MSHT Approximate N3LO PDFs: Updates and Consequences for Phenomenology

TL;DR

This work addresses how newly computed Mellin-moment updates to singlet splitting functions and exact transition matrix elements influence the MSHT approximate N3LO PDFs. The authors incorporate $10$ Mellin moments for the singlet $P_{ij}$, update TMEs to exact results, and assess the resulting changes in PDFs and PDF luminosities. They find only minor shifts, with the gluon and charm PDFs changing at the percent level and the overall fit quality remaining substantially better than NNLO, thereby validating the robustness of the aN3LO framework for LHC phenomenology. The results support the use of these updated aN3LO PDFs for precise Higgs and related cross-section predictions, while highlighting small, targetable MHOU-related adjustments for future refinements.

Abstract

We present updates to the MSHT approximate N3LO PDFs focusing upon recent developments, examining the impacts of newly determined splitting function and transition matrix element calculations, performed since the public MSHT20aN3LO PDF set was released. We observe only small changes to the output PDFs, at most of similar size to their quoted uncertainties and typically notably less. Finally, we also present the impacts on the PDF luminosities, where changes are generally further reduced.

Figures (3)

• Figure 1: Comparison of our previous approximations of (a) $P_{gg}$ and (b) $A_{Hg}$ - with our prior/posterior determination in MSHT20aN3LO McGowan:2022nag shown in green/blue with associated error bands. In (a) the new updated approximate determination of FHMRUVV Falcioni:2024qpd is shown and in (b) the new updated parameterised version of the exact determination of Ablinger:2023aheAblinger:2024xtt is shown, both in red.
• Figure 2: Comparison of the updated PDFs with only the new FHMRUVV splitting functions (red dotted), only the new transition matrix elements (green dashed), and both of these updates (grey dash-dotted), against those with our original approximations for these pieces (blue) McGowan:2022nag. Note the latter is described as "MSHT20aN3LO new" as it has some updates in the data and methodology relative to the public set, as described in Cridge:2023ryvCridge:2023ozx.
• Figure 3: Comparison of the updated PDF luminosities at 14 TeV with only the new FHMRUVV splitting functions (red dotted), only the new transition matrix elements (green dashed), and both of these updates (grey dash-dotted), with our original approximations for these pieces (blue) McGowan:2022nag. Note the latter is described as "MSHT20aN3LO new" as it has some updates in the data and methodology relative to the public set, as described in Cridge:2023ryvCridge:2023ozx.