Academic literature on the topic 'Next-to-next-to-leading order (NNLO)'

For processes involving structure functions and/or fragmentation functions, arguments that over a range of a proper kinematic variable, there is a part that dominates the next-to-leading order (NLO) corrections, are briefly reviewed. The arguments are tested against more recent NLO and in particular complete next-to-next-to-leading order (NNLO) calculations. A critical examination of when these arguments may not be useful is also presented.

The next-to-leading order electro-weak radiative corrections to the µ±e- → µ±e- process are reviewed and their relevance is discussed for the MUonE experiment, proposed at CERN. The aim of MUonE is the high precision measurement of the QED running coupling constant in the space-like region, from which the full hadronic contribution can be extracted and used to provide a new and independent determination of the leading-order hadronic correction to the muon g − 2. In this context, the required accuracy demands that radiative corrections are accounted for at the highest level of precision and implemented into a Monte Carlo event generator for data analysis. The first step towards the final goal of theoretical precision, which will require the full set of NNLO corrections and resummation of higher orders, is the inclusion of NLO electro-weak corrections.

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum p2, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.

We present a determination of the strong coupling constant αS( $ m_{Z^0 } $ ) using a global fit of theory predictions in next-to-next-next-leading-order (NNLO) combined with resummed predictions at the next-to-next-leading-log level (NNLL) [bibrR11]. The predictions are compared to distributions of energy-energy correlations measured in e+e−annihilation to hadronic final states by experiments at the e+e−colliders LEP, PETRA, TRISTAN and PEP. The predictions are corrected for hadronisation effects using the modern generator programs Sherpa 2.2.4 and Herwig 7.1.1.

Predictions of fiducial cross sections, differential cross sections, and lepton charge asymmetry are presented for the production ofW±bosons with leptonic decay up to next-to-next-to-leading order (NNLO) in perturbative QCD. Differential cross sections ofW±bosons andWboson lepton charge asymmetry are computed as a function of lepton pseudorapidity for a defined fiducial region inppcollisions ats=13 TeV. Numerical results of fiducialW±cross section predictions are presented with the latest modern PDF models at next-to-leading order (NLO) and NNLO. It is found that the CT14 and NNPDF 3.0 predictions with NNLO QCD corrections are about 4% higher than the NLO CT14 and NNPDF 3.0 predictions while MMHT 2014 predictions with NLO QCD corrections are smaller than its NNLO QCD predictions by approximately 6%. In addition, the NNLO QCD corrections reduce the scale variation uncertainty on the cross section by a factor of 3.5. The prediction of central values and considered uncertainties are obtained using FEWZ 3.1 program.

I present a unified approach to calculating the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections to cross-sections for electroweak, Higgs, QCD, and SUSY processes. I derive master formulas that can be used for any of these processes in hadron–hadron and lepton–hadron collisions. The formulas are based on a unified threshold resummation formalism and can be applied to both total and differential cross-sections for processes with either simple or complex color flows and for various factorization schemes and kinematics. As a test of the formalism, I rederive known NNLO results for Drell–Yan and Higgs production, deep inelastic scattering, and W+γ production, and I obtain expressions for several two-loop anomalous dimensions and other quantities needed in next-to-next-to-leading-logarithm (NNLL) resummations. I also present new results for the production of supersymmetric charged Higgs bosons; massive electroweak vector bosons; photons; heavy quarks in lepton–hadron and hadron–hadron collisions and in flavor-changing neutral current processes; jets; and squarks and gluinos. The NNLO soft and virtual corrections are often dominant, especially near threshold, and they reduce the scale dependence of the cross-section. Thus, a unified approach to these corrections is important in the search for new physics at present and future colliders.

Abstract This paper presents high-accuracy predictions for the differential cross ss as a function of the key observable ϕ η * of the neutral-current Drell-Yan (DY) dilepton production in proton-proton (pp) collisions. The differential distributions for the ϕ η * are presented by using the state-of-the-art predictions from the combined calculations of fixed-order perturbative quantum chromodynamics (QCD) corrections at next-to-next-to-leading order (NNLO) accuracy and resummation of large logarithmic terms at next-to-next-to-leading logarithmic (NNLL) and next-to-NNLL (N3LL) accuracies, i.e., NNLO+NNLL and NNLO+N3LL, respectively. The predicted distributions are reported for a thorough set of the DY dilepton invariant mass m ll ranges, spanning a wide kinematic region of 50 < m ll < 1000 GeV both near and away from the Z-boson mass peak, and rapidity y ll ranges in the central detector acceptance region of ∣y ll ∣ < 2.4. The differential ϕ η * distributions in the wide m ll and y ll ranges offer stringent tests to assess the reliability of the predictions, where the m ll and y ll are closely correlated with the parton distribution functions (PDFs) of the incoming partons. The matched predictions through NNLO+N3LL are observed to provide good description of the 13 TeV pp collision data for the ϕ η * (including the dilepton transverse momentum p T ll as well) distributions in almost the entire m ll and y ll ranges, apart from the intermediate- to high- ϕ η * region in the lowest mass range 50–76 GeV which is assessed to constitute a challenge for the presented predictions. The predictions at NNLO+N3LL are also reported at 14 TeV for the upcoming high-luminosity running era of the Large Hadron Collider (LHC), in which increasing amount of data is expected to require more accurate and precise theoretical description. The most recent PDF models MSHT20 and CT18, in addition to the NNPDF3.1, are tested for the first time for the matched predictions of the ϕ η * distribution. The differential distributions by the combined predictions through NNLO QCD+NLO EW are finally provided to enable assessment of the impact of the EW corrections for the ϕ η * .

We discuss the most recent calculations of the top quark total cross section and transverse momentum distributions at the Tevatron and the LHC. These calculations include the soft-gluon corrections at next-to-next-to-leading order (NNLO). The soft NNLO corrections stabilize the scale dependence of the cross section.

In this short review, the calculation of the next-to-next-to-leading order QCD corrections to the inclusive radiative decay [Formula: see text] is described. We summarize the salient features of the calculational framework adopted, discuss the results obtained in the last few years, and indicate the technical tools that made the NNLO calculations possible. We conclude by comparing the current NNLO theoretical estimate for the branching ratio with the experimental measurement and by briefly discussing the size and origin of the residual theoretical uncertainty.

Prediction of Z→l+l- production cross section (where l±=e±,μ±) in proton-proton collisions at s=14 TeV is estimated up to next-to-next-to-leading order (NNLO) in perturbative QCD including next-to-leading order (NLO) electroweak (EW) corrections. The total inclusive Z boson production cross section times leptonic branching ratio, within the invariant mass window 66<mll<116 GeV, is predicted using NNLO HERAPDF2.0 at NNLO QCD and NLO EW as σZTot=2111.69-26.92+26.31 (PDF) ±11 (αs) ±17 (scale) -30.98+57.41 (parameterization and model). Theoretical prediction of the fiducial cross section is further computed with the latest modern PDF models (CT14, MMHT2014, NNPDF3.0, HERAPDF2.0, and ABM12) at NNLO for QCD and NLO for EW. The central values of the predictions are based on DYNNLO 1.5 program and the uncertainties are extracted using FEWZ 3.1 program. In addition, the cross section is also calculated as functions of μR and μF scales. The choice of μR and μF for scale variation uncertainty is further discussed in detail.

In questo lavoro presento le implementazioni di due processi di produzione di una coppia di bosoni elettrodeboli (EW) dallo scattering di due adroni in due diversi generatori di eventi Monte Carlo all'ordine next-to-next-to-leading (NNLO) nella cromodinamica quantistica (QCD) combinati con la parton shower (PS). Nella prima parte della tesi discuto l'implementazione del processo di produzione di due coppie di leptoni privi di massa con lo stesso sapore e carica opposta dallo scattering protone-protone all'interno del generatore di eventi Monte Carlo Geneva. Dopo aver brevemente introdotto il metodo Geneva, fornisco una descrizione dettagliata di due delle sue funzioni recentemente implementate. Dopo aver passato gli eventi attraverso la parton shower di Pythia8, mostro infine diverse distribuzioni di interesse fenomenologico e le confronto con i dati degli esperimenti ATLAS e CMS al Large Hadron Collider (LHC). Il generatore di eventi Geneva consente di abbinare il calcolo NNLO con la resummazione all'ordine logaritmico next-to-next-to-leading primo (NNLL') della zero-jettiness e quella all'ordine logaritmico next-to-leading (NLL) della one-jettiness. Poiché il contributo della risommazione è differenziale nel solo parametro della N-jettiness, può essere utilizzato per generare eventi soltanto dopo aver fornito la sua dipendenza dall'intero spazio delle fasi di radiazione. Le funzioni utilizzate a questo scopo sono dette funzioni di splitting e devono essere normalizzate in modo da non compromettere l'accuratezza della risommazione. In questo lavoro presento un modo per normalizzarle on the fly, che fornisce una migliore stabilità all'integrazione Monte Carlo. Tuttavia, tale metodo richiede il calcolo analitico di diversi limiti dello spazio delle fasi che dipendono dalle mappe utilizzate per proiettare le configurazioni con N+1 partoni di stato finale su quelle con N partoni di stato finale. Dopo aver descritto tutte le proiezioni attualmente disponibili in Geneva, presento un calcolo dettagliato della normalizzazione delle corrispondenti funzioni di splitting. Successivamente discuto la sottrazione all'ordine next-to-leading (NLO) delle singolarità infrarosse di QCD per qualsiasi processo di produzione di un singoletto di colore. Poiché Geneva richiede l'integrazione Monte Carlo on-the-fly delle ampiezze reali sottratte, mostro un modo per ottimizzare l'efficienza dell'integrazione che può essere particolarmente utile per i processi in cui il calcolo degli elementi di matrice reali è computazionalmente impegnativa. Nella seconda parte della tesi discuto l'implementazione del processo di produzione di una coppia di fotoni da uno scattering protone-protone all'interno del generatore di eventi Monte Carlo Powheg Box + MiNNLOPS. Tale processo richiede un trattamento dedicato poiché è afflitto da divergenze di elettrodinamica quantistica (QED) nel limite in cui qualsiasi fotone diventa collineare a un quark. Dopo aver brevemente introdotto il generatore di eventi Powheg Box e il metodo MiNNLOPS, presento gli strumenti appositamente creati per questo calcolo. Comincio descrivendo una tecnica generale per trattare qualsiasi processo con una sezione d'urto Born divergente nel generatore di eventi Powheg Box senza applicare alcun taglio a livello di generazione. Presento quindi una mappa che impedisce che le configurazioni finite dal punto di vista della QED con un partone di stato finale siano proiettate su configurazioni singolari senza partoni di stato finale. Infine discuto alcune modifiche alla versione originale del metodo MiNNLOPS volte a ridurre l'impatto dei contributi spuri oltre il NNLO. Dopo aver passato gli eventi attraverso la parton shower di Pythia8, concludo mostrando diverse distribuzioni di interesse fenomenologico e confrontandole con i dati di LHC più recenti dall'esperimento ATLAS.
In this work, I present the implementations of two processes of electroweak (EW) boson pair production from hadronic scattering within two different Monte Carlo event generators at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) combined with parton showers (PS). In the first part of the work, I discuss the implementation of the process of production of two same-flavor opposite-charge pairs of massless leptons from proton-proton scattering within the Geneva Monte Carlo event generator. After briefly introducing the Geneva method, I provide a detailed description of two of its newly-implemented features. After passing the events through the Pythia8 parton shower, I finally show several distributions of phenomenological interest and compare them with the data from the ATLAS and CMS experiments at the Large Hadron Collider (LHC). The Geneva event generator provides a framework for matching the NNLO calculation with the next-to-next-to-leading logarithmic prime (NNLL') resummation of the zero-jettiness and next-to-leading logarithmic (NLL) resummation of the one-jettiness. Since the contribution from the resummation is only differential in the N-jettiness parameter, it can be used for generating events only after providing its dependence on the full radiation phase space. The functions used for this purpose are called splitting functions and must be normalized so as not to spoil the accuracy of the resummation. In this work, I present a way of normalizing them on the fly, which provides better stability to the Monte Carlo integration. However, such a method requires the analytic computation of several phase-space boundaries, which depend on the mappings used for projecting the configurations with N+1 final-state partons onto those with N final-state partons. After describing all the mappings currently available in Geneva, I present a detailed calculation of the normalization of the corresponding splitting functions. I then discuss the next-to-leading order (NLO) subtraction of the infrared QCD singularities for any process of production of a color singlet. Since Geneva requires the on-the-fly Monte Carlo integration of the subtracted real amplitudes, I show a way to optimize the efficiency of the integration, which can be particularly useful for processes where the evaluation of the real matrix elements is computationally demanding. In the second part of the work, I discuss the implementation of the process of production of a photon pair from a proton-proton scattering within the Powheg Box + MiNNLOPS Monte Carlo event generator. Such a process requires a dedicated treatment since it is plagued by quantum electrodynamics (QED) divergences in the limit where any photons become collinear to a quark. After briefly introducing the Powheg Box event generator and the MiNNLOPS method, I present the dedicated tools devised for this calculation. I begin by describing a generic way to deal with any process with a divergent Born cross section in the Powheg Box event generator without applying any generation-level cuts. I then present a mapping that prevents QED-finite configurations with one final-state parton from being projected to singular configurations with no final-state partons. Finally, I discuss several modifications to the original version of the MiNNLOPS method aimed at reducing the size of spurious contributions beyond NNLO. After passing the events through the Pythia8 parton shower, I conclude by showing several distributions of phenomenological interest and comparing them with the most recent LHC data from the ATLAS experiment.

Cette thèse présente une étude dédiée du rayonnement supplémentaire dans les événements e⁺e⁻ → µ⁺µ⁻γ et e⁺e⁻ → π⁺π⁻γ avec un rayonnement dans l’état initial (ISR). L’étude est basée sur les données recueillies par le détecteur BABAR, correspondant à une luminosité intégrée de 424,2 fb⁻¹ et 43,9 fb⁻¹ à la résonance Y(4S) et en dessous de la résonance, respectivement. Les événements ISR à deux corps sont sélectionnés en exigeant que l’énergie du photon ISR dans le système du centre de masse E^*_ γISR soit supérieure à 4 GeV et que ISR l’angle polaire dans le laboratoire soit compris entre 0,35 et 2,4 rad, et qu’il y ait exactement deux traces avec les charges opposées, chacune avec une impulsion transverse p_T > 0,1 GeV et dans la plage angulaire entre 0,4 et 2,45 rad. Dans les événements avec deux candidats photons ISR, le photon ISR est choisi comme étant celui avec l’énergie E^*_ γISR la plus élevée. Des ajustements cinématiques d’ordre suivant (NLO) et d’ordre supérieur (NNLO) sont effectués pour étudier le rayonnement d’un ou deux photons respectivement dans les états initiaux et finals en plus du photon ISR. Plusieurs arbres de décision boostés (BDTs) basés sur la technique multivariée sont réalisés pour (1) déterminer les facteurs de normalisation des bruits de fonds multihadrons simulés à partir des processus qqbar et 3π, (2) séparer les signaux dimuon et dipion des bruits de fond dans un plan bidimensionnel en χ² d’ajustements cinématiques avec un photon supplémentaire à petit ou grand angle, et (3) supprimer les contributions des bruits de fond dans des échantillons de dipions avec deux photons supplémentaires. Suivant les méthodes de l’analyse précédente de BABAR, de nouveaux résultats sont présentés sur les processus NLO et comparés aux prédictions, en comparaison avec les prédictions des générateurs Monte Carlo (MC) PHOKHARA et AFKQED. La comparaison révèle des écarts dans les taux et également dans les distributions angulaires du photon supplémentaire entre les données et le générateur PHOKHARA. Le désaccord observé a un effet négligeable sur la mesure BABAR de la section efficace du dipion, mais il pourrait affecter de manière plus significative d’autres mesures basées sur la méthode ISR. Pour approfondir les résultats de l’analyse NLO, une analyse 0C basée sur la reconstruction cinématique à zéro contrainte de l’échantillon complet de muons est effectuée et valide le désaccord observé. Les contributions substantielles de NNLO sont étudiées et quantifiées dans les processus dimuon et dipion. Les implications de ces résultats pour d’autres expériences sont brièvement discutées et comparées
This thesis presents a dedicated study of additional radiation in e⁺e⁻ → µ⁺µ⁻γ and e⁺e⁻ → π⁺π⁻γ initial-state-radiation (ISR) events. This study is based on the data collected by the BABAR detector, corresponding to an integrated luminosity of 424.2 fb⁻¹ and 43.9 fb⁻¹ at and below the Y(4S) resonance, respectively. Two-body ISR events are selected by requiring the ISR photon energy in the center-of-mass frame E^*_ γISR be greater than 4 GeV and the laboratory polar angle in the range 0.35-2.45 rad, and exactly two opposite charged tracks, each with transverse momentum p_T > 0,1 GeV and within the angular range 0.40-2.45 rad. In the events with two ISR photon candidates, the ISR photon is chosen to be that with the higher E^*_ γISR. Kinematic fits of next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) are performed to probe the radiation of one or two photons respectively in the initial and final states in addition to the ISR photon. Several boosted decision trees (BDTs) based on the multivariate technique are performed to (1) determine the normalization factors for simulated multihadron backgrounds from qqbar and 3π processes, (2) separate dimuon and dipion signals from backgrounds in a two-dimensional χ² plane of kinematic fits with a small-or large-angle additional photon, and (3) suppress background contributions in dipion samples with two additional photons. New results are presented for processes at NLO following the previous BABAR analysis, comparing with predictions from PHOKHARA and AFKQED Monte Carlo (MC) generators. The comparison reveals discrepancies in the one-photon rates and the PHOKHARA generator. The observed disagreement has a negligible effect on the BABAR measurement of the dipion cross section, but it could affect other ISR-based measurements more significantly. To further investigate the results from the NLO analysis, a 0C analysis which stands for zero constraint kinematic reconstruction of the full muon sample is performed and validates the observed disagreement. Substantial NNLO contributions are studied and quantified in both dimuon and dipion processes. Implications of these results for other experiments are briefly discussed and compared