Next-to-leading Order Predictions Research Articles

Studies of Z boson decay into double ϒ mesons at the NLO QCD accuracy

In this paper, we employ the nonrelativistic quantum chromodynamics (QCD) factorization to conduct a comprehensive examination of the Z boson decay into a pair of ϒ mesons, achieving accuracy at the next-to-leading-order (NLO) in αs. Our calculations demonstrate that the quantum electrodynamics (QED) diagrams are indispensable in comparison to the pure QCD diagrams, and the implementation of QCD corrections markedly enhances the QCD results, whereas it substantially diminishes the QED results. To ensure consistency with the experimental methodology, we have taken into account the feed-down transitions originating from higher excited states, which exhibit significant relevance. Combining all the contributions, we arrive at the NLO prediction of BZ→ϒ(nS)+ϒ(mS)∼10−11, which is notably lower than the upper limits set by CMS. Published by the American Physical Society 2024

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions.

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Predictions for exclusive varUpsilon photoproduction in ultraperipheral {textrm{Pb}}+{textrm{Pb}} collisions at the LHC at next-to-leading order in perturbative QCD

We present predictions for the rapidity-differential cross sections of exclusive varUpsilon photoproduction in ultraperipheral collisions (UPCs) of lead ions at the Large Hadron Collider (LHC). We work in the framework of collinear factorization at next-to-leading order (NLO) in perturbative QCD, modeling the generalized parton distributions (GPDs) through the Shuvaev transform of nuclear parton distribution functions (nPDFs). Our direct NLO predictions depend significantly on nPDF uncertainties and on the choices of the factorization and renormalization scales, but to a much lesser degree on GPD modeling. To tame the scale dependence and to account for the fact that the NLO calculations generally underpredict the photoproduction measurements on protons, we also present alternative, data-driven predictions. In this approach the underlying photoproduction cross sections on lead are found by combining their nuclear modifications calculated at NLO with the measured photoproduction cross sections on protons. The data-driven strategy reduces the uncertainties associated with the scale choices, and essentially eliminates the effects of GPD modeling thereby leaving the cross sections sensitive mainly to the input nPDFs. Our estimates indicate that the process is measurable in {textrm{Pb}}+{textrm{Pb}} collisions at the LHC.

Determination of diffractive PDFs from a global QCD analysis of inclusive diffractive DIS and dijet cross-section measurements at HERA

We present an updated set of {\tt SKMHS} diffractive parton distribution functions (PDFs). In addition to the diffractive deep-inelastic scattering (diffractive DIS) data sets, the recent diffractive dijet cross sections measurements by the H1 experiment from the HERA collider are added to the data sample. The new set of diffractive PDFs, entitled {\tt SKMHS23} and {\tt SKMHS23-dijet}, are presented at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. Since the gluons directly contribute to jet production through the boson-gluon fusion process, the data on diffractive dijet production in inclusive DIS help to constrain the gluon density, allowing for the determination of both the quark and gluon densities with better accuracy. The NLO and NNLO theory predictions calculated using both {\tt SKMHS23} and {\tt SKMHS23-dijet} are compared to the analyzed data showing excellent agreements. The effect arising from the inclusion of diffractive dijet data and higher order QCD corrections on the extracted diffractive PDFs and data/theory agreements are clearly examined and discussed.

Multiplicity dependence of charged-particle jet production in pp collisions at mathbf {sqrt{s}}=mathbf {13~TeV}

The multiplicity dependence of jet production in pp collisions at the centre-of-mass energy of sqrt{s} = 13 {mathrm {TeV}} is studied for the first time. Jets are reconstructed from charged particles using the anti-k_mathrm {T} algorithm with resolution parameters R varying from 0.2 to 0.7. The jets are measured in the pseudorapidity range |eta _{mathrm{jet}}|< 0.9-R and in the transverse momentum range 5<p_mathrm {T,jet}^{mathrm{ch}}<140 {mathrm {GeV}}/c. The multiplicity intervals are categorised by the ALICE forward detector V0. The p_{mathrm T} differential cross section of charged-particle jets are compared to leading order (LO) and next-to-leading order (NLO) perturbative quantum chromodynamics (pQCD) calculations. It is found that the data are better described by the NLO calculation, although the NLO prediction overestimates the jet cross section below 20 {mathrm {GeV}}/c. The cross section ratios for different R are also measured and compared to model calculations. These measurements provide insights into the angular dependence of jet fragmentation. The jet yield increases with increasing self-normalised charged-particle multiplicity. This increase shows only a weak dependence on jet transverse momentum and resolution parameter at the highest multiplicity. While such behaviour is qualitatively described by the present version of PYTHIA, quantitative description may require implementing new mechanisms for multi-particle production in hadronic collisions.

Differential distributions for single top quark production at the LHeC

We present a phenomenological study of the single top (anti-)quark production with leptonic decays at the Large Hadron electron Collider (LHeC) at the next-to-leading-order (NLO) in QCD. We focus on various differential distributions in a fiducial region. The NLO corrections can reduce the fiducial cross section by 14%. We find the NLO predictions exhibit strong stability under scale variations for most observables considered while the scale variations at the leading-order (LO) dominated in the theoretical uncertainties. We propose a method of determining the top-quark mass using the measurement of the average transverse momentum of the charged lepton. The scale variations at the NLO induce a theoretical uncertainty of about 1.3 GeV of the extracted top-quark mass. The statistical error of the extracted top-quark mass amounts to 1.1 GeV. We also investigate the impact of the QCD corrections and the scale variations in searches of the anomalous Wtb couplings.

Curing the unphysical behaviour of NLO quarkonium production at the LHC and its relevance to constrain the gluon PDF at low scales

We address the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-to-Leading Order (NLO) in alpha _s which we attribute to an over-subtraction in the factorisation of the collinear singularities inside the PDFs in the overline{text {MS}} scheme. Such over- or under-subtractions have a limited phenomenological relevance in most of the scattering processes in particle physics. On the contrary, it is particularly harmful for P_T-integrated charmonium hadroproduction which renders a wide class of NLO results essentially unusable. Indeed, in such processes, alpha _s is not so small, the PDFs are not evolved much and can be rather flat for the corresponding momentum fractions and, finally, some process-dependent NLO pieces are either too small or too large. We propose a scale-fixing criterion which avoids such an over-subtraction. We demonstrate its efficiency for eta _{c,b} but also for a fictitious light elementary scalar boson. Having provided stable NLO predictions for eta _{c,b}P_T-integrated cross sections, sigma ^{mathrm{NLO}}_{eta _Q}, and discussed the options to study eta _{b} hadroproduction, we argue that their measurement at the LHC can help better determine the gluon PDF at low scales and tell whether the local minimum in conventional NLO gluon PDFs around x=0.001 at scales below 2 GeV is physical or not.

$${W}^{{\pm}}{/Z}$$ Cross Section Ratios Through (N)NLO Predictions in QCD

This paper presents $$W^{\pm}/Z$$ cross section ratio predictions for the $$W$$ and $$Z$$ boson productions in their subsequent electron decay channels with next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) calculations in perturbative QCD. The predicted ratios from the fiducial cross sections are primarily compared with the ATLAS measurement based on 13 TeV LHC proton–proton collisions. The predicted fiducial ratios for 14 TeV proton–proton collisions are also presented at (N)NLO accuracies. The 13 TeV and 14 TeV differential distributions for the ratios are provided as a function of the boson transverse momentum at NNLO using different parton distribution functions (PDFs). The 13 TeV and 14 TeV differential distributions for the ratios are also provided for the boson production in association with at least one jet as functions of the first leading jet transverse momentum and absolute pseudorapidity at NLO using various PDF sets. The focus is to predict the ratios more precisely in terms of the reduced theoretical scale uncertainties for the fiducial calculations and to assess sensitivity of the ratios to different PDF sets for the differential calculations. The 13 TeV ratio is predicted as 10.55 $$\pm$$ 0.35 at NLO and 10.57 $$\pm$$ 0.07 at NNLO and found to be in good agreement with the ATLAS data. The 14 TeV ratio is predicted consistently as 10.50 $$\pm$$ 0.36 at NLO and 10.37 $$\pm$$ 0.07 at NNLO. Estimated scale uncertainties are reduced to less than percent level at NNLO in the fiducial ratios. The differential ratios distributions are consistently predicted by using different PDF sets at both 13 TeV and 14 TeV. The differential ratios exhibit more sensitivity to choice of PDF sets in higher regions of the distributions.

Parton distributions with theory uncertainties: general formalism and first phenomenological studies

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology. In addition, we also compare the results based on the theory covariance matrix formalism to those obtained by performing PDF determinations based on different scale choices.

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We present an event-file format for the dissemination of next-to-leading-order (NLO) predictions for QCD processes at hadron colliders. The files contain all information required to compute generic jet-based infrared-safe observables at fixed order (without showering or hadronization), and to recompute observables with different factorization and renormalization scales. The files also make it possible to evaluate cross sections and distributions with different parton distribution functions. This in turn makes it possible to estimate uncertainties in NLO predictions of a wide variety of observables without recomputing the short-distance matrix elements. The event files allow a user to choose among a wide range of commonly-used jet algorithms and jet-size parameters.We provide event files for a W or Z boson accompanied by up to four jets, and for pure-jet events with up to four jets. The files are for the Large Hadron Collider with a center of mass energy of 7 or 8 TeV.A C++ library along with a Python interface for handling these files is also provided and described in this article. The library allows a user to read the event files and recompute observables transparently for different pdf sets and factorization and renormalization scales.Program title: nTupleReaderCatalogue identifier: AESC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 62761No. of bytes in distributed program, including test data, etc.: 442886Distribution format: tar.gzProgramming language: C++ with Python interface.Computer: Workstations.Operating system: Linux, MacOS.RAM: Varying bytesClassification: 11.1, 11.5.External routines: ROOT, LHAPDFNature of problem:NLO QCD predictions for vector boson + jets and jet processes for generic observables.Solution method:Event files containing all information required to compute generic jet-based infrared-safe observables at fixed order and to recompute observables with different factorization and renormalization scales are provided. The library provides an interface to access the information in these files.Running time:The runtime scales linearly with the file size.

Inclusive hc production and energy spectrum from e+e− annihilation at a super B factory

We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^+e^-$ annihilation at Super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO short-distance coefficient (SDC) accompanying the color-octet production operator $\mathcal{O}_8^{h_c}(^1S_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphysical endpoint singularity. With the aid of the soft-collinear effective theory, those large endpoint logarithms are resummed to the next-to-leading logarithmic (NLL) accuracy. Consequently, further supplemented with the non-perturbative shape function, we obtain the well-behaved predictions for the $h_c$ energy spectrum in the entire kinematic range, which awaits the examination by the forthcoming Belle II experiment.

Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD

Hard processes in diffractive deep-inelastic scattering can be described by a factorisation into parton-level subprocesses and diffractive parton distributions. In this framework, cross sections for inclusive dijet production in diffractive deep-inelastic electron–proton scattering (DIS) are computed to next-to-next-to-leading order (NNLO) QCD accuracy and compared to a comprehensive selection of data. Predictions for the total cross sections, 40 single-differential and four double-differential distributions for six measurements at HERA by the H1 and ZEUS collaborations are calculated. In the studied kinematical range, the NNLO corrections are found to be sizeable and positive. The NNLO predictions typically exceed the data, while the kinematical shape of the data is described better at NNLO than at next-to-leading order (NLO). A significant reduction of the scale uncertainty is achieved in comparison to NLO predictions. Our results use the currently available NLO diffractive parton distributions, and the discrepancy in normalisation highlights the need for a consistent determination of these distributions at NNLO accuracy.

The Matrix Element Method at next-to-leading order QCD for hadronic collisions: single top-quark production at the LHC as an example application

Recently, a general algorithm to extend the Matrix Element Method (MEM) by taking into account next-to-leading-order (NLO) corrections in quantum chromodynamics (QCD) has been presented. In this article, the algorithm is applied to the most general case that coloured partons are encountered in the initial as well as the final state. This represents a substantial extension compared to previous work. As a concrete example, the production of single top quarks at the LHC is studied. We present in detail the generation of unweighted events following the NLO predictions. By treating these events as the result of a toy experiment, we show the first proof-of-principle application of the Matrix Element Method at NLO QCD for hadronic jet production. As an illustration, we study the determination of the top-quark mass. We find that — apart from elevating the powerful MEM to a sound theoretical foundation at NLO — the inclusion of the NLO corrections can lead to sizeable effects compared to the Matrix Element Method relying on leading-order predictions only. Furthermore, we find that the incorporation of the NLO corrections is mandatory to obtain reliable estimates of the theoretical uncertainties. In addition, this work shows that measuring the top-quark mass using the MEM in single top-quark production offers an interesting alternative to mass measurements in top-quark pair production.

Next-to-leading-order QCD and electroweak corrections to WWW production at proton-proton colliders

Triple-W-boson production in proton-proton collisions allows for a direct access to the triple and quartic gauge couplings and provides a window to the mechanism of electroweak symmetry breaking. It is an important process to test the Standard Model (SM) and might be background to physics beyond the SM. We present a calculation of the next-to-leading order (NLO) electroweak corrections to the production of WWW final states at proton-proton colliders with on-shell W bosons and combine the electroweak with the NLO QCD corrections. We study the impact of the corrections to the integrated cross sections and to kinematic distributions of the W bosons. The electroweak corrections are generically of the size of 5-10% for integrated cross sections and become more pronounced in specific phase-space regions. The real corrections induced by quark-photon scattering turn out to be as important as electroweak loops and photon bremsstrahlung corrections, but can be reduced by phase-space cuts. Considering that prior determinations of the photon parton distribution function (PDF) involve rather large uncertainties, we compare the results obtained with different photon PDFs and discuss the corresponding uncertainties in the NLO predictions. Moreover, we determine the scale and total PDF uncertainties at the LHC and a possible future 100 TeV pp collider.

Accurate predictions for charged Higgs production: Closing the [formula omitted] window

We present predictions for the total cross section for the production of a charged Higgs boson in the intermediate-mass range (mH±∼mt) at the LHC, focusing on a type-II two-Higgs-doublet model. Results are obtained at next-to-leading order (NLO) accuracy in QCD perturbation theory, by studying the full process pp→H±W∓bb¯ in the complex-(top)-mass scheme with massive bottom quarks. Compared to lowest-order predictions, NLO corrections have a sizeable impact: they increase the cross section by roughly 50% and reduce uncertainties due to scale variations by more than a factor of two. Our computation reliably interpolates between the low- and high-mass regime. Our results provide the first NLO prediction for charged Higgs production in the intermediate-mass range and therefore allow to have NLO accurate predictions in the full mH± range. The extension of our results to different realisations of the two-Higgs-doublet model or to the supersymmetric case is also discussed.

Charge and matter form factors of two-neutron halo nuclei in halo effective field theory at next-to-leading order

Using halo effective field theory (EFT), an expansion in $R_{core}/R_{halo}$, where $R_{core}$ is the radius of the core and $R_{halo}$ the radius of the halo nucleus, we calculate the charge and neutron form factors of the two-neutron halo nuclei $^{11}$Li, $^{14}$Be, and $^{22}$C to next-to-leading-order (NLO) by treating them as an effective three-body system. From the form factors we extract the point charge and point matter radii, inter-neutron distance, and neutron opening angle. Agreement is found with existing experimental extractions. Results are given for the point charge and point matter radii for arbitrary neutron core scattering effective range, $\rho_{cn}$, that can be used for predictions once $\rho_{cn}$ is measured. Estimates for $\rho_{cn}$ are also used to make NLO predictions. Finally, our point charge radii are compared to other halo-EFT predictions, and setting the core mass equal to the neutron mass our point charge radius is found to agree with an analytical prediction in the unitary limit.

Differential Higgs boson pair production at next-to-next-to-leading order in QCD

We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at 14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp -> HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%.

Global analysis of the experimental data onχcmeson hadroproduction

We carry out a global analysis of the experimental data on the $\chi_c$ production cross section and the ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ at the LHC and the Tevatron. The related long-distance matrix elements (LDMEs) at both leading order (LO) and next-to-leading order (NLO) in the QCD coupling constant are renewed. We also present the transverse momentum distribution of the $\chi_c$ production cross section and the ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ for several experimental conditions and find that NLO predictions agree with all sets of experimental data. By contrast, at LO, one cannot explain all the data with a unique value of the color-octet LDME. A brief analysis of the nonrelativistic QCD scale dependence of the cross sections shows that, for the conditions we are concerned with in this paper, the dependence can be almost totally absorbed into the LDME.

Hadronic production ofWandZbosons at large transverse momentum

We introduce a modified factorization formalism in quantum chromodynamics for hadronic production of $W$ and $Z$ bosons at large transverse momentum $p_T$. When $p_T$ is much larger than the invariant mass $Q$ of the vector boson, this new factorization formalism systematically resums the large fragmentation logarithms, $\alpha_s^m\ln^m(p_T^2/Q^2)$, to all orders in the strong coupling $\alpha_s$. Using our modified factorization formalism, we calculate the next-to-leading order (NLO) predictions for $W$ and $Z$ boson production at high $p_T$ at the CERN Large Hadron Collider and at a future 100 TeV proton-proton collider. Our NLO results are about $5\%$ larger in normalization, and they show improved convergence and moderate reduction of the scale variation compared to the NLO predictions derived in a conventional fixed-order perturbative expansion.

Higgs boson decay into four leptons at NLOPS electroweak accuracy

In view of precision studies of the Higgs sector at the Run II of the LHC, the improvement of the accuracy of the theoretical prediction is becoming a pressing issue. In this framework, we detail a calculation of the full Next-to-Leading Order (NLO) electroweak corrections to Higgs boson decay into four charged leptons, by considering the gold-plated channel H → Z (∗) Z (∗) → 2l2l ′ , l, l ′ = e, μ. We match the NLO corrections with a QED Parton Shower (PS), in order to simulate exclusive multiple photon emission and provide novel results at NLOPS electroweak accuracy. We compare our NLO predictions to those of the program Prophecy4f and present NLOPS phenomenological results relevant for Higgs physics studies, with particular attention to precision measurements of the Higgs boson mass, spin-parity assignment and tests of the Standard Model. Our calculation is implemented in a new code, Hto4l, which can be easily interfaced to any generator describing Higgs boson production. As an example, we provide illustrative results for Higgs production and decay in the process gg → H → 4l using POWHEG with NLOPS accuracy in the production mode.