducial region used by experimental collaborations and in a more inclusive phase space, where the differences among the various approximations lead to more sizeable effects. Afterwards, we turn to predictions matched to parton showers, at LO and NLO: we show that on the one hand, the inclusion of NLO QCD corrections leads to more stable predictions, but on the other hand the details of the matching and of the parton-shower programs cause differences which are considerably larger than those observed at fixed order, even in the experimental fiducial region. We conclude with recommendations for experimental studies of vector-boson scattering processes., Comment: Data and input files are available at: https://github.com/VBSCanAction/VBSComparison/ . 28 pages including figures and references. Matches the journal version

The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a recent paper, we showed how the photon PDF could be determined in terms of the electromagnetic proton structure functions $F_2$ and $F_L$ measured in electron-proton scattering experiments, and gave an explicit formula for the PDF including all terms up to next-to-leading order. In this paper we give details of the derivation. We obtain the photon PDF using the factorisation theorem and applying it to suitable BSM hard scattering processes. We also obtain the same PDF in a process-independent manner using the usual definition of PDFs in terms of light-cone Fourier transforms of products of operators. We show how our method gives an exact representation for the photon PDF in terms of $F_2$ and $F_L$, valid to all orders in QED and QCD, and including all non-perturbative corrections. This representation is then used to give an explicit formula for the photon PDF to one order higher than our previous result. We also generalise our results to obtain formul\ae\ for the polarised photon PDF, as well as the photon TMDPDF. Using our formula, we derive the $P_{\gamma i}$ subset of DGLAP splitting functions to order $\alpha \alpha_s$ and $\alpha^2$, which agree with known results. We give a detailed explanation of the approach that we follow to determine a photon PDF and its uncertainty within the above framework., Comment: 75 pages, 25 figures, data files corresponding to the figures available at http://doi.org/10.5281/zenodo.837233, LUXqed17 PDF files available in LHAPDF, references added in v2

We examine the constraints on the trilinear Higgs coupling $\lambda$ that originate from associated ($Vh$) and vector boson fusion (VBF) Higgs production in $pp$ collisions in the context of the Standard Model effective field theory. The 1-loop contributions to $pp \to V h$ and $pp \to jj h$ that stem from insertions of the dimension-6 operator $O_6 = - \lambda \left (H^\dagger H \right )^3$ are calculated and combined with the ${\cal O} (\lambda)$ corrections to the partial decay widths of the Higgs boson. Employing next-to-next-to-leading order QCD predictions, we analyse the sensitivity of current and forthcoming measurements of the signal strengths in $Vh$ and VBF Higgs production to changes in $\lambda$. We show that future LHC runs may be able to probe modifications of $\lambda$ with a sensitivity similar to the one that is expected to arise from determinations of double-Higgs production. The sensitivity of differential $Vh$ and VBF Higgs distributions to a modified $h^3$ coupling is also studied., Comment: 23 pages, 7 figures; v2: matches published version

It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton ($ep$) scattering data, in effect viewing the $ep\to e+X$ process as an electron scattering off the photon field of the proton. To this end, we consider an imaginary, beyond Standard Model process with a flavour changing photon-lepton vertex. We write its cross section in two ways, one in terms of proton structure functions, the other in terms of a photon distribution. Requiring their equivalence yields the photon distribution as an integral over proton structure functions. As a result of the good precision of $ep$ data, we constrain the photon PDF at the level of 1-2% over a wide range of momentum fractions., Comment: 6 pages, 5 figures; v3 includes small textual changes and an updated CT14 comparison in Fig. 4, as published. LUXqed_PDF4LHC15_nnlo_100 set available from LHAPDF, further information at http://cern.ch/luxqed/

We present the first next-to-next-to-leading logarithmic resummation for the two-jet rate in $e^+e^-$ annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ARES method to observables involving any global, recursively infrared and collinear safe jet algorithm in e^+e^- collisions. As opposed to other methods, this approach does not require a factorization theorem for the observables. We present predictions matched to next-to-next-to-leading order, and a comparison to LEP data., Comment: 15 pages, 4 figures

We present a simulation program for the production of a pair of W bosons in association with a jet, that can be used in conjunction with general-purpose shower Monte Carlo generators, according to the POWHEG method. We have further adapted and implemented the MINLO' method on top of the NLO calculation underlying our WW+jet generator. Thus, the resulting simulation achieves NLO accuracy not only for inclusive distributions in WW+jet production but also WW production, i.e. when the associated jet is not resolved, without the introduction of any unphysical merging scale. This work represents the first extension of the MINLO' method, in its original form, to the case of a genuine underlying 2->2 process, with non-trivial virtual corrections., Comment: 22 pages, 9 figures

We present a new release of the QCDLoop library based on a modern object-oriented framework. We discuss the available new features such as the extension to the complex masses, the possibility to perform computations in double and quadruple precision simultaneously, and useful caching mechanisms to improve the computational speed. We benchmark the performance of the new library, and provide practical examples of phenomenological implementations by interfacing this new library to Monte Carlo programs., Comment: 20 pages, 7 figures, accepted for publication in CPC. Code available from http://cern.ch/qcdloop

We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross Section Working Group., Comment: Minor changes, plots updated, matches the version published in JHEP

We present new results for the jet-veto efficiency and zero-jet cross section in Higgs production through gluon fusion. We incorporate the N$^3$LO corrections to the total cross section, the NNLO corrections to the 1-jet rate, NNLL resummation for the jet $p_t$ and LL resummation for the jet radius dependence. Our results include known finite-mass corrections and are obtained using the jet-veto efficiency method, updated relative to earlier work to take into account what has been learnt from the new precision calculations that we include. For 13 TeV collisions and using our default choice for the renormalisation and factorisation scales, $\mu_0=m_H/2$, the matched prediction for the jet-veto efficiency increases the pure NNNLO prediction by about 2% and the two have comparable uncertainties. Relative to NNLO+NNLL results, the new prediction is 2% smaller and the uncertainty reduces from more than 10% to less than 5%. Results are also presented for the central scale $\mu_0=m_H$., Comment: 30 pages, 16 figures