## MSHT20 PDFs: LHAPDF grids

Here we enclose the LHAPDF 6 grid files corresponding to the MSHT20 PDFs, published in arXiv:2012.04684, arXiv:2106.10289, arXiv:2111.05357, arXiv:2207.04739 and arXiv:2312.07665. See below for futher details.

Please reference the appropropriate papers if you use the PDFs for a publication.

We provide NLO and NNLO grids for the central fit and 64 eigenvectors sets (corresponding to 32 eigenvectors in the '+' and '-' directions), for a 68% confidence interval. LO grids are provided with 60 eigenvector sets. Grids for the central fit + eigenvectors are provided for α_{S}=0.130 at LO, α_{S}=0.118 and 0.120 at NLO and α_{S}=0.118 at NNLO.

Note that a list of corrections/updates to the publicly available grids is provided at the end of this page.

### MSHT global PDF fit

The MSHT20 PDFs, resulting from a QCD fit up to NNLO order, published in arXiv:2012.04684:

#### Central + eigenvector sets

### Strong coupling and heavy quark mass variations

In addition, alongside the MSHT20 paper we provided central grids for a short ranges of α_{S} values at NLO and NNLO. At NLO α_{S}=0.115-0.122 and at NNLO α_{S}=0.115-0.121, in increments of 0.001. Again for these a formatting issue lead to the α_{S} grid for LHAPDF interpolation being incorrect in version 1 of certain grids. In addition, the set index has been updated in some cases to be better consistent with the LHAPDF numbering system.

Following our paper on the α_{S} and heavy quark mass dependence, published in arXiv:2106.10289, we also provide further LHAPDF 6 grids corresponding to these variations as well as some cases with 3 and 4 flavours only, if you use any of these please reference this paper (as well as the original MSHT20 paper):

#### Central sets for small α_{S} ranges

- MSHT20nnlo_as_smallrange
- MSHT20nlo_as_smallrange
- MSHT20nnlo_as_smallrange_nf3
- MSHT20nlo_as_smallrange_nf3
- MSHT20nnlo_as_smallrange_nf4
- MSHT20nlo_as_smallrange_nf4

#### Central sets for large α_{S} ranges

#### Central sets for m_{c,b} ranges

- MSHT20nnlo_mcrange_nf3
- MSHT20nnlo_mcrange_nf4
- MSHT20nnlo_mcrange_nf5
- MSHT20nnlo_mbrange_nf3
- MSHT20nnlo_mbrange_nf4
- MSHT20nnlo_mbrange_nf5
- MSHT20nlo_mcrange_nf3
- MSHT20nlo_mcrange_nf4
- MSHT20nlo_mcrange_nf5
- MSHT20nlo_mbrange_nf3
- MSHT20nlo_mbrange_nf4
- MSHT20nlo_mbrange_nf5
- MSHT20nlo_as120_mcrange_nf3
- MSHT20nlo_as120_mcrange_nf4
- MSHT20nlo_as120_mcrange_nf5
- MSHT20nlo_as120_mbrange_nf3
- MSHT20nlo_as120_mbrange_nf4
- MSHT20nlo_as120_mbrange_nf5

#### Central + eigenvector sets for 3 and 4 flavours

### MSHT20 QED PDF sets

Here we provide PDF sets including QED corrections to DGLAP evolution, and a photon PDF, as described in arXiv:2111.05357. Please reference this, as well as the original MSHT20 publication, if you make use of these sets. These include the baseline set, as well as sets with only the elastic or inelastic photon PDF included. In addition, a set of neutron PDFs, again including the elastic or inelastic photon PDF only, are provided (The set index has again now been updated in some cases to be better consistent with the LHAPDF numbering system):

- MSHT20qed_nnlo
- MSHT20qed_nnlo_elastic
- MSHT20qed_nnlo_inelastic
- MSHT20qed_nnlo_neutron
- MSHT20qed_nnlo_neutron_elastic
- MSHT20qed_nnlo_neutron_inelastic

### MSHT20 aN^{3}LO PDF sets

Here we provide PDF sets including approximate N^{3}LO corrections to DGLAP evolution, transition matrix elements, and hard cross sections, as described in arXiv:2207.04739. Please reference this, as well as the original MSHT20 publication, if you make use of these sets. Each of the two sets includes a central set and 52 eigenvector pairs, corresponding to 32 PDF parameters and 20 parameters representing theoretical uncertainties. In the first of these the 5 pairs of parameters representing N^{3}LO K-factors for 5 types of hard scattering process are decorrelted from other parameters, while in the second all 52 parameters are correlated. In both cases the full uncertainty is obtained by considering each of the 52 eigenvector pairs as orthogonal as in the situatuons where only PDF parameters are considered.
The grids below are updated with the correction of a minor bug in a non-singlet splitting function leading to very small changes at high-x. The grids below therefore supersede any previous versions of MSHT20aN3LO PDFs downloaded before 22/09/2022.

_{S}values are also provided below:

### MSHT20 QED + aN^{3}LO PDF sets

Here we provide PDF sets combining approximate N^{3}LO QCD and QED corrections, as described in arXiv:2312.07665. Each set includes a central set and 48 eigenvector pairs, corresponding to 32 PDF parameters, 10 (non-K-factor) theoretical uncertainties associated with the approximate N

^{3}LO QCD corrections, and 6 eigenvectors associated with the uncertainty on the input photon PDF, i.e. the QED corrections. Sets corresponding to the (default) total and elastic/inelastic breakdowns of the photon PDF are also provided: As the data and theoretical settings have been updated somewhat since the MSHT20aN

^{3}LO analysis, we also provide on the website alone the supplementary set corresponding to the QCD--only fit considered here:

in case the user is interested in isolating the relative impact of QED effects. However, to maintain consistency the public MSHT20aN^{3}LOrelease remains the official release.

### MSHT20 QED + LO PDF sets

Here we provide PDF sets combining LO QCD and QED corrections, as described in arXiv:2312.07665. Each set includes a central set and 34 eigenvector pairs, corresponding to 28 PDF parameters and 6 eigenvectors associated with the uncertainty on the input photon PDF, i.e. the QED corrections. Sets corresponding to the (default) total and elastic/inelastic breakdowns of the photon PDF are also provided:### Corrections/updates

- A formatting issue lead to the α
_{S}grid for LHAPDF interpolation being incorrect in version 1 of the baseline MSHT20 (LO to NNLO) grids. This has now been fixed in version 2. - For a small selection of sets (MSHT20nnlo_as118, MSHT20lo_as130, MSHT20qed_nnlo_elastic, MSHT20qed_nnlo_neutron) 1-2 eigenvectors were repeated due to an outputting error in the lhapdf grid production. The impact on the PDF uncertainties is very small, at the level of 1% of the PDF error (i.e. if the relative PDF error is 2% then the change is at most 0.02% in the PDF error with respect to the previous result), however this has now been corrected in Dataversion (4,4,3,3) with respectively, for the sets listed above.