An investigation of the and heavy quark mass dependence in the MSHT20 global PDF analysis

T. Cridge; L. A. Harland-Lang; A. D. Martin; R. S. Thorne

doi:10.1140/epjc/s10052-021-09533-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 744
https://doi.org/10.1140/epjc/s10052-021-09533-7

Regular Article - Theoretical Physics

An investigation of the $α_{S}$ $\alpha _S$ and heavy quark mass dependence in the MSHT20 global PDF analysis

T. Cridge¹^a, L. A. Harland-Lang², A. D. Martin³ and R. S. Thorne¹

¹ Department of Physics and Astronomy, University College London, WC1E 6BT, London, UK
² Rudolf Peierls Centre, Beecroft Building, Parks Road, OX1 3PU, Oxford, UK
³ Institute for Particle Physics Phenomenology, Durham University, DH1 3LE, Durham, UK

^a t.cridge@ucl.ac.uk

Received: 1 July 2021
Accepted: 6 August 2021
Published online: 17 August 2021

Abstract

We investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ 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 $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ , spanning the range $α_{S} (M_{Z}^{2}) = 0.108$ $\alpha _S(M_Z^2)=0.108$ to 0.130 in units of 0.001. We make all resulting PDFs sets available. We find that the best fit values are $α_{S} (M_{Z}^{2}) = 0.1203 \pm 0.0015$ $\alpha _S(M_Z^2)=0.1203\pm 0.0015$ and $0.1174 \pm 0.0013$ $0.1174\pm 0.0013$ at NLO and NNLO respectively. We investigate the relationship between the variations in $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ 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 $Δ m_{c} = 0.05 G e V$ $\Delta m_c =0.05~\mathrm GeV$ and $Δ m_{b} = 0.25 G e V$ $\Delta m_b =0.25~\mathrm GeV$ , using the pole mass definition of the quark masses. As for varying $α_{S} (M_{Z}^{2})$ $\alpha _S(M_Z^2)$ 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.

© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.