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Journal articles on the topic 'NLO/NNLO calculation'
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1
WANG, JIAN, GUOMING CHEN, and WEIMIN WU. "THE IMPACT OF LO, NLO AND NNLO FOR THE HIGGS SEARCHING AT $\sqrt{s} = 7$ TeV OF LHC." Modern Physics Letters A 25, no. 36 (2010): 3027–31. http://dx.doi.org/10.1142/s0217732310034146.
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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
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Contogouris, A. P., and G. Grispos. "Approximate calculation of corrections at NLO and NNLO." Nuclear Physics B - Proceedings Supplements 96, no. 1-3 (2001): 94–97. http://dx.doi.org/10.1016/s0920-5632(01)01115-x.
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Eskola, K. J., V. J. Kolhinen, P. V. Ruuskanen, and R. L. Thews. "Effects of Shadowing on Drell–Yan Dilepton Production in High Energy Nuclear Collisions." International Journal of Modern Physics E 12, no. 02 (2003): 197–209. http://dx.doi.org/10.1142/s0218301303001260.
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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.
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Ocalan, Kadir. "Accurate prediction of the Drell-Yan ϕη* distribution in wide dilepton mass and rapidity ranges in pp collisions through NNLO+N3LL". Physica Scripta 96, № 12 (2021): 125323. http://dx.doi.org/10.1088/1402-4896/ac3e19.
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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 * .
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CONTOGOURIS, A. P., and Z. MEREBASHVILI. "APPROXIMATE NEXT-TO-LEADING ORDER AND NEXT-TO-NEXT-TO-LEADING ORDER CORRECTIONS." International Journal of Modern Physics A 18, no. 06 (2003): 957–66. http://dx.doi.org/10.1142/s0217751x03013983.
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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.
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Kovalenko, O. "Neutral Meson and Direct Photon Measurements with the ALICE Experiment." Ukrainian Journal of Physics 64, no. 7 (2019): 602. http://dx.doi.org/10.15407/ujpe64.7.602.
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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.
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Altowyan, Mezna Saleh, Saied M. Soliman, Jamal Lasri, et al. "A New Pt(II) Complex with Anionic s-Triazine Based NNO-Donor Ligand: Synthesis, X-ray Structure, Hirshfeld Analysis and DFT Studies." Molecules 27, no. 5 (2022): 1628. http://dx.doi.org/10.3390/molecules27051628.
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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.
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Babazadeh, Shahrouz, Tanya Furman, John M. Cottle, Davood Raeisi, and Ianna Lima. "Magma chamber evolution of the Ardestan pluton, Central Iran: evidence from mineral chemistry, zircon composition and crystal size distribution." Mineralogical Magazine 83, no. 6 (2019): 763–80. http://dx.doi.org/10.1180/mgm.2019.44.
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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.
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Campbell, John, Tobias Neumann, and Zack Sullivan. "Single-top-quark production in the t-channel at NNLO." Journal of High Energy Physics 2021, no. 2 (2021). http://dx.doi.org/10.1007/jhep02(2021)040.
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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.
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Lansberg, Jean-Philippe, Maxim Nefedov, and Melih A. Ozcelik. "Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections." Journal of High Energy Physics 2022, no. 5 (2022). http://dx.doi.org/10.1007/jhep05(2022)083.
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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.
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Valeshabadi, Ramin Kord, Majid Modarres, and Somayeh Rezaie. "Three-photon productions within the $$k_t$$-factorization at the LHC." European Physical Journal C 81, no. 11 (2021). http://dx.doi.org/10.1140/epjc/s10052-021-09771-9.
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AbstractRecently, the ATLAS data of isolated three-photon production showed that the next-to-leading order (NLO) collinear factorization is not enough to describe experimental data. Therefore, one needs to calculate the cross section beyond the NLO, and as showed later, these data can be well described by the NNLO calculation within the collinear factorization framework. However, it is shown that the $$k_t$$ k t -factorization can be quite successful in describing exclusive and high energy collision processes, henceforth we decided to calculate isolated three-photon production within this framework. In this work we use the Martin, Ryskin, and Watt unintegrated parton distribution functions (MRW UPDFs) at LO and NLO levels, in addition to parton branching (PB) UPDFs in order to calculate cross section which we utilize the KATIE parton level event generator. It will be shown that in contrast to collinear factorization, the $$k_t$$ k t -factorization can describe quiet well the three-photon production ATLAS data. Interestingly our results using the NLO-MRW and PB UPDFs can cover the data within their uncertainty bands, similar to the NNLO collinear results.
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Chawdhry, Herschel A., Michał Czakon, Alexander Mitov, and Rene Poncelet. "NNLO QCD corrections to diphoton production with an additional jet at the LHC." Journal of High Energy Physics 2021, no. 9 (2021). http://dx.doi.org/10.1007/jhep09(2021)093.
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Abstract We calculate the NNLO QCD corrections to diphoton production with an additional jet at the LHC. Our calculation represents the first NNLO-accurate prediction for the transverse momentum distribution of the diphoton system. The improvement in the accuracy of the theoretical prediction is significant, by a factor of up to four relative to NLO QCD as estimated through scale variations. Our calculation is exact except for the finite remainder of the two-loop amplitude which is included at leading color. The numerical impact of this approximated contribution is small. The results of this work are expected to further our understanding of the Higgs boson sector and of the behavior of higher-order corrections to LHC processes.
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Sirunyan, A. M., A. Tumasyan, W. Adam, et al. "Extraction and validation of a new set of CMS pythia8 tunes from underlying-event measurements." European Physical Journal C 80, no. 1 (2020). http://dx.doi.org/10.1140/epjc/s10052-019-7499-4.
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AbstractNew sets of CMS underlying-event parameters (“tunes”) are presented for the pythia8 event generator. These tunes use the NNPDF3.1 parton distribution functions (PDFs) at leading (LO), next-to-leading (NLO), or next-to-next-to-leading (NNLO) orders in perturbative quantum chromodynamics, and the strong coupling evolution at LO or NLO. Measurements of charged-particle multiplicity and transverse momentum densities at various hadron collision energies are fit simultaneously to determine the parameters of the tunes. Comparisons of the predictions of the new tunes are provided for observables sensitive to the event shapes at LEP, global underlying event, soft multiparton interactions, and double-parton scattering contributions. In addition, comparisons are made for observables measured in various specific processes, such as multijet, Drell–Yan, and top quark-antiquark pair production including jet substructure observables. The simulation of the underlying event provided by the new tunes is interfaced to a higher-order matrix-element calculation. For the first time, predictions from pythia8 obtained with tunes based on NLO or NNLO PDFs are shown to reliably describe minimum-bias and underlying-event data with a similar level of agreement to predictions from tunes using LO PDF sets.
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Buccioni, Federico, Jean-Nicolas Lang, Jonas M. Lindert, et al. "OpenLoops 2." European Physical Journal C 79, no. 10 (2019). http://dx.doi.org/10.1140/epjc/s10052-019-7306-2.
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Abstract We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD–EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree–loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications.
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Dasgupta, Mrinal, Basem Kamal El-Menoufi, and Jack Helliwell. "QCD resummation for groomed jet observables at NNLL+NLO." Journal of High Energy Physics 2023, no. 1 (2023). http://dx.doi.org/10.1007/jhep01(2023)045.
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Abstract We use a direct QCD approach to carry out the next-to-next-to-leading logarithmic (NNLL) resummation for observables groomed with the modified mass-drop tagger (Soft Drop β = 0). We focus on observables which are additive given an arbitrary number of soft-collinear emissions. For this class of observables, we arrange the structure of the NNLL terms into two distinct categories. The first defines a simplified inclusive tagger, whereby the NNLL collinear structure is directly related to ungroomed observables. The second defines a clustering correction which takes a particularly simple form when the Cambridge-Aachen (C/A) algorithm is used to cluster the jets. We provide, in addition to the QCD resummation of groomed jet mass, the first NNLL resummed predictions, matched to NLO, for a range of groomed jet angularities with mMDT grooming. Moreover, we also include for the first time in the same calculation, finite zcut effects computed at NLL level alongside the small zcut NNLL results which simultaneously improves upon both of the calculations used for groomed jet mass phenomenological studies to date. While for simplicity we focus on e+e− collisions, the essential NNLL resummation we develop is process independent and hence with the appropriate NLO matching our results are also applicable for hadron collider phenomenology.
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Pozzorini, Stefano, Natalie Schär, and Max Zoller. "Two-loop amplitude generation in OpenLoops." SciPost Physics Proceedings, no. 7 (June 21, 2022). http://dx.doi.org/10.21468/scipostphysproc.7.018.
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Numerical tools, such as OpenLoops, provide NLO scattering amplitudes for a very wide range of hard scattering amplitudes in a fully automated way. In order to match the numerical precision of current and future experiments, however, the higher precision of NNLO calculations is essential, and their automation in a similar tool highly desirable.In our approach, D-dimensional amplitudes are decomposed into loop-momentum tensor integrals with coefficients constructed in four dimensions and rational terms. We present a fully generic algorithm for the efficient numerical construction of the tensor coefficients, which constitutes an important building block for an automated NNLO tool.
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Hu, YaLu, ChuanLe Sun, XiaoMin Shen, and Jun Gao. "Hadronic decays of Higgs boson at NNLO matched with parton shower." Journal of High Energy Physics 2021, no. 8 (2021). http://dx.doi.org/10.1007/jhep08(2021)122.
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Abstract We present predictions for hadronic decays of the Higgs boson at next-to-next-to-leading order (NNLO) in QCD matched with parton shower based on the POWHEG framework. Those include decays into bottom quarks with full bottom-quark mass dependence, light quarks, and gluons in the heavy top quark effective theory. Our calculations describe exclusive decays of the Higgs boson with leading logarithmic accuracy in the Sudakov region and next-to-leading order (NLO) accuracy matched with parton shower in the three-jet region, with normalizations fixed to the partial width at NNLO. We estimated remaining perturbative uncertainties taking typical event shape variables as an example and demonstrated the need of future improvements on both parton shower and matrix element calculations. The calculations can be used immediately in evaluations of the physics performances of detector designs for future Higgs factories.
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Prestel, Stefan. "Matching N3LO QCD calculations to parton showers." Journal of High Energy Physics 2021, no. 11 (2021). http://dx.doi.org/10.1007/jhep11(2021)041.
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Abstract The search for new interactions and particles in high-energy collider physics relies on precise background predictions. This has led to many advances in combining precise fixed-order cross-section calculations with detailed event generator simulations. In recent years, fixed-order qcd calculations of inclusive cross sections at n3lo precision have emerged, followed by an impressive progress at producing differential results. Once differential results become publicly available, it would be prudent to embed these into event generators to allow the community to leverage these advances. This note offers some concrete thoughts on me+ps matching at third order in qcd. As a method for testing these thoughts, a toy calculation of e+e− → u$$ \overline{u} $$ u ¯ at $$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 ) is constructed, and combined with an event generator through unitary matching. The toy implementation may serve also as blueprint for high-precision qcd predictions at future lepton colliders. As a byproduct of the n3lo matching formula, a new nnlo+ps formula for processes with “additional” jets is obtained.
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Saleev, Vladimir. "Production of three isolated photons in the high-energy factorization approach." SciPost Physics Proceedings, no. 8 (July 14, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.167.
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We study large-p_TpT three-photon production at the LHC at the center-of-mass energy \sqrt{s}=8s=8 TeV. We use the LO approximation of the parton Reggeization approach consistently merged with the real NLO corrections. For numerical calculations use the parton-level generator KaTie and modified KMR-type unintegrated parton distribution functions. We find good agreement between our predictions and data with the same accuracy as in the NNLO calculations based on the collinear parton model of QCD. At higher energies (\sqrt{s}=13s=13 and 27 TeV) parton Reggeization approach predicts larger cross sections, up to \sim 10∼10 % and \sim 20∼20 %, respectively.
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Alioli, Simone, Alessandro Broggio, and Matthew A. Lim. "Zero-jettiness resummation for top-quark pair production at the LHC." Journal of High Energy Physics 2022, no. 1 (2022). http://dx.doi.org/10.1007/jhep01(2022)066.
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Abstract We study the resummation of the 0-jettiness resolution variable $$ \mathcal{T} $$ T 0 for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $$ \mathcal{T} $$ T 0 → 0 limit. We then calculate the $$ \mathcal{O} $$ O (αs) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ ($$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ NNLL a ′ ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t$$ \overline{t} $$ t ¯ +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ NNLL a ′ +NLO accuracy.
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Abdul Khalek, Rabah, Richard D. Ball, Stefano Carrazza, et al. "A first determination of parton distributions with theoretical uncertainties." European Physical Journal C 79, no. 10 (2019). http://dx.doi.org/10.1140/epjc/s10052-019-7364-5.
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Abstract The parton distribution functions (PDFs) which characterize the structure of the proton are currently one of the dominant sources of uncertainty in the predictions for most processes measured at the Large Hadron Collider (LHC). Here we present the first extraction of the proton PDFs that accounts for the missing higher order uncertainty (MHOU) in the fixed-order QCD calculations used in PDF determinations. We demonstrate that the MHOU can be included as a contribution to the covariance matrix used for the PDF fit, and then introduce prescriptions for the computation of this covariance matrix using scale variations. We validate our results at next-to-leading order (NLO) by comparison to the known next order (NNLO) corrections. We then construct variants of the NNPDF3.1 NLO PDF set that include the effect of the MHOU, and assess their impact on the central values and uncertainties of the resulting PDFs.
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Cridge, T., L. A. Harland-Lang, A. D. Martin, and R. S. Thorne. "An investigation of the $$\alpha _S$$ and heavy quark mass dependence in the MSHT20 global PDF analysis." European Physical Journal C 81, no. 8 (2021). http://dx.doi.org/10.1140/epjc/s10052-021-09533-7.
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AbstractWe investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) , spanning the range $$\alpha _S(M_Z^2)=0.108$$ α S ( M Z 2 ) = 0.108 to 0.130 in units of 0.001. We make all resulting PDFs sets available. We find that the best fit values are $$\alpha _S(M_Z^2)=0.1203\pm 0.0015$$ α S ( M Z 2 ) = 0.1203 ± 0.0015 and $$0.1174\pm 0.0013$$ 0.1174 ± 0.0013 at NLO and NNLO respectively. We investigate the relationship between the variations in $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) and the uncertainties on the PDFs, and illustrate this by calculating the cross sections for key processes at the LHC. We also perform fits where we allow the heavy quark masses $$m_c$$ m c and $$m_b$$ m b to vary away from their default values and make PDF sets available in steps of $$\Delta m_c =0.05~\mathrm GeV$$ Δ m c = 0.05 G e V and $$\Delta m_b =0.25~\mathrm GeV$$ Δ m b = 0.25 G e V , using the pole mass definition of the quark masses. As for varying $$\alpha _S(M_Z^2)$$ α S ( M Z 2 ) values, we present the variation in the PDFs and in the predictions. We examine the comparison to data, particularly the HERA data on charm and bottom cross sections and note that our default values are very largely compatible with best fits to data. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard value of 5 flavours.
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Broggio, Alessandro, Sebastian Jaskiewicz, and Leonardo Vernazza. "Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold." Journal of High Energy Physics 2021, no. 10 (2021). http://dx.doi.org/10.1007/jhep10(2021)061.
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Abstract We calculate the generalized soft functions at $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact d-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining the soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N3LO, finding agreement.
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Kidonakis, Nikolaos, and Nodoka Yamanaka. "QCD corrections in $$tq\gamma $$ production at hadron colliders." European Physical Journal C 82, no. 8 (2022). http://dx.doi.org/10.1140/epjc/s10052-022-10643-z.
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AbstractWe study QCD corrections for the associated production of a single top quark and a photon ($$tq\gamma $$ t q γ 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.
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Meng, Rui-Qing, Sheng-Quan Wang, Ting Sun, Chao-Qin Luo, Jian-Ming Shen, and Xing-Gang Wu. "QCD improved top-quark decay at next-to-next-to-leading order." European Physical Journal C 83, no. 1 (2023). http://dx.doi.org/10.1140/epjc/s10052-023-11224-4.
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AbstractWe analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative QCD predictions. The PMC renormalization scales of the coupling constant $$\alpha _s$$ α s are determined by absorbing the non-conformal $$\beta $$ β terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale $$Q_\star =15.5$$ Q ⋆ = 15.5 GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice $$\mu _r=m_t$$ μ r = m t , reflecting the small virtuality of the QCD dynamics of the top-quark decay process. Moreover, due to the non-conformal $$\beta $$ β terms disappear in the pQCD series, there is no renormalon divergence and the NLO QCD correction term is greatly increased while the NNLO QCD correction term is suppressed compared to the conventional results obtained at $$\mu _r=m_t$$ μ r = m t . By further including the next-to-leading (NLO) electroweak corrections, the finite W boson width and the finite bottom quark mass, we obtain the top-quark total decay width $$\Gamma ^{\textrm{tot}}_t=1.3112^{+0.0190}_{-0.0189}$$ Γ t tot = 1 . 3112 - 0.0189 + 0.0190 GeV, where the error is the squared averages of the top-quark mass $$\Delta m_t=\pm 0.7$$ Δ m t = ± 0.7 GeV, the coupling constant $$\Delta \alpha _s(M_Z)=\pm 0.0009$$ Δ α s ( M Z ) = ± 0.0009 and the estimation of unknown higher-order terms using the PAA method with [N/M]=[1/1]. The PMC improved predictions for the top-quark decay are complementary to the previous PMC calculations for top-quark pair production and helpful for detailed studies of properties of the top-quark.
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Baranowski, Daniel, Maximilian Delto, Kirill Melnikov, and Chen-Yu Wang. "On phase-space integrals with Heaviside functions." Journal of High Energy Physics 2022, no. 2 (2022). http://dx.doi.org/10.1007/jhep02(2022)081.
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Abstract We discuss peculiarities that arise in the computation of real-emission contributions to observables that contain Heaviside functions. A prominent example of such a case is the zero-jettiness soft function in SCET, whose calculation at next-to-next-to-next-to-leading order in perturbative QCD is an interesting problem. Since the zero-jettiness soft function distinguishes between emissions into different hemispheres, its definition involves θ-functions of light-cone components of emitted soft partons. This prevents a direct use of multi-loop methods, based on reverse unitarity, for computing the zero-jettiness soft function in high orders of perturbation theory. We propose a way to bypass this problem and illustrate its effectiveness by computing various non-trivial contributions to the zero-jettiness soft function at NNLO and N3LO in perturbative QCD.
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Ball, Richard D., Stefano Carrazza, Juan Cruz-Martinez, et al. "The path to proton structure at 1% accuracy." European Physical Journal C 82, no. 5 (2022). http://dx.doi.org/10.1140/epjc/s10052-022-10328-7.
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AbstractWe present a new set of parton distribution functions (PDFs) based on a fully global dataset and machine learning techniques: NNPDF4.0. We expand the NNPDF3.1 determination with 44 new datasets, mostly from the LHC. We derive a novel methodology through hyperparameter optimization, leading to an efficient fitting algorithm built upon stochastic gradient descent. We use NNLO QCD calculations and account for NLO electroweak corrections and nuclear uncertainties. Theoretical improvements in the PDF description include a systematic implementation of positivity constraints and integrability of sum rules. We validate our methodology by means of closure tests and “future tests” (i.e. tests of backward and forward data compatibility), and assess its stability, specifically upon changes of PDF parametrization basis. We study the internal compatibility of our dataset, and investigate the dependence of results both upon the choice of input dataset and of fitting methodology. We perform a first study of the phenomenological implications of NNPDF4.0 on representative LHC processes. The software framework used to produce NNPDF4.0 is made available as an open-source package together with documentation and examples.
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Aebischer, Jason, Christoph Bobeth, and Andrzej J. Buras. "On the importance of NNLO QCD and isospin-breaking corrections in $$\varepsilon '/\varepsilon $$." European Physical Journal C 80, no. 1 (2019). http://dx.doi.org/10.1140/epjc/s10052-019-7549-y.
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AbstractFollowing the 1999 analysis of Gambino, Haisch and one of us, we stress that all the recent NLO analyses of $$\varepsilon '/\varepsilon $$ε′/ε in the Standard Model (SM) suffer from the renormalization scheme dependence present in the electroweak penguin contributions as well as from scale uncertainties in them related to the matching scale $$\mu _W$$μW and in particular to $$\mu _t$$μt in $$m_t(\mu _t)$$mt(μt). We also reemphasize the important role of isospin-breaking and QED effects in the evaluation of $$\varepsilon '/\varepsilon $$ε′/ε. Omitting all these effects, as done in the 2015 analysis by RBC-UKQCD collaboration, and choosing as an example the QCD penguin ($$Q_6$$Q6) and electroweak penguin ($$Q_8$$Q8) parameters $$B_6^{(1/2)}$$B6(1/2) and $$B_8^{(3/2)}$$B8(3/2) to be $$B_6^{(1/2)}= 0.80 \pm 0.08$$B6(1/2)=0.80±0.08 and $$B_8^{(3/2)}= 0.76 \pm 0.04$$B8(3/2)=0.76±0.04 at $$\mu = m_c=1.3\,\, \text {GeV}$$μ=mc=1.3GeV, we find $$(\varepsilon '/\varepsilon )_\mathrm{SM} = (9.4 \pm 3.5) \times 10^{-4}$$(ε′/ε)SM=(9.4±3.5)×10-4, whereas including them results in $$(\varepsilon '/\varepsilon )_\mathrm{SM} = (5.6\pm 2.4)\times 10^{-4}$$(ε′/ε)SM=(5.6±2.4)×10-4. This is an example of an anomaly at the $$3.3\,\sigma $$3.3σ level, which would be missed without these corrections. NNLO QCD contributions to QCD penguins are expected to further enhance this anomaly. We provide a table for $$\varepsilon '/\varepsilon $$ε′/ε for different values of $$B_6^{(1/2)}$$B6(1/2) and the isospin-breaking parameter $${\widehat{\Omega }}_\text {eff}$$Ω^eff, that should facilitate monitoring the values of $$\varepsilon '/\varepsilon $$ε′/ε in the SM when the RBC-UKQCD calculations of hadronic matrix elements including isospin-breaking corrections and QED effects will improve with time.
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Buckley, A., X. Chen, J. Cruz-Martinez, et al. "A comparative study of Higgs boson production from vector-boson fusion." Journal of High Energy Physics 2021, no. 11 (2021). http://dx.doi.org/10.1007/jhep11(2021)108.
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Abstract The data taken in Run II at the Large Hadron Collider have started to probe Higgs boson production at high transverse momentum. Future data will provide a large sample of events with boosted Higgs boson topologies, allowing for a detailed understanding of electroweak Higgs boson plus two-jet production, and in particular the vector-boson fusion mode (VBF). We perform a detailed comparison of precision calculations for Higgs boson production in this channel, with particular emphasis on large Higgs boson transverse momenta, and on the jet radius dependence of the cross section. We study fixed-order predictions at next-to-leading order and next-to-next-to-leading order QCD, and compare the results to NLO plus parton shower (NLOPS) matched calculations. The impact of the NNLO corrections on the central predictions is mild, with inclusive scale uncertainties of the order of a few percent, which can increase with the imposition of kinematic cuts. We find good agreement between the fixed-order and matched calculations in non-Sudakov regions, and the various NLOPS predictions also agree well in the Sudakov regime. We analyze backgrounds to VBF Higgs boson production stemming from associated production, and from gluon-gluon fusion. At high Higgs boson transverse momenta, the ∆yjj and/or mjj cuts typically used to enhance the VBF signal over background lead to a reduced efficiency. We examine this effect as a function of the jet radius and using different definitions of the tagging jets. QCD radiative corrections increase for all Higgs production modes with increasing Higgs boson pT, but the proportionately larger increase in the gluon fusion channel results in a decrease of the gluon-gluon fusion background to electroweak Higgs plus two jet production upon requiring exclusive two-jet topologies. We study this effect in detail and contrast in particular a central jet veto with a global jet multiplicity requirement.
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Marxer, Felix, and Peter Ulmer. "Crystallisation and zircon saturation of calc-alkaline tonalite from the Adamello Batholith at upper crustal conditions: an experimental study." Contributions to Mineralogy and Petrology 174, no. 10 (2019). http://dx.doi.org/10.1007/s00410-019-1619-x.
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Abstract The understanding of the geochemical and petrophysical evolution of magmas forming intermediate calc-alkaline batholiths at shallow crustal levels critically depends on knowledge of the phase equilibria relations along the liquid line of descent. Here, we present experimental results for a tonalitic system at a pressure of 200 MPa and under water-saturated conditions. Melting experiments were performed at temperatures between 700 and 1000 °C in externally heated HCM pressure vessels, with oxygen fugacity controlled close to the Ni–NiO buffer equilibrium (NNO) employing an argon–methane mixture as pressure medium and Co–Pd redox sensors to verify fO2 conditions. Natural rock powder of a medium-K tonalite from the Adamello Batholith in Northern Italy served as experimental starting material. Based on compositional data of stable phases in the run products and images of entire run charges, mass balance calculations as well as image processing were performed to investigate the evolution of the crystal/melt ratio with respect to temperature. Furthermore, compositional trends of minerals as well as the liquid line of descent of residual melts were obtained. Orthopyroxene, clinopyroxene and plagioclase were identified as near-liquidus phases (below 990 °C). At 900 °C, amphibole joins the solid-phase assemblage at the expense of clinopyroxene, indicating the existence of a peritectic relationship. After an initial near-linear decrease with temperature, residual melt fractions exhibit a plateau of 45–55 vol. % between 750 and 850 °C, followed by a rapid decrease coinciding with quartz saturation at 725 °C. Compositions of residual liquids evolve along a typical calc-alkaline differentiation trend with decreasing temperature (increasing SiO2 and decreasing TiO2, Al2O3, CaO, MgO and FeO contents) and become peraluminous below 900 °C. Intermediate to acidic rocks from the Adamello follow the experimental liquid line of descent indicating that the observed compositional spread of the natural intermediate composition rock record can be explained by low-pressure magma differentiation and liquid extraction. Experimentally determined zircon saturation levels are at low temperatures distinctly lower compared to existing and often used Zr-saturation models, but fully consistent with observed and modelled Zr-evolution trends from the natural rock record of the Southern Adamello Batholith inferring that zircon saturation in these intermediate to felsic plutonic rocks occurred at 800–830 °C corresponding to a melt fraction of about 50 vol. %.