# A new simple PDF parametrization: improved description of the HERA data

## TL;DR

This paper introduces a new flexible PDF parametrization that significantly improves the fit quality to HERA data, highlighting the importance of parametrization choices at small-x and the benefits of small-x resummation.

## Contribution

A novel PDF parametrization implemented in xFitter that outperforms the default in describing HERA data and reveals parametrization biases at small-x.

## Key findings

- Reduced chi-squared by over 60 units with only four additional parameters.
- Parametrization bias at small-x affects PDF accuracy for high-energy colliders.
- Small-x resummation further improves fit quality by about 30 chi-squared units.

## Abstract

We introduce a new parametrization for the parton distribution functions (PDFs) designed to be flexible in the small-x region. We implement it in the xFitter open-source PDF fitting tool, and compare it to the default xFitter parametrization, widely used for many PDF studies, and notably for the HERAPDF determination. We find that we can describe the combined inclusive HERA I+II data using NNLO theory with a significantly higher quality than HERAPDF2.0: the $\chi^2$ is reduced by more than 60 units, having used only four more parameters. Our result highlights a significant parametrization bias in the default xFitter parametrization at small x, which would lead to even more dramatic effects when used for higher energy colliders, where the small-x region is more relevant. We also find that the inclusion of small-x resummation, that was shown in previous studies to lead to similar improvements in the fit quality, further reduces the $\chi^2$ by approximately 30 extra units.