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\title[Towards NNPDF4.0]{Towards NNPDF4.0:\\
The Structure of the Proton to One-Percent Accuracy
{\scriptsize XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects}}
\date[April 13, 2021]{April 13, 2021}
\author[Emanuele R. Nocera]{Emanuele R. Nocera\\ {\scriptsize School of Physics and Astronomy, The University of Edinburgh\\ on behalf of the NNPDF Collaboration}}

\setbeamertemplate{frametitle}[default][center]

\begin{document}
\beamertemplatenavigationsymbolsempty

%TITLEPAGE-------------------------------------------------------------------------------------------------------
\begin{frame}
\titlepage
\vspace{0.7cm}
\begin{flushright}
 \includegraphics[scale=0.15]{plots/nnpdf_logo_official}\\
\end{flushright}
\vspace{-0.7cm}
\end{frame}

%Slide
\begin{frame}
 \frametitle{From NNPDF3.1 to NNPDF4.0}
 \footnotesize
 \centering
 \scriptsize
 \vspace{-0.1cm}
 \begin{equation}
  \mathcal{L}_{ij}(M_X,y,\sqrt{s})=\frac{1}{s}\sum_{i,j}
  f_i\left(\frac{M_Xe^y}{\sqrt{s}},M_X\right) 
  f_j\left(\frac{M_Xe^{-y}}{\sqrt{s}},M_X \right)
  \nonumber
 \end{equation}
 \footnotesize
 \begin{overlayarea}{\textwidth}{5.2cm}
  \only<1>
  {
  \centering
  \underline{SINGLET}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_qq}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_qq}\\    
   \end{column}
  \end{columns}
  }
  \only<2>
  {
  \centering
  \underline{SINGLET}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_qqbar}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_qqbar}\\    
   \end{column}
  \end{columns}  
  }
  \only<3>
  {
  \centering
  \underline{FLAVOURS}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_udbar}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_udbar}\\    
   \end{column}
  \end{columns}  
  } 
  \only<4>
  {
  \centering
  \underline{FLAVOURS}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_dubar}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_dubar}\\    
   \end{column}
  \end{columns}  
  }   
  \only<5>
  {
  \centering
  \underline{GLUON}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_gg}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_gg}\\    
   \end{column}
  \end{columns}  
  } 
  \only<6>
  {
  \centering
  \underline{GLUON}\\
  \begin{columns}[c]
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF3.1 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF31_gq}\\
   \end{column}
   \begin{column}{0.5\textwidth}
    \centering
        NNPDF4.0 (NNLO)\\
        \vspace{0.1cm}
        \includegraphics[width=\columnwidth]{plots/plot_lumi2d_uncertainty_NNPDF40_gq}\\    
   \end{column}
  \end{columns}  
  }   
 \end{overlayarea}
 \begin{alertblock}{}
  \centering
  Steady progress towards 1\% relative uncertainties on $\mathcal{L}_{ij}$ on a broad kinematic range\\
 \end{alertblock}
 \vspace{-0.1cm}
 \begin{block}{}
  \centering
  How are we getting there?\\
 \end{block}
\end{frame}

%Slide
\begin{frame}
 \frametitle{NNPDF4.0: data set extension}
 \footnotesize
 \centering
 \includegraphics[width=\textwidth]{plots/Markers0_plot_xq2}\\
 $\mathcal{O}(50)$ data sets investigated; $\mathcal{O}(400)$ data points more in NNPDF4.0 than in NNPDF3.1
\end{frame}

%Slide
\begin{frame}
 \frametitle{NNPDF4.0: new data sets}
 \tiny
 \vspace{0.1cm}
 %\renewcommand*{\arraystretch}{1.15}
 \begin{tabularx}{\textwidth}{llXr}
 \toprule
 Process    & Experiment & Description                                         & Reference\\
 \midrule
 DIS        
            & HERA        & Combined reduced $c$ and $b$ cross sections                      & [{\textcolor{salmon}{EPJ\,C78\,(2018)\,473}}]\\
            & NOMAD$^*$   & $\mathcal{R}_{\mu\mu}(E)=\sigma_{\mu\mu}(E)/\sigma_{\rm CC}(E)$  & [{\textcolor{salmon}{NPB\,876\,(2013)\,339}}]\\
 DY          
            & ATLAS       & $W,Z$ central/forward rapidity distr., {\bf 7~TeV}               & [{\textcolor{salmon}{EPJ\,C77\,(2017)\,367}}]\\
            & ATLAS       & $\{m_{\ell\ell},|y_{\ell\ell}|\}$ $Z$ high-mass distribution, {\bf 8~TeV} & [{\textcolor{salmon}{JHEP\,08\,(2016)\,009}}]\\
            & ATLAS       & $\{m_{\ell\ell},|y_{\ell\ell}|\}$ $Z$ distribution, {\bf 8~TeV}  & [{\textcolor{salmon}{JHEP\,12\,(2017)\,059}}]\\            
            & ATLAS       & $W$ rapidity distr., {\bf 8~TeV}                                 & [{\textcolor{salmon}{EPJ\,C79\,(2019)\,760}}]\\
            & ATLAS       & $W$ and $Z$ total cross section, {\bf 13~TeV}                    & [{\textcolor{salmon}{PLB\,759\,(2016)\,601}}]\\
            & LHCb        & $y_Z$ distribution, $2e$ and $2\mu$, {\bf 13~TeV}                & [{\textcolor{salmon}{JHEP\,09\,(2016)\,136}}]\\  
 $W$+c 
            & ATLAS$^\dag$& $|\eta^\ell|$ distribution  {\bf 7~TeV}                          & [{\textcolor{salmon}{JHEP\,05\,(2014)\,068}}]\\
            & CMS$^\dag$  & $|\eta^\mu|$ distribution  {\bf 13~TeV}                          & [{\textcolor{salmon}{EPJ\,C79\,(2019)\,269}}]\\ 
 single-jet 
            & ATLAS       & $\{p_T, |y|\}$ distribution, {\bf 8~TeV}                         & [{\textcolor{salmon}{JHEP\,09\,(2017)\,020}}]\\
 $t\bar{t}$ 
            & CMS         & total inclusive cross section, {\bf 5~TeV}                       & [{\textcolor{salmon}{JHEP\,03\,(2018)\,115}}]\\
            & CMS         & normalised $\{m_{t\bar{t}},y_t\}$ distribution, {\bf 8~TeV}      & [{\textcolor{salmon}{EPJ\,C77\,(2017)\,459}}]\\
            & CMS         & normalised $y_t$ distribution (dilepton), {\bf 13~TeV}           & [{\textcolor{salmon}{JHEP\,02\,(2019)\,149}}]\\
            & CMS         & normalised $y_t$ distribution (lepton+jet), {\bf 13~TeV}         & [{\textcolor{salmon}{PRD\,97\,(2018)\,112003}}]\\ 
 \midrule
 \alert{single top} 
            & ATLAS       & $R_t$ {\bf 7, 8, 13~TeV}                                         & [{\textcolor{salmon}{JHEP\,04\,(2017)\,086}}]\\
            & ATLAS       & normalised $y_t$ and $y_{\bar{t}}$ distributions, {\bf 7, 8~TeV} & [{\textcolor{salmon}{PRD\,90\,(2014)\,112006; EPJ\,C77\, (2017)\,531}}]\\
            & CMS         & $t+\bar{t}$ cross section, {\bf 7~TeV}                           & [{\textcolor{salmon}{JHEP\,12\,(2012)\,035}}]\\
            & CMS         & $R_t$ {\bf 8, 13~TeV}                                            & [{\textcolor{salmon}{JHEP\,06\,(2014)\,090; PLB\,772\,(2017)\,752}}]\\
 \alert{$W$+jet}    
            & ATLAS       & $p_T$ distribution, {\bf 8~TeV}                                  & [{\textcolor{salmon}{JHEP\,05\,(2018)\,077}}]\\        
 \alert{isolated photon} 
            & ATLAS       & $\{E_T^\gamma,|\eta^\gamma|\}$ distribution, {\bf 13~TeV}        & [{\textcolor{salmon}{PLB\,770\,(2017)\,473}}]\\     
 \alert{di-jets}    
            & ATLAS       & $\{m_{12},y^*\}$ distribution {\bf 7~TeV}                        & [{\textcolor{salmon}{JHEP\,05\,(2014)\,059}}]\\
            & CMS         & $\{m_{12},|y_{\rm max}|\}$ distribution {\bf 7~TeV}              & [{\textcolor{salmon}{PRD\,87\,(2013)\,112002}}]\\
            & CMS         & $\{p_{\rm T,avg},y_b,y^*\}$ distribution {\bf 8~TeV}             & [{\textcolor{salmon}{EPJ\,C77\,(2017)\,746}}]\\           
 \alert{DIS+jets}   
            & H1$^*$      & Single- and di-jet differential distributions                    & [{\textcolor{salmon}{EPJ\,C75\,(2015)\,65; C77\,(2017)\,215}}]\\
 \bottomrule 
 \multicolumn{3}{l}{$^*$Not in baseline fit; studied via reweighting}                        &
 \multicolumn{1}{l}{$^\dag$Only NLO fit}\\
 \multicolumn{4}{l}{Processes highlighted in \alert{red} correspond to processes NOT in NNPDF3.1}\\
 \end{tabularx}
% \vspace{-0.2cm}
% \scriptsize
% \begin{block}{}
%  \centering
%  Selection of data sets based on weighted fits\\
%  %{\scriptsize Example: D0 $W$ electron asymmetry no longer in NNPDF4.0}\\
% \end{block}
\end{frame}

%Slide
\begin{frame}
 \frametitle{NNPDF4.0: theoretical and methodological features}
 \footnotesize
 \begin{itemize}
  \item \underline{Refined} theoretical framework~{\tiny{[{\textcolor{salmon}{EPJ\,C79\,(2019)\,282; EPJ\,C81\,(2021)\,37; EPJ\,C80\,(2020)\,1168;}}]}}\\
  {\scriptsize $\rightarrow$ nuclear uncertainties for both deuteron and heavy nuclei included by default}\\
  {\scriptsize $\rightarrow$ NNLO charm-quark massive corrections implemented (a bug in the NLO corrected)}\\
  {\scriptsize $\rightarrow$ EW corrections not included to ensure consistency with data, but carefully checked}\\
  {\scriptsize $\rightarrow$ charm PDF parametrised on the same footing as other PDFs}\\
  \item \underline{Improved} implementation of PDF properties~{\tiny{[{\textcolor{salmon}{JHEP\,11\,(2020)\,129}}]}}\\
  {\scriptsize $\rightarrow$ extended positivity constraints for light quark/antiquark and gluon PDFs}\\
  {\scriptsize $\rightarrow$ extended integrability constraints of non-singlet light quark PDF combinations}\\
  \item \underline{New} PDF parametrisation and optimisation~{\tiny{[{\textcolor{salmon}{EPJ\,C79\,(2019)\,676}}]}} \\
  {\scriptsize $\rightarrow$ single neural network to parametrise eight independent PDF combinations}\\
  {\scriptsize $\rightarrow$ check of the independence of the results from the chosen parametrisation basis}\\
  {\scriptsize $\rightarrow$ new optimisation strategy based on gradient descent rather than genetic algorithms}\\
  {\scriptsize $\rightarrow$ scan of the hyperparameter space to find the optimal minimisation settings}\\
  \item \underline{Complete} statistical validation of PDF uncertainties~{\tiny{[{\textcolor{salmon}{Acta\,Phys.Polon.\,B52\,(2021)\,243}}]}}\\
  {\scriptsize $\rightarrow$ (multi-)closure tests to validate PDF uncertainties in the data region}\\
  {\scriptsize $\rightarrow$ future tests to check the sensibleness of PDF uncertainties in extrapolation regions}\\
  \item \underline{More efficient} compression tool for PDF set delivery~{\tiny{[{\textcolor{salmon}{arXiv:2104.04535}}]}}
 \end{itemize}
 {\tiny{[{\color{salmon}{See also talks by R.L. Pearson later today and by C. Schwan and F. Heckhorn tomorrow.}}]}}\\
\end{frame}

%Slide
\begin{frame}
 \frametitle{NNPDF4.0: Fit quality -- NNLO}
 \footnotesize
 \centering
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
  \tiny
  \renewcommand*{\arraystretch}{1.08}
   \begin{tabularx}{\columnwidth}{Xrc}
   \toprule
   Data set                   & $N_{\rm dat}$ & $\chi^2/N_{\rm dat}$ \\
   \midrule
   Fixed-target DIS           & 1881 & 1.10 \\
   HERA                       & 1208 & 1.21 \\
   \ $\sigma_c$               &   37 & 2.11 \\
   \ $\sigma_b$               &   26 & 1.48 \\
   Fixed-target Drell-Yan     &  189 & 1.00 \\
   CDF                        &   28 & 1.31 \\
   D0                         &   37 & 1.00 \\
   ATLAS                      &  621 & 1.18 \\
   \ Drell-Yan, 7, 8, 13~TeV  &  153 & 1.32 \\
   \ $W$+jet, 8~TeV           &   32 & 1.15 \\
   \ single top, 7, 8, 13~TeV &   14 & 0.36 \\
   \ di-jets, 7~TeV           &   90 & 1.93 \\
   \ jets, 8~TeV              &  171 & 0.61 \\
   \ top pair, 7, 8, 13~TeV   &   16 & 2.30 \\
   \ $Zp_T$, 8~TeV            &   92 & 0.86 \\
   \ direct photon, 13~TeV    &   53 & 0.72 \\
   CMS                        &  411 & 1.40 \\
   \ Drell-Yan, 7, 8~TeV      &  154 & 1.34 \\
   \ single top, 7, 8, 13~TeV &    3 & 0.43 \\
   \ di-jets, 7~TeV           &   54 & 1.67 \\
   \ di-jets, 8~TeV           &  122 & 1.50 \\
   \ top pair, 5, 7, 8~TeV    &   29 & 0.84 \\
   \ top pair, 13~TeV         &   21 & 0.67 \\
   \ $Zp_T$, 8~TeV            &   28 & 1.42 \\
   LHCb                       &  116 & 1.53 \\
   \midrule
   Total                      & 4491 & 1.17 \\
   \bottomrule 
   \end{tabularx}
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \footnotesize
   Overall good description of the data sets\\
   \vspace{0.1cm}
   Two exceptions:\\
   HERA $\sigma_c$ and ATLAS top pair\\
   \vspace{0.1cm}
   Weighted fits analysis:\\
   {\scriptsize in case of HERA $\sigma_c$:}\\
   {\scriptsize lack of small-$x$ resummation}\\
   \vspace{0.1cm}
   {\scriptsize in case of ATLAS top pair:\\ slight tension with (di-jet) data sets}\\
   {\scriptsize poor fit if all distributions are included}\\
   {\scriptsize normalised rapidity distributions retained}\\
   {\scriptsize although their $\chi^2/N_{\rm dat}$ of order 3}\\
   {\scriptsize CMS top pair data almost insensitive to all this}\\
   \vspace{0.1cm}
   General remark:\\
   {\scriptsize as statistical uncertainties become smaller}\\
   {\scriptsize a good control of systematic uncertainties}\\ 
   {\scriptsize and their correlations becomes fundamental}\\ 
   {\scriptsize to interpret the sensibleness of the fit}\\
   \vspace{0.2cm}
   \begin{block}{}
    \centering
    {\scriptsize All results in the sequel are obtained at NNLO}\\
   \end{block}
  \end{column}
 \end{columns}
\end{frame}

%Slide07
\begin{frame}
 \frametitle{From NNPDF3.1 to NNPDF4.0}
 \footnotesize
 \centering
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \begin{overlayarea}{\columnwidth}{4cm}
    \only<1>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/qq_lumi_31vs40}\\    
    }
    \only<2>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/qq_lumi_31}\\    
    }
   \end{overlayarea}
  \end{column}
  \begin{column}{0.5\textwidth}
   \begin{overlayarea}{\columnwidth}{4cm}
    \only<1>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/qqbar_lumi_31vs40}\\    
    }
    \only<2>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/qqbar_lumi_31}\\    
    }
   \end{overlayarea}   
  \end{column} 
 \end{columns}
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \begin{overlayarea}{\columnwidth}{4cm}
    \only<1>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/gg_lumi_31vs40}\\
    }
    \only<2>
    {
     \centering
     \includegraphics[width=0.95\columnwidth]{plots/gg_lumi_31}\\    
    }
   \end{overlayarea}   
  \end{column}
  \begin{column}{0.5\textwidth}
   \begin{overlayarea}{\columnwidth}{4cm}
    \only<1>
    {
     \centering
     \tiny
     \renewcommand*{\arraystretch}{1.35}
     \begin{tabular}{lcc}
      \toprule
       \backslashbox{data set ($N_{\rm dat}$)}{methodology} & NNPDF3.1         & NNPDF4.0        \\
       \midrule
       NNPDF3.1 (4093)                                     & \alert{\bf 1.19} &            1.12  \\
       NNPDF4.0 (4491)                                     &      1.25        & \alert{\bf 1.17} \\
      \bottomrule
     \end{tabular}\\
     \vspace{0.3cm}
     \scriptsize
     \underline{Consistency} between PDF sets\\
     \vspace{0.2cm}
     NNPDF4.0 \underline{more precise}\\
     (combination of data set and methodology)\\
     \vspace{0.2cm}
     NNPDF4.0 \underline{more accurate}\\
     (superiority of the NNPDF4.0 methodology)\\
    }
    \only<2>
    {
      \centering
     \tiny
     \renewcommand*{\arraystretch}{1.35}
     \begin{tabular}{lcc}
      \toprule
       \backslashbox{data set ($N_{\rm dat}$)}{methodology} & NNPDF3.1         & NNPDF4.0        \\
       \midrule
       NNPDF3.1 (4093)                                      &            1.19  &            1.12  \\
       NNPDF4.0 (4491)                                      & \alert{\bf 1.25} & \alert{\bf 1.17} \\
      \bottomrule
     \end{tabular}\\
     \vspace{0.3cm}
     \scriptsize
     \underline{Consistency} between PDF sets\\
     \vspace{0.2cm}
     NNPDF4.0 \underline{more precise}\\
     (combination of data set and methodology)\\
     \vspace{0.2cm}
     NNPDF4.0 \underline{more accurate}\\
     (superiority of the NNPDF4.0 methodology)\\  
    }
   \end{overlayarea}   
  \end{column}   
 \end{columns}
\end{frame}

%Slide
\begin{frame}
 \frametitle{The gluon PDF: impact of data}
 \footnotesize
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   jet and $t\bar{t}$ data\\
   \includegraphics[width=0.95\columnwidth]{plots/gluon_1}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   $Zp_T$ and direct photon data\\
   \includegraphics[width=0.95\columnwidth]{plots/gluon_2}\\   
  \end{column}
 \end{columns}
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   di-jets vs single-inclusive jets\\
   \includegraphics[width=0.95\columnwidth]{plots/gluon_3}\\   
  \end{column}
  \begin{column}{0.5\textwidth}
  \centering
  Hierarchical impact of different data sets\\
  {\scriptsize di-jet measurements have the largest pull}\\
  {\scriptsize $t\bar{t}$ and $Zp_T$ measurements have a comparatively small pull, which is consistent with the global fit}\\
  {\scriptsize direct photon measurements almost immaterial}\\ 
  \vspace{0.3cm}
  Inclusion of di-jet measurements is preferred over single-inclusive jet measurements\\
  {\scriptsize given their greater theoretical accuracy and the avoidance of decorrelation models}\\
  {\scriptsize For details, see~{\tiny{[{\color{salmon}{EPJ C80 (2020) 8}}]}}}\\
  \end{column}
 \end{columns}
\end{frame}

%Slide
\begin{frame}
 \frametitle{Quark flavour decomposition: impact of data}
 \footnotesize
  \centering
  Quarks\\
  \includegraphics[width=0.48\textwidth]{plots/flavour_u}
  \includegraphics[width=0.48\textwidth]{plots/flavour_d}\\ 
  Antiquarks\\
  \includegraphics[width=0.48\textwidth]{plots/flavour_baru}
  \includegraphics[width=0.48\textwidth]{plots/flavour_bard}\\ 
\end{frame}

%Slide
\begin{frame}
 \frametitle{Sea quark asymmetry: SeaQuest}
 \centering
 \includegraphics[width=\textwidth]{plots/seaquest}\\
 \vspace{-1cm}
 \begin{flushright}
  {\tiny{[{\color{salmon}{Nature\,590\,(2021)\,561; plot by courtesy of J. Rojo}}]}}
 \end{flushright}
\end{frame}

%Slide
\begin{frame}
 \frametitle{The strange PDF: impact of data}
 \footnotesize
 \centering
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/strange_1}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/strange_2}\\
  \end{column}
 \end{columns}
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/ks-Q_1p6GeV}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \footnotesize
   Enhanced $s$ and $\bar{s}$ PDFs w.r.t. NNPDF3.1\\
   {\scriptsize effect of ATLAS $W,Z$ and $W$+jet data}\\
   \vspace{0.2cm}
   Good consistency with NNPDF3.1str\\
   {\scriptsize no nuclear uncertainties in NNPDF3.1str}\\
   {\scriptsize no NOMAD data in NNPDF4.0}\\
   \vspace{0.2cm}
   Good consistency of $K_s$ across PDF sets\\ 
   \vspace{0.1cm}
   $K_s(Q^2)=\frac{\int_0^1\,dx[s(x,Q^2)+\bar{s}(x,Q^2)]}{\int_0^1\,dx[\bar{u}(x,Q^2)+\bar{d}(x,Q^2)]}$\\
   \begin{flushright}
    {\tiny{See also [{\color{salmon}{EPJ\,C80\,(2020)\,1168}}]}}
   \end{flushright}
  \end{column}
 \end{columns} 
\end{frame}

%Slide13
\begin{frame}
 \frametitle{Impact of theory: perturbative vs fitted charm}
 \footnotesize
 \centering
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/charm_1}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   Striking evidence of intrinsic charm\\
   {\scriptsize even w/o EMC $F_2^c$ data}\\
   \vspace{0.2cm}
   Perturbative charm alters the flavour decomposition and deteriorates the fit\\
   \vspace{0.1cm}
   {\scriptsize $\chi^2_{\rm fitted\,charm}=1.17\to \chi^2_{\rm pert.\,charm}=1.19$}\\
   \vspace{0.2cm}
   {\scriptsize mainly due to a worsening\\ of the LHC $W,Z$ and top pair data sets}\\
  \end{column}
 \end{columns}
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/charm-Q_1p6GeV}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/qqbar_lumi_pch}\\
  \end{column}
 \end{columns}
\end{frame}

%Slide
\begin{frame}
 \frametitle{NNPDF4.0: implications for LHC phenomenology}
 \footnotesize
 \centering
 \vspace{0.2cm}
 \includegraphics[width=0.43\textwidth]{plots/NNPDF40_HIGGS_WM-global}
 \ \ \ \ \ \ \ \ \ 
 \includegraphics[width=0.43\textwidth]{plots/NNPDF40_TTBAR-global}\\
 \begin{flushright}
  \tiny{[{\color{salmon}{Plots by courtesy of C.~Schwan}}]}
 \end{flushright}
\end{frame}

%Slide
\begin{frame}
 \frametitle{Conclusions}
 \footnotesize
 \centering
 NNPDF4.0 is the next generation parton set of the NNPDF family.\\
 \vspace{0.3cm}
 It achieves 1\% accuracy in an unprecedentedly broad kinematic range\\
 by consistently improving the previous NNPDF3.1 parton set.\\
 \vspace{0.3cm}
 This result builds upon an extensive LHC data set\\ 
 combined with deep-learning optimisation models.\\
 \vspace{0.3cm}
 Its faithfulness in representing PDF uncertainties is completely validated by closure tests.\\
 \vspace{0.3cm}
 1\% PDF uncertainties challenge the accuracy of theoretical predictions\\
 and demand an increasing effort towards the systematic inclusion in the fit of\\ 
 theoretical uncertainties (nuclear, higher orders, physical parameters, \dots)\\
 and higher-order QCD and EW corrections.\\
 \vspace{0.3cm}
 \begin{block}{}
 \centering
 The {\bf NNPDF code} used to produce the NNPDF4.0 parton set\\ 
 {\bf will be made publicly available} with its documentation.\\
 \end{block}
 \vspace{1cm}
 \begin{overlayarea}{\textwidth}{0.5cm}
  \only<1>
  {
  }
  \only<2>
  {
  \centering
  \Large\bf Thank you
  }
 \end{overlayarea}
\end{frame}

\appendix

%Slide10
\begin{frame}
 \frametitle{Individual data sets: $\chi^2$ breakdown}
 \tiny
 \renewcommand*{\arraystretch}{1.15}
 \begin{tabularx}{\textwidth}{Xcccccccc}
  \toprule
  \backslashbox{fit}{data set} & ATLAS jets & CMS jets & ATLAS top & CMS top & ATLAS $Z p_T$ & CMS $Z p_T$ & ATLAS dir. phot. & total\\
  \midrule
  NNPDF4.0        &  1.06  &  1.55  &  2.29  &  0.77  &  0.86  &  1.41  &  0.71  & 1.17 \\
  (no jets)       & [1.71] & [3.70] &  1.54  &  1.00  &  0.86  &  1.35  &  0.72  & 1.14 \\
  (no top)        &  1.08  &  1.57  & [3.51] & [0.91] &  0.86  &  1.43  &  0.74  & 1.18 \\
  (no $Zp_T$)     &  1.08  &  1.57  &  2.30  &  0.76  & [0.99] & [1.41] &  0.69  & 1.14 \\
  (no dir. phot.) &  1.06  &  1.55  &  2.30  &  0.77  &  0.86  &  1.42  & [0.71] & 1.18 \\
  \bottomrule
 \end{tabularx}
 \vfill
 \tiny
 \renewcommand*{\arraystretch}{1.15}
 \begin{tabularx}{\textwidth}{Xccccccccc}
  \toprule
  \backslashbox{fit}{data set}     & ATLAS 2j & CMS 2j & ATLAS 1j (7~TeV) & ATLAS 1j (8~TeV) & CMS 1j & $Z p_T$ & top & total\\
  \midrule
  NNPDF4.0                         &  1.93  &  1.56  & [1.28] [3.42]$^*$ & 0.61 [2.82]$^*$ & [1.31]  &  0.99  &  1.17  &  1.17 \\
  (single-jets instead of di-jets) & [2.41] & [2.68] & {\color{white}{[}}1.23{\color{white}{]}} [3.36]$^*$ & 0.85 [3.10]$^*$ &  1.07   &  0.99  &  1.19  &  1.14 \\
  \bottomrule
  $^*$No decorrelation model & \\
 \end{tabularx}
 \vfill
 \tiny
 \renewcommand*{\arraystretch}{1.15}
 \begin{tabularx}{\textwidth}{Xccccccccc}
  \toprule
  \backslashbox{fit}{data set}     & FT DIS & HERA & FT DY & Tevatron & ATLAS $W,Z$ & CMS $W,Z$ & LHCb & single top & total\\
  \midrule
  NNPDF4.0                         & 1.10 & 1.21 &  1.00  &  1.14  &  1.28  &  1.33  &  1.54  &  0.37  & 1.17 \\
  (no LHCb)                        & 1.08 & 1.21 &  0.97  &  1.27  &  1.34  &  1.35  & [2.60] &  0.34  & 1.16 \\      
  (no ATLAS/CMS $W,Z$)             & 1.05 & 1.20 &  0.85  &  1.02  & [2.14] & [1.36] &  1.39  &  0.37  & 1.11 \\
  \midrule
  DIS-only                         & 1.03 & 1.21 & [1.40] & [1.22] & [4.15] & [3.83] & [2.96] & [0.33] & 1.10 \\
  \bottomrule
 \end{tabularx} 
\end{frame}

%Slide11
\begin{frame}
 \frametitle{Quark flavour separation: nuclear uncertainties}
 \footnotesize
 \centering
 \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/nuclear_baru}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/nuclear_bard}\\
  \end{column}
 \end{columns}
  \begin{columns}[c]
  \begin{column}{0.5\textwidth}
   \centering
   Effect of nuclear uncertainties relevant\\ at large $x$\\
   to reconcile FT DIS with LHC DY data\\
   \vspace{0.1cm}
   {\scriptsize $\chi^2_{\rm tot}=1.17\to \chi^2_{\rm tot}=1.26$ (no nucl. uncs.)}\\
   {\scriptsize $\chi^2_{\rm LHCb}=1.54\to \chi^2_{\rm tot}=1.76$ (no nucl. uncs.)}\\
   \vspace{0.2cm}
   The bulk of the effect is due to nuclear uncertainties for heavy nuclei\\
   {\scriptsize deuteron uncertainties have a comparatively smaller effect at inermediate values of $x$}\\
  \end{column}
  \begin{column}{0.5\textwidth}
   \centering
   \includegraphics[width=\columnwidth]{plots/nuclear_d}\\   
  \end{column}
 \end{columns}
\end{frame}

%Slide14
\begin{frame}
 \frametitle{NNPDF4.0: parton luminosities}
 \footnotesize
 \centering
 \begin{overlayarea}{\textwidth}{10cm}
  \only<1>
  {
   \includegraphics[width=0.48\textwidth]{plots/lumi_qq_1}
   \includegraphics[width=0.48\textwidth]{plots/lumi_qqbar_1}\\
   \includegraphics[width=0.48\textwidth]{plots/lumi_gq_1}
   \includegraphics[width=0.48\textwidth]{plots/lumi_gg_1}\\
  }
  \only<2>
  {
   \includegraphics[width=0.48\textwidth]{plots/lumi_qq_2}
   \includegraphics[width=0.48\textwidth]{plots/lumi_qqbar_2}\\
   \includegraphics[width=0.48\textwidth]{plots/lumi_gq_2}
   \includegraphics[width=0.48\textwidth]{plots/lumi_gg_2}\\  
  }
 \end{overlayarea}
\end{frame}

%Slide
%%%%%%%%%%%%%%%%%%%%%%%
%\section{PDF properties and their implementation}
%\input{felix_positivity/positivity}
%\input{pos_integ/main}

%%%%%%%%%%%%%%%%%%%%%%%
%\section{PDF determination methodology}
%\input{juan_future_hyperopt/hyperopt}
%\input{roy_pdf_correlations/pdf_corr}

%%%%%%%%%%%%%%%%%%%%%%%
%\section{PDF validation}
%\input{closure_test/closure_test}
%\input{juan_future_hyperopt/future}

%%%%%%%%%%%%%%%%%%%%%%%
%\section{Dataset selection}
%%%%%\input{weight_fits/talk}








\end{document}



