On improving NLO merging for $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $$ production

We introduce an improvement to the FxFx matrix element merging procedure for pp →$$ t\overline{t}W $$ t t ¯ W production at NLO in QCD with one and/or two additional jets. The main modification is an improved treatment of jets that are not logarithmically enhanced in the low transverse-momentum regime. We provide predictions for the inclusive cross section and the $$ t\overline{t}W $$ t t ¯ W differential distributions including parton-shower effects. Taking also the NLO EW corrections into account, this results in the most-accurate predictions for this process to date. We further proceed to include the on-shell LO decays of the $$ t\overline{t}W $$ t t ¯ W including the tree-level spin correlations within the narrow-width approximation, focusing on the multi-lepton signatures studied at the LHC. We find a ∼30% increase over the NLO QCD prediction and large non-flat K-factors to differential distributions.

Measurements of the inclusive and differential production cross sections of a top-quark–antiquark pair in association with a Z boson at $$\sqrt{s} = 13$$ TeV with the ATLAS detector

Measurements of both the inclusive and differential production cross sections of a top-quark–antiquark pair in association with a Z boson ($$t{\bar{t}}Z$$ t t ¯ Z ) are presented. The measurements are performed by targeting final states with three or four isolated leptons (electrons or muons) and are based on $$\sqrt{s} = 13$$ s = 13 TeV proton–proton collision data with an integrated luminosity of 139 $$\hbox {fb}^{-1}$$ fb - 1 , recorded from 2015 to 2018 with the ATLAS detector at the CERN Large Hadron Collider. The inclusive cross section is measured to be $$\sigma _{t{\bar{t}}Z} = 0.99 \pm 0.05$$ σ t t ¯ Z = 0.99 ± 0.05 (stat.) $$\pm \, 0.08$$ ± 0.08 (syst.) pb, in agreement with the most precise theoretical predictions. The differential measurements are presented as a function of a number of kinematic variables which probe the kinematics of the $$t{\bar{t}}Z$$ t t ¯ Z system. Both absolute and normalised differential cross-section measurements are performed at particle and parton levels for specific fiducial volumes and are compared with theoretical predictions at different levels of precision, based on a $$\chi ^{2}/$$ χ 2 / ndf and p value computation. Overall, good agreement is observed between the unfolded data and the predictions.

Applications of pT-xR Variables in Describing Inclusive Cross Sections at the LHC

Invariant inclusive single-particle/jet cross sections in p–p collisions can be factorized in terms of two separable dependences, a [pT−s] sector and an [xR−pT−s] sector. Here, we extend our earlier work by analyzing more extensive data to explore various s-dependent attributes and other systematics of inclusive jet, photon and single particle reactions. Approximate power laws in s,pT and xR are found. Physical arguments are given which relate observations to the underlying physics of parton–parton hard scattering and the parton distribution functions in the proton. We show that the A(s,pT) function, introduced in our earlier publication to describe the pT dependence of the inclusive cross section, is directly related to the underlying hard parton–parton scattering for jet production, with little influence from soft physics. In addition to the A-function, we introduce another function, the F(s,xR) function that obeys radial scaling for inclusive jets and offers another test of the underlying parton physics. An application to heavy ion physics is given, where we use our variables to determine the transparency of cold nuclear matter to penetrating heavy mesons through the lead nucleus.

Matching in $$ pp\to t\overline{t}W/Z/h+ $$ jet SMEFT studies

In this paper, we explore the impact of extra radiation on predictions of $$ pp\to \mathrm{t}\overline{\mathrm{t}}\mathrm{X},\mathrm{X}=\mathrm{h}/{\mathrm{W}}^{\pm }/\mathrm{Z} $$ pp → t t ¯ X , X = h / W ± / Z processes within the dimension-6 SMEFT framework. While full next-to-leading order calculations are of course preferred, they are not always practical, and so it is useful to be able to capture the impacts of extra radiation using leading-order matrix elements matched to the parton shower and merged. While a matched/merged leading-order calculation for $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{X} $$ t t ¯ X is not expected to reproduce the next-to-leading order inclusive cross section precisely, we show that it does capture the relative impact of the EFT effects by considering the ratio of matched SMEFT inclusive cross sections to Standard Model values, $$ {\sigma}_{\mathrm{SM}\mathrm{EFT}}\left(\mathrm{t}\overline{\mathrm{t}}\mathrm{X}+\mathrm{j}\right)/{\sigma}_{\mathrm{SM}}\left(\mathrm{t}\overline{\mathrm{t}}\mathrm{X}+\mathrm{j}\right)\equiv \mu $$ σ SMEFT t t ¯ X + j / σ SM t t ¯ X + j ≡ μ . Furthermore, we compare leading order calculations with and without extra radiation and find several cases, such as the effect of the operator $$ \left({\varphi}^{\dagger }i{\overleftrightarrow{D}}_{\mu}\varphi \right)\left(\overline{t}{\gamma}^{\mu }t\right) $$ φ † i D ↔ μ φ t ¯ γ μ t on $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{h} $$ t t ¯ h and $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $$ t t ¯ W , for which the relative cross section prediction increases by more than 10% — significantly larger than the uncertainty derived by varying the input scales in the calculation, including the additional scales required for matching and merging. Being leading order at heart, matching and merging can be applied to all operators and processes relevant to $$ pp\to \mathrm{t}\overline{\mathrm{t}}\mathrm{X},\mathrm{X}=\mathrm{h}/{\mathrm{W}}^{\pm }/\mathrm{Z}+\mathrm{jet} $$ pp → t t ¯ X , X = h / W ± / Z + jet , is computationally fast and not susceptible to negative weights. Therefore, it is a useful approach in $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{X} $$ t t ¯ X + jet studies where complete next-to-leading order results are currently unavailable or unwieldy.

Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e+e− → $$ d\overline{d} $$ d d ¯ . We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 → 2 + X scalar scattering process.

Single-top-quark production in the t-channel at NNLO

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.

Resummed inclusive cross-section in ADD model at N3LL

We present three loop soft-plus-virtual (SV) corrections to the spin-2 production at the Large Hadron Collider (LHC). For this calculation, we make use of the recently computed quark and gluon three loop form factors for the spin-2 production, the universal soft-collinear coefficients as well as the mass factorization kernels. The SV coefficients are presented up to next-to-next-to-next-to leading order (N3LOsv). We also use these coefficients at three loops to compute the resummed prediction for inclusive cross-section to next-to-next-to-next-to leading logarithmic accuracy (N3LL) matched to N3LOsv. We use the standard technique to derive the Mellin N-dependent coefficients and also the N-independent coefficients to achieve the resummation using the minimal prescription matching procedure. Considering the spin-2 propagator in the large extra dimensional (ADD) model, we also study the numerical impact of these three-loop SV corrections as well as the resummed predictions on the di-lepton invariant mass distribution at the 13 TeV LHC. We find that the conventional scale uncertainties in the N3LOsv +N3LL resummed results substantially get reduced to as low as 2% in the high invariant mass region. We also estimate the PDF uncertainties in our predictions that will be useful in the experimental searches for large extra dimensions.

Resummed Drell-Yan cross-section at N3LL

We present the resummed predictions for inclusive cross-section for Drell-Yan (DY) production as well as onshell Z, W± productions at next-to-next-to-next-to leading logarithmic (N3LL) accuracy. Using the standard techniques, we derive the N-dependent coefficients in the Mellin-N space as well as the N-independent constants and match the resummed result through the minimal prescription procedure with the fixed order results. In addition to the standard ln N exponentiation, we study the numerical impacts of exponentiating N-independent part of the soft function and the complete $$ {\overline{g}}_0 $$ g ¯ 0 that appears in the resummed predictions in N space. All the analytical pieces needed in these different approaches are extracted from the soft-virtual part of the inclusive cross section known to next-to-next-to-next-to leading order (N3LO). We perform a detailed analysis on the scale and parton distribution function (PDF) variations and present predictions for 13 TeV LHC for the neutral Drell-Yan process as well as onshell charged and neutral vector boson productions.

Precision inclusive Higgs physics at e+e− colliders with tracking detectors and without calorimetry

A primary goal of a future e+e− collider program will be the precision measurement of Higgs boson properties. For practical reasons it is of interest to determine the minimal set of detector specifications required to reach this and other scientific goals. Here we investigate the precision obtainable for the e+e−Zhμ+μ−X inclusive cross section and the Higgs boson mass using the di-muon recoil method, considering a detector that has only an inner tracking system within a solenoidal magnetic field, surrounded by many nuclear interaction lengths of absorbing material, and an outer muon identification system. We find that the sensitivity achievable in these measurements with such a tracking detector is only marginally reduced compared to that expected for a general purpose detector with additional electromagnetic and hadronic calorimeter systems. The difference results mainly from multi-photon backgrounds that are not as easily rejected with tracking detectors. We also comment on the prospects for an analogous measurement of the e+e−→Zh→e+e−X inclusive cross section. Finally, we study searches for light scalars utilizing the di-muon recoil method, estimating the projected reach with a tracking or general purpose detector.