# Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV

## TL;DR

This paper introduces a non-quadratic Hessian PDF reweighting method that accounts for non-quadratic terms in the initial fit and applies it to CMS dijet data at 5.02 TeV, improving PDF constraints.

## Contribution

It extends the Hessian reweighting technique by including non-quadratic components, enhancing the accuracy of PDF updates using new data.

## Key findings

- Reweighted CT14 PDFs improve agreement with CMS dijet data.
- Data constrains gluon nuclear shadowing and antishadowing effects.
- Proton-PDF modifications impact pPb dijet predictions.

## Abstract

Hessian PDF reweighting, or "profiling", has become a widely used way to study the impact of a new data set on parton distribution functions (PDFs) with Hessian error sets. The available implementations of this method have resorted to a perfectly quadratic approximation of the initial $\chi^2$ function before inclusion of the new data. We demonstrate how one can take into account the first non-quadratic components of the original fit in the reweighting, provided that the necessary information is available. We then apply this method to the CMS measurement of dijet pseudorapidity spectra in proton-proton (pp) and proton-lead (pPb) collisions at 5.02 TeV. The measured pp dijet spectra disagree with next-to-leading order (NLO) theory calculations using the CT14 NLO PDFs, but upon reweighting the CT14 PDFs, these can be brought to a much better agreement. We show that the needed proton-PDF modifications also have a significant impact on the predictions for the pPb dijet distributions. Taking the ratio of the individual spectra, the proton-PDF uncertainties effectively cancel, giving a clean probe of the PDF nuclear modifications. We show that these data can be used to further constrain the EPPS16 nuclear PDFs and strongly support gluon nuclear shadowing at small $x$ and antishadowing at around $x \approx 0.1$.