\chapter{Experimental Setup}
	\label{chapter_experimental_section}
\section{The DESY Laboratory}
	The analysis presented in this thesis was performed with data from the ZEUS detector, which was situated on the Hadron-Elektron Ring Anlage (HERA), at The Deutsches Elekronen-Synchrotron (DESY) Laboratory in Hamburg Germany.  DESY is part of the Helmholtz Association, and has two locations in Germany: one in Hamburg, and one in Zeuthen.  DESY's facilities are used primarily for the study of natural sciences, specifically pertaining to the use of particle accelerators of varying size to probe the structure of matter.  DESY hosted on average approximately 3000 scientists from 33 different countries for research related to HERA and HASYLAB, the associated synchrotron complex.
\section{The HERA Accelerator}
	HERA was the world's first and only lepton-nucleon beam collider, and was the largest accelerator at the DESY complex.  A nearly circular construction with a circumference of 6.3km, HERA was approved for construction in 1984, and built between 1984 and 1991. The commissioning of the electron ring and proton ring occurred in 1989 an 1991, respectively.  HERA provided luminosity to its experiments from mid 1992 until 2 July, 2007, when it was decommissioned.  Figure~\ref{fig_HERA_schematic} is a schematic representation of HERA and the pre-accelerator elements.  Particles were produced at low energies, and sequentially passed between different pre-accelerators before reaching HERA, as described below.
\begin{figure}
  \begin{center}
	\includegraphics[draft=false, width=1.\textwidth]{/home/hwolfe/thesis/figures/experimental/hera_schematic_rotate}
  \end{center}
	\caption[Schematic Diagram of the DESY Accelerator Complex]{
		\fixspacing{Schematic of the DESY Accelerator Complex % Source~\cite{slac_ep_inelastic}
		}
	}
	\label{fig_HERA_schematic}
\end{figure}
\subsection{Proton Injection and Acceleration}
	To produce protons for collisions, hydrogen gas was ionized and accelerated in the LINAC III linear accelerator to 50~MeV.  The ions were passed through a thin metal foil to strip the remaining electron, and passed to the DESY III synchrotron for further acceleration to 7.5~GeV.   DESY III is a 317~m circumference storage ring which could hold up to 11 proton bunches with approximately $10^{11}$ protons per bunch.  From DESY III, protons were injected into PETRA II, which accelerated bunches up to 40~GeV.  Protons were then injected into HERA for acceleration up to and maintained at their final energy.  HERA operated at several different proton energies during its lifetime, but all data presented in this thesis arise from collisions with 920~GeV protons.  
\subsection{Lepton Injection and Acceleration}
	During periods of electron-proton collisions, electrons were produced by a hot metal filament.  During periods of positron-proton collisions, positrons were produced by scattering electrons on tungsten sheets, resulting in the production of $e^+e^-$ pairs by Bremsstrahlung.  HERA provided both electron-proton and positron-proton collisions during separate periods.  Throughout the rest of this chapter, the term {\it electron} will denote separately to either electrons or positrons, unless otherwise stated.  After production, electrons were accelerated up to an energy of 450~MeV in the LINAC II accelerator, which is a 70~m linear accelerator.   They were then gathered in PIA, a 29~m accumulator.  Bunches of approximately $3.5\times 10^{10}$ electrons were then injected into DESY II, a 293~m circumference synchrotron, which accelerated them to an energy of 8~GeV.  From DESY II, electrons were injected into PETRA II, a 2.3~km circumference synchrotron, which accelerated  bunches to 12~GeV.  Electrons were then injected into HERA, and were accelerated to and maintained at an energy of 27.5~GeV.
\subsection{Beam Circulation and Collisions}
	Within HERA, electron and proton beams were stored in separate beam pipes, each with a vacuum pressure of approximately $3\times10^{-11}$~Torr.  The bunches circulated in opposite directions, with a separation of approximately 28.8 m, which in time is 96~ns, and a frequency of 10.4 MHz.  HERA could theoretically have held 210 electron and 210 proton bunches, but in practice about 10 bunches of each type were left unfilled to so that a filled bunch of the opposing type could circulate without collisions.  This allowed the HERA Machine group to study beam dynamics separately from interactions.  Additionally, approximately 15 successive bunches of each type were left unfilled to allow time for deflection magnets to energize for beam dumps. 

	At two places on the ring, labled north and south halls in Figure~\ref{fig_HERA_schematic}, the two beam pipes merged into one and the beams were brought together with nearly zero crossing angle.  Two experiment halls were located at the intersection points, providing space for the general purpose detectors H1 and ZEUS.  Two other experiments, HERMES and HERA-B detectors were located at experiment halls labeled east and west, respectively.  HERA-B studied collisions between the proton beam and wire targets to study $B$ hadron production, while HERMES studied collisions between the electron beam and a proton gas jet to study the spin structure of the proton.  

	Between 1992 and 1997, HERA collided 27.52~GeV leptons with 820~GeV protons, providing $ep$ collisions with a CME of $s\approx \sqrt{4E_pE_e}\approx 300$~GeV.  The energy of the protons from 1997 to 2007 920~GeV, $ep$ collisions with a CME of approximately 320~GeV.  During the last periods of operation in 2007, The proton energy was lowered to 450 and 575~GeV, in order to investigate a previously unexplored region of phase space.
\subsection{HERA Luminosity}
	HERA began operation providing electron-proton collisions, and has alternately provided positron-proton collisions.
	%as outlined in Table~\ref{table_lumi}.    
	The {\it Instantaneous luminosity}, $L$ can be described as the incoming flux of particles participating in a reaction.  At a two-particle intersecting storage ring collider like HERA, this can be estimated as $L=f\left(N_1N_2/A\right)$, where $f$ is the frequency of bunch crossings, $N_i$ is the number of particles in each bunch in beam $i$, and $A$ is the area of overlap of the two beams.  Thus, the instantaneous luminosity of HERA based on its design characteristics would be \
	\begin{equation}
		L_{HERA} = f\frac{N_1N_2}{A} \approx 10.4\times 10^6\frac{10^{20}}{3.36\times10^{-5}cm^2 } = 3.1\times10^{31} cm^{-2}s^{-1}
	\end{equation}
	The average specific luminosity during the period 1992 to 2000 was approximately $2\times 10^{31}$~cm$^{-2}$~s$^{-1}$. Between 2000 and 2002, HERA underwent a luminosity upgrade, which was primarily achieved by installing improved focusing magnets which diminished the interaction area of the two beams.  The periods before and after the upgrades are referred to as {\it HERA~I} and {\it HERA~II}, respectively.  The resulting specific luminosity for HERA II was approximately $3.8\times 10^{31}$~cm$^{-2}$~s$^{-1}$.  Direct detection of the instantaneous luminosity during HERA operation is described in section~\ref{subsection_luminosity_mon_and_pol}.

\subsection{Polarized Collisions}
	The electron beam at HERA became naturally polarized transversely polarized due to the Sokolov-Ternov effect\cite{ref_sokolov_ternov}.  The characteristic build-up time expected for the HERA accelerator was approximately 40 minutes.  During the 200-2002 luminosity upgrade, spin rotators on either side of the H1 and ZEUS detectors were installed to change the electron polarization from transverse to longitudinal and back, providing collisions with longitudinally polarized electrons.  Measurement of the electron polarization is described in section~\ref{subsection_luminosity_mon_and_pol}.
%\section{Detection of Particles}
%\subsection{Particle Tracking }
%\subsection{Electromagnetic Showers }
%\subsection{Hadronic Showers}
%\subsection{A Generic Particle Detector}

\section{The ZEUS Detector}
% \begin{figure}
%   \begin{center}
% 	\includegraphics[draft=false, width=1.\textwidth]{/home/hwolfe/thesis/figures/chapter3/zeus3D}
%   \end{center}
% 	\caption[A Diagram of The ZEUS Detector]{\fixspacing{A Diagram of The ZEUS Detector}}
% 	\label{diagram_zeus_detector}
% \end{figure}

	The ZEUS detector was a general purpose detector designed for studying various aspects of electron-proton scattering, and was located at the HERA south experiment hall.  It was constructed from several independent subdetectors, which were built by universities from more than 11 countries.  
	
	The ZEUS collaboration used a right-handed Cartesian coordinate system to describe the design and operation of the ZEUS detector.  The origin is located at the nominal interaction point, the positive $z$-axis pointed in the direction of the proton beam, the positive $y$-axis pointed upwards, and the $x$-axis pointed toward the center of HERA.  The polar angle, $\theta$,  is defined by $0^{\circ}$ in the direction of the proton beam, and $90^{\circ}$ in the direction of the positive $y$-axis.  The azimuthal angle, $\phi$ is defined as being $0^{\circ}$ in the direction of the positive $x$-axis, and $90^{\circ}$ in the direction of the positive $y$-axis.  The direction of positive and negative $z$ will sometimes be referred to as {\it forward} and {\it backward}, respectively.  Objects in these halves of the coordinate system will be described as being in the {\it front} and {\it back} of the detector, respectively.  Because the central part of the ZEUS detector is cylindrically shaped, objects this region will be referred to as in the {\it barrel}.

	The ZEUS detector was built around the HERA beampipe at the nominal interaction point, and was roughly symmetric in $\phi$.  The most central components were, in order from the beam pipe to the outside, the micro-vertex detector, tracking system, toroid magnet, and calorimeter.  These components were directly used in this analysis and will be described in more detail in the sections which follow.  Around the calorimeter are the iron yoke/backing calorimeters, muon chambers, and the concrete encasement.  In the negative $z$ direction, in the direction which protons enter the detector, the "veto wall" detector was located to cancel the recording of data caused by particles associated with the proton beam, but not caused by $ep$ interactions.   

\subsection{ZEUS Tracking Detectors}
\begin{figure}
  \begin{center}
	\includegraphics[draft=false, width=.5\textwidth]{/home/hwolfe/thesis/figures/chapter3/ctd_xy}
  \end{center}
	\caption[A Diagram of The ZEUS CTD]{\fixspacing{A Diagram of The ZEUS CTD, as viewed in the direction of the electron beam.}}
	\label{diagram_zeus_ctd}
\end{figure}
	During the period of data taking relevant to this thesis, the tracking system of the ZEUS detector consisted of a silicon vertex detector, Three drift chamber detectors, and a straw-tube tracker.  The drift chamber tracking detectors covered  three regions: the forward (FTD), barrel, or central (CTD), and rear (RTD).   The CTD is of greatest importance to this thesis, and the FTD and RTD will not be discussed here.

	The silicon-strip micro vertex detector (MVD), was installed in 2001 during the HERA upgrade shutdown.  The MVD was designed to improve the overall precision of the tracking system and allow the identification of events containing secondary vertices from decays of long-lived particles\cite{ref_mvd}.      The MVD was split into two sections: barrel (BMVD) and forward (FMVD).  
	
	The BMVD was 64 cm long and covers a polar angle between $30^\circ$ and $150^\circ$.  It consisted of three layers of silicon sensors arranged in concentric planes around the interaction point. The inner layer was placed at a radius between 3 and 5 cm from the CTD axis.  Because of space restrictions cause by the elliptical beam pipe not being centered on the interaction point, the inner layer did not completely surround the beam pipe in $\phi$. The second and third layers were placed at r=8.6 cm  and r=12.3 cm, respectively, and each completely surrounded the beam pipe in $\phi$.     The BMVD was equipped with 600 single-sided strip silicon sensors of approximately  $64 \times 64$ mm$^2$ and 320 $\mu m$-thick with p+ strips implanted into n-type bulk.    Each sensor was covered with 3082 strips with a pitch of  20 $\mu m$. Two sensors were glued together next to each other with perpendicular strips on the same side. When placed in the barrel MVD, the sensors parallel to the beam pipe give the $r-\phi$ coordinate of a hit while the perpendicular ones gave the $z$ information.  

	The FMVD consisted of four planes referred to as wheels, which were perpendicular to the beam axis. The four wheels were positioned at z=32, 45, 47 and 75 cm. Each wheel consisted of two back to back layers of 14 silicon sensors of the same type as in the barrel section but with a trapezoidal shape. There were 480 readout strips per sensor.  The FMVD extended the polar coverage of the MVD down to $7^\circ$.


	The CTD was a cylindrical drift chamber which is filled with a mixture of argon, $CO_2$ and ethane.  It had an active volume with length $205$~cm, inner radius of $18.2$~cm and an outer radius of $79.4$~cm,  covering a polar angle range from $15^{\circ}$ to $164^{\circ}$.  It was divided into eight sections called {\it octants}, which occupied $45^{\circ}$ of azimuthal angle each, spanning the entire length of the CTD, this is depicted in figure~\ref{diagram_zeus_ctd}.  Each octant was divided into nine radial {\it super layers}, numbered one to nine, numbered from central to exterior.  Each odd-numbered superlayer contained wires which were parallel to the beam axis.  Each even-numbered superlayer contained wires which were tilted relative to the beam axis by an angle of $4.98^{\circ}$, $-5.53^{\circ}$,  $-5.51^{\circ}$, and $5.62^{\circ}$ for layers 2,4,6,8, respectively.  These angles are referred to as a {\it stereo angle}, because the path of particles which caused a signal in two adjacent superlayers could be identified within $2$~mm in the $z$ direction.

	The CTD operated in a $1.43 T$ magnetic field, which caused charged particles to arc as they passed. The momentum and charge of the particles could then be determined by this curvature.  As particles passed though the CTD, they imparted energy to the gas, and their energy loss as a function of distance, $\frac{dE}{dx}$, was also used in particle identification.   %The resolution of the measured momentum for particles in the CTD was
% 	\begin{equation}
% 		Somethin, Somethin.
% 	\end{equation}
\subsection{The ZEUS Calorimeter}
	\label{subsection_ZEUS_CAL}
	Similar to the Tracking system, the ZEUS uranium calorimeter (CAL) was constructed in three separate parts: forward (FCAL), barrel (BCAL), and rear (RCAL).  This is depicted schematically in Figure~\ref{figure_ZEUS_CAL}. These covered polar angles of $2.2^\circ-39.9^\circ$, $36.7^\circ-128.1^\circ$, and $128.1^\circ-176.5^\circ$ respectively.  Each of these three main main regions were constructed from independent sections called {\it modules}, which were further divided into sections called {\it CAL towers}, which were then divided into {\it cells}.   Each tower in the CAL was subdivided into electromagnetic {\it EMC} or hadronic {\it HAC} sections.  In the FCAL and BCAL Each EMC section contained four longitudinal separations into EMC cells, while each HAC section was transversely separated into two HAC cells.  In the RCAL each tower contains only two EMC cells and one HAC.  In terms of readout, cells are the most fundamental unit of the CAL. 
\begin{figure}
	\label{figure_ZEUS_CAL}
	\begin{center}
		%\epsfig{file=figures/introduction/pdg_ratio_n_colors.ps,width=.8\textwidth}
		\includegraphics[draft=false, width=.7\textwidth]{/home/hwolfe/thesis/figures/experimental/ZEUS_CAL}
		%http://pdg.lbl.gov/2007/reviews/hadronicrpp.pdf
	\end{center}
		\caption[Schematic of the ZEUS Calorimeter]{
			\fixspacing{  
				A $z$-$y$ schematic diagram of the ZEUS Calorimeter.  
			}
		}
\end{figure}
	Each cell was roughly shaped like a rectangular prism, and was constructed of alternating layers of $3.3$~mm thick absorber plates and $2.6$~mm thick plastic scintillator.  Each absorber plate was constructed by encasing the depleted uranium $^{238}U$ in a steel jacket.  Incident particles on the absorber showered, producing many more particles, which stimulated the scintillator tiles, producing light.  Light from the scintillators was passed from two opposite sides of each cell along two separate wavelength shifters.  Each wavelength shifter was attached to one photo-multiplier tube (PMT), located on the exterior of the CAL.  The two PMTs for each cell were labled as {\it left} and {\it right}.  
	%The scintillator material was designed to produce a spectrum centered on $???$~nm.  As light travelled down a wavelength shifter from a cell to one of its two PMTs, the peak wavelength of the spectrum became slightly longer, proportional to the distance it travelled. Based on the resultant peak of the wavelength spectrum, a rough $r$ position of the energy deposit, with an uncertainty smaller than the size of the cell could be made.   Wrong says Wesley.  Luiville?
	Using timing information between left and right channels for each cell, improvement in three dimensional positioning could be made.  The agreement between pairs of PMTs also allowed a systematic check of response, and redundancy in case of noise.

	 $^{238}U$ was chosen as absorber material for its density, stability, radiation-hardness and its own natural low level radiation.  This low radiation provided a stable and well understood signal for calibration of the readout.  Hadrons incident on  $^{238}U$ create a high number of spallation neutrons, which can then excite the hydrogen nuclei of a scintillator.  Electrons do not radiate the same manner because they mostly interact with atomic electrons, rather than nuclei.  These EM interactions typically produce photons and $e^+e^-$ pairs.  The CAL was designed with a careful balance between the quantity of uranium and steel in each absorber plate which allowed the CAL to reach a nearly equal response from hadronic and leptonic energy.  Test beam studies showed the response to be equal within $3\%$.  This is important for jet physics, because it removes the need for assumptions about the leptonic and hadronic content of jets.  The single particle energy resolution for electrons  and hadrons was determined in test-beams to be $\frac{\sigma_E^e}{E} = 18\%/\sqrt{E}$ and $\frac{\sigma_E^h}{E/\GeV} = 35\%/\sqrt{E/\GeV}$, respectively~\cite{ref_cal}.  This can be contrasted with the equivalent H1 energy resolutions of $\frac{\sigma_E^e}{E} = 12\%/\sqrt{E}$, $\frac{\sigma_E^h}{E} = 50\%/\sqrt{E}$~\cite{nim:a386:310,nim:a386:397}.  
\subsection{Luminosity Monitor and Polarimeters}
	\label{subsection_luminosity_mon_and_pol}
	   The {\it luminosity} of a data sample, $L = N/\sigma$, is defined as the number of particles produced from a process, divided by the cross section for that process.  Thus in order to determine a cross section from experimental data, one must know the luminosity used to generate that measurement.  At HERA, the luminosity of $ep$ collisions was determined by measuring the rate of Bremsstrahlung photons from the Bethe-Heitler process $ep\rightarrow ep\gamma$.  The theoretical cross section for this process is known to an accuracy of $.5\%$, so a precise measurement of this process allowed a precise measurement of the luminosity.  
\begin{figure}
	\label{figure_ZEUS_lumi_system}
	\begin{center}
		%\epsfig{file=figures/introduction/pdg_ratio_n_colors.ps,width=.8\textwidth}
		\includegraphics[draft=false, width=1.\textwidth]{/home/hwolfe/thesis/figures/experimental/ZEUS_lumi_system}
		%http://pdg.lbl.gov/2007/reviews/hadronicrpp.pdf
	\end{center}
		\caption[Schematic of the ZEUS Luminosity System]{
			\fixspacing{  
				Schematic of the ZEUS Luminosity System.  
			}
		}
\end{figure}


	The Bethe-Heitler measurement was performed at $-107$~m in the ZEUS coordinate system by a lead-scintillator calorimeter, depicted in Figure~\ref{figure_ZEUS_lumi_system}.  The lumi-$\gamma$ system, gathered photons with a polar angle $\theta_\gamma < 0.5$~mrad with an test-beam energy resolution of $18\%/\sqrt{E}$~\cite{ref_lumi}.  It was determined that the protective carbon/lead synchrotron radiation filter caused a slight degradation of performance to $18\%/\sqrt{E}$.  The lumi-$\gamma$ detector had 1cm scintillator strips located $.7\chi_0$ inside, granting the ability to resolve the impact position of photons to .2cm in $x$ and $y$.  This system was also used to measure the electron beam-tilt and measure photons from initial-state radiation (ISR).  In addition to the lumi-$\gamma$ calorimeter, a second lead-scintillator calorimeter called lumi-$e$ was located at $-27m$, which captured electrons which were deflected from the beam by the HERA bending magnets.  This was originally designed to compliment the lumi-$\gamma$ system, but was found to be unnecessary for luminosity measurement.  The total uncertainty in the luminosity measurement was determined for this analysis to be $~2.5\%$.  

	The electron beam polarization was measured using two independent polarimeters, referred to as the longitudinal polarimeter (LPOL)~\cite{nim:a479:334,tech:pol2000prc} and transverse polarimeter (TPOL)~\cite{nim:a329:79,tech:pol2000prc}.  Both devices exploited the spin-dependent cross section for Compton scattering of circularly polarized photons off of electrons.  The polarimeters were able to measure the polarization in times much shorter than the polarization build-up time. The two independent devices were found to agree with each other within 2\%~\cite{Gharibyan:2003yv}
\subsection{Veto Wall and C5 Counter}
	The veto wall is was a large wall of iron positioned -7m, designed to shield the ZEUS detector from particles produced in the proton beam halo.  It measured $8\times 7.6\times 0.86$~m, with a square hole of dimension $0.95$~m at the center to accommodate the beam pipe and magnets.  Scintillators on either side of the wall provided information about the rate of incident particles, allowing veto information for events contaminated by these particles.  The C5 counter was a scintillator attached to the C5 collimator at $z = -3.15$~m which provided timing information used to synchronize the HERA and ZEUS clocks.  The C5 counter also provided veto information for beam halo interactions.
\subsection{Trigger and Data Acquisition}
\label{section_zeus_trigger}
	Assuming that ZEUS recorded one event from every crossing, it would have produced data at a rate of approximately $1$~MB $\times$ 10MHz$=10$TB$/$s.  Because the data transmission from the detector to the event reconstruction computing farm (described in the next section) was less than 1MB/s, the rate of data was forced to be reduced by a factor of $10^6$.   A faster transmission rate would not have been beneficial, because not every crossing produced an $ep$ interaction, and some that did produced products deemed uninteresting, or which were contaminated by signal from non-$ep$ sources.  Deciding which events were worth full reconstruction and storage was accomplished by the a 3-level trigger system, depicted in Figure~\ref{figure_ZEUS_trigger}. 
\begin{figure}
	\label{figure_ZEUS_trigger}
	\begin{center}
		%\epsfig{file=figures/introduction/pdg_ratio_n_colors.ps,width=.8\textwidth}
		\includegraphics[draft=false, width=1.\textwidth]{/home/hwolfe/thesis/figures/experimental/ZEUS_trigger}
		%http://pdg.lbl.gov/2007/reviews/hadronicrpp.pdf
	\end{center}
		\caption[Schematic of the ZEUS Trigger System]{
			\fixspacing{  
				Schematic of the ZEUS System System.  
			}
		}
\end{figure}
	The ZEUS First Level Trigger (FLT) was a digital hardware trigger, designed to reduce the event rate to $~1kHz$.  In order to hold the data while electronics make a decision, raw data was stored on the detector in an analog pipeline for $5\mu s$.  This allows a decision to move data off the detector to be made roughly every 50 bunch crossings.  The time during the first 25 of these 50 crossings is allocated to individual component FLTs.  The rest of the cycles are given to the Global First Level Trigger (GFLT), which collected decisions from the subdetector-specific FLTs, and issued global accept or abort requests.  This was performed with almost zero deadtime.  If a particular event was accepted by the FLT, it was then digitized and transferred to the Second Level Trigger (SLT).  Due to finite transfer of data between the components deadtime occurs here at $~1-2\%$
	\label{section_SLT}
	The SLT used more complete information than the first level trigger.   It was designed to reduce the event rate to less than $100Hz.$  Similarly to the FLT, each subdetector has its own SLT which passes information to the Global Second Level Trigger (GSLT).  If the event is accepted by the SLT, all components send all information to the event builder (EVB), which then combines all data into a single event record to ADAMO database tables.  

	Data was then passed to the Third Level Trigger (TLT), which was a purely software based trigger.  The TLT partially reconstructed kinematic variables, and reduced the eventrate to ~1Hz.   If the event was accepted by the TLT, then it was passed to the ZEUS Physics Reconstruction Program (ZEPHYR), which uses calibration constant tables for each component to interpret detector signals as energies, times, and positions, and the event was written to data tape for storage and analysis.
