# kocolosk/thesis

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
408 lines (367 sloc) 23.4 KB
 \chapter{Experimental Facilities} \section{The Relativistic Heavy Ion Collider (RHIC)} \begin{figure} \begin{center} \includegraphics[width=0.8\textwidth]{figures/rhic-from-above} \end{center} \caption{The RHIC accelerator complex. Polarized protons are generated in OPPIS (not shown) and pass through the Linac, Booster, and AGS on their way to RHIC.} \label{fig:rhic} \end{figure} The Relativistic Heavy Ion Collider (RHIC) is an intersecting storage ring located at Brookhaven National Laboratory in Upton, New York. Unusually versatile for a collider, RHIC uses two independent superconducting rings to collide beams of ions with mass numbers separately ranging from one to 197. Recent beam configurations include protons on protons, deuterons on gold, copper on copper, and gold on gold. Figure \ref{fig:rhic} shows a schematic view of the RHIC accelerator complex. The main RHIC ring has a 3.8 kilometer circumference and is comprised of six straight sections and six curved sections. Collisions between the beams occur in the middle of each straight section; four experimental halls are situated at the two (BRAHMS), six (STAR), eight (PHENIX), and ten o'clock (PHOBOS) positions. RHIC relies on a complex of smaller accelerators to prepare ion beams for injection into the main ring. This work focuses on the systems used to polarize and accelerate beams of protons, thus avoiding further discussion of the Tandem Van de Graff generator used exclusively in heavy ion operations. Polarized protons are produced using OPPIS \cite{Zelenski:2002gb, Zelenski:2008zza}, an optically-pumped polarized ion source which typically generates 0.5 mA, 400 $\mu$s pulses of ions, corresponding to $\mathrm{9x10^{11}}$ ions per pulse. The pulsed nature of the beam is crucial to achieving the RHIC design luminosity of $\mathrm{2x10^{32}~cm^{-2}~s^{-1}}$. OPPIS polarizes protons by passing them through a rubidium vapor pumped with circularly polarized laser light in a strong magnetic field. The $\mathrm{H^+}$ ions pick up a polarized rubidium electron through collisions in the vapor, and magnetic fields cause the electron polarization to be transferred to the nucleus. Finally, the hydrogen atoms are ionized to $\mathrm{H^-}$ when they pass through a sodium vapor. The pulses of 35 keV $\mathrm{H^-}$ ions produced by OPPIS are accelerated by the LINAC, Booster, and AGS on their way to RHIC. The LINAC strips off the electrons and accelerates the protons to a kinetic energy of 200 MeV with an efficiency of approximately 50\%. It injects the remaining $\sim \mathrm{4x10^{11}}$ ions into the Booster ring in a single bunch. The Booster accelerates the protons to 1.5 GeV and passes them on to the Alternating Gradient Synchrotron (AGS), which accelerates them to the RHIC injection energy of 25 GeV. RHIC propels the $\sim \mathrm{2x10^{11}}$ protons remaining in each bunch to the desired collision energy, which can range from 30 GeV to 250 GeV. This work analyzes data collected with a beam energy of 100 GeV. More details of the RHIC accelerator complex are available in \cite{Harrison:2003sb}. \subsection{Spin Dynamics and Siberian Snakes} The evolution of the spin direction of a beam of polarized protons in external magnetic fields is governed by the Thomas-BMT equation \cite{Thomas:1927yu, Bargmann:1959gz}, % \begin{equation} \frac{d\vec{P}}{dt} = -\left(\frac{e}{\gamma m}\right)[(G\gamma + 1) \vec{B}_{\perp} + (G + 1) \vec{B}_{\parallel}] \times \vec{P}. \end{equation} % Comparing this equation with the Lorentz force equation governing the orbital motion, % \begin{equation} \frac{d\vec{v}}{dt} = -\left(\frac{e}{\gamma m}\right)[\vec{B}_{\perp}] \times \vec{v}, \end{equation} % one realizes that, in a pure vertical magnetic field, the spin rotates G$\gamma$ + 1 times faster than the orbital motion. This factor, referred to as the spin tune $\nu_{sp}$, gives the number of full spin precessions for every orbit. An accelerating beam in a storage ring encounters depolarizing resonances whenever the spin tune is equal to an integer multiple of the frequency with which a spin-depolarizing magnetic field is encountered. In the simplest case, a depolarizing field can be introduced by a magnet error or misalignment. For these \textit{imperfection resonances}, the resonance condition is just $G\gamma = n$. If $G\gamma$ is non-integral, the beam sees the depolarizing field at a different point in its precession on each revolution, and the effects tend to cancel out. The focusing fields themselves can also be a source of depolarization; for these \textit{intrinsic resonances} the resonance condition is $G\gamma = kP \pm \nu_y$, where $k$ is an integer, $\nu_y$ is the vertical betatron tune, and $P$ is the superperiodicity. The stable spin direction in an accelerating beam normally coincides with the vertical magnetic field (longitudinal polarization at the interaction points being achieved through the use of spin rotator magnets), but near a resonance it is perturbed away from the vertical by the resonance driving fields. The polarization loss when a beam is accelerated through one of these resonances can be calculated analytically \cite{Froissart:1960zz}: % \begin{equation} \frac{P_f}{P_i} = 2 e^{-\pi |\epsilon|^2 / 2\alpha} -1. \end{equation} % Here $\epsilon$ is the resonance strength and $\alpha$ is the change of the spin tune per radian of the orbit angle. When the beam is slowly accelerated ($\alpha \ll |\epsilon|^2$) the stable spin direction changes adiabatically and the result is a spin flip. In contrast, techniques such as a betatron tune jump effectively result in $|\epsilon|^2 \ll \alpha$ and thus preserve the polarization through the resonance. At high energies, the number and strength of the resonances encountered make these traditional techniques impractical. Instead, the RHIC rings employ Siberian Snake'' magnets \cite{Derbenev:1978hv} which generate a $$180^\circ$$ spin rotation about a horizontal axis when the beam passes through them. In effect, the Siberian Snakes ensure that the spin tune is an energy-independent half-integer, thus avoiding all imperfection resonances as well as intrinsic resonances with an appropriate choice of the betatron tune. RHIC is designed to achieve 70\% polarization; the datasets analyzed in this work were taken with 45\% - 55\% polarized beams, as certain elements of the accelerator complex (notably, a Siberian Snake in the AGS) were still being commissioned. \subsection{Polarimetry Systems\label{sec:polarimeters}} RHIC polarimetry relies on the observation of small angle elastic scattering in the Coulomb-Nuclear Interference (CNI) region. Two complementary varieties of target are used: a thin carbon ribbon \cite{Jinnouchi:2004up} and a hydrogen gas jet (H-Jet) \cite{Zelenski:2005mz, Okada:2006dd}. The carbon ribbon boasts a large scattering cross section which allows a statistically precise measurement of the beam polarization in a few seconds, but the theoretical prediction for the analyzing power of this measurement includes an unknown contribution from a hadronic spin flip amplitude. In contrast, the hydrogen gas jet has a well-understood analyzing power but a much smaller scattering cross section. The natural solution, then, is to calibrate the results of the p+C CNI polarimeters with a measurement from the H-jet polarimeter. The p+C polarization measurements are performed using individual carbon ribbon targets in each beam that are a mere 150 $\mathrm{\mathring{A}}$ thick. Scatterings occur at a momentum transfer of 0.002 - 0.010 $\mathrm{GeV}^2$, resulting in a small forward scattering angle for the proton and a recoil carbon nucleus with less than 1 MeV of kinetic energy. Detection of the scattered proton is not possible without drastic changes to the beam profile at the polarimeter location, but the thinness of the target allows the recoil nucleus to escape the target and reach one of a set of silicon strip detectors arranged around it. The use of a thin target also allows the measurement to be performed multiple times over the course of a beam store with acceptable losses in luminosity. The theoretical uncertainty in the analyzing power of the p+C measurements is estimated to be less than 10\% \cite{Alekseev:2003sk}, but this uncertainty can be mitigated by calibrating the results from the p+C polarimeter against measurements performed using the hydrogen gas jet target. The use of identical beam and target particles allows the polarization of the beam to be directly expressed in terms of the target polarization, % \begin{equation} P_{beam} = -P_{target}\frac{\epsilon_{beam}}{\epsilon_{target}}, \end{equation} % and since the target polarization is precisely measured using a Breit-Rabi polarimeter, this approach eliminates the uncertainties from the non-perturbative hadronic spin flip amplitude. A single H-Jet polarimeter measures the polarization in both beams. The polarimeter requires an integration time of twenty hours to achieve a 2\% statistical uncertainty for a single beam, but because the scattering cross section is so small this measurement can occur concurrently with experimental data taking. \subsection{Cogging and Bunch Patterns} The RHIC beams are configured into 120 RF buckets capable of storing bunches injected from the AGS. In practice, not all of these 120 buckets are filled; a small number must be left empty as an abort gap'' to allow a controlled dumping of the beam when the luminosity has dropped below a useful level for physics data-taking. The two beams are cogged so that bunches from each beam can pass through one another at the RHIC interaction points. During a given RHIC store a given bunch from the Yellow'' beam always collides with the same bunch from the Blue'' beam. The polarization of each bunch is independently controlled at injection time, and the mapping of polarization states to bunch numbers can vary from fill to fill, enabling a powerful control on spin-dependent systematic uncertainties at the experiments. \section{The Solenoidal Tracker at RHIC (STAR)} STAR \cite{Ackermann:2002ad} is a general-purpose collider detector with several subsystems capable of investigating a wide range of phenomena from multiple collision types. A schematic of the detector is shown in Figure \ref{fig:star-schematic}. STAR acquires data in \textit{runs}, typically of 30 to 45 minutes duration, in which several hundred thousand events will be recorded. If a problem is discovered with a run during acquisition, reconstruction, or analysis, that run can be cleanly discarded without the loss of a large number of good events. Five STAR subsystems are of interest in this work: the Beam-Beam Counters (BBCs), Zero Degree Calorimeters (ZDCs), Barrel Electromagnetic Calorimeter (BEMC), Endcap Electromagnetic Calorimeter (EEMC), and STAR's flagship subsystem, the Time Projection Chamber (TPC). The BBCs and BEMC identify interesting events online and trigger the detector to read them out, while the BEMC, EEMC and TPC are used to reconstruct the final state of the event offline. The BBCs and ZDCs also allow a bunch crossing-dependent measure of the beam luminosities, which is essential to normalize spin-dependent asymmetries. These and other subsystems are described in greater detail in \cite{Harrison:2003sb}. \begin{figure} \includegraphics[width=1.0\textwidth]{figures/star-schematic-new} \caption{Schematic overview of the STAR detector, identifying many of the detector subsystems and defining the STAR coordinate system.} \label{fig:star-schematic} \end{figure} \subsection{Trigger System} STAR has a 3 level hardware trigger system (L0, L2, L3) \cite{Bieser:2002ah, Adler:2002ab} allowing for the selection of rare events from the large pool of minimum bias (MB) interactions. While the TPC and other tracking detectors have long readout times compared to the interaction rate, the BBCs and the BEMC are fast detectors that sample each bunch crossing at the STAR IR, and can thus be used for efficient selection of high $p_T$ events. A typical trigger mix consists of $\sim$10-20 separate triggers running in parallel. Significant improvements to the STAR data acquisition system (DAQ) beyond design specifications enabled the experiment to record events in the 2005 and 2006 experimental runs at a rate of 30-50 Hz with a dead-time fraction of $\sim$50\%. The L0 trigger operates on coarse-granularity data from fast detectors and builds a decision tree capable of completing its analysis in time with the 119 nanosecond RHIC bunch crossing interval. If the L0 trigger issues an accept the full trigger detector data is sent to L2 for further analysis. In contrast to L0, the L2 trigger runs on commodity hardware and its algorithms can be written in C. It applies preliminary calibrations and can do some primitive jet finding in the course of making its decision, but must issue that decision in no more than 5 milliseconds. If the L2 trigger issues an accept, the slow detectors are read out and the full event is recorded to tape. The L3 trigger \cite{Adler:2002ab} enables online TPC track finding using a farm of commodity servers. It was at one time a necessary component of the trigger system, but upgrades to the data acquisition system have increased the throughput from STAR to the RHIC Computing Facility (RCF) to the point where the $\sim$50 Hz of events selected by the L0 and L2 trigger algorithms can be recorded to tape. The L3 tracking output continues to serve as a useful qualitative monitoring tool in the STAR control room. \subsection{Beam Beam Counters\label{sec:bbc}} The BBCs \cite{Kiryluk:2003aw} consist of two hexagonal scintillator arrays, one immediately outside each magnet poletip 3.7~m from the interaction point. Each array is tiled from 36 individual hexagonal scintillators read out by wave length shifting fiber and a photomultiplier tube. The beam pipe passes through the center of the array. The region 9.6~cm to 48~cm from the beam axis ($3.3 < |\eta| < 5.0$) is covered by 18 small hexagonal tiles. The remaining region out to 193~cm from the beam pipe ($2.1 < |\eta| < 3.3$) is covered by 18 large hexagonal tiles. Only the small tiles are used in this analysis. Thresholds are set well below the signal deposited by a single ionizing particle in a tile, and a bunch crossing is recorded as having a hit based on the relative timing between the first signal from any of the small tiles on one side with the first signal from any of the small tiles on the other. The timing resolution is $\sim$2~ns, sufficient to separate beam backgrounds which should hit the two counters in succession vs. particles from a collision which should result in both counters being struck simultaneously. A timing cut 8~ns wide selects only coincidences with collision timing, and individual scalers are kept for each timing bin in addition to the total in the timing gate, thus allowing for more selective cuts offline. In addition to defining the MB trigger condition, coincident signals in the BBCs also serve as a luminosity monitor. In particular, tracking the number of BBCs hits per bunch crossing allows one to measure the luminosities for each combination of the spin states of the two beams. The ratios of these luminosities are a crucial element in the extraction of single- and double-spin physics asymmetries at RHIC. The absolute luminosity seen by the BBCs is calibrated by measuring the size of the beams and the number of colliding protons. The coincident cross section was found to be 26.1 $\pm$ 1.8(stat) $\pm$ 1.8(syst)~mb, representing $87\pm8\%$ of the non-singly diffractive pp cross section \cite{Adams:2003kv}. This translates into a typical BBC coincidence rate for 2005 (2006) data of $\sim$180 ($\sim$500)~kHz. \subsection{Zero Degree Calorimeters\label{sec:zdc}} The ZDCs \cite{Adler:2003sp} are hadron calorimeters placed 18~m upstream on each side of the the STAR interaction point. This places them on a line with the colliding beams but outside the final bending magnets between the two beam lines. They are 6 hadronic interaction lengths in depth but only 10~cm wide extending $\pm$2.7~mrad from the beam. As with the BBCs, a hit is recorded based on a coincidence between the two ZDCs with timing consistent with particles arriving simultaneously from the interaction point. These devices are designed to be sensitive to neutrons from heavy ion reactions and thus are not used as trigger detectors in the pp program. They do serve as a secondary luminosity monitor useful for many systematic error checks. They typically count a factor of 100 less than the BBC. \subsection{Scaler System\label{sec:scalers}} Signals from the L0 Trigger and the BBCs and ZDCs are processed by a set of 12 Scaler Boards \cite{scalers}. A Board is a custom VME histogramming module with 24 input bits, the combination of which maps to one of $$2^{24}$$ 40 bit memory locations on the module. 7 input bits are reserved for an encoding of the bunch crossing number, leaving 17 for detector-specific logic. The memory location addressed by a particular 24 bit input pattern is incremented when an event satisfies that bit pattern. The scaler system typically tracks hits in the East and West halves of the luminosity monitors separately, as well as a variety of coincidences with different $$\Delta T$$ requirements. Some of the boards are in continuous operation during a STAR run, while others sample at discrete intervals. \subsection{Electromagnetic Calorimeters} Electromagnetic calorimetry is an essential element of the trigger system at STAR and is also important for many final state analyses (especially, for the purposes of this thesis, jet reconstruction). We will focus on two calorimeter subsystems: the BEMC \cite{Beddo:2002zx}, covering $|\eta| < 1.0$, and the EEMC \cite{Allgower:2002zy}, which is installed only on the West side of STAR and spans $1.09 < \eta < 2.0$. Both the BEMC and EEMC are segmented sampling calorimeters with lead absorber layers and active plastic scintillator layers. The BEMC is divided into 4800 projective towers spanning $\Delta \eta \times \Delta \phi = 0.05 \times 0.05$, while the EEMC's 720 projective towers each span 0.1 in azimuth and range in pseudorapidity coverage from $\Delta \eta = 0.057$ at $\eta = 1.09$ to $\Delta \eta = 0.099$ at $\eta = 2.0$. Both calorimeters have a depth of at least twenty radiation lengths. At Level 0, the BEMC and EEMC implement trigger conditions based on thresholds in single high towers, 4x4 (4x2) trigger patches, and 20x20 (12x10) jet patches. At Level 2 the calorimeters drive a wide variety of trigger algorithms ranging from dijet reconstructions that span seamlessly across the two calorimeters to heavy flavor searches doing online calculations of tower pair invariant masses. The primary calorimeter trigger condition used in this work is the BEMC jet patch (JP) trigger, which requires an energy sum above threshold in one of twelve fixed collections of 400 towers each spanning $\Delta \eta \times \Delta \phi = 1.0 \times 1.0$. In this case the Level 2 trigger algorithm is a simple accept, and the EEMC is used only for final state jet reconstruction. %% This table is probably not a good idea anyway. % \begin{table} % \begin{center} % \begin{tabular}{c|cc} % & BEMC & EEMC\\ % \hline % depth & $\geq 20~\chi_0$ & $\geq 20~\chi_0$ % \end{tabular} % \end{center} % \caption{PID Selection Windows} % \label{tbl:pid-selection-windows} % \end{table} \subsection{Time Projection Chamber} The TPC \cite{Anderson:2003ur} is the primary detector subsystem at STAR, providing full azimuthal tracking of charged particles with transverse momentum above $\sim 100$ MeV/c and $|\eta| < 1.8$, and particle identification through measurements of ionization energy loss. It is a 4.2 meter long volume of gas bounded by an inner field cage at a radius of 50 centimeters and an outer field cage at 200 centimeters. The end caps of the detector are held at ground potential and the central cathode membrane at -28kV; metal rings connected by precision resistors in the field cages ensure a uniform electric field of $\approx 135$ V/cm. The TPC sits inside a solenoid with a field strength of 0.5 Tesla. Charged particles ionize the P10 gas (a mix of 90\% argon and 10\% methane) as they traverse the volume of the TPC, producing secondary electrons that drift to the nearest end cap of the detector. The $z$ coordinate of each point along the track is calculated by measuring the time required for the electrons to reach the end cap and dividing by the drift velocity. The drift velocity varies with electric field strength and with the temperature, pressure, and composition of the gas, so measurements of it are performed every few hours using the TPC laser system \cite{Abele:2003aa}. Radial laser beams at known positions along the length of the TPC ionize trace organic substances in the P10 gas; the time difference between the arrival of electrons liberated by lasers at two different positions allows a calculation of the drift velocity. % could say a little more about how electron drift time is measured ... e.g. time buckets for readout pads Each end cap is divided into twelve sectors, positioned as the hours on a clock face, and each sector contains 45 rows of cathode pads (5,692 pads per sector). The cathode pads are mounted on anode wires; the secondary electrons avalanche near the anode wires, and the positive ions produced in this avalanche generate a temporary image charge on several nearby pads. The image charge is measured, and an analysis of the charge sharing between the pads allows the original track $x$ and $y$ coordinates along the wire to be reconstructed to within a small fraction of a pad width. Finally, the charge deposited on each pad is used to calculate the particle's energy loss per unit length due to ionization, or dE/dx. \begin{figure} \includegraphics[width=1.0\textwidth]{figures/tpc} \caption{The STAR Time Projection Chamber (TPC). The end-caps are divided into twelve sectors, each with an inner and outer sub-sector. The TPC is divided into two by a central cathode membrane spanning the gas volume between the inner and outer field cages.} \label{fig:tpc} \end{figure} \subsection{Computing Facilities} The aggregate raw data produced by all detector subsystems in STAR is on the order of 100 MB per event. The STAR Data Acquisition System (DAQ) \cite{Landgraf:2002zw} reduces the event size through hardware-based zero suppression, resulting in a 10x savings for the highest multiplicity heavy ion collisions and substantially greater savings (100x or more) for the proton-proton collisions analyzed in this work. It then organizes the data into DAQ files and transfers these files to tape in the RHIC Computing Facility's HPSS hierarchical storage system, which provides 8 PB of storage and a throughput of over 300 MB per second to the RHIC and USATLAS experiments. Event reconstruction and data analysis takes place on a Linux compute farm with over 3300 cores and 1.7 PB of local storage. The STAR reconstruction software is written in C++ and runs on Scientific Linux, a version of Red Hat Enterprise Linux maintained by the particle physics community. The event reconstruction code loads DAQ files from HPSS into local storage, performs tracking and applies a variety of detector calibrations, and generates micro Data Storage Tapes'' or $\mu$DSTs'', which contain higher-level physics objects such as particle tracks, event vertices, and calorimeter clusters. $\mu$DSTs are implemented using ROOT \cite{Brun:1997pa} TTrees, allowing efficient ad-hoc and batch data analysis. The analysis presented here was performed on a set of TTrees generated from $\mu$DSTs using a mix of custom C++ libraries and Python scripts interfacing with the ROOT data analysis framework.