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

TL;DR

The paper extends Hessian PDF reweighting by incorporating the first non-quadratic terms of the original fit’s $\chi^2$ via $\delta z^{\pm}_k$ information, and applies the method to CMS 5.02 TeV dijet data. The non-quadratic extension (cubic–quadratic) is exercised on CT14 NLO and EPPS16 nPDFs, showing substantial modifications to high-$x$ gluons improve pp data description and propagate to pPb predictions, while dramatically reducing uncertainties in the gluon sector of EPPS16. The results provide evidence for small-$x$ gluon shadowing and mid-$x$ antishadowing in nuclei and demonstrate the potential of non-quadratic reweighting to sharpen nuclear PDF constraints; the authors advocate publishing the original fit’s parameter-shift information to enable higher-order reweighting in future global analyses.

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 $χ^2$ 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 $x \approx 0.1$.

Figures (13)

• Figure 1: An illustration for the response of $\chi^2$ (top) and $y_i$ (bottom) with respect to a change of parameter $z_k$ in quadratic--linear (red, long dashed), quadratic--quadratic (blue, short dashed) and cubic--quadratic (black, solid) approximations.
• Figure 2: Upper panels: Distributions of dijets in 5.02 TeV proton--proton collisions against $\eta_{\rm dijet}$ and normalized to unity in each bin of $p_{\rm T}^{\rm ave}$. The imposed kinematic cuts are discussed in text. Black markers show the data from the CMS measurement Sirunyan:2018qel with vertical bars showing the statistical and systematical uncertainties added in quadrature. Solid orange lines represent the results from the NLO pQCD calculation using the central set of the CT14 NLO PDFs Dulat:2015mca with $\mu = p_{\rm T}^{\rm ave}$ scale choice, light orange boxes the associated PDF uncertainties from the CT14 NLO error sets. Lower panels: Difference to the central CT14 result. Dashed hollow boxes show the dependence of NLO predictions on factor two upward and downward variations of the scale choice. Dotted lines represent the results from the respective LO pQCD calculation. The results with $\mu = M_{\rm dijet}$ scale choice and its factor two variations are indicated in green.
• Figure 3: The impact of reweighting on CT14 NLO PDFs at $Q^2 = 10^4~{\rm GeV}^2$. The original CT14 PDFs are shown in orange, with the solid line representing the central set PDFs, the ratio to which is shown in each panel. The corresponding PDFs obtained with quadratic--quadratic reweighting using $\Delta\chi^2 = 100$ are shown in red and the central set of the reweighting with $\Delta\chi^2 = 10$ is presented with a solid purple line.
• Figure 4: Upper panels: The impact of reweighting on CT14 predictions of pp dijet spectra. The original predictions are shown in orange and the results obtained with quadratic--quadratic reweighting using $\Delta\chi^2 = 100$ are shown in red. In both cases the solid lines corresponding to the central set and the shaded boxes showing the PDF uncertainty. In addition, resulting spectra from reweighting with $\Delta\chi^2 = 10$ are shown as purple lines. Lower panels show again the difference to the original central CT14 results.
• Figure 5: Comparison of the NLO gluon PDFs of the original and reweighted CT14 sets with those from the MMHT14, NNPDF3.1 and 5-flavour ABMP16 analyses. The uncertainty bands of the latter have been scaled with a factor 1.64 to nominally match with the 90% confidence level definition of the CT14 analysis.