In-Situ Calibration of the CMS Electromagnetic Calorimeter

The in-situ intercalibration of the PbWO 4 crystals of the CMS electromagnetic calorimeter will be performed using three techniques: An energy-ﬂow method will be used at startup to intercalibrate to a precision of around 2% within about three hours. The energy/momentum measurement of isolated electrons from W → e ν events will then be used to obtain the design goal precision of 0.5% within about two months. Global intercalibration of different regions of the calorimeter and the determination of the absolute energy scale will be performed using energetic electrons from Z → e + e − events.


Introduction
The CMS Electromagnetic Calorimeter consists of 75848 lead tungstate crystals. To achieve the target energy resolution, precise in-situ intercalibration of the individual crystals using physics events is required. The importance of this can be seen by considering, for example, the potential discovery and mass measurement of an intermediate mass Higgs boson in the H→ γγ channel, which would greatly benefit from an energy resolution with a constant term of less than about 0.5%. The intercalibration error goes directly into this constant term with very little scaling, because most of the energy goes into a single crystal.

The CMS Electromagnetic Calorimeter
A detailed description of the CMS ECAL can be found in [1]. Figure 1 shows a transverse section of the ECAL. The endcap consists of identically shaped crystals, slightly shorter (220 mm, 24.7 X 0 ) and a little larger in cross-section than the barrel crystals, grouped in mechanical units of 5 × 5 crystals arranged in a rectangular xy grid, with the crystal axes off-pointing from the nominal vertex by angles between 2 • and 5 • . A 3X 0 silicon strip preshower detector is situated in front of most of the endcap (|η| > 1.653).

The Electron/Photon High Level Trigger
The online reconstruction and selection of physics objects will be performed using the CMS High Level Trigger (HLT), described in detail in [2]. This will be done flexibly using a single online CPU farm, made up of approximately 2000 processors, using the same object-oriented environment and code as the offline software. The CPU time targets are already being met. 2 The Electron/Photon HLT selection is performed in three stages: 1. "Level-2": Clusters of crystals are constructed using a bump-finding algorithm. The spray of bremsstrahlung energy radiated in the tracker material is collected in "super-clusters". At low luminosity, the transverse energy of the super-cluster is required to be greater than 26.0 (14.5) GeV for single (double) triggers.
2. "Level-2.5": The energy-weighted average impact point of the super-cluster is propagated back to the nominal vertex point and hits in the pixel detector are sought. If at least two pixel hits are found, the candidate is classified as an electron, otherwise it is classified as a photon. For the photon stream at low luminosity, the transverse energy of the supercluster is required to be greater than 80 (20) GeV for single (double) triggers.
3. "Level-3": For electrons, tracks are reconstructed and cuts are applied on the ratio of the super-cluster energy to the track momentum and on the difference in pseudorapidity, η, between the extrapolated track and the super-cluster position. Isolation requirements are made for both electrons and photons. Table 1 shows the electron and photon rates output by the HLT at both low and high luminosity. The single electron background comes from π ± /π 0 overlap, π 0 conversions and genuine electrons from b/c → e. The efficiency for H→ γγ for m H =115 GeV at low luminosity after the complete selection chain is 77% for events with both photons in the fiducial region, and 84% for events for which the photons also pass the offline p T cuts to be used for Higgs searches. 4 Intercalibration Strategy

Precalibration
The raw intercalibration precision obtained from laboratory measurements of the APD gains and crystal light yields is ∼4.5%. The precision obtained from the transfer of the test beam precalibration to the assembled detector is predicted to be ∼2%. However, the present construction schedule implies that less than one quarter of the calorimeter elements can be precalibrated.

In-Situ Intercalibration Using Electrons From W→ eν Events
The standard technique which will be used to obtain high-precision local intercalibration of the CMS ECAL is to use the E/p of electrons from W→ eν decays, where E is the energy measured in the calorimeter and p is the measured momentum of the reconstructed track.
There are two dominating issues. The first is that the inclusion of electrons with large losses due to bremsstrahlung in the tracker material results in a large tail in the E/p distribution, leading to a tradeoff between electron efficiency and the width of the distribution. Electrons which radiate significantly can be removed by applying very hard cuts on ECAL shower shape variables.
Since the amount of bremsstrahlung depends on the amount of material, which varies with η, the strategy is to intercalibrate crystals within small η regions first with loose bremsstrahlung cuts, and then to intercalibrate between the regions with much tighter cuts.
The second issue is that each electron shower involves up to 25 crystals 1) , so there is a need to deconvolute the 25 individual calibration constants used to reconstruct the energy of each electron. The deconvolution is performed using an iterative algorithm which was used to solve the same problem in the L3 experiment at LEP. The algorithm was tested for electrons simulated in a 10 × 10 crystal matrix. Figure 2 shows the calibration errors as a function of the number of W → eν events per channel. A few tens of events per channel are sufficient to obtain an intercalibration precision better than the target of 0.5%. The time required depends on the cuts applied to remove electrons with large bremsstrahlung losses. Conservative calculations indicate a time scale of around two months at low luminosity.

φ-Symmetry Intercalibration
The standard W→ eν intercalibration requires approximately two months of stable running at 2 × 10 33 cm −2 s −1 luminosity and requires the entire detector to be functioning optimally (e.g. perfect tracker alignment), conditions which may take some time to achieve. φ-symmetry intercalibration [3] is proposed as a method to rapidly achieve a target intercalibration precision of 2% at startup, by exploiting the uniformity of energy deposition in minimum-bias events to intercalibrate pairs of rings of crystals at fixed | η |. Minimum-bias crossings are used to avoid trigger bias, but the use of jet-triggers, which have the advantage of much larger energy deposits, is also being investigated. The number of intercalibration constants can thus be reduced from 75848 (no. of crystals) to 125 (no. of fixed | η | ring pairs). Ring-to-ring intercalibration will then be performed using Z→ e + e − events (Section 4.4).
Distributions of the total transverse energy deposited in each crystal from 18 million fully simulated minimum-bias events are formed for 85 (40) pairs of rings in the barrel (endcaps). The summations do not include energy deposits below 150 MeV in the barrel and below 750 MeV in the endcaps in order to exclude noise. The intercalibration precision attainable for each pair of rings is determined from the Gaussian width of the distribution via an empirically determined constant of proportionality.
The technique has been directly tested by performing a complete simulation of the method to a pair of rings with miscalibrations assigned randomly from a Gaussian of width 6%. Figure 3(a) shows the residual miscalibration after a single iteration of the method.
If the symmetry were exact the attainable precision would be proportional to 1/ √ N , where N is the number of events. In reality, a limiting precision is reached when the inhomogeneity of tracker material breaks the φ-symmetry of the energy deposition. This limit can be calculated for each pair of rings by fitting the precision as a function of 1/ √ N to a function of the form where m is a constant and s is the limiting precision. This procedure is illustrated in Figure 3  The intercalibration precision which can be obtained with 18 million minimum-bias events, and the limit on the precision are shown as a function of η in Figure 4. The precision with 18 million events is between 1.2% and 3.5% throughout the fiducial region. Allocating 1kHz of Level-1 bandwidth for minimum-bias, 18 million events could be taken in less than three hours. Complete ignorance of the tracker material distribution is assumed. With knowledge of the distribution after precise independent W→ eν intercalibration, there is the potential for rapid and repeated high-precision intercalibration (<1% every few hours).