\chapter{Conclusions}
	\label{chapter_conclusions}

%   The Standard Model is by no means complete, however, and many researchers are searching for extentions to the Standard Model or alternatives which might subsume it.  Along with theoretical work, this process requires new measurements which illuminate the Standard Model's strengths and shortcomings, as well as measurements which extract its undetermined parameters.  The measurements presented in this analysis give important information about the content of the proton, the knowledge of which is invaluable to studies at the Large Hadron Collider in the near future.


Measurements of polarized and unpolarized integrated and
differential multi-jet cross sections in CC $e^{\pm}p$ DIS
were made using $0.36~\mbox{fb}^{-1}$ of data collected with the ZEUS
detector at HERA, covering the entire HERA II data sample. The measurements were made in
the kinematic region defined by $Q^2>200~\GeV^2$ and $y<0.9$.
Jets were identified in the laboratory frame using the $k_{T}$ cluster
algorithm in the longitudinally invariant inclusive mode. 

Polarized differential and integrated inclusive-jet cross sections were measured over
the phase-space region as functions of $\rapjet$, $\etjet$, $Q^2$ and $x$ for jets with $\etjet>14$
GeV and $-1<\rapjet<2.5$.  The measured cross sections are in good agreement with the SM predictions provided by {\mepjet}~2.1~\cite{ref_mepjet} calculations. The ratios of the differential cross sections for negative and positive longitudinally-polarized lepton beams are also well described by the same predictions.

Unpolarized differential inclusive-jet cross sections were
measured as functions of $\rapjet$, $\etjet$, $Q^2$ and $x$ for jets with $\etjet>14$
GeV and $-1<\rapjet<2.5$. The ratio of the differential cross sections for $e^-p$ and $e^+p$
collisions as a function of $\rapjet$ is $\approx 2$ in the range $-1 < \rapjet < 2.5$, as predicted by the SM predictions provided by {\mepjet}~2.1 calculations. The ratio as a function of
$\etjet$ ($Q^2$) increases as $\etjet$ ($Q^2$) increases, in agreement
with the expected increased contribution from the valence-quark
densities in the proton at high $x$ and the fact that both reactions
are sensitive to different quark flavors. 

NLO QCD predictions for inclusive-jet CC DIS computed using the {\mepjet}~2.1 program were observed to provide a good description of the measured cross sections.  A detailed study of the theoretical uncertainties was performed: they are dominated by the uncertainty contributed by the ZEUS-S~\cite{epj:c42:1} PDF set. The predictions from the MRST2001~\cite{pr:d50:6734} and CTEQ5D~\cite{epj:c12:375, Pumplin:2002vw, Stump:JHEP0310} PDF sets were also compared to the measured inclusive-jet cross sections, and show differences between predictions on the order of the uncertainties from the ZEUS-S set.  The uncertainties due to the PDFs are larger for $e^+p$ than for $e^-p$ collisions, due to the larger relative uncertainty of the $d$ PDF~\cite{epj:c42:1}.  Therefore, these measurements, if used together with other data in global PDF fits such as CTEQ or MSTW, have the potential to constrain the flavor content of the proton at $x\gtrsim 10^{-2}$.

 Unpolarized Dijet differential cross sections were measured for jets with $\etjeta>14$ GeV, $\etjetb>5$ GeV and  $-1<\rapjet<2.5$.  These cross sections were measured as functions of $Q^2$, dijet invariant mass, mean $\etjet$, and mean $\rapjet$ of the two jets.  The comparison of NLO QCD predictions computed using the {\mepjet}~2.1 program with the measured dijet differential cross sections shows a poor agreement in both shape and normalization.   Because these dijet distributions contain significant contributions from boson-gluon fusion, they are sensitive to the gluon content of the proton.

Three-jet differential cross sections were measured for the first time in CC DIS.  The cross sections were measured for jets with $\etjeta>14$ GeV, $\etjetb>5$ GeV, $\etjetc>5$ GeV and $-1<\rapjet<2.5$. The LO QCD predictions provide a good description of the shape of the data, but do not describe the normalization.  The dominant source of theoretical uncertainty was due to higher order terms not present in the calculations.  

The three-jet sample also contains eleven candidates with a fourth jet of $\etjet>5$ GeV in the range $-1<\rapjet<2.5$.  This represents the first observation of 4-jet events in CC DIS.  This number cannot be accurately predicted with present calculations, but the naive comparison of the ratio of the number of 4-jet events to the number of trijet events is similar to the same ratio for trijets and dijets.

The largest source of uncertainty in the measured cross sections are statistical.  The natural suggestion to improve the present study would then be increased statistics, but because no other $ep$ collider is currently approved for funding, this increase must come from alteration of event selection over the existing data.  The trigger selection for the present sample was observed to be $\sim 95\%$ efficient, and the final sample was observed to contain negligible contamination by other processes.  The event selection after triggering, however, showed significant reduction in efficiency to $~60\%$ for inclusive-jets, so improvements to the selection could prove beneficial.  The present value of $\ptmiss$ cut is already optimized because of trigger conditions.  The minimum $\etjet$ cut for inclusive jets or the highest $\etjet$-jet are predetermined by the $\ptmiss$ cut due to kinematic correlation between $\ptmiss$ and the $E_T$ of the highest $\etjet$-jet.  The choice of the phase space cut $y<0.9$ is needed to ensure proper reconstruction of $Q^2$, and very few events are present above this cut.  Increasing statistics of the sample would therefore imply the improvement of cleaning cuts, which is challenging due to the large variety of $ep$ and non-$ep$ background sources.  Because the cleaning cuts chosen have already been optimized, any alternative method would risk introducing additional systematic uncertainty.

The measurements contained in this work represent the largest sample of Multi-jets in CC DIS, from the world's first and only $ep$ collider. These results are at present the only published sample of jets in CC DIS with longitudinally-polarized leptons.   While the theoretical predictions match the data within uncertainties for inclusive-jet production, the uncertainty due to the choice of PDFs dominates, and the data shows the capacity to differentiate between competing PDF sets, specifically the $d$ PDF.  It is therefore extremely important that the results presented here be included to PDF extractions to global data.
