Approximate NNLO Research Articles

SMEFT chromomagnetic dipole operator contributions to tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t{{\\bar{t}}}$$\\end{document} production at approximate NNLO in QCD

We study higher-order QCD corrections for the production of a top–antitop quark pair (tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t{{\\bar{t}}}$$\\end{document} production) at the Large Hadron Collider in the Standard Model Effective Field Theory. We consider effects of new physics parametrized by the top-quark chromomagnetic dipole operator. We calculate new physics contributions to the total cross section at approximate NNLO, with second-order soft-gluon corrections added to the complete NLO result, including uncertainties from scale dependence and from parton distributions. We also calculate new physics contributions at approximate NNLO for differential distributions in top-quark transverse momentum.

QCD analysis of valence structure functions using deep inelastic lepton-nucleon scattering

A new “” nonsinglet QCD analysis of the structure functions at the NNLO approximation is performed, utilizing the global fit of the data from various charged lepton scattering experiments. We extract the valence parton distribution functions (PDFs) and provide a parametrization of them, along with the correlated errors for a wide range of x and Q2. We compare valence PDFs and their uncertainties with those from different PDF sets provided by various groups. We also obtain valence PDFs and the strong coupling constant αs(MZ2), taking into account the nuclear correction concerning large x as well as the target mass correction (TMC) and higher twist (HT) effects at the NNLO. In the large x region, we extract the higher twist contributions of xF3(x,Q2), F2p(x,Q2), and F2d(x,Q2). We determine αs(MZ2) without and with considering the TMC and HT corrections and perform a comparison with the world average of αs(MZ2) and other reported results. The extracted results concerning valence PDFs with their uncertainties and αs(MZ2) value agree with available theoretical models. Published by the American Physical Society 2024

Soft-gluon corrections in [formula omitted] production

We study higher-order QCD corrections for the associated production of a top-antitop quark pair and a W boson (tt¯W production) in proton-proton collisions. We calculate approximate NNLO (aNNLO) and approximate N3LO (aN3LO) cross sections, with second-order and third-order soft-gluon corrections added to the exact NLO QCD result, and we also include electroweak (EW) corrections through NLO. We calculate uncertainties from scale dependence, which are reduced at higher orders, and from parton distributions, and we also provide separate results for tt¯W+ and tt¯W− production. We compare our results to recent measurements from the LHC, and we find that the aN3LO QCD + NLO EW predictions provide improved agreement with the data. We also calculate differential distributions in top-quark transverse momentum and rapidity and find significant enhancements from the higher-order corrections. This is the first calculation of soft-gluon corrections in single-particle-inclusive kinematics for a 2→3 process where all final-state particles are massive.

Charged Higgs-boson decays into quarks

We consider the full genuine next-to-leading order SUSY–QCD corrections to the charged Higgs decays into quarks supplemented by the NNLO corrections to the effective top and bottom Yukawa couplings. The NNLO corrections to the effective top Yukawa coupling are a new ingredient of our analysis. We arrive at an approximate NNLO prediction for MSSM charged Higgs decays after including the N4LO QCD corrections for large charged Higgs masses. The residual uncertainties are in the percent range or below, depending on the particular MSSM scenario.

Soft-gluon corrections for tqZ production

We study soft-gluon corrections for the associated production of a single top quark and a Z boson (tqZ production) at hadron colliders. We find that the radiative corrections are dominated by soft-gluon emission. We derive an approximate NNLO (aNNLO) cross section by adding second-order soft-gluon corrections to the exact NLO result. We calculate the aNNLO cross section at LHC energies, including uncertainties from scale dependence and from parton distributions. We also calculate differential distributions in top-quark rapidity. We show that the aNNLO corrections are significant and they enhance the NLO cross section while decreasing theoretical uncertainties.

The NNLO QCD analysis of gluon density at small-x

In this paper, a next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) calculation of gluon distribution function at small-[Formula: see text] is presented. The gluon distribution function is explored analytically in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi approach by a Taylor expansion at small-[Formula: see text] as two first-order partial differential equations in two variables: Bjorken [Formula: see text] and [Formula: see text][Formula: see text]. We have solved the system of equations at LO, NLO and NNLO, respectively, by Lagrange’s method. The resulting analytical expressions are compared with the available global parton distribution function fits as well as with the results of the Block–Durand–McKay model. We have further performed an [Formula: see text] test to check the compatibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small-[Formula: see text] region.

Color dipole cross section in the DGLAP improved saturation model

We show that the geometric scaling of the dipole cross section can be explained using standard DGLAP perturbative evolution. The DGLAP-improved saturation model due to the Laplace transform method is considered at LO and NNLO approximations from the experimental data by relying on a Froissart-bounded parametrization of F_{2}(x,Q^{2}). These results are comparable with the Golec-Biernat–Wddot{mathrm {u}}sthoff (GBW) model in a wide kinematic region rQ_{s} which takes into account charm mass. The successful description of {sigma }_{mathrm {dip}}(x,r)/sigma _{0} and {sigma }_{mathrm {dip}}(rQ_{s})/sigma _{0} are presented.

QCD corrections in tqgamma production at hadron colliders

We study QCD corrections for the associated production of a single top quark and a photon (tqgamma production) at hadron colliders. We calculate the NLO cross section at LHC and future collider energies for a variety of kinematical cuts, and we estimate uncertainties from scale dependence and from parton distributions. We also calculate differential distributions in top-quark transverse-momentum and rapidity as well as photon energy. Finally, we study higher-order corrections from soft-gluon emission for this process, and we provide approximate NNLO (aNNLO) results for the cross section and top-quark differential distributions. We also compare our calculations with recent measurements from CMS and ATLAS at the LHC and find that the aNNLO corrections improve the comparison between the data and the Standard Model predictions.

Factorization and Sudakov resummation in leptonic radiative B decay — a reappraisal

The B-meson light-cone distribution amplitude is an important non- perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of B mesons, such as B− → γℓ− overline{nu} . We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the B decay processes at leading order in ΛQCD/mb is most directly contained in the distribution amplitude in Laplace space evaluated near the origin, we propose a convenient parameterization of this object in terms of a small set of uncorrelated hadronic parameters. Using recent results on the three-loop anomalous dimension for heavy-light current operators, we derive an expression for the convolution integral appearing in the B− → γℓ− overline{nu} factorization formula that is explicitly scale independent, and we evaluate this formula at (approximate) NNLO.

Towards a Global QCD Analysis of Fragmentation Functions at Next-to-Next-to-Leading Order Accuracy.

We carry out a global QCD analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order (NNLO) accuracy by performing a fit to the combined set of single-inclusive electron-positron annihilation and, for the first time, semi-inclusive deep-inelastic scattering multiplicity data. For the latter, we utilize the approximate NNLO QCD corrections that were derived recently within the threshold resummation formalism. We explore the impact of the NNLO corrections on the description of the semi-inclusive deep-inelastic scattering datasets in various kinematic regimes and on the resulting pion fragmentation functions.

Higher order approximations to the longitudinal structure function FL from the parametrization of F2 based on the Laplace transformation

We describe the determination of the longitudinal structure function $F_{L}$ at NLO and NNLO approximations, using Laplace transform techniques, into the parametrization of $F_{2}(x,Q^{2})$ and its derivative with respect to $\ln{Q^{2}}$ at low values of the Bjorken variable $x$. The obtained results are comparable with others by considering the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_{f}=4$. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_{L}(x,Q^{2})$ at small $x$ in a wide range of $Q^{2}$ values and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos. The obtained longitudinal structure functions with and without the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, LHeC Collaboration and FCC-he Study Group, P. Agostini et al., J. Phys. G: Nucl. Part. Phys. {\bf48}, 110501(2021).] are compared with the H1 Collaboration data [Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model at NLO and NNLO approximations.

Approximate NNLO QCD corrections to semi-inclusive DIS

We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic (NNLL) accuracy, including the two-loop hard factor. The approximate NNLO terms are obtained by expansion of the resummed expression. They include all terms in Mellin space that are logarithmically enhanced at threshold, or that are constant. In terms of the customary SIDIS variables $x$ and $z$ they include all double distributions (that is, "plus" distributions and $\delta$-functions) in the partonic variables. We also investigate corrections that are suppressed at threshold and we determine the dominant terms among these. Our numerical estimates suggest much significance of the approximate NNLO terms, along with a reduction in scale dependence.

Anomalous couplings in Higgs-boson pair production at approximate NNLO QCD

We combine NLO predictions with full top-quark mass dependence with approximate NNLO predictions for Higgs-boson pair production in gluon fusion, including the possibility to vary coupling parameters within a non-linear Effective Field Theory framework containing five anomalous couplings for this process. We study the impact of the anomalous couplings on various observables, and present Higgs-pair invariant-mass distributions at seven benchmark points characterising different mhh shape types. We also provide numerical coefficients for the approximate NNLO cross section as a function of the anomalous couplings at sqrt{s} = 14 TeV.

Nonlinear corrections on the parametrization methods

We present nonlinear corrections (NLCs) to the distribution functions at low values of x and Q^{2} using the parametrization F_{2}(x,Q^{2}) and F_{L}(x,Q^{2}). We use a direct method to extract nonlinear corrections to the ratio of structure functions and the reduced cross section in the next-to-next-to-leading order (NNLO) approximation with respect to the parametrization method (PM). Comparisons between the nonlinear results with the bounds in the color dipole model (CDM) and HERA data indicate the consistency of the nonlinear behavior of the gluon distribution function at low x and low Q^{2}. The nonlinear longitudinal structure functions are comparable with the H1 Collaboration data in a wide range of Q^{2} values. Consequently, the nonlinear corrections at NNLO approximation to the reduced cross sections at low and moderate Q^{2} values show good agreement with the HERA combined data. These results at low x and low Q^{2} can be applied to the LHeC region for analyses of ultra-high-energy processes.

Soft-gluon corrections for the associated production of a single top quark and a Higgs boson

We discuss soft-gluon resummation for the associated production of a single top quark and a Higgs boson ($tqH$ production) in single-particle-inclusive (1PI) kinematics. We present analytical results for the higher-order corrections and numerical results for the cross sections at LHC energies. We calculate approximate NNLO total rates, including scale dependence and uncertainties from parton distributions, as well as top-quark transverse-momentum and rapidity distributions. In all cases we find that the soft-gluon corrections are dominant and provide important contributions to the total and differential cross sections.

Higher-order corrections for tW production at high-energy hadron colliders

We discuss cross sections for tW production in proton-proton collisions at the LHC and at higher-energy colliders with energies of up to 100 TeV. We find that, remarkably, the soft-gluon corrections are numerically dominant even at very high collider energies. We present results with soft-gluon corrections at approximate NNLO and approximate N3LO matched to complete NLO results. These higher-order corrections are large and need to be included for better theoretical accuracy and smaller scale dependence. Total cross sections as well as top-quark and W-boson transverse-momentum and rapidity distributions are presented using various recent sets of parton distribution functions.

QCD analysis of structure functions in deep inelastic neutrino-nucleon scattering without using the orthogonal polynomials approach

A nonsinglet QCD analysis of neutrino-nucleon structure function is performed based on all the data for charged current neutrino-nucleon deep inelastic scattering (DIS) corresponds to NLO and NNLO approximations, with taking into account the nuclear and higher twist corrections. In this analysis, we extract $xu_v(x,Q^2)$ and $xd_v(x,Q^2)$ valence parton distribution functions (PDFs) in a wide range of $x$ and $Q^2$, and determine their parametrization with the correlated errors using the xFitter framework. Our results regarding valence-quark densities with their uncertainties are compared to the prediction extracted using other PDF sets from different groups. We determine $\alpha_{s}(M_Z^2)$= 0.1199 $\pm$ 0.0031 and 0.1185 $\pm$ 0.0023 with considering the nuclear and higher twist corrections at the NLO and NNLO, respectively, and perform a comparison with other reported results. The extracted results regarding valence-quark distributions and the value of $\alpha_{s}(M_Z^2)$ are in good agreement with available theoretical models.

Thrust distribution in Higgs decays at the next-to-leading order and beyond

We present predictions for the thrust distribution in hadronic decays of the Higgs boson at the next-to-leading order and the approximate next-to-next-to-leading order. The approximate NNLO corrections are derived from a factorization formula in the soft/collinear phase-space regions. We find large corrections, especially for the gluon channel. The scale variations at the lowest orders tend to underestimate the genuine higher order contributions. The results of this paper is therefore necessary to control the perturbative uncertainties of the theoretical predictions. We also discuss on possible improvements to our results, such as a soft-gluon resummation for the 2-jets limit, and an exact next-to-next-to-leading order calculation for the multi-jets region.

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard 'Hessian error' propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering dataset and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$.

Higher-order radiative corrections for bb¯→H−W+

I present higher-order radiative corrections from collinear and soft gluon emission for the associated production of a charged Higgs boson with a $W$ boson. The calculation uses expressions from resummation at next-to-leading-logarithm accuracy. From the resummed cross section I derive analytical formulas at approximate NNLO and N$^3$LO. Total cross sections are presented for the process $b{\bar b} \rightarrow H^- W^+$ at various LHC energies. The transverse-momentum and rapidity distributions of the charged Higgs boson are also calculated.