Harland-Lang L A, Cridge T, Thorne R S
Department of Physics and Astronomy, University College London, London, WC1E 6BT UK.
Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany.
Eur Phys J C Part Fields. 2025;85(3):316. doi: 10.1140/epjc/s10052-025-13934-3. Epub 2025 Mar 18.
We present a first global closure test of the fixed parameterisation (MSHT) approach to PDF fitting. We find that the default MSHT20 parameterisation can reproduce the features of the input set in such a closure test to well within the textbook uncertainties. This provides strong evidence that parameterisation inflexibility in the MSHT20 fit is not a significant issue in the data region. We also present the first completely like-for-like comparison between two global PDF fits, namely MSHT and NNPDF, where the only difference is guaranteed to be due to the fitting methodology. To achieve this, we present a fit to the NNPDF4.0 data and theory inputs, but with the MSHT fixed parameterisation. We find that this gives a moderately, but noticeably, better fit quality than the central NNPDF4.0 fits, both with perturbative and fitted charm, and that this difference persists at the level of the PDFs and benchmark cross sections. The NNPDF4.0 uncertainties are found to be broadly in line with the MSHT results if a textbook tolerance is applied, but to be significantly smaller if a tolerance typical of the MSHT20 fit is applied. This points to an inherent inconsistency between these approaches. We discuss the need for an enlarged tolerance criterion in global PDF fits in detail, and demonstrate the impact of data/theory inconsistencies in the closure test setting; namely, these do not lead to any increase in the PDF uncertainty. We also investigate the impact of restricting the PDF parameterisation to have fewer free parameters than the default MSHT20 case, and find this can be significant at the level of both closure tests and the full fit.
我们展示了对用于部分子分布函数（PDF）拟合的固定参数化（MSHT）方法的首次全局闭合测试。我们发现，在这种闭合测试中，默认的MSHT20参数化能够将输入集的特征重现到教科书不确定性范围内。这有力地证明了在数据区域中，MSHT20拟合中参数化的不灵活性并非重大问题。我们还展示了两种全局PDF拟合（即MSHT和NNPDF）之间的首次完全同类比较，其中唯一的差异必定源于拟合方法。为实现这一点，我们展示了对NNPDF4.0数据和理论输入的拟合，但采用MSHT固定参数化。我们发现，无论是对于微扰粲夸克还是拟合粲夸克，这都给出了比NNPDF4.0中心拟合适度但明显更好的拟合质量，并且这种差异在部分子分布函数和基准截面水平上持续存在。如果应用教科书公差，发现NNPDF4.0的不确定性与MSHT结果大致相符，但如果应用MSHT20拟合的典型公差，则明显更小。这表明这些方法之间存在内在不一致性。我们详细讨论了在全局PDF拟合中扩大公差标准的必要性，并展示了闭合测试设置中数据/理论不一致性的影响；即，这些不会导致部分子分布函数不确定性增加。我们还研究了将部分子分布函数参数化限制为比默认的MSHT20情况具有更少自由参数的影响，发现在闭合测试和完整拟合水平上这都可能很显著。
