Complete $$ {N}_f^2 $$ contributions to four-loop pure-singlet splitting functions

Gehrmann, Thomas; von Manteuffel, Andreas; Sotnikov, Vasily; Yang, Tong-Zhi

doi:10.1007/jhep01(2024)029

J. High Energ. Phys.

2024

DOI: 10.1007/jhep01(2024)029

|View full text |Cite

Complete $$ {N}_f^2 $$ contributions to four-loop pure-singlet splitting functions

Thomas Gehrmann,

Andreas von Manteuffel,

Vasily Sotnikov

et al.

Abstract: The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting fu… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 7 publications

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Four-loop splitting functions in QCD – The quark-to-gluon case

Falcioni,

Herzog,

Moch

et al. 2024

Physics Letters B

View full text Add to dashboard Cite

Four-loop splitting functions in QCD – The quark-to-gluon case

Falcioni,

Herzog,

Moch

et al. 2024

Physics Letters B

View full text Add to dashboard Cite

The impact of LHC jet and Z $$p_T$$ data at up to approximate N$${}^3$$LO order in the MSHT global PDF fit

Cridge,

Harland-Lang,

Thorne

2024

Eur. Phys. J. C

View full text Add to dashboard Cite

We present an analysis of two key sets of data constraining the high x gluon at up to approximate N$${}^3$$ 3 LO in QCD within the MSHT global PDF fitting framework. We begin with LHC 7 and 8 TeV inclusive jet and dijet production at both NNLO and aN$${}^3$$ 3 LO. This makes use of the formalism established in the previous global MSHT20aN$${}^3$$ 3 LO PDF fit, but now considers the role of dijet production for the first time at this order. We present a detailed comparison of the fit quality and PDF impact for both cases, and consider the role that electroweak corrections, and the scale choice for inclusive jet production has. Some mild tension between these data sets in the impact on the high x gluon is seen at NNLO, but this is largely eliminated at aN$${}^3$$ 3 LO. While a good fit quality to the dijet data is achieved at both orders, the fit quality to the inclusive jet data is relatively poor. We examine the impact of including full colour corrections in a global PDF fit for the first time, finding this to be relatively mild. We also revisit the fit to the ATLAS 8 TeV Z$$p_T$$ p T data, considering the role that the $$p_T$$ p T cuts, data selection and different aspects of the aN$${}^3$$ 3 LO treatment have on the fit quality and PDF impact. We observe that in all cases the aN$${}^3$$ 3 LO fit quality is consistently improved relative to the NNLO, indicating a clear preference for higher order theory for these data.

show abstract

The path to $$\hbox {N}^3\hbox {LO}$$ parton distributions

Ball,

Barontini,

Candido

et al. 2024

Eur. Phys. J. C

View full text Add to dashboard Cite

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order ($$\hbox {aN}^3\hbox {LO}$$ aN 3 LO ). We construct an approximation to the $$\hbox {N}^3\hbox {LO}$$ N 3 LO splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known $$\hbox {N}^3\hbox {LO}$$ N 3 LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $$\mathcal {O}\left( \alpha _s^3\right) $$ O α s 3 accuracy. We determine a set of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of $$\hbox {N}^3\hbox {LO}$$ N 3 LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs from the MSHT group. We examine the phenomenological impact of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Complete $$ {N}_f^2 $$ contributions to four-loop pure-singlet splitting functions

Cited by 7 publications

References 74 publications

Four-loop splitting functions in QCD – The quark-to-gluon case

Four-loop splitting functions in QCD – The quark-to-gluon case

The impact of LHC jet and Z $$p_T$$ data at up to approximate N$${}^3$$LO order in the MSHT global PDF fit

The path to $$\hbox {N}^3\hbox {LO}$$ parton distributions

Contact Info

Product

Resources

About