-- LuisLebolo - 25 Jul 2008

Introduction

The Standard Model of Particle Physics has unified the electromagnetic interaction (carrier: photon, γ) and the weak interaction (carriers: W+, W-, Z0) [1]. However, the four carriers are exceptionally diverse: the γ is massless whereas the W± and Z0 are relatively massive. In the framework of the Standard Model, particles acquire mass through their interaction with the Higgs field. This implies the existence of a new particle: the Higgs boson (H0). The theory provides a general, upper mass limit of about 1 TeV; but it also predicts its production rate and decay modes for each possible mass. The European Organization for Nuclear Research’s (CERN) Large Hadron Collider (LHC) is a particle accelerator that will probe deep into matter. Scheduled to switch on in 2008, the LHC will allow the development of physics in an unprecedented energy range. It will ultimately collide beams of protons at an energy of 7 TeV (14 TeV in the center of mass). The prime motivation of the LHC is to elucidate the nature of electroweak symmetry breaking for which the Higgs mechanism is presumed to be responsible. The experimental study of the Higgs mechanism can also shed light on the mathematical consistency of the Standard Model at energy scales above about 1 TeV. Furthermore, there are high hopes for discoveries that could pave the way toward a unified theory. These discoveries could take the form of supersymmetry or extra dimensions. There are many compelling reasons to investigate the TeV energy scale and the Compact Muon Solenoid (CMS) detector will these high-energy proton-proton collisions.

Compact Muon Solenoid

CMS is a general-purpose detector designed to run at the LHC’s highest luminosity. The fundamental components of CMS are central tracking, the electromagnetic calorimeter, the hadronic calorimeter, and the muon system.

Figure 1: CMS Layout and Detectors [1] Source: <http://cmsinfo.cern.ch/Welcome.html/CMSdocuments/CMSbrochure/CMS-Brochure03.pdf>

Essentially, there are six types of particles observed in CMS with their detection methods given in Table 1 and Figure 2:

Table 1: Observable Particles in CMS [2] Source: <http://cmsinfo.cern.ch/Welcome.html/CMSdocuments/ForGuides/CMSdocumentforGuides.pdf>

Figure 2: CMS Slice Through [3] Source: <http://cmsinfo.cern.ch/Welcome.html/CMSdocuments/CMSdocuments.html>

Most particles will leave a track in the central tracking before electrons, photons, and hadrons are stopped by the calorimeters; allowing their energy to be measured [4]. The first calorimeter layer is the electromagnetic calorimeter and is designed to measure the energies of electrons and photons with high precision. Hadrons, which interact via the strong force, deposit most of their energy in the surrounding hadronic calorimeter (HCAL). After most particles are stopped by the calorimeters, the muon system will track muons adjacent to the superconducting solenoid.

The Hadron Calorimeter

Figure 3: Longitudinal view of the CMS detector showing the locations of the hadron barrel (HB), endcap (HE), outer (HO), and forward (HF) calorimeters.

The HCAL plays an essential role in the identification and measurement of quarks, gluons, and neutrinos by measuring the energy/direction of jets and the missing transverse energy in events [4]. Missing energy forms a crucial signature of new particles, like the supersymmetric partners of quarks and gluons. The HCAL will also aid in the identification of electrons, photons, and muons when used in conjunction with the rest of the subdetectors. The HCAL is divided into four sections: Hadron Barrel (HB), Hadron Endcap (HE), Hadron Outer (HO) and Hadron Forward (HF) (see Figure 3) [2]. HB and HE are sampling calorimeters containing brass plates interleaved with plastic scintillators. This central calorimetry is complemented by a tail-catcher in the barrel region (HO) ensuring that hadronic showers are sampled with large hadronic interaction lengths. Full geometric coverage for the measurement of the transverse energy in the event is provided by an iron/quartz-fiber calorimeter (HF). The scintillators emit blue-violet light, where the amount of light is proportional to the energy of the incident hadron. The scintillation light is converted by wavelength shifting fibers (WLS) that are then spliced to clear fibers (see Figure 4). The clear fiber goes to an optical connector at the end of the scintillator tray. The optical cable takes the light to an optical decoding unit that arranges the fibers into read-out towers and brings the light to a photodetector. These photodetectors are called hybrid photodiodes (HPDs), which provide gain and can operate in high axial magnetic fields. An additional fiber enters each HPD for direct injection of light using either a laser or a light emitting diode (LED). On the other hand, HF uses Cerenkov light emitted in the quartz fibers and is detected by photomultiplier tubes (PMTs). A charge-integrating Analog-to-Digital Converter (ADC) - called the Charge-Integrator and Encoder (QIE) - converts the analog signal from the HPD (or PMT) to a digital signal. The QIE internally contains four capacitor banks that are connected in turn to the input, i.e. one every 25 ns bunch crossing (should I mention more about bunch crossings and basic LHC beam parameters/physics?). The integrated charge from the capacitor is converted to a seven-bit non-linear scale to cover the large dynamic range of the detector.

Figure 4: Schematic of HB optics

Background

At design luminosity, approximately twenty inelastic collisions will be superimposed on an event of interest [TDR]. This implies that roughly one thousand charged particles will emerge from the interaction region every 25 ns. The products of an interaction may be confused with those from other interactions in the same bunch crossing (called pile-up). This problem clearly becomes more severe when the response time of a detector element and its electronic signal is longer than 25 ns. Using high-granularity detectors with good time resolution can reduce the effect of this pile-up. However, the resulting large number of detector electronic channels requires superb synchronization. An essential component of the HCAL is the laser calibration system, which can be used to synchronize channels, monitor QIE linearity, and examine the calorimeter’s performance [5]. This is done in part by exciting the scintillators using an ultraviolet (UV) nitrogen laser with a wavelength of 337 nm. The laser system can illuminate an entire half-barrel (HB+ or -), a single endcap (HE+ or -), an outer hadron ring (HO +2, +1, 0, -1, or -2), or a forward calorimeter (HF+ or -) at once through a series of optical splitters.

Laser Setup

Figure 4: Photograph of Laser System (Better pic/labels?).

The alignment of all optical components must be exceptionally accurate, where small vibrations or tensions in the table could prove detrimental. Therefore, the laser calibration system is constructed on an optical breadboard that dampens vibrations and prevents warping under heavy loads. The laser emits pulses where the pulse-to-pulse energy variations are specified to be 4% and the beam-spot size is originally 8 x 8 mm. In order to control the intensity of the light (and map out the QIE linearity), the laser ray is incident upon a continuously varying neutral density (ND) filter wheel. Normally the attenuation would not be uniform across the beam-spot, due to the initially large beam-spot size. Therefore, two anti-correlated filter wheels are utilized. Each filter wheel is controlled by a rotary stepping motor and is specified to be linear in optical density (log10(S/S0)) as the wheel is changed by equal angles. The level of attenuation increases with the rotational angle. Subsequently, the ray passes through a focusing lens with a focal length of 20 cm. This focuses the beam-spot down to several hundred micrometers in diameter to better match the quartz fibers. The ray is then incident upon the first beam sampler, which is held by a mirror gimbal. The gimbal has three axes of rotation and allows the angle of incidence to be controlled.

Figure 5: Optical Ray Trace of Perfect Alignment (w/ Fresnel Amplitude Coefficients)

The beam is then reflected, transmitted, and split as described by the laws of optics (i.e. Fresnel equations). The first sampler reflects two beams to the second sampler and transmits one beam to the fiber harness. The fiber harness, controlled with a linear stepping motor, can be moved such that the beam enters one of the 30 possible fibers held within. Each reflection beam incident upon the second sampler creates two additional reflection beams and one transmission beam. Adjacent to the second sampler are two L-brackets that hold quartz fiber optic cables and route the light to pin diodes. The pin diodes allow us to measure the intensity of the light - independently from the detector - via an oscilloscope or data acquisition system. Thus, at the L-brackets, there are a total of two transmission beams (2 and 3) and four reflection beams (4 through 7).

Figure 6: Beam Sampler/Splitter, T = 5 mm. Made of UV fused silica (quartz), the splitter picks off approximately 5% of the incident beam at 45°. The back surface is wedged to eliminate internal fringes and anti-reflective coated to remove ghosting [6]. Source: <http://www.thorlabs.com/images/PDF/v17_662.pdf>

Fiber Optic Path

Table 2: Fiber Optics Lengths and Transmissions Fiber Path Length (m) Diameter (um) Trans. HBHE at Fiber Harness In 200 to Laser Box Panel ? in 200 out 250 ? in Delay Box 15-30 250? ? to Patch Panel 50-100 in 250 out 300 7.50% to Laser Distribution Box 20 300 ? in Laser Distribution Box (1-to-18 Splitter) ? in 400 out 250 2.20% to Calibration Box (1 per RBX) 35-40 300 50% At Calibration Box in 400 ?

HB in Calibration Box Megatile 1-to-4 Splitter for each 5° Sector ? in 800 out 250 7.50% to Megatile (layer 9) ? 300 ? in Megatile 1-to-16 Splitter for each eta tower ? in 800 out 100 ?

HE?

Figure 7: Fiber Optic Path (Can’t read megatile captions)

In the barrel/endcap region, the laser can be directed either straight onto an internal scintillator block connected to the HPD or into a collection of scintillator tiles (a megatile). For the megatiles, the quartz fibers that lead from the laser to the detector have been carefully controlled to equalize the optical path length to each wedge. This allows us to flatten the timing of the detector for time-of-flight studies. As an example, the optics fiber path for HBHE is as follows (see Figure 7). Laser light enters a fiber at the fiber harness (FH) where it is then connected to fibers at the delay box. The equalization of the fiber lengths takes place in the delay box. The light is then fed into the patch panel (PP) that connects the laser room fibers to the detector fibers (for HB, the patching actually occurs on the detector). The light is then routed to the laser distribution box (LDB) where it is split to each of the 18 wedges/RBXes. Inside each RXB is a Calibrration Box (CalBox). In the CalBox, the HPD fiber is fed onto a scintillator block that is connected directly to the HPD (this is the same scintillator block in which the LED is placed). The megatile fiber is fed into a one-to-four splitter, which routes the light to the four 5° sectors of each wedge. Each phi-sector has seventeen layers of scintillators, however the laser light is fed into the ninth layer. Once the light is fed into the megatile, it is fanned out as shown in Figure 8 - and distributed to all tiles. The light signal produced by a UV flash in the scintillator is similar to the signal induced by a charged particle. Therefore one can mimic the time-of-flight of a particle from the interaction region. This arrangement allows the timing of HCAL to be flattened and monitored. The laser also allows a performance check of the entire optical route from scintillator to electronics. It provides an important technique to check for defective channels and to track possible degradation of calorimeter gain (due to component aging, temperature dependence, and radiation damage).

Figure 8A: Design of HB scintillator tray

Figure 8B: Design of HE scintillator tray

Fresnel Equations

Relative intensity calculations of the seven outgoing, split beams allow us to determine misalignments in the optical setup. Therefore, it is important to understand the nature of these reflected/transmitted beams. At a dielectric interface, Fresnel equations relate the amplitudes of reflection and transmission to the amplitude of the incident electromagnetic wave [7]. In general, when a wave reaches a boundary between two different dielectric constants, part of the wave is reflected and part is transmitted; the sum of the energies in these two waves equal to that of the original wave [8]. Since electromagnetic waves are transverse, there are separate coefficients in the directions perpendicular and parallel to the surface of the dielectric. The coefficients for reflection and transmission of the transverse electric field are termed S-polarized, while the coefficients for reflection and transmission of the transverse magnetic field are termed P-polarized.

Figure 9: The Plane of Incidence and Field Components [7] Source: <http://scienceworld.wolfram.com/physics/FresnelEquations.html> For P-polarization, the ratio of amplitudes for reflected and transmitted waves (rP and tP, respectively) are (1) , (2) where (in terms of the transmitted and incident angles, θT and θI) (3) . (4) Equation 3 was simplified using Snell’s Law ( ). In Equation 4, the permeability ‘μ’ of most dielectrics is approximately equal to unity. The intensity, I, is defined (by means of the time-averaged Poynting vector), as , (5) where ε is the electric permittivity and v is speed of the wave. The reflectance and transmittance are then (6) . (7)

Similarly, for S-polarization, (8) (9) (10) . (11) As a measurement of misalignment, the relative intensities of a theoretically perfect alignment were compared to intensities produced by the setup.

Results

Misalignment

Beam intensities were calculated using the preceding Fresnel equations. However, several corrections were required*. First, it was ensured that pin diode 1 and pin diode 2 (PD1 and PD2, respectively) were normalized and reading the same amount of charge. The intensities of beams 2 and 3 are much greater than those of beams 4 through 7. To account for this, each pin diode’s signal is split into 3 channels – where each successive channel is electrically attenuated by approximately 64x. The signal is then readout by a Charge Analog-to-Digital-Converter (QADC). Therefore, if a QADC channel is saturated, we simply readout the next channel and correct for the attenuation. Errors for the theoretical intensities were calculated by assuming that the incident beams were off from perfect alignment (45°) by 5° at both samplers. Moreover, the splitters have an anti-reflective coating that slightly distorts the beam and must be accounted for. Far more complex corrections include the optical path lengths and focusing of the beam-spots. For example, in Figure 5, beam 3 has a longer optical path than beam 2. Therefore, the diameter of beam 3’s spot at PD2 will differ from that of beam 2. Indeed, the optical geometry provides the following relationship , (13) where D is the diameter of the spot, b is the diameter of the incident beam (6000 µm), d is the total optical path length of the beam, and f is the focal length of the lens (20 cm). Since the width of the fiber is 200 µm (used to be 300 µm? This was in the 2004 setup – old fiber harness), corrections must be made for beams that have a greater width than the fiber (assuming circular dimensions for both fiber and beam). The optical lengths of most beams were optimized so that the spot diameters were less than 200 µm; therefore only beam 4 had to be corrected in this manner.

Table 2A: Path Lengths and Spot Diameters Path Segment Distance (mm) Traversal through Splitter (T) 5.717 Focuser to Splitter 1 (FS1) 51.190 Splitter 1 to Splitter 2 (S1S2) 77.070 Splitter 2 to Pin Diode 1 (S2PD1) 60.740 Splitter 2 to Pin Diode 2 (S2PD2) 65.410

Beam Optical Path Length (cm) Spot Diameter (µm) 2 FS1 + S1S2 + T + S2PD1 19.472 158.480

3 FS1 + 2*T + S1S2 + T + S2PD1 20.615 184.559

4 FS1 + 2*T + S1S2 + 2*T + S2PD2 21.654 496.179

5 FS1 + 2*T + S1S2 + S2PD2 20.511 153.139

6 FS1 + S1S2 + 2*T + S2PD2 20.511 153.139

7 FS1 + S1S2 + S2PD2 19.367 189.900

Table 2B: Data for Intensity Calculations Indexes of Refraction and Angles Filter Wheel Position # ND Angle (°) Air (n1) 1.00029 2 19 342 Quartz (n2) 1.45850 3 11 198 θI 45°

Data Beam Signal ( C ) Low ( C ) High ( C ) Pin 3 - ND 0.4 2 3.416E-10 3.158E-10 3.708E-10

1. 2.577E-10 2.332E-10 2.806E-10

Pin 2 - ND 0.0 4 1.296E-10 1.168E-10 1.403E-10

1. 2.436E-10 2.235E-10 2.603E-10
2. 2.012E-10 1.832E-10 2.182E-10
3. 2.982E-10 2.755E-10 3.175E-10

Data Beam Pedestal ( C ) Low ( C ) High ( C ) Pin 3 - ND 0.4 2 5.800E-12 -2.375E-12 1.508E-11

1. 5.400E-12 -2.750E-12 1.471E-11

Pin 2 - ND 0.0 4 1.060E-11 1.350E-13 1.963E-11

1. 8.600E-12 -5.750E-12 2.022E-11
2. 1.000E-11 -1.780E-12 2.172E-11
3. 1.000E-11 -1.750E-12 2.050E-11

Ped Subtracted ( C ) Focal Corrected ( C ) Pin 3 - ND 0.4 2 3.358E-10 3.358E-10

1. 2.523E-10 2.523E-10

Pin 2 - ND 0.0 4 1.190E-10 3.255E-10

1. 2.350E-10 2.350E-10
2. 1.912E-10 1.912E-10
3. 2.882E-10 2.882E-10 Sum N/A 1.628E-09

Pin Diode Normalizations (Beam 3) FILTERED Motor 2 - 14 Motor 3 - 11 Pin 3 - ND .4

Pin Signal ( C ) Low ( C ) High ( C ) 3 3.622E-11 3.350E-11 3.829E-11 2 2.914E-10 2.718E-10 3.075E-10

Pin Pedestal ( C ) Low ( C ) High ( C ) 3 1.412E-12 6.750E-13 2.038E-12 2 1.080E-11 -3.800E-12 2.375E-11

Pin Total Signal ( C ) Low Error ( C ) High Error ( C ) 3 3.481E-11 2.719E-12 2.072E-12 2 2.806E-10 1.965E-11 1.610E-11 Pin 2 / Pin 3 8.061

Pin Beam Pin Equalized Normalized 7 3 2 2.707E-09 9.393

1. 2.034E-09 7.057

2 4 3.255E-10 1.130

1. 2.350E-10 0.815
2. 1.912E-10 0.663
3. 2.882E-10 1.000 Sum 5.781E-09 N/A

Calculations Beam S-Intensity P-Intensity Total Intensity Normalized 7 Pin 1 2 6.918E-02 6.653E-03 7.584E-02 11.171

1. 5.829E-02 6.563E-03 6.485E-02 9.553

Pin 2 4 4.787E-03 4.426E-05 4.831E-03 0.712

1. 5.681E-03 4.486E-05 5.726E-03 0.843
2. 5.681E-03 4.486E-05 5.726E-03 0.843
3. 6.743E-03 4.547E-05 6.789E-03 1.000 Sum N/A N/A 1.638E-01 N/A

After taking these corrections and errors into account, the theoretical calculations vs. the actual intensities measured were compared. This provided us with a measurement of our misalignment (as a deviation from perfect alignment). As a result, beams 2 and 7 are utilized for further data collection; they require the least amount of correction, have minimal sources of error, and have relatively diverse intensities.

Figure 10: Intensity Data vs. Calculation

Linearity

The QIE linearity was measured by varying the laser’s optical density. Each filter wheel was mapped throughout thirteen (we may do a continuous sweep) equally spaced positions in order to confirm its linearity. The specifications of the filter wheels are: • Filter wheel 1: 0.00 - 3.00 B over 315° (45° - 360°) • Filter wheel 2: 0.04 - 4.00 B over 270° (90° - 360°). The current filter wheels are specified to be for visible light (400 nm to 700 nm). Therefore, new wheels will be purchased that are sensitive to UV light (337 nm) and that have a greater dynamic range. A finer mapping of these new filter wheels will then be performed.

Figure 11: Linearity of filter wheels

As can be seen in Figure 10, the filter wheels are confirmed to be linear within 5%. The outlier data points at higher attenuations are expected; higher attenuation means less photostatistics. However, there are two problems currently under investigation. In filter wheel 1, the nonlinearity of the data point at -1.75 B is not understood. Also, a sinusoidal pattern is seen in both filter wheels, which suggests a systematic error. This can either be an incorrectly mounted wheel, an incorrectly manufactured filter, an imperfection in the glass (due to scratches/smudges), or the fact that we are currently using filter wheels specified for the visible light range. For QIE linearity, the mean value of the signal’s pulse height distribution was fit to a line (log scale) over various attenuations. The chi-squared values (a measurement of fit) were large due to nonlinearities. Therefore, residuals were plotted to substantiate these errors.

Figure 12: OLD DATA! Typical Optical Density and Residual Plot. The errors bars get larger as the rotor angle increases because there are fewer photoelectrons at high attenuation (they go as ).

OLD DATA! A similar trend was seen for all channels and their residuals were scatter plotted. Excluding the lowest and highest attenuations (energies), less than 5% deviation in linearity was confirmed (as specified by the manufacturer). However, a sinusoidal pattern was seen across all channels and implied a systematic error in the setup. This could have meant that the wheel was off-center when mounted or fabricated. Nevertheless, a finer mapping of the wheel would be required and another set of runs is planned for the near future.

Figure 13: OLD DATA! Residuals for all channels

Resolution

The resolution of the laser to HPD was also analyzed. A standard form of the resolution function was used, where the terms were added in quadrature. It can be seen, from Figure 14, that the constant term confines the resolution at high energy and the noise term dominates at low energies. For collision data, the basic contributions to the stochastic term are event-to-event fluctuations in the lateral shower containment and photostatistic contributions. The most important contributions to the constant term are non-uniformity of light collection, intercalibration errors, and leakage of energy from the back of the detector. The noise term consists of electronics, digitization and pileup noise.

Figure 14: OLD DATA! Typical Resolution Plots

OLD DATA! Initially, the ROOT scripts were allowed to fit all parameters freely. However, a two to three peak structure for the stochastic term was observed. The constant term was known to be 4% from the laser variation and the noise term was available from the pedestal data, hence these values were constrained and a clear structure to the stochastic term was evident.

Figure 15: OLD DATA! Histogram of Resolution Parameters: (LEFT) All Parameters Free (RIGHT) Constant and Noise Parameters Constrained

To further investigate, a scatter plot was made of the stochastic term vs. channel. For HB, there were eight HPDs. As a result, differences corresponding to individual HPDs were observed. The units of the stochastic term are photoelectrons/GeV. Therefore, it is related to the quantum efficiency of the photodiodes. Unfortunately, only the central towers of HE were instrumented and a general mapping of those HPDs was attained. Note that - excluding the two outliers - the stochastic term is roughly 40%. From Poisson statistics, one can correlate the stochastic term to a more direct function of efficiency as follows: , (12) where E is the energy and N is the number of photoelectrons. Therefore, for 1 GeV of energy, 6.25 photoelectrons are obtained. The calorimeter was originally calibrated to 18 photoelectrons per GeV of energy deposit (note that two HB HPDs were worse).

Figure 16: Stochastic Term v. Channel

Discussion and Conclusions

Three aspects of the calibration system were examined:

• Intensity/Misalignment: An understanding of the sampling arrangement was essential. There were many factors to take into consideration, the most probable sources of error were determined, and these errors were then minimized. This is imperative since the system has numerous optical components and thus numerous places for things to go wrong. The deviation from perfect alignment allows a certain confidence in the setup. Finally, data collection beams were chosen due to their relatively diverse intensities and lack of corrections required. • Linearity: The linearity of the filter wheels was confirmed to be within 5%, in general. There are ongoing investigations for the two outlier data points and systematic errors. New QIE linearity analysis conclusions... • Resolution: The resolution of the laser to HPD was analyzed, separating it into its noise, constant, and stochastic contributions. The aspects of the energy resolution that govern certain regions of energy and intensity are now known and may be controlled. The pin diodes, for example, will allow us to manage the constant term. Furthermore, the quantum efficiency of the HPDs was found to be approximately 40%, with two HPDs having poorer efficiency. New HPD resolution conclusions… Knowing the efficiency of the HPDs provides a way to check on the calorimeter’s stability over time. Closing words

Bibliography

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