Academic literature on the topic 'NLO/NNLO calculation'

Most of current Monte Carlo studies on the Higgs searching are based on LO, or NLO calculation. However, in recent years, the next-to-next-to-leading order (NNLO) corrections have been computed for some physics process, and found that the cross section increases the kinematics changes. As the results, the analysis results could be impacted by these high order QCD corrections. We use standard Monte Carlo generator for LO, as well as MC@NLO for NLO and ResBos for NNLO at 7 TeV of LHC to evaluate this impact for physics channel of the Higgs, mass at 165 GeV, to WW, then W decay to lepton and neutrino as the final states. We found the signal rate could be effected by ratio of 1:2.6:3.4 for LO, NLO and NNLO using the same standard H→WW→lνlν searching analysis process.6

We compute cross sections for the Drell–Yan process in nuclear collisions at next-to-leading order (NLO) in αs. The effects of shadowing on the normalization and on the mass and rapidity dependence of these cross sections are presented. An estimate of higher order corrections is obtained from next-to-next-to-leading order (NNLO) calculation of the rapidity-integrated mass distribution. Variations in these predictions resulting from choices of parton distributions sets are discussed. Numerical results for mass distributions at NLO are presented for RHIC and LHC energies, using appropriate rapidity intervals. The shadowing factors in the dilepton mass range 2 < M < 10 GeV are predicted to be substantial, typically 0.5 - 0.7 at LHC, 0.7 - 0.9 at RHIC, and approximately independent of the choice of parton distribution sets and the order of calculation.

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 * .

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 ALICE experiment is designed to study the properties of the matter created in proton-proton and heavy-ion collisions at the LHC. Neutral mesons can be reconstructed in ALICE in a wide range of transverse momenta via two-photon decays. Neutral meson measurements in pp collisions give an opportunity to validate the NLO or NNLO pQCD calculations and to constrain the parton distribution functions and the parton fragmentation functions. Neutral meson spectra measured in pA and AA collisions allow us to test a modification of the parton distribution functions in nuclei and the parton energy loss in the hot matter created in AA collisions. The recent results from ALICE on direct photon measurements in the Pb–Pb, neutral pion and n meson productions in pp, p-Pb, and Pb–Pb collisions are presented.

The reaction of PtCl2 with s-triazine-type ligand (HTriaz) (1:1) in acetone under heating afforded a new [Pt(Triaz)Cl] complex. Single-crystal X-ray diffraction analysis showed that the ligand (HTriaz) is an NNO tridentate chelate via two N-atoms from the s-triazine and hydrazone moieties and one oxygen from the deprotonated phenolic OH. The coordination environment of the Pt(II) is completed by one Cl−1 ion trans to the Pt-N(hydrazone). Hirshfeld surface analysis showed that the most dominant interactions are the H···H, H···C and O···H intermolecular contacts. These interactions contributed by 60.9, 11.2 and 8.3% from the whole fingerprint area, respectively. Other minor contributions from the Cl···H, C···N, N···H and C···C contacts were also detected. Among these interactions, the most significant contacts are the O···H, H···C and H···H interactions. The amounts of the electron transfer from the ligand groups to Pt(II) metal center were predicted using NBO calculations. Additionally, the electronic spectra were assigned based on the TD-DFT calculations.

AbstractThe Oligo–Miocene Ardestan quartz diorite to tonalite is part of widespread Cenozoic magmatism within the Urumieh–Dokhtar Magmatic Assemblage of Iran. The Ardestan pluton is composed mainly of varying proportions of plagioclase feldspar (normally zoned from bytownite to andesine), amphibole (magnesio-hornblende) and biotite. Biotite exhibits a range of Al values (~2–2.8 apfu) over very restricted Fe# ratios (0.42–0.56) which are characteristic of continental arc magmatic suites. High Ti2O contents of biotite (<6.1 wt.%) suggest a magmatic origin. Ti-in-biotite geothermometery gives a mean crystallisation temperature of 730 ± 56°C, slightly higher than calculated TZr.Ti°C (716 ± 50°C) and similar to the average TZr.sat°C (735 ± 26°C). These results are consistent with the low bulk-rock SiO2 contents, which provide minimum estimates of temperature and indicate zircon crystallised from a fractionated magma. Zircons from the Ardestan pluton have high (Sm/La)N (>10) ratios suggesting a magmatic origin. T–$f_{{\rm O}_{\rm 2}}$ calculations of oxygen fugacity between –13.6 to –16.9 indicate oxidising crystallisation conditions between the Ni–NiO (NNO) and Fe2O3–Fe3O4 (HM) buffers. Tight linear trends of log (XF/XOH), log (XCl/XOH) and log (XCl/XOH) vs. XMg represent a narrow range of $f_{{\rm H}_2O}$, fHF and fHCl, clearly indicating that physico-chemical conditions were essentially constant throughout the formation of magmatic biotite. The shape of crystal size distribution curves along with the medium Al and Mg contents in amphibole and biotite, respectively, are consistent with a history of magma mixing involving injections of basic magma into the evolving felsic chamber. Calculated residence time for Ardestan plagioclase crystals of ~630 years support field evidence that these plutons were emplaced at shallow depths.

Abstract We present a calculation of t-channel single-top-quark production and decay in the five-flavor scheme at NNLO. Our results resolve a disagreement between two previous calculations of this process that found a difference in the inclusive cross section at the level of the NNLO coefficient itself. We compare in detail with the previous calculations at the inclusive, differential and fiducial level including b-quark tagging at a fixed scale μ = mt. In addition, we advocate the use of double deep inelastic scattering (DDIS) scales (μ2 = Q2 for the light-quark line and μ2 = Q2 + $$ {m}_t^2 $$ m t 2 for the heavy-quark line) that maximize perturbative stability and allow for robust scale uncertainties. All NNLO and NLO⊗NLO contributions for production and decay are included in the on-shell and vertex-function approximation. We present fiducial and differential results for a variety of observables used in Standard Model and Beyond Standard Model analyses, and find an important difference between the NLO and NNLO predictions of exclusive t + n-jet cross sections. Overall we find that NNLO corrections are crucial for a precise identification of the t-channel process.

Abstract The energy dependence of the total hadroproduction cross section of pseudoscalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to $$ {\alpha}_s^n{\ln}^{n-1} $$ α s n ln n − 1 (1/z), to the CF hard-scattering coefficient, where z = M2/$$ \hat{s} $$ s ̂ with M and $$ \hat{s} $$ s ̂ being the quarkonium mass and the partonic center-of-mass energy squared. The resummation is performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic (DL) approximation, which is a subset of the leading logarithmic ln(1/z) approximation. Doing so, one remains strictly consistent with the NLO and NNLO DGLAP evolution of the PDFs. By improving the treatment of the small-z asymptotics of the CF coefficient function, the resummation cures the unphysical results of the NLO CF calculation. The matching is directly performed in the z-space and, for the first time, by using the Inverse-Error Weighting (InEW) matching procedure. As a by-product of the calculation, the NNLO term of the CF hard-scattering coefficient proportional to $$ {\alpha}_s^2 $$ α s 2 ln(1/z) is predicted from HEF.

La tesi si occupa delle correzioni di potenza calcolate su un parametro-soglia di momento trasverso che interessano calcoli perturbativi di ordine superiore nella costante di accoppiamento forte. In particolare, si impone un parametro-soglia di momento trasverso, qt_cut, su uno stato finale bianco e si calcolano le correzioni di potenza sul parametro-soglia, fino alla quarta potenza, per la sezione d'urto inclusiva al primo ordine sottodominante in QCD. Inoltre, si considera lo stesso processo al secondo ordine sottodominante in QCD, limitandosi al contributo reale-virtuale, e si calcolano le correzioni di potenza per la sezione d'urto inclusiva sino alla seconda potenza sul parametro-soglia. Lo studio della dipendenza della sezione d'urto dal parametro-soglia permette di approfondire il comportamento della prima nei limiti dello spazio delle fasi, dando indizi sulla struttura a tutti gli ordini nella costante di accoppiamento forte e sull'identificazione di caratteristiche universali. La conoscenza delle correzioni di potenza è poi un ingrediente fondamentale per ridurre la dipendenza delle sezioni d'urto di QCD dal parametro-soglia quando viene applicato un metodo slicing come la sottrazione-qt. Si presentano, quindi, risultati analitici per la produzione di un bosone vettore e per la produzione di un bosone di Higgs al primo ordine sottodominante in QCD, e per la parte reale-virtuale del canale qg per la produzione di un bosone vettore al secondo ordine. Nel dettaglio, si illustra una procedura generale per il calcolo delle correzioni di potenza sul parametro-soglia. Per mostrare l'impatto numerico di tali correzioni, si presentano dei risultati numerici e si discute di come la dipendenza residuale da qt_cut interessi la sezione d'urto totale della produzione di un bosone Z o di un bosone di Higgs presso LHC. La seconda parte della tesi, complementare alla prima, è dedicata allo sviluppo di un'interfaccia tra MadGraph5_aMC@NLO e POWHEG BOX, al fine di coniugare la flessibilità di MadGraph quando genera gli elementi di matrice per processi del Modello Standard o di sue estensioni, con tutte le caratteristiche di POWHEG BOX. Tra di esse, la possibilità di generare eventi con peso positivo è fondamentale e rende POWHEG uno dei metodi più usati quando sono necessari campioni molto numerosi. Al fine di testare l'interfaccia, si studia la produzione di un bosone di spin 0 assieme a due getti, con accoppiamenti che violano CP. Si discutono delle distribuzioni che caratterizzano le proprietà del bosone e alcuni risultati ottenuti con la funzione di ripesamento di POWHEG BOX. Infine, si presentano alcune distribuzioni ottenute con il metodo MiNLO.<br>The thesis deals with the power corrections in a transverse-momentum cutoff that affect perturbative calculations at higher orders in the strong coupling constant. In particular, we impose a transverse-momentum cutoff, qt_cut, on a colourless final state and we compute the power corrections for the inclusive QCD next-to-leading-order cross section in the cutoff, up to the fourth power. We also consider the same production process at next-to-next-to-leading order in QCD, restricting ourselves to the real-virtual contribution, and we compute the power corrections up to the second power in the cutoff for the inclusive cross section. The study of the dependence of the cross section on qt_cut allows for an understanding of its behaviour at the boundaries of the phase space, giving hints on the structure at all orders in the strong coupling constant and on the identification of universal patterns. The knowledge of such power corrections is also a required ingredient in order to reduce the dependence on the transverse-momentum cutoff of the QCD cross sections at higher orders, when the qt-subtraction method, i.e. a slicing scheme, is applied. We present analytic results for both Drell-Yan vector-boson and Higgs-boson production in gluon fusion at next-to-leading order in QCD, and for the real-virtual part of the qg-initiated channel of vector-boson production at NNLO in QCD. In particular, we illustrate a process-independent procedure for the calculation of the all-order power corrections in the cutoff. In order to show the impact of the power-correction terms, we present selected numerical results and discuss how the residual dependence on qt_cut affects the total cross section for Drell-Yan Z production and Higgs boson production via gluon fusion at the Large Hadron Collider. A second and complementary part of the thesis is devoted to the development of an interface between MadGraph5_aMC@NLO and the POWHEG BOX framework, in order to match the flexibility of MadGraph for the generation of matrix elements for Standard-Model processes and for several of its extensions, to all features of the POWHEG BOX framework. Among those, it is essential the possibility, via the POWHEG method, to generate events with positive weights, which makes it the method of choice when large samples of events are needed. As a proof of concept, we provide a phenomenological study for the production of a spin-0 Higgs-like boson, in association with up to two jets, with CP-violating couplings. We discuss a few distributions able to characterise the spin-0 boson CP properties, and discuss a few results obtained using the POWHEG BOX reweighting feature. We also present a few distributions obtained with the MiNLO method.

In this thesis the task of computing higher order corrections to QCD scattering processes for the LHC is considered, specifically Next-to Leading Order (NLO) and Next-toNext-to Leading Order (NNLO) perturbative QCD corrections. The infrared (IR) divergent behaviour of the cross section is isolated using the antenna subtrac- tion formalism. This method has previously been used at NNLO in the calculation of jet production in the context of e+e− annihilation and for the leading colour contribution to dijet production via pure gluon scattering. The research presented in this thesis extends the formalism to include scattering processes involving quarks with initial-state partons. General formulae, including sub-leading colour contributions, are presented for the isolation and cancellation of IR and singularities when calculating the production of colourless final-states at the LHC at NLO and NNLO accuracy. The leading colour NNLO correction to the sub-process qq ̄ → gg is calculated and numerical results are presented to demonstrate the convergence of the physical cross section and the subtraction terms in the various unresolved limits. The calculations are organised with the aid of convenient quantities, referred to as integrated antenna strings. Using these quantities, the full calculation displays a clear and predictive structure, in particular at the double virtual level where the structures presented are new.

The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation. Our main results include explicit formulas for a subset of the integral coefficients, expressing them as products of tree-level amplitudes integrated over specific contours in the complex plane. We give a general selection principle for determining these contours. This principle is then applied to obtain the coefficients of integrals with the topology of a double box. We show that, for four-particle scattering, each double-box integral in the two-loop basis is associated with a uniquely defined complex contour, referred to as its master contour. We provide a classification of the solutions to setting all propagators of the general double-box integral on-shell. Depending on the number of external momenta at the vertices of the graph, these solutions are given as a chain of pointwise intersecting Riemann spheres, or a torus. This classification is needed to define master contours for amplitudes with arbitrary multiplicities. We point out that a basis of two-loop integrals with as many infrared finite elements as possible allows substantial technical simplications, in terms of obtaining the coefficients of the integrals, as well as for the analytic evaluation of the integrals themselves. We compute two such integrals at four points, obtaining remarkably compact expressions. Finally, we provide a check on a recently developed recursion relation for the all-loop integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory, examining the two-loop six-gluon MHV amplitude and finding agreement. The validity of the approach to two-loop amplitudes developed in this thesis extends to all four-dimensional gauge theories, in particular QCD. The approach is suited for obtaining compact analytical expressions as well as for numerical implementations.

In this thesis we consider the phenomenology of the theory of strong interactions, Quantum Chromodynamics (QCD), with particular reference to the ongoing experimental program at the Large Hadron Collider in CERN. The current progress in precision measurement of Standard Model processes at the LHC experiments must be matched with corresponding precision in theoretical predictions, and to this end we present calculations at next-to-next-to-leading order in perturbation theory of observable quantities involving quarks and gluons, the strongly interacting particles of the SM. Such calculations form the most important class of corrections to observables and are vital if we are to untangle signals of New Physics from LHC data. We consider in particular the amplitudes for five parton interactions at 1- and 2-loop order and present full (in the 1-loop case) and partial (in the 2-loop case) analytic results in terms of rational functions of kinematic invariants multiplying a basis of master integrals. We address the problem of the solution of a system of integration-by-parts identities for Feynman integrals and demonstrate how some current difficulties may be overcome. We consider also the properties of the top quark, and present the NNLO, real-virtual contributions to the calculation of its decay rate. The results are presented as helicity amplitudes so that the full behaviour of the top spin is retained. These amplitudes constitute a necessary ingredient in the complete calculation of top quark pair production and decay at NNLO which will be an important theoretical input to many experimental analyses. Turning to a more phenomenological study, we consider the extraction of two important SM parameters, the top mass and the strong coupling constant, from measurements of top pair production at the ATLAS and CMS experiments. We compare with NNLO theory predictions and use a least-squares method to extract the values of the parameters simultaneously. We find best fit values of the parameters which are compatible with previous extractions performed using top data with the current world averages published by the Particle Data Group. We consider the issue of PDF choice and the circumstances in which a heavy quark can be considered a constituent of the proton. In particular, we look at the production of a Higgs boson in association with bottom quarks in four and five flavour schemes, in which the b may or may not be included in the initial state. We show that theoretical predictions in both schemes are well-motivated and appropriate in different scenarios, and moreover that results in the schemes are consistent provided a judicious choice of the renormalisation and factorisation scales is made. We suggest a typical scale choice motivated by considerations of consistency and find it to be somewhat lower than the typical hard scale of the process.