Source-linked AI summary
HATHOR for single top-quark production: Updated predictions and uncertainty estimates for single top-quark production in hadronic collisions
P. Kant, O. M. Kind, T. Kintscher, T. Lohse, T. Martini, S. Mölbitz, P. Rieck, P. Uwer
TL;DR
Single-top measurements require precise theoretical predictions and systematic uncertainty estimates for comparison with collider data. The paper extends HATHOR with NLO single-top calculations and studies PDFs, independent scale variations, and mass extraction. It provides a fast framework for inclusive cross-section studies, while full NNLO improvements remain dependent on estimated uncalculated terms.
Problem
Precise comparisons with increasingly accurate single-top measurements require detailed predictions and systematic studies of theoretical uncertainties.
Method
The analysis extends HATHOR using NLO QCD calculations, efficient partonic cross-section evaluation, PDF comparisons, and independent renormalisation- and factorisation-scale variations.
Results
The framework evaluates inclusive single-top cross sections and assesses scale, PDF, strong-coupling, and top-quark-mass dependence against recent measurements.
Takeaways & Limitations
HATHOR enables fast and systematic total-cross-section studies that can support Standard Model fits and related parameter analyses.
Takeaways & Limitations
Possible improvements from the full NNLO calculation are estimated using an educated guess for an uncalculated coefficient.
Abstract
from arXiv · showhide
We present updated predictions for single top-quark production in hadronic collisions. The analysis is based on next-to-leading order QCD calculations. The input parameters are fixed to recent measurements. We compare different PDF sets and investigate the related uncertainties. The impact of uncalculated higher orders is estimated using an independent variation of the renormalisation and factorisation scale. The theoretical predictions are compared with recent measurements from Tevatron and LHC. Furthermore, the cross section measurements are used to estimate the top-quark mass. To perform the analysis we extended the publicly available HatHor program to single top-quark production. We thus provide a unified framework for the fast numerical evaluation of total cross sections for top-quark production, which may be used for example in Standard Model fits. For future extensions towards NNLO accuracy, we include already all scale dependent terms at NNLO. We briefly describe how to use the program and provide all required tools to repeat the aforementioned analysis.
1 Introduction
Single-top production is experimentally challenging but scientifically valuable, motivating precise theoretical predictions and uncertainty studies across its three production channels. The paper situates updated NLO calculations and HATHOR extensions within existing work on channel-specific corrections and higher-order QCD effects.
- Single-top rates are about one third of inclusive top-pair rates, but complicated signatures and sizeable backgrounds make measurements challenging.
- Single-top production probes the V−A charged-current structure, provides direct access to Vtb, and supplies highly polarised top quarks.
- The t-channel dominates at both the Tevatron and LHC, while Wt is second at the LHC and the s-channel is second at the Tevatron.
- Existing work covers NLO inclusive and differential predictions, decay effects, parton showers, flavour schemes, and soft-gluon or partial NNLO corrections.
- Increasingly precise measurements require detailed theory comparisons, including PDF uncertainties and independent renormalisation- and factorisation-scale variations.
2 Theoretical setup
The theoretical setup computes inclusive single-top cross sections in the QCD improved parton model and extracts NLO partonic cross sections from numerical calculations. It also validates complementary extraction methods and incorporates parameter, PDF, and scale-dependence handling for HATHOR.
- Theoretical setup: Inclusive cross sections are factorised into PDFs and partonic cross sections, using five massless flavours with a massless b-quark in the initial state.The top-quark mass is renormalised in the on-shell scheme, and µR and µF denote renormalisation and factorisation scales.
- NLO partonic cross sections: At NLO, numerical phase-space integrations of virtual and real corrections replace unavailable compact analytic expressions for inclusive cross sections.The calculation uses Catani-Seymour subtraction so soft and collinear singularities cancel in the summed result, despite additional convolutions obscuring partonic-energy identification.
- NLO partonic cross sections: Three complementary approaches extract NLO partonic cross sections: pseudo-PDF probing, modified MCFM integration, and a private virtual-correction code.Pseudo-PDFs use narrow Gaussian distributions to probe a chosen partonic centre-of-mass energy, while the modified-MCFM approach removes PDF integrations for greater numerical efficiency.
- Validation: The extraction methods agree within less than 1 ‰ across all production channels and corresponding initial states for a fixed top-quark mass.The private code also agrees with the two other methods for s- and t-channel production.
- Input parameters: Single-top production retains dependence on mt, mW, weak couplings, and CKM elements, so its full mass dependence cannot be encoded in a one-dimensional scaling function.Most parameter values and PDF sets can be varied in HATHOR, while the W mass is fixed to its current world average.
3 HATHOR for single top-quark production
HATHOR 2.0 extends the program to inclusive single-top production while preserving a common calculation interface and adding configurable inputs. It supports LO and NLO predictions, compares HATHOR with MCFM, and exposes tools for parameter studies and reproducible use.
- Program extension: HATHOR 2.0 introduces dedicated classes for the t-channel, s-channel, and associated Wt single-top production channels.These classes share a common base with the existing Hathor class and provide the same calculation methods.
- Validation: HATHOR predictions for pp collisions at √s=14TeV are compared with corresponding MCFM results for t-channel, s-channel, and associated Wt production.The validation presents relative deviations as a function of the top-quark mass, with the uncertainty bands indicating MCFM's statistical integration error.
- Configuration: The program evaluates inclusive top-quark and anti-quark production and lets users select TOPQUARK, ANTITOPQUARK, or BOTH.Additional methods allow users to inspect and modify the CKM matrix, whose defaults follow recent PDG world averages.
- Perturbative predictions: Users can select LO or NLO perturbative contributions through setScheme, combining the NLO option with LO to obtain the full NLO cross section.LO uses analytic partonic cross sections, while NLO partonic cross sections are sampled from MCFM and include calculated scale-dependent terms.
- Use and distribution: HATHOR provides examples, a graphical user interface, and a downloadable release for repeating calculations and obtaining reference cross sections.The package includes the demo sgtop.cxx file and asks users to cite the underlying NLO calculations when publishing results.
4 Results
HATHOR evaluates single-top cross sections and their theoretical sensitivities at NLO, covering scale, mass, strong-coupling, and PDF variations. The results compare predictions with measurements and use cross-section dependence to assess top-quark mass extraction.
- Program and setup: HATHOR enables fast computations of total cross-section dependencies on varied model parameters.The program is used to study scale, mass, strong-coupling, and PDF effects.
- Scale dependence: Independent renormalisation- and factorisation-scale variation shows less than five per cent variation for t- and s-channel production under reasonable scale changes.Diagonal scale variation can underestimate uncertainties, especially for the s- and Wt-channels.
- Top-quark mass: Single-top cross sections are calculated at NLO with CT10nlo, while top-quark pair production is calculated at NNLO with CT10nnlo for mass comparisons.The mass study covers a range around the measured top-quark mass and extends up to 1TeV.
- Top-quark mass: The parameter A determines the sensitivity of single-top cross sections to the extracted top-quark mass, with the s-channel showing the strongest mass dependence.The extracted masses have large uncertainties but are consistent with the world average within uncertainties.
- Strong coupling and PDFs: A one per cent uncertainty in αs roughly produces a one per cent cross-section uncertainty, while ABM11 gives significantly larger cross-section predictions.The cross-section dependence on αs is approximately linear with a slope close to one.
- Strong coupling and PDFs: PDF uncertainties are about ±1 per cent at high energies for the s- and t-channels but significantly larger for associated Wt production.CT10 predictions are slightly below MSTW08 and NNPDF23, whereas ABM11 gives larger high-energy t-channel cross sections; results remain marginally consistent within uncertainty bands.
5 Summary
The paper extends HATHOR to fast single-top cross-section calculations across all three production channels and QCD orders through NLO. It also supports systematic studies of scales, model parameters, PDFs, top-quark mass, and αs.
- 5 Summary: HATHOR computes t-channel, s-channel, and associated Wt production cross sections at LO and NLO in QCD.The extension covers all three single-top production channels.
- 5 Summary: The calculated results agree with other programs to better than 1 ‰ despite requiring little computing time.
- 5 Summary: Complete renormalisation- and factorisation-scale dependence is implemented through NNLO.The paper also collects the corresponding equations for future NNLO extensions.
- 5 Summary: HATHOR enables fast systematic variations of scales, model parameters, PDFs, perturbative orders, top-quark mass, and αs.The paper applies these capabilities to cross-section and uncertainty studies, including top-quark-mass estimates from measurements.
A Scaling functions in NNLO
This appendix specifies scale-dependent terms for the s-channel and associated Wt production used in the NNLO-oriented cross-section framework.
- A Scaling functions in NNLO: The s-channel scale-dependent terms are specified for indices i ∈ {20,21,22}.
- A Scaling functions in NNLO: For associated Wt production, κ is set to zero for all partonic channels.
B Additional figures
The appendix provides additional figures for partonic contributions, LO/NLO cross sections, and αs and PDF dependence in single-top production.
- B Additional figures: Figure 10 shows NLO partonic cross-section contributions for s-channel and Wt production versus partonic centre-of-mass energy at mt = 172.5 GeV.The renormalisation and factorisation scales are both set to the top-quark mass.
- B Additional figures: Figure 11 compares LO and NLO HATHOR cross sections using CT10nlo with scale uncertainty and recent collider measurements.The comparisons include s-channel measurements from CMS and the Tevatron, plus Wt measurements from the LHC.
- B Additional figures: Figure 12 presents NLO s-channel and Wt cross sections for different αs values and NLO PDF sets at √s = 14 TeV in pp scattering.
- B Additional figures: The αs plots mark each PDF set’s best fit and full PDF uncertainty, alongside the world-average αs value and uncertainty at the Z pole.
C Parametrization of the top-quark mass dependence
This appendix supplies coefficients for fast evaluations of the top-quark-mass dependence, using NLO cross sections and a reference mass from the current world average.
- C Parametrization of the top-quark mass dependence: Table 3 lists coefficients for fast cross-section evaluations using Eq. (41), with all cross-section values given in pb.The table uses NLO calculations.
- C Parametrization of the top-quark mass dependence: The reference top-quark mass used for the PDF parametrization is the current world average, mt = 173.5 GeV.
D Example of HATHOR usage
The example configures HATHOR for NLO single-top production at a 14 TeV proton–proton collider using the CT10nlo PDF set, then computes and prints a cross section with its error.
- The example includes the HATHOR header and the standard iostream library.
- It initializes the CT10nlo PDF set and configures HATHOR for proton–proton collisions at 14,000 GeV with LO and NLO schemes at low precision.
- The calculation sets the top-quark mass, factorisation scale, and renormalisation scale all to 173 GeV before requesting the cross section.
- The resulting cross section and its numerical error are retrieved and printed in picobarns.