aN³LO Parameterisations for MSHT20 aN³LO PDFs

This repository contains the Fortran routines for transition matrix elements and splitting functions up to approximate N³LO (aN³LO).

Feel free to raise an issue in this space in the event of any questions, requests, comments or bug fixes.

This code is provided as supplementary material to the MSHT20 approximate N³LO PDFs.

These approximations are not exact and allow for a level of variation by the input parameter "a" in all cases. These subroutines here use a simple method of simultaneous equations in order to produce the approximations and therefore may well be superseded in the future by more robust and equally/more efficient approximations or indeed, the exact functions when available.

Please refer to arXiv:2207.04739 for the full details of how these approximations are determined.

Note that these can and will be continually updated with any
extra exact calculations that are made available, which will increase the accuracy of these approximations.

When using these approximations, please reference the following.

aN³LO Transition Matrix Element References:

• J. McGowan, et. al., arXiv:2207.04739
• H. Kawamura, et. al., arXiv:1205.5727
• I. Bierenbaum, et. al., arXiv:0904.3563
• J. Ablinger, et. al., arXiv:1406.5654
• J. Ablinger, et. al., arXiv:1409.1135
• J. Ablinger, et. al., arXiv:1402.0359

aN³LO Splitting Functions References:

• J. McGowan, et. al., arXiv:2207.04739
• S. Moch, et. al., arXiv:1707.08315
• A. Vogt, et. al., arXiv:1808.08981
• S. Catani, et. al., hep-ph/9405388
• L. N. Lipatov, Sov. J. Nucl. Phys. (1976)
• E. A. Kuraev, et. al., JETP (1977)
• I. I. Balitsky, et. al., Sov. J. Nucl. Phys. (1978)
• V. S. Fadin, et. al., hep-ph/9802290
• M. Ciafaloni, et. al., hep-ph/9803389