Chapter 2 Theory
3.2 The Compact Muon Solenoid
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must have the ability to reconstruct and identify leptons, photons, jets, and missing transverse energy with high precision, efficiency and geometric hermeticity over a wide angular range. The challenge of CMS is to operate in the harsh environment of approximately 20 inelastic pp collisions producing about 1000 charged particles every 25 ns. CMS also has to be able to reduce the total interaction rate from the 1 GHz delivered by the LHC by a factor of nearly 106 down to about 1.5 kHz that can affordably be processed and stored. This requires a very fast, granular, and radiation resistant apparatus whose large number of channels are well synchronized.
CMS consists of several sub-systems with different roles, see Figure 3.7. They
crystals-based electromagnetic calorimeter.
The coordinate system adopted by CMS has the origin centered at the nominal collision point inside the experiment, they-axis pointing vertically upward, and thex-axis pointing radially inward toward the center of the LHC. Thus, thez-axis points along the beam direction toward the Jura mountains from LHC Point 5. The azimuthal angle is measured from thex-axis in thex-yplane and the radial coordinate in this plane is denoted byr. The polar angle
✓is measured from thez-axis. Pseudorapidity is defined as⌘= ln tan(✓/2). Thus, the momentum and energy transverse to the beam direction, denoted bypTandET, respectively, are computed from thexandycomponents.
The imbalance of energy measured in the transverse plane is denoted byEmissT .
2 General concept
An important aspect driving the detector design and layout is the choice of the magnetic field configuration for the measurement of the momentum of muons. Large bending power is needed to measure precisely the momentum of high-energy charged particles. This forces a choice of superconducting technology for the magnets.
The overall layout of CMS [1] is shown in Fig. 1. At the heart of CMS sits a 13-m-long, 6-m-inner-diameter, 4-T superconducting solenoid providing a large bending power (12 Tm) before the muon bending angle is measured by the muon system. The return field is large enough to saturate 1.5 m of iron, allowing 4 muonstationsto be integrated to ensure robustness and full geometric coverage. Each muon station consists of several layers of alu- minium drift tubes (DT) in the barrel region and cathode strip chambers (CSC) in the endcap region, complemented by resistive plate chambers (RPC).
C ompact Muon S olenoid
Pixel Detector Silicon Tracker Very-forward
Calorimeter
Electromagnetic Calorimeter Hadron
Calorimeter
Preshower
Muon Detectors Superconducting Solenoid
Figure 1: A perspective view of the CMS detector.
The bore of the magnet coil is large enough to accommodate the inner tracker and the calorimetry inside. The tracking volume is given by a cylinder of 5.8-m length and 2.6-m diameter. In order to deal with high track multiplicities, CMS employs 10 layers of silicon microstrip detectors, which provide the required granularity and precision. In addition, 3 layers of silicon pixel detectors are placed close to the interaction region to improve the measurement of the impact parameter of charged-particle tracks, as well as the position of secondary vertices. The expected muon momentum resolution using only the muon system, using only the inner tracker, and using both sub-detectors is shown in Fig. 2.
2
Figure 3.7: A schematic overview of the CMS detector with average-sized physi- cists [67].
are arranged in an onion-like layered structure around the nominal interaction point.
Particles produced in collisions at the geometrical center of CMS cross these layers as they propagate from the inside out. The presence or lack of signals along their trajectories depends on the type of the particle and of the given subsystem. Combin- ing information from the various detectors enables inferences about the underlying particle trajectory, kinematics and types, cf. Figure 3.8.
1m 2m 3m 4m 5m 6m 7m 0m
Transverse slice through CMS
2T 4T
Superconducting Solenoid Hadron
Calorimeter Electromagnetic
Calorimeter Silicon
Tracker
Iron return yoke interspersed with Muon chambers
Key: Electron
Charged Hadron (e.g. Pion) Muon
Photon
Neutral Hadron (e.g. Neutron)
Figure 3.8: Transverse slice of the CMS detector depicting interaction of particles of different types with the various sub-systems [74].
A characteristic feature of the CMS design is the arrangement of its magnetic field.
To reach sufficient bending power for precise momentum measurement of charged particles, and unambiguous charge assignment for muons of transverse momentum up to pT ≈ 1 TeV, CMS chose a large superconducting solenoid. To reduce the amount of material in front of the calorimeters, they are located inside of the solenoid together with the inner tracking system. The size of the solenoid limits the size of the calorimeters, leading to a use of very dense materials in their active volume that can contain electrons, photons and hadrons with sufficiently high efficiencies. So it is the design of CMS that is compact in contrast to ATLAS rather than its overall dimensions of 21.6 m length, 14.6 m diameter, and 12.5 kt.
The CMS design is not only compact, it is also modular. The various CMS detector elements were constructed on the surface, lowered into the experimental cavern, and then assembled in a fashion resembling LEGO building blocks.
CMS uses a right-handed Cartesian coordinate system with the origin at the nominal interaction point at the geometrical center of the detector. Thex-axis points inward to the center of the LHC ring, the y-axis upward, and the z-axis tangentially to the direction of the beams. The right-handedness leads to a counter-clockwise direction of thez-axis looking from above.
Based on the Cartesian coordinates, we define cylindrical ones with the radial dis- tance from the beam r = p
x2+y2, the azimuthal angle φ = arctan(y/x) measured from the positive end of thex-axis, and thez-axis. We also define a spherical coordi- nate system with the radial distance to the origin ρ=p
x2+y2 +z2, the azimuthal angle φ, and the polar angle θ = arccos(z/r) measured from the positive end of the z-axis.
Another often used coordinate is the pseudorapidity defined as:
η =−ln tanθ
2, (3.5)
which, in the limit E → |p|, is equal to therapidity:
y= 1
2lnE+pz
E −pz. (3.6)
It has the advantage that particle production rate is roughly constant as a function of it, in the region around η = 0, and its differences are Lorentz invariant with respect to boosts along the beam axis. This is especially important at hadron colliders where the center-of-mass momentum component along this direction is unknown and differs event-by-event. Pseudorapidity η = 0 corresponds to the x-y plane and it tends to η → +∞ for the direction along the positive z-axis and η → −∞ for the negative z-axis with most of the fiducial volume covered by small numerical values of η.