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\begin{document}

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\begin{titlepage}
 
\noindent
%HERAPDF2.0Jets NNLO, the completion of the HERAPDF2.0 family\hfill\\
%\ \\
%DESY-15-039 \\
%June 5, 2015 \\
H1prelim-19-041 \\
ZEUS-prel-19-001 \\

\vspace*{1.0cm}

\begin{center}
\begin{Large}


  {\bfseries Preliminary Writeup, April 4, 2019 }

  {\bfseries HERAPDF2.0Jets NNLO (prel.), the completion of the HERAPDF2.0 family}

  
\vspace*{1cm}

H1, ZEUS and NNLOJET Collaborations


\end{Large}
\end{center}

\vspace*{1cm}
\begin{abstract} \noindent
  The HERAPDF2.0 family, introduced in 2015, is completed
  with fits HERAPDF2.0Jets NNLO (prel.) based on inclusive
  HERA data and selected jet production data.
  The result of a fit with the strong coupling constant, $\asmz$, free is
  $\asmz = 0.1150 \pm 0.0008{\rm (exp)} ^{+0.0002}_{-0.0005}$ 
  (model/parameterisation) $\pm 0.0006{\rm (hadronisation)} \pm 0.0027 {\rm (scale)}$.
  Sets of parton density functions, PDFs, from fits with fixed
  $\asmz = 0.115$ and  $\asmz = 0.118$ are presented and compared.
  The PDFs from the fit with fixed $\asmz = 0.118$ are also compared
  to the PDFs from HERAPDF2.0 NNLO.
  Predictions from the PDFs of HERAPDF2.0Jets NNLO (prel.) with
  fixed $\asmz = 0.115$ are compared to the jet production data used as
  input. The predictions describe the data very well.

\end{abstract}

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\section{Introduction \label{sec:int}}

Deep inelastic scattering (DIS) of electrons
%\footnote{In this write-up, 
%the word ``electron" refers to both electrons and positrons, 
%unless otherwise stated.} 
on protons, $ep$, at centre-of-mass energies of up to $\sqrt{s} \approx 320\,$GeV
at HERA has been central to the exploration
of proton structure and quark--gluon dynamics as
described by perturbative Quantum Chromo Dynamics (pQCD)~\cite{saturation}. 

The combination of H1 and ZEUS data on inclusive $ep$ scattering
and the subsequent pQCD analysis, introducing the family of 
parton density functions (PDFs) known as HERAPDF2.0,
was a milestone for the exploitation\cite{HERAPDF20} of the HERA data.
The preliminary work presented here represents a completion of the 
HERAPDF2.0 family~\cite{HERAPDF20} with a fit at NNLO to
HERA inclusive~\cite{HERAPDF20} and jet production data
published separately by the
ZEUS and H1 collaborations.
This was not possible at the time of the original introduction of HERAPDF2.0
because a treatment at NNLO of jet production in 
$ep$ scattering was not available then.

The name HERAPDF stands for a pQCD analysis within the
DGLAP~\cite{Gribov:1972ri,Gribov:1972rt,Lipatov:1974qm,Dokshitzer:1977sg,Altarelli:1977zs}
formalism, where predictions from pQCD are fitted to data.
These predictions
are obtained by solving the DGLAP evolution 
equations at LO, NLO and NNLO in the \msbar scheme~\cite{MSbar}.

\section{Procedure and Data}

The inclusive and dijet production
data~\cite{zeus9697jets,zeusdijets,h1highq2oldjets,h1lowq2jets,h1highq2newjets},
which were already
used for HERAPDF2.0Jets NLO were again used for the analysis presented here.
A new data set~\cite{h1lowq2newjets} published by the 
H1~collaboration on 
jet production in low~$Q^2$ events, 
where $Q^2$ is the four-momentum-transfer squared,
was added as input to the fits. 
All data sets on jet production, which were used, 
are listed in Table~\ref{tab:jet-data}.
The charm data, which were included in the analysis at NLO, were not used
for the analysis presented here.
Their influence will be studied in a future analysis. 

The fits presented here were done in almost exactly the same way 
as for all other members of the HERAPDF2.0 family~\cite{HERAPDF20},
and especially for the HERAPDF2.0Jets NLO fit. This includes
the $\chi^2$ definition which was taken from equation\,32 
of~\cite{HERAPDF20}.

The fits were performed using the programme 
QCDNUM~\cite{QCDNUM} within the xFitter, formerly HERAFitter,
framework~\cite{HERAfitter} and an independent
programme, which was also already used as a second program in the
HERAPDF2.0 analysis.
The results obtained by the two programmes, as previously
for all HERAPDF2.0 fits~\cite{HERAPDF20}, 
were in excellent agreement, well within fit uncertainties.
All numbers presented here were obtained using xFitter. 
Only cross sections for $Q^2$ starting at $Q^2_{min} = 3.5$\,GeV$^2$ 
were used in the analysis. 
All parameter setting were the same as for the HERAPDF2.0Jets NLO fit.
The analysis of uncertainties was also performed in exactly the same way.

There were some modifications with respect to the analysis at NLO.
They were driven by the usage of
the newly available treatment of jet production at NNLO.
The jet data were included in the fits at NNLO  by calculating
predictions for the jet cross sections
within the  Applfast framework using the NNLO extension of
NLOjet++~\cite{nlojet1,nlojet2},
which was interfaced to FastNLO~\cite{fastnlo1,fastnlo2,fastnlo3} 
in order to achieve the speed necessary
for iterative PDF fits.
As done previously, the predictions were multiplied by corrections
for hadronisation and 
$Z^0$ exchange before they were used in the fits.
A running electro-magnetic $\alpha$ as implemented in the 2012 version of 
the programme EPRC~\cite{Spiesberger:95} was used for the treatment
of the jet cross sections.

The new treatment of inclusive jet and dijet production at NNLO was only 
applicable to a slightly reduced phase space compared to 
HERAPDF2.0Jets NLO. All data points 
with $\sqrt{\langle p_T^2 \rangle +Q^2} \le 13.5$\,GeV were excluded,
where $p_T$ is the transverse energy of the jets. 
In addition, six data points, the lowest $\langle p_T \rangle$ 
bin for each $Q^2$ region, were excluded from the ZEUS dijet
data set because the NNLO  predictions for these points were
deemed unreliable.
The resulting reduction of data points is listed in Table~\ref{tab:jet-data}.
In addition, the trijet data~\cite{h1highq2newjets} which were used as input
to HERAPDF2.0Jets NLO had to be excluded as their treatment at NNLO was not available.

The choice of scales was also adjusted to the NNLO analysis.
At NLO, the factorisation scale was chosen as 
$\mu_{\rm f}^2 = Q^2$,
while the renormalisation scale was linked to the transverse
momenta, $p_T$, of the jets by $\mu_{\rm r}^2 = (Q^2 + p_{T}^2)/2$.
For the NNLO analysis, $\mu_{\rm f}^2 =\mu_{\rm r}^2= Q^2 + p_{T}^2$
was chosen.



\section{Determination of the strong coupling constant}
\label{sec:as}

Jet production data are essential for the determination of
the strong coupling constant, $\asmz$.
In pQCD fits to inclusive DIS data alone, the gluon PDF is determined 
via the DGLAP equations only, using the observed scaling violations.
This results in a strong correlation between the shape of the 
gluon distribution and the value of $\asmz$. 
Data on jet production cross sections provide an independent constraint
on the gluon distribution.
Jet and dijet production are also directly sensitive to $\asmz$ and 
thus  such data allow for an accurate simultaneous determination of $\asmz$
and the gluon distribution.

The HERAPDF2.0Jets NNLO (prel.) fit with free $\asmz$
gave a value of
\begin{eqnarray}
\nonumber
\asmz =0.1150 \pm 0.0008{\rm (exp)} ^{+0.0002}_{-0.0005}{\rm (model/parameterisation)} \\
\nonumber
 ~~~~ \pm 0.0006{\rm (hadronisation)}~~ \pm 0.0027 {\rm (scale)}~~.
\end{eqnarray}
This result on $\asmz$ is compatible with the world average~\cite{PDG18} 
and it is competitive to other determinations at NNLO. The ``exp'' denotes
the experimental uncertainty which is taken as the fit uncertainty.

The HERAPDF2.0Jets NNLO (prel.) fit with free $\asmz$  uses
1343 data points and has a
$\chi^2/$d.o.f.\,$= 1599/1328 = 1.203$. This can be compared
to the $\chi^2/$d.o.f.\,$= 1363/1131 = 1.205$ for HERAPDF2.0 NNLO based on
inclusive data only~\cite{HERAPDF20}.
The similarity of the $\chi^2/$d.o.f. values indicates that 
the data on jet production do not introduce any tension.

The experimental uncertainty was determined from the fit.
The $\chi^2$ scan in $\asmz$ shown in Fig.~\ref{fig:alphasscan}a) confirmed
the value of $\asmz$ and the experimental, i.e.\ fit,
uncertainty.
The clear minimum coincides with the value as determined
by the fit and the dependence of $\chi^2$ on $\asmz$ confirms the fit uncertainty.
The model/parameterisation and hadronisation uncertainties also shown
in Fig.~\ref{fig:alphasscan}a)
were determined
with similar scans in the respective parameter spaces. 

A strong motivation to determine
$\asmz$ at NNLO was the hope to substantially reduce scale uncertainties.
This uncertainty
was evaluated by varying the renormalisation and factorisation 
scales by a factor of two,
both separately and simultaneously, 
and taking the maximal positive and negative deviations.
The uncertainties were assumed to be 
50\,\% correlated and 50\,\% uncorrelated
between bins and data sets.
The result is also shown in Fig.~\ref{fig:alphasscan}a).
The scale uncertainty still dominates the uncertainties.

As the input data were changed for the NNLO
analysis and the choice of scales were changed with respect to the NLO analysis,
a detailed comparison of scale uncertainties will be published after
the appropriate reanalysis of the data at NLO.
However, the scale uncertainty of $\pm 0.0027$ is significantly lower
than the $+0.0037,-0.0030$ previously observed for the HERAPDF2.0Jets
NLO analysis.
If the NNLO determination of $\asmz$ was performed with the old
choice of scales, the value of $\asmz$ was reduced to 0.1135.
This is well within scale uncertainties.


The question whether data with relatively low $Q^2$ bias the
determination of $\asmz$ arose within the context of the
HERAPDF2.0 analysis~\cite{HERAPDF20}.
Figure~\ref{fig:alphasscan}b) shows scans with  
$Q^2_{min}$ set to 3.5\,GeV$^2$, 10\,GeV$^2$ and 20\,GeV$^2$
for the inclusive data. Clear minima are visible which coincide within
uncertainties.

%Figure~\ref{fig:alphasscan}c) shows similar scans with  
%$Q^2_{min}$ set to 3.5\,GeV$^2$, 10\,GeV$^2$ and 20\,GeV$^2$
%not only applied to the inclusive data but also to normalised jet data.
%Clear minima are, again, visible. The minima are slightly shifted to low
%$\asmz$ for the two higher $Q^2_{min}$, but the difference is still within
%uncertainties.


\section{The PDFs of HERAPDF2.0Jets NNLO (prel.)}

The PDFs resulting from the HERAPDF2.0Jets NNLO (prel.)  fit with
fixed $\asmz = 0.115$ are shown in Fig.~\ref{fig:as0-115} at a scale of
$Q^2=10$\,GeV$^2$.
The results of a full analysis of uncertainties obtained from
the respective fits are also shown.
This includes experimental, i.e.\ fit, uncertainties,
model and parameterisation uncertainties as 
well as additional hadronisation uncertainties on the jet data,
all as defined for the HERAPDF2.0 family~\cite{HERAPDF20}.
%Scale uncertainties are not considered.

The PDFs resulting from the HERAPDF2.0Jets NNLO (prel.) fit with
fixed $\asmz = 0.118$,
the value used for HERAPDF2.0Jets NLO,
are shown in Fig.~\ref{fig:as0-118} at a scale of
$Q^2=10$\,GeV$^2$. Also shown are the results of a full analysis of
uncertainties.
A comparison between the PDFs obtained for $\asmz = 0.115$ and $\asmz = 0.118$
is provided in Figs.~\ref{fig:as0-115vsas0-118} 
and~\ref{fig:as0-115vsas0-118-mz} for the scale 10\,GeV$^2$ and $M_Z^2$,
respectively.
Here, only total uncertainties
are shown. At the lower scale, 
a significant difference is  observed in the gluon distributions,
where the distribution for $\asmz = 0.115$  is above the distribution for
$\asmz = 0.115$ for $x$ less than $\approx 10^{-2}$.

A comparison between the PDFs obtained by HERAPDF2.0Jets NNLO (prel.) with
$\asmz = 0.118$ and the PDFs of HERAPDF2.0 NNLO based on inclusive data only
is provided in Fig.~\ref{fig:as0-118vsherapdf2}. Again, only total uncertainties
are shown. These two sets of PDFs do not show any significant difference.


\section{Comparison of HERAPDF2.0Jets NNLO (prel.) to jet data}
\label{sec:comp:fit:jets} 
%
Comparisons of the predictions of HERAPDF2.0Jets NNLO (prel.) with
fixed $\asmz = 0.115$
to the data on jet production used as input to the fits 
are shown in Figs.~\ref{fig:h1old-jet-data}, \ref{fig:h1-jet-data-highQ2},
\ref{fig:h1-jet-data-low-Q2} and \ref{fig:zeus-jet-data}.
The H1 collaboration published most of their jet cross sections
normalised to the inclusive NC cross sections.

All analyses were performed using the assumption of massless 
jets, i.e. the transverse energy, $E_T$, and the transverse momentum
of a jet, $p_T$, are equivalent. 
For inclusive jet analyses, each jet is entered separately with its
$p_T$. For dijet %and trijet
analyses, the average 
of the transverse momenta, $\langle p_T \rangle $ is used.
In these cases, $\langle p_T \rangle $ was also used to set the
the factorisation and renormalisation scales to
$\mu_{\rm f}^2 =\mu_{\rm r}^2= Q^2 + \langle p_{T} \rangle^2$
for calculating predictions.
Scale uncertainties were not considered for
the comparisons to data.

The predictions from HERAPDF2.0Jets NNLO (prel.) agree very well
with all data on jet production
used as input to the fit.

\section{Summary}

The HERA data set on inclusive $ep$ scattering  as introduced by the 
ZEUS and H1 collaborations~\cite{HERAPDF20}, 
together with selected data on jet production, published separately by 
the two collaborations, were used as input to NNLO fits
called HERAPDF2.0Jets NNLO (prel.). They complete the HERAPDF2.0 family.
A fit with free $\asmz$ gave
$\asmz = 0.1150 \pm 0.0008{\rm (exp)} ^{+0.0002}_{-0.0005} {\rm (mo-} $
${\rm del/parameterisation)} \pm 0.0006{\rm (hadronisation)}~~ \pm 0.0027 {\rm (scale)}$.
A preliminary set of PDFs with a full analysis of uncertainties was
obtained from a HERAPDF2.0Jets NNLO (prel.) fit with fixed $\asmz = 0.115$.
These PDFs were compared to PDFs from a similar fit with fixed $\asmz = 0.118$
and the PDFs from HERAPDF2.0 NNLO based on inclusive data only. All these PDFs
are very similar.
The predictions from HERAPDF2.0Jets NNLO (prel.) were compared to the
jet production data used as input. The predictions describe the data
very well.

 
\section{Acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

We are grateful to the HERA machine group whose outstanding
efforts have made the ZEUS and H1 experiments possible.
We appreciate the contributions to the construction, 
maintenance and operation of the H1 and ZEUS detectors of 
many people who are not listed as authors.
We thank our funding agencies for financial 
support, the DESY technical staff for continuous assistance and the 
DESY directorate for their support and for the hospitality they 
extended to the non-DESY members of the collaborations. 
We would like to give credit to all partners contributing to the 
EGI computing infrastructure for their support.

\clearpage
\bibliography{H1prelim-19-041}




\clearpage



\begin{table}
\begin{center}
\begin{scriptsize}
\begin{tabular}{|lr|rr|c|c|c|c|c|c|c|}
\hline
Data Set & taken~~~~ &\multicolumn{2}{ c|}{$Q^2 [$GeV$^2$] range}&${\cal L}$ & $e^+/e^-$ & $\sqrt{s}$ & norma-& all & used & Ref.\\
\multicolumn{2}{|r|}{from ~~~~ to~~~}          & from   & to     & pb$^{-1}$ &       & GeV    & lised  & points & points & \\
\hline
 H1 HERA\,I normalised jets & 1999 -- 2000 & $150$  &$15000$ & $65.4$  &$e^+p$   & $319$  & yes & 24 & 24 &\cite{h1highq2oldjets} \\
 H1 HERA\,I jets at low  $Q^2$    & 1999 -- 2000 &   $5$  &  $100$ & $43.5$  &$e^+p$   & $319$  & no  & 28 & 16 &\cite{h1lowq2jets} \\
 H1 normalised inclusive jets at high $Q^2$  & 2003 -- 2007 & $150$  &$15000$ & $351$  &$e^+p$/$e^-p$   & $319$  & yes & 30 & 24 &\cite{h1highq2newjets},
\cite{h1lowq2newjets} \\
 H1 normalised dijets at high $Q^2$  & 2003 -- 2007 & $150$  &$15000$ & $351$  &$e^+p$/$e^-p$   & $319$  & yes & 24 & 24 &\cite{h1highq2newjets}\\
 H1 normalised inclusive jets at low $Q^2$  & 2005 -- 2007 & $5.5$    &   $80$ & $290$  &$e^+p$/$e^-p$   & $319$  & yes & 48 & 32 & \cite{h1lowq2newjets}\\
 H1 normalised dijets at low $Q^2$     & 2005 -- 2007  & $5.5$    &   $80$ & $290$  &$e^+p$/$e^-p$   & $319$  & yes & 48 & 32 &\cite{h1lowq2newjets}\\
\hline
ZEUS inclusive jets  & 1996 -- 1997 & $125$  &$10000$ & $38.6$  &$e^+p$    & $301$ & no  & 30 & 30 &\cite{zeus9697jets}  \\
ZEUS dijets ~~~~~~~~~~~~~~~~~~ 1998 --2000 \& & 2004 -- 2007 & $125$  &$20000$ & $374$&$e^+p$/$e^-p$& $318$ & no  & 22 & 16 &\cite{zeusdijets} \\
\hline
\end{tabular}
\end{scriptsize}
\end{center}
\caption{\label{tab:jet-data}
The data sets on jet production from H1 and ZEUS  
used for the HERAPDF2.0Jets NNLO (prel.) fits.
}
\end{table}


\clearpage

%JETS
%alpha-scans

\begin{figure}
  \centering
  \setlength{\unitlength}{0.1\textwidth}
%  \begin{picture} (9,12)
  \begin{picture} (9,8)
  \put(1.2,5.0){\includegraphics[width=0.65\textwidth]{H1prelim-19-041.fig1a.eps%
}}
  \put(1.2,0.0){\includegraphics[width=0.70\textwidth]{H1prelim-19-041.fig1b.eps}}
  \put (0.6,5.9) {a)}
  \put (0.6,0.9) {b)}
  \end{picture}
\caption {$\Delta \chi^2 = \chi^2 - \chi^2_{\rm min}$ vs.\ $\asmz$ for
HERAPDF2.0Jets NNLO (prel.) fits with fixed $\asmz$ with a) the standard
$Q^2_{min}$ of 3.5\,GeV$^2$ b) with $Q^2_{min}$ set to
3.5\,GeV$^2$, 10\,GeV$^2$ and 20\,GeV$^2$ for the inclusive data.
In a), the result and all uncertainties determined for
the HERAPDF2.0Jets NNLO (prel.) fit
with free $\asmz$ are also shown.
In b), not all scan points for $Q^2_{min}$ of 3.5\,GeV$^2$ are plotted
for better visibility.
}
\label{fig:alphasscan}
\end{figure}

\clearpage

%%%PDFs

\begin{figure}[tbp]
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (11,10)
  \put(0.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig2a.pdf%
}}
  \put(5.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig2b.pdf}}
  \put(0.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig2c.pdf}}
  \put(5.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig2d.pdf}}
  \put (0.6,5.5) {a)}
  \put (5.6,5.5) {b)}
  \put (0.6,0.5) {c)}
  \put (5.6,0.5) {d)}
  \end{picture}
%\vspace{-0.5cm} 
\caption { 
The parton distribution functions 
a) $xu_v$, b) $xd_v$, c) $xg$ and d) $x\Sigma=x(\bar{U}+\bar{D})$ of
HERAPDF2.0Jets NNLO (prel.) with $\asmz$ fixed to 0.115, the
value determined in the NNLO fit with free $\asmz$
at the scale $Q^2 = 10$\,GeV$^{2}$.
The uncertainties are given as differently shaded bands.
}
\label{fig:as0-115}
\end{figure}

\clearpage
%\put for abc
\begin{figure}[tbp]
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (11,10)
  \put(0.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig3a.pdf%
}}
  \put(5.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig3b.pdf}}
  \put(0.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig3c.pdf}}
  \put(5.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig3d.pdf}}
  \put (0.6,5.5) {a)}
  \put (5.6,5.5) {b)}
  \put (0.6,0.5) {c)}
  \put (5.6,0.5) {d)}
  \end{picture}
%%\vspace{-0.5cm} 
\caption { 
The parton distribution functions 
$xu_v$, $xd_v$, $xg$ and $x\Sigma=x(\bar{U}+\bar{D})$ of  
HERAPDF2.0Jets NNLO (prel.) with $\asmz$ fixed to 0.118, the
value determined in the HERAPDFJets NLO fit with free $\asmz$,
at the scale $Q^2 = 10$\,GeV$^{2}$.
The uncertainties are given as differently shaded bands.
}
\label{fig:as0-118}
\end{figure}



\clearpage
\begin{figure}[tbp]
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (11,10)
  \put(0.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig4a.pdf%
}}
  \put(5.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig4b.pdf}}
  \put(0.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig4c.pdf}}
   \put(5.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig4d.pdf}}
  \put (0.6,5.5) {a)}
  \put (5.6,5.5) {b)}
  \put (0.6,0.5) {c)}
  \put (5.6,0.5) {d)}
  \end{picture}
\vspace{-0.5cm} 
\caption { 
Comparison of the parton distribution functions 
a) $xu_v$, b) $xd_v$, c) $xg$ and d) $x\Sigma=x(\bar{U}+\bar{D})$ of 
HERAPDF2.0Jets NNLO (prel.) with fixed $\asmz = 0.115$ and $\asmz = 0.118$
at the scale $Q^{2} = 10\,$GeV$^{2}$.
The total uncertainties are shown as differently hatched bands.
}
\label{fig:as0-115vsas0-118}
\end{figure}


\clearpage
\begin{figure}[tbp]
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (11,10)
  \put(0.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig5a.pdf%
}}
  \put(5.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig5b.pdf}}
  \put(0.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig5c.pdf}}
   \put(5.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig5d.pdf}}
  \put (0.6,5.5) {a)}
  \put (5.6,5.5) {b)}
  \put (0.6,0.5) {c)}
  \put (5.6,0.5) {d)}
  \end{picture}
\vspace{-0.5cm} 
\caption { 
Comparison of the parton distribution functions 
a) $xu_v$, b) $xd_v$, c) $xg$ and d) $x\Sigma=x(\bar{U}+\bar{D})$ of 
HERAPDF2.0Jets NNLO (prel.) with fixed $\asmz = 0.115$ and $\asmz = 0.118$
at the scale $Q^{2} = M_Z^2$.
The total uncertainties are shown as differently hatched bands.
}
\label{fig:as0-115vsas0-118-mz}
\end{figure}

\clearpage


\begin{figure}[tbp]
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (11,10)
  \put(0.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig6a.pdf%
}}
  \put(5.0,5.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig6b.pdf}}
  \put(0.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig6c.pdf}}
   \put(5.0,0.0){\includegraphics[width=0.6\textwidth]{H1prelim-19-041.fig6d.pdf}}
  \put (0.6,5.5) {a)}
  \put (5.6,5.5) {b)}
  \put (0.6,0.5) {c)}
  \put (5.6,0.5) {d)}
  \end{picture}
\vspace{-0.5cm} 
\caption { 
Comparison of the parton distribution functions 
a) $xu_v$, b) $xd_v$, c) $xg$ and d) $x\Sigma=x(\bar{U}+\bar{D})$ of 
HERAPDF2.0Jets NNLO (prel.) 
and HERAPDF2.0 NNLO based
on inclusive data only, both with fixed $\asmz = 0.118$,
at the scale $Q^{2} = 10\,$GeV$^{2}$.
The total uncertainties are shown as differently hatched bands.
}

\label{fig:as0-118vsherapdf2}
\end{figure}

\clearpage

%%%%%%%% DATA
%%%%%%% H1 old jets

\begin{figure}
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (9,12)
  \put(0,0){\includegraphics[width=0.9\textwidth]{H1prelim-19-041.fig7a.eps%
}}
  \put(0,7){\includegraphics[width=0.9\textwidth]{H1prelim-19-041.fig7b.eps}}
  \put (0.1,7.2) {a)}
  \put (0.1,0.2) {b)}
  \end{picture}
%\centerline{
%\epsfig{file=figures/h1lowq2.eps,width=0.9\textwidth}}
%\vspace*{1cm}
%\centerline{
%\epsfig{file=figures/h1norm-h1.eps,width=0.9\textwidth}}
%\vspace{0.5cm}
\caption{
a) Differential jet cross sections, ${\rm d}\sigma/{\rm d}p_T$, normalised to 
   NC inclusive cross sections, in bins of $Q^2$ 
   between 150 and 15000\,GeV$^2$ as measured by H1.
b) Differential jet cross sections, ${\rm d}\sigma/{\rm d}p_T$, 
   in bins of $Q^2$ between 5 and 100\,GeV$^2$ as measured by H1. 
Also shown are predictions from HERAPDF2.0Jets NNLO (prel.). 
The bands represent the total uncertainties on the predictions
excluding scale uncertainties.
Only data used in the fit are shown.
}
\label{fig:h1old-jet-data}
\end{figure}
\clearpage


% H1 normalised jets

\begin{figure}
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (9,11)
  \put(1,5.3){\includegraphics[width=0.8\textwidth]{H1prelim-19-041.fig8a.eps%
}}
  \put(1,0){\includegraphics[width=0.8\textwidth]{H1prelim-19-041.fig8b.eps}}
  \put (0.6,5.8) {a)}
  \put (0.6,0.5) {b)}
  \end{picture}
\caption{
  Differential normalised
  a) inclusive jet cross sections, ${\rm d}\sigma/{\rm d}p_T$, 
  b) differential dijet cross-sections, ${\rm d}\sigma/{\rm d}\langle p_T \rangle_2$, 
     in bins of $Q^2$ between 150 and 15000\,GeV$^2$ as measured by H1.
     The variable $\langle p_T \rangle_2$ 
     denote the average $p_T$ of the two jets. 
     All cross sections are normalised to NC inclusive cross sections and 
     devided by the bin-width.
     Also shown are predictions from HERAPDF2.0Jets NNLO (prel.). 
     The bands represent the total uncertainties on the predictions
     excluding scale uncertainties; they are mostly invisible.
     Only data used in the fit are shown.
}
\label{fig:h1-jet-data-highQ2}
\end{figure}
\clearpage



\begin{figure}
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (9,11)
  \put(1,5){\includegraphics[width=0.8\textwidth]{H1prelim-19-041.fig9a.eps%
}}
  \put(1,0){\includegraphics[width=0.8\textwidth]{H1prelim-19-041.fig9b.eps}}
  \put (0.6,5.5) {a)}
  \put (0.6,0.5) {b)}
  \end{picture}
\caption{
  Differential normalised
  a) inclusive jet cross sections, ${\rm d}\sigma/{\rm d}p_T$, 
  b) differential dijet cross-sections, ${\rm d}\sigma/{\rm d}\langle p_T \rangle_2$, 
     in bins of $Q^2$ between 5 and 80\,GeV$^2$ as measured by H1.
     The variable $\langle p_T \rangle_2$ 
     denote the average $p_T$ of the two jets. 
     All cross sections are normalised to NC inclusive cross sections. 
     Also shown are predictions from HERAPDF2.0Jets NNLO (prel.). 
     The bands represent the total uncertainties on the predictions
     excluding scale uncertainties; they are mostly invisible.
     Only data used in the fit are shown.
}
\label{fig:h1-jet-data-low-Q2}
\end{figure}
\clearpage



%%%%%%%%%%%%%% ZEUS jets
\begin{figure}
  \centering
  \setlength{\unitlength}{0.1\textwidth}
  \begin{picture} (9,11)
  \put(0,6.5){\includegraphics[width=0.9\textwidth]{H1prelim-19-041.fig10a.eps%
}}
  \put(0,0.0){\includegraphics[width=0.9\textwidth]{H1prelim-19-041.fig10b.eps}}
  \put (0.1,6.7) {a)}
  \put (0.1,0.2) {b)}
  \end{picture}
%\centerline{
%\epsfig{file=figures/zeus-incl.eps,width=0.8\textwidth}}
%\vspace*{1.0cm}
%\centerline{
%\epsfig{file=figures/zeus-dijets.eps,width=0.8\textwidth}}
%\vspace{0.5cm}
\caption {
a) Differential jet cross sections, ${\rm d}\sigma/{\rm d}p_T$, 
   in bins of $Q^2$ between 125 and 10000\,GeV$^2$ 
   as measured by ZEUS.
b) Differential dijet cross sections, $d\sigma/{\rm d} \langle p_T \rangle_2$, 
   in bins of $Q^2$ between 125 and 20000\,GeV$^2$ as measured by ZEUS.
   The variable $\langle p_T \rangle_2$ denotes the average 
   $p_T$ of the two jets. 
Also shown are predictions from HERAPDF2.0Jets NNLO (prel.). 
The bands represent the total uncertainty on the predictions
excluding scale uncertainties; they are mostly invisible.
Only data used in the fit are shown.
}
\label{fig:zeus-jet-data}
\end{figure}
\clearpage

%=============== Additional Material==================

{\huge \bf Additional Material:}

{\bf Alpha Scan plotted with experimental/fit uncertainties only:}

\begin{figure} [h]
\center
\includegraphics[width=0.65\textwidth]{H1prelim-19-041.fig11.eps%%
}
\caption {$\Delta \chi^2 = \chi^2 - \chi^2_{\rm min}$ vs.\ $\asmz$ for
HERAPDF2.0Jets NNLO (prel.) fits with fixed $\asmz$ with the standard
$Q^2_{min}$ of 3.5\,GeV$^2$.
The result and the experimental/fit uncertainty determined for
the HERAPDF2.0Jets NNLO (prel.) fit
with free $\asmz$ are also shown.
}
\label{fig:alphasscan-exp}
\end{figure}

\vskip 1cm
{\bf Alpha Scan plotted in old style:}

\begin{figure} [h]
\center
 \includegraphics[width=0.75\textwidth]{H1prelim-19-041.fig12.eps%%
}
\vskip -7cm
 \caption {$\Delta \chi^2 = \chi^2 - \chi^2_{\rm min}$ vs.\ $\asmz$ for
  HERAPDF2.0 NNLO (prel.) fits with fixed $\asmz$ with
   $Q^2_{min}$ set to 3.5\,GeV$^2$, 10\,GeV$^2$ and 20\,GeV$^2$ for 
   the inclusive data.}
\label{fig:alphasscan-oldstyle}
\end{figure}



\clearpage


\end{document}

