A team proposes replacing tabulated, interpolated proton parton distribution functions (PDFs) with analytic expressions in (x, Q²), obtained by promoting the parameters of a standard x-space parametrisation to functions of the scale. The coefficients are reconstructed from the HERAPDF2.0 NLO set using machine-assisted fitting techniques, covering 10⁻⁴ ≤ x ≤ 0.65 and scales up to 1 TeV.

PDFs are non-perturbative inputs whose scale dependence is fixed by the DGLAP equations, and their numerical evaluation usually relies on interpolation of tabulated grids. The new representation, dubbed ML-PDFs, reproduces integrated distributions with deviations below 1% for most flavours, although the strange quark reaches differences of about 1.5% at the highest scales. Valence and momentum sum rules are satisfied at the percent level.

In concrete applications, representative pp → π and pp → γπ cross sections are reproduced within approximately 2% and 5%, respectively, in the kinematic regions studied. The practical advantage is cost: direct evaluation of the analytic expressions, rather than interpolation through LHAPDF, reduces total Monte Carlo run time by about 11% in the first case and 30% in the second.

The speed-up is relevant for the event generators that feed LHC simulations, where PDF evaluation is a recurrent bottleneck. The work opens the door to analytic parametrisations of other PDF sets and to their direct integration into simulation chains, although their behaviour outside the explored x and Q² range, and with higher-precision PDF sets, remains to be tested.