- Email: [email protected]
The performance of the CDF luminosity monitor
Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
The performance of the CDF luminosity monitor D. Acostaa, S. Klimenkoa,*, J. Konigsberga, A. Korytova, G. Mitselmakhera, V. Neculaa, A. Nomerotskya, A. Pronkoa, A. Sukhanova, A. Safonova, D. Tsybycheva, S.M. Wanga, M. Wongb a
University of Florida, Corner of Museum Road & North-South Drive, Gainesville, FL 32611-8440, USA b Fermi National Laboratory, Batavia, IL, USA
Abstract We describe the initial performance of the detector used for the luminosity measurement in the CDF experiment in Run II at the Tevatron. The detector consists of low-mass gaseous Cherenkov counters with high light yield (B100 photoelectrons) and monitors the process of inelastic pp% scattering. It allows for several methods of precise luminosity measurements at peak instantaneous luminosities of 2 1032 cm2 s1 ; corresponding to an average of six pp% interactions per bunch crossing. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Hadron; Collider; Luminosity; Cherenkov
1. Introduction At hadron collider experiments the beam luminosity, traditionally, has been measured using the process of inelastic pp% scattering. It has a large cross-section sin B60 mb; measured at the Tevatron energy (1:8 TeV) by the CDF, E710 and E811 experiments [1–3] with an uncertainty of B3%: The rate of inelastic pp% interactions is given by mfBC ¼ sin L
2. CLC detector
ð1Þ
where L is the instantaneous luminosity, fBC is the rate of bunch crossings in the Tevatron and m is the average number of pp% interactions per bunch crossing. To detect inelastic pp% events efficiently a dedicated detector at small angles, operating at high rate and occupancy, is required. In Run II the *Corresponding author. E-mail address: [email protected]fl.edu (S. Klimenko).
Cherenkov luminosity counters (CLC) are being used by CDF to measure the Tevatron luminosity. The CLC is designed to measure m accurately (within a few percent) all the way up to the high luminosity regime LB2 1032 cm2 s1 expected in Run II [4,5].
There are two CLC modules in the CDF detector, installed at small angles in the proton (East) and anti-proton (West) directions with rapidity coverage between 3.75 and 4.75. Each module consists of 48 thin, long, gas-filled, Cherenkov counters. The counters are arranged around the beam-pipe in three concentric layers, with 16 counters each, and pointing to the center of the interaction region. They are built with reflective aluminized mylar sheets of 0:1 mm thick
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 1 4 4 5 - 6
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
58 200 180
photoelectrons
90000
isobutane at 1.2 atm.
160 140
80000
120 100
70000
80 60
60000
20 0
0
10
20
30
40
50
60
70
80
90
channel
Fig. 1. Number of photoelectrons produced by single particles traversing the full length of the CLC counters measured for all 96 counters.
events
40
50000 40000 30000 20000 10000
and have a conical shape. The cones in two outer layers are about 180 cm long and the inner layer counters (closer to the beam pipe) have the length of 110 cm: The Cherenkov light is detected with fast, 2:5 cm diameter, photomultiplier tubes (Hamamatsu R5800Q). The tubes have a concave– convex, 1 mm thick, quartz window for efficient collection of the ultra-violet part of Cherenkov spectra and operate at a gain of 2 105 : The performance of a single Cherenkov counter at the testbeam and the CLC design are described in detail in Refs. [6,7]. The counters are mounted inside a thin pressure vessel made of aluminum and filled with isobutane. The nominal operation point is near atmospheric pressure. However, if more light is desired, the vessel is designed to operate at maximum pressure of two atmospheres. We use isobutane as a radiator because it has one of the largest indexes of refraction for commonly available gases (1.00143) and good transparency for photons in the ultra-violet part of spectra where most of the Cherenkov light is emitted. The Cherenkov angle is 3:11 and the momentum threshold for light emission is 9:3 MeV c1 for electrons and 2:6 GeV c1 for pions. Fig. 1 shows the large light yield (B100 photoelectrons) for relativistic particles, from pp% collisions, traversing the full length of the counters.
3. CLC amplitude and occupancy for p%p collisions Since there are no Landau fluctuations for the Cherenkov light emission, we expect a narrow
0
0
0.5
1 1.5 2 amplitude, spp units
2.5
3
Fig. 2. Amplitude distribution of Cherenkov counters: solid— data, dots—simulation.
peak in the CLC amplitude distribution corresponding to single particles crossing the full length of the counters. The width (rms) of the single particle peak (SPP) is determined by the photoelectron statistics, light collection uniformity and the amplitude resolution of the photomultipliers (with B10% contribution from each source). By measuring the SPP mean values we can calibrate the CLC amplitude in units of a single particle peak. However, due to secondary interactions of particles from pp% collisions in the material surrounding the CLC, the distribution of amplitudes in the counters does not show a clear single particle peak (see Fig. 2). Secondary particles are mainly electrons and positrons from electromagnetic showers produced by p0 -gg decays in the beam pipe and vertex detector material. They contribute low amplitudes when particles traverse the counters at large angle and also create long tails at high amplitude when several particles hit the same counter. To suppress the showers and observe the single particle peak we applied an isolation cut, requiring amplitudes in the counters around a selected counter to be less than 20 photoelectrons. Fig. 3 show the amplitude distribution for one of the CLC counters after the isolation cut. The single particle peak is clearly
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62 Qie 20
10
2
40
number of hits
Chi2 / ndf = 18.45 / 32 Prob = 0.9732 p0 = 0.996 ± 0.4417 p1 = 0.01512 ± 0.002215 p2 = 370.2 ± 10.12 p3 = 13.23 ± 1.511 p4 = 73.6 ± 7.876 p5 = 0.5722 ± 0.2167
50
Entries
59
p2 - SPP position p4 - SPP width 30
20
10
10
0
0
200
400
600
800
1000
ADC counts
Fig. 3. Amplitude distribution for one of the Cherenkov counters after an isolation cut: histogram—data; smooth curve—fit.
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
threshold, spp units
Fig. 4. Number of hits as a function of threshold: triangles— data; dots—simulation.
seen and it can be used for the amplitude calibration of the counters. As can be seen from Fig. 2, the full simulation of the detector, using the MBR event generator,1 compares well with the amplitude distributions in the data. The Cherenkov counters are not sensitive to beam halo, photons or neutrons, nor to soft charged particles which fall under the Cherenkov threshold. Still a considerable number of secondary particles is produced in the beam pipe and detected by CLC affecting significantly the occupancy. Fig. 4 shows the average number of counters (hits) fired by a pp% event in the two CLC modules as a function of the amplitude threshold used to count hits. The CLC occupancy for a pp% event is around 25% for an amplitude threshold of 0.5 (in the SPP units described above).
have an effective cross-section sa : The average number of such interactions per bunch crossing, ma ; satisfies ma fBC ¼ sa ðmÞL;
sa ðmÞ ¼ sin ea ðmÞ
ð2Þ
where ea ðmÞ is the probability to register a pp% collision in the CLC. For low luminosity we expect that ea ðm-0Þ ¼ ea ; where ea is the probability to detect a single pp% interaction (the CLC ‘‘acceptance’’). Then, ea ðmÞ ¼ ea da ðmÞ; where the term da ðmÞ describes the non-linearity of the CLC cross-section due to pile-up from multiple interactions (see Section 5). The acceptance ea can be factorized as ea ¼
eha sh þ eda sd þ edd a sdd ; sin
sin ¼ sh þ sd þ sdd ð3Þ
4. CLC acceptance Inelastic pp% interactions2 that satisfy some selection criteria a to be registered in the CLC, 1 MBR is a CDF ‘‘minimum-bias’’ event generator that includes diffractive processes and that has been tuned to reproduce CDF’s data. 2 The CLC has zero acceptance for elastic pp% events.
where sh ; sd ; sdd are the hard core, diffractive and double diffractive inelastic scattering crosssection, respectively, and eha ; eda ; edd are their a acceptances. Table 1 shows the calculated acceptances for the different inelastic processes as given by the MBR generator. The CLC is most sensitive to the hard core pp% interactions, with small contributions from diffractive processes, especially when the East–West coincidence (eEW ) is required.
60
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
Table 1 Acceptances for CLC and CLC+plug detectors calculated for different inelastic processes. The CLC amplitude threshold is 0.5 SPP and the plug energy threshold is 3 GeV: A coincidence of the East and West detectors (EW) is required. Only statistical errors are shown Detector
ehEW (%)
edd EW (%)
edEW (%)
eEW (%)
CLC CLC+plug
88.670.5 97.370.2
31.870.7 44.770.7
9.170.4 20.570.6
69.670.2 79.370.2
350 300 250 "particles", hits
The systematic error of the CLC acceptance is dominated by the error on eha : It might be relatively large if obtained solely from the simulation which is sensitive to the accurate modeling of pp% interactions and the detector material. To reduce the uncertainty on the CLC acceptance we use a reference detector with an acceptance for hard core events close to 100%: Then measuring the ratio R of pp% events detected in the CLC to those detected in the reference detector, we have ea ¼ er R; where er is the acceptance of the reference detector. Using the CLC and the CDF plug calorimeters as a reference detector, from simulation, the combined acceptance for hard core interactions is about 97%: Therefore, we expect that er can be calculated with an uncertainty better than 2%; which translates into the same level of uncertainty for the CLC acceptance.
200 150 100 50 0
0
1
2
3
4
5 µ
6
7
8
9
10
Fig. 5. The average number of hits (data: open circles, simulation: filled circles) and number of particles reconstructed from the total CLC amplitude (data: open triangles, simulation: filled squares) as a function of m:
5. Luminosity measurements 5.1. Counting of empty bunch crossings The number of pp% interactions ðnÞ in a bunch crossing follows Poisson statistics with mean m: Bunch crossings with n ¼ 0 are empty and the probability of empty crossings is P0 ðmÞ ¼ em : By measuring the fraction of empty crossings we can find m and therefore the luminosity. An equivalent method (measuring the collision rate) was used by CDF during Run I [8]. The determination on whether a bunch crossing is empty or not depends on the CLC selection criteria. For a coincidence of two CLC modules the experimental probability to see empty crossings is PEW ðmÞ ¼ ð2ee1 m 1Þeð1e0 Þm
ð4Þ
where e0 is the probability to detect no hits in both CLC modules, and e1 is the probability to detect at least one hit exclusively in one module.3 In the low luminosity approximation, when m-0; we obtain PEW ðmÞ-eeEW m ; where eEW ; is the probability of a coincidence of two CLC modules. The advantage of this method is its weak dependence on the amplitude threshold. The disadvantage is a very small probability of empty crossings at high luminosity, which becomes difficult to measure with precision due to pile-up of multiple pp% interactions and beam losses. At low luminosity the systematic uncertainty is dominated by the uncertainty on the acceptance eEW ðB2%Þ and this 3
Assuming the CLC modules are identical.
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
method is equivalent to other methods discussed below. 5.2. Counting of hits For a specific selection criteria a; which defines a collision and threshold on the amplitude of the CLC hits, the average number of pp% interactions per bunch crossing can be estimated as ma ¼ N% a =N% sa ; where N% a is the measured average number of hits per bunch crossing and N% sa is the average number of hits from a single pp% collision, which can be measured at low luminosity when m51: The CLC occupancy grows with luminosity and eventually saturates due to the finite number of counters. Therefore, an accurate measurement of the ma non-linearity is required. In order to construct bunch crossings with large m we have superimposed the counters response from many bunch crossings recorded at low luminosity. Fig. 5 shows the saturation of the number of hits for
61
increasing m; calculated for a coincidence of two CLC modules and an amplitude threshold of 0.5 SPP. We observe an excellent agreement between the data and simulation. At m ¼ 5 a correction of about 40% is needed to compensate for the nonlinearity. This could contribute a systematic uncertainty of a few percent in the luminosity measurement. At low luminosity, the hit counting method is equivalent to particle counting. In this case the systematic error of ma is dominated by variations of the CLC amplitude and by the contribution from beam losses. Since the amplitude variations are corrected with the measurements of the SPP, and since we suppress losses with the time of flight cut, we expect to reduce this systematic error down to the 1% level. During the first part of Run II we have used both the counting of empty crossings and hits for real-time luminosity measurements. Fig. 6 shows the luminosity measured in real-time by the counting of hits for one of the Tevatron stores.
Fig. 6. Real-time pp% luminosity for one of the Tevatron stores.
62
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
5.3. Counting of particles By dividing a counter’s amplitude by its SPP mean value, we can calibrate it in units of the effective number of particles crossing the counter. Then the total normalized amplitude Ap of the counters, which passed the selection criteria, is proportional to the actual number of particles detected by CLC and therefore, to the luminosity. We expect that the Ap does not saturate at high luminosity as it happens for hits. However, it may not be a linear function of m as well. Fig. 5 shows the total amplitude Ap (‘‘particles’’) as a function of m: Bunch crossings with large m were constructed from collisions recorded at low luminosity. Approximately a 7% correction needs to be applied to the luminosity (for mE5), which is much smaller than the equivalent correction for hit counting. This method is thus suitable for use at very high luminosities. The systematic uncertainty arising from the Ap non-linearity is expected to be less than 2%.
6. Conclusion The CDF luminosity monitor is a novel detector, based on gas Cherenkov counters, capable of an accurate measurement of the Tevatron luminosity in Run II by detecting inelastic pp% collisions. It allows instantaneous amplitude calibration to track detector gain drifts
and provides several methods suitable for measurements both at low and high luminosity. The detector has performed very well during the first part of Run II and the feasibility of these measurements has been demonstrated. The systematic error of the luminosity measurement is dominated by the uncertainties of the inelastic pp% cross-section ðB3%Þ; the CLC acceptance ea ðB2%Þ and the non-linearity of the CLC acceptance da ðo2%Þ: The total systematic error is expected to be below the 5% level. Work remains to be done to more accurately estimate these uncertainties. Although we did not discuss it in this paper, the process of W -boson production, with W decaying leptonically, will be used for an independent cross-check of the absolute normalization of the luminosity measured with the CLC.
References [1] [2] [3] [4] [5] [6] [7] [8]
F. Abe, et al., Phys. Rev. D 50 (1994) 5550. N. Amos, et al., Phys. Rev. Lett. 68 (1992) 2433. C. Avila, et al., Phys. Lett. B 445 (1999) 419. CDF collaboration, F. Abe, et al., Nucl. Instr. and Meth. A 271 (1988) 387. The CDF II Technical Design Report, Fermilab-Pub-96390-E, November 1996. J. Elias, et al., Nucl. Instr. and Meth. A 441 (2000) 366. D. Acosta, et al., Nucl. Instr. and Meth. A 461 (2001) 540. D. Cronin-Hennessy, et al., Nucl. Instr. and Meth. A 443 (2000) 37.
The performance of the CDF luminosity monitor D. Acostaa, S. Klimenkoa,*, J. Konigsberga, A. Korytova, G. Mitselmakhera, V. Neculaa, A. Nomerotskya, A. Pronkoa, A. Sukhanova, A. Safonova, D. Tsybycheva, S.M. Wanga, M. Wongb a
University of Florida, Corner of Museum Road & North-South Drive, Gainesville, FL 32611-8440, USA b Fermi National Laboratory, Batavia, IL, USA
Abstract We describe the initial performance of the detector used for the luminosity measurement in the CDF experiment in Run II at the Tevatron. The detector consists of low-mass gaseous Cherenkov counters with high light yield (B100 photoelectrons) and monitors the process of inelastic pp% scattering. It allows for several methods of precise luminosity measurements at peak instantaneous luminosities of 2 1032 cm2 s1 ; corresponding to an average of six pp% interactions per bunch crossing. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Hadron; Collider; Luminosity; Cherenkov
1. Introduction At hadron collider experiments the beam luminosity, traditionally, has been measured using the process of inelastic pp% scattering. It has a large cross-section sin B60 mb; measured at the Tevatron energy (1:8 TeV) by the CDF, E710 and E811 experiments [1–3] with an uncertainty of B3%: The rate of inelastic pp% interactions is given by mfBC ¼ sin L
2. CLC detector
ð1Þ
where L is the instantaneous luminosity, fBC is the rate of bunch crossings in the Tevatron and m is the average number of pp% interactions per bunch crossing. To detect inelastic pp% events efficiently a dedicated detector at small angles, operating at high rate and occupancy, is required. In Run II the *Corresponding author. E-mail address: [email protected]fl.edu (S. Klimenko).
Cherenkov luminosity counters (CLC) are being used by CDF to measure the Tevatron luminosity. The CLC is designed to measure m accurately (within a few percent) all the way up to the high luminosity regime LB2 1032 cm2 s1 expected in Run II [4,5].
There are two CLC modules in the CDF detector, installed at small angles in the proton (East) and anti-proton (West) directions with rapidity coverage between 3.75 and 4.75. Each module consists of 48 thin, long, gas-filled, Cherenkov counters. The counters are arranged around the beam-pipe in three concentric layers, with 16 counters each, and pointing to the center of the interaction region. They are built with reflective aluminized mylar sheets of 0:1 mm thick
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 1 4 4 5 - 6
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
58 200 180
photoelectrons
90000
isobutane at 1.2 atm.
160 140
80000
120 100
70000
80 60
60000
20 0
0
10
20
30
40
50
60
70
80
90
channel
Fig. 1. Number of photoelectrons produced by single particles traversing the full length of the CLC counters measured for all 96 counters.
events
40
50000 40000 30000 20000 10000
and have a conical shape. The cones in two outer layers are about 180 cm long and the inner layer counters (closer to the beam pipe) have the length of 110 cm: The Cherenkov light is detected with fast, 2:5 cm diameter, photomultiplier tubes (Hamamatsu R5800Q). The tubes have a concave– convex, 1 mm thick, quartz window for efficient collection of the ultra-violet part of Cherenkov spectra and operate at a gain of 2 105 : The performance of a single Cherenkov counter at the testbeam and the CLC design are described in detail in Refs. [6,7]. The counters are mounted inside a thin pressure vessel made of aluminum and filled with isobutane. The nominal operation point is near atmospheric pressure. However, if more light is desired, the vessel is designed to operate at maximum pressure of two atmospheres. We use isobutane as a radiator because it has one of the largest indexes of refraction for commonly available gases (1.00143) and good transparency for photons in the ultra-violet part of spectra where most of the Cherenkov light is emitted. The Cherenkov angle is 3:11 and the momentum threshold for light emission is 9:3 MeV c1 for electrons and 2:6 GeV c1 for pions. Fig. 1 shows the large light yield (B100 photoelectrons) for relativistic particles, from pp% collisions, traversing the full length of the counters.
3. CLC amplitude and occupancy for p%p collisions Since there are no Landau fluctuations for the Cherenkov light emission, we expect a narrow
0
0
0.5
1 1.5 2 amplitude, spp units
2.5
3
Fig. 2. Amplitude distribution of Cherenkov counters: solid— data, dots—simulation.
peak in the CLC amplitude distribution corresponding to single particles crossing the full length of the counters. The width (rms) of the single particle peak (SPP) is determined by the photoelectron statistics, light collection uniformity and the amplitude resolution of the photomultipliers (with B10% contribution from each source). By measuring the SPP mean values we can calibrate the CLC amplitude in units of a single particle peak. However, due to secondary interactions of particles from pp% collisions in the material surrounding the CLC, the distribution of amplitudes in the counters does not show a clear single particle peak (see Fig. 2). Secondary particles are mainly electrons and positrons from electromagnetic showers produced by p0 -gg decays in the beam pipe and vertex detector material. They contribute low amplitudes when particles traverse the counters at large angle and also create long tails at high amplitude when several particles hit the same counter. To suppress the showers and observe the single particle peak we applied an isolation cut, requiring amplitudes in the counters around a selected counter to be less than 20 photoelectrons. Fig. 3 show the amplitude distribution for one of the CLC counters after the isolation cut. The single particle peak is clearly
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62 Qie 20
10
2
40
number of hits
Chi2 / ndf = 18.45 / 32 Prob = 0.9732 p0 = 0.996 ± 0.4417 p1 = 0.01512 ± 0.002215 p2 = 370.2 ± 10.12 p3 = 13.23 ± 1.511 p4 = 73.6 ± 7.876 p5 = 0.5722 ± 0.2167
50
Entries
59
p2 - SPP position p4 - SPP width 30
20
10
10
0
0
200
400
600
800
1000
ADC counts
Fig. 3. Amplitude distribution for one of the Cherenkov counters after an isolation cut: histogram—data; smooth curve—fit.
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
threshold, spp units
Fig. 4. Number of hits as a function of threshold: triangles— data; dots—simulation.
seen and it can be used for the amplitude calibration of the counters. As can be seen from Fig. 2, the full simulation of the detector, using the MBR event generator,1 compares well with the amplitude distributions in the data. The Cherenkov counters are not sensitive to beam halo, photons or neutrons, nor to soft charged particles which fall under the Cherenkov threshold. Still a considerable number of secondary particles is produced in the beam pipe and detected by CLC affecting significantly the occupancy. Fig. 4 shows the average number of counters (hits) fired by a pp% event in the two CLC modules as a function of the amplitude threshold used to count hits. The CLC occupancy for a pp% event is around 25% for an amplitude threshold of 0.5 (in the SPP units described above).
have an effective cross-section sa : The average number of such interactions per bunch crossing, ma ; satisfies ma fBC ¼ sa ðmÞL;
sa ðmÞ ¼ sin ea ðmÞ
ð2Þ
where ea ðmÞ is the probability to register a pp% collision in the CLC. For low luminosity we expect that ea ðm-0Þ ¼ ea ; where ea is the probability to detect a single pp% interaction (the CLC ‘‘acceptance’’). Then, ea ðmÞ ¼ ea da ðmÞ; where the term da ðmÞ describes the non-linearity of the CLC cross-section due to pile-up from multiple interactions (see Section 5). The acceptance ea can be factorized as ea ¼
eha sh þ eda sd þ edd a sdd ; sin
sin ¼ sh þ sd þ sdd ð3Þ
4. CLC acceptance Inelastic pp% interactions2 that satisfy some selection criteria a to be registered in the CLC, 1 MBR is a CDF ‘‘minimum-bias’’ event generator that includes diffractive processes and that has been tuned to reproduce CDF’s data. 2 The CLC has zero acceptance for elastic pp% events.
where sh ; sd ; sdd are the hard core, diffractive and double diffractive inelastic scattering crosssection, respectively, and eha ; eda ; edd are their a acceptances. Table 1 shows the calculated acceptances for the different inelastic processes as given by the MBR generator. The CLC is most sensitive to the hard core pp% interactions, with small contributions from diffractive processes, especially when the East–West coincidence (eEW ) is required.
60
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
Table 1 Acceptances for CLC and CLC+plug detectors calculated for different inelastic processes. The CLC amplitude threshold is 0.5 SPP and the plug energy threshold is 3 GeV: A coincidence of the East and West detectors (EW) is required. Only statistical errors are shown Detector
ehEW (%)
edd EW (%)
edEW (%)
eEW (%)
CLC CLC+plug
88.670.5 97.370.2
31.870.7 44.770.7
9.170.4 20.570.6
69.670.2 79.370.2
350 300 250 "particles", hits
The systematic error of the CLC acceptance is dominated by the error on eha : It might be relatively large if obtained solely from the simulation which is sensitive to the accurate modeling of pp% interactions and the detector material. To reduce the uncertainty on the CLC acceptance we use a reference detector with an acceptance for hard core events close to 100%: Then measuring the ratio R of pp% events detected in the CLC to those detected in the reference detector, we have ea ¼ er R; where er is the acceptance of the reference detector. Using the CLC and the CDF plug calorimeters as a reference detector, from simulation, the combined acceptance for hard core interactions is about 97%: Therefore, we expect that er can be calculated with an uncertainty better than 2%; which translates into the same level of uncertainty for the CLC acceptance.
200 150 100 50 0
0
1
2
3
4
5 µ
6
7
8
9
10
Fig. 5. The average number of hits (data: open circles, simulation: filled circles) and number of particles reconstructed from the total CLC amplitude (data: open triangles, simulation: filled squares) as a function of m:
5. Luminosity measurements 5.1. Counting of empty bunch crossings The number of pp% interactions ðnÞ in a bunch crossing follows Poisson statistics with mean m: Bunch crossings with n ¼ 0 are empty and the probability of empty crossings is P0 ðmÞ ¼ em : By measuring the fraction of empty crossings we can find m and therefore the luminosity. An equivalent method (measuring the collision rate) was used by CDF during Run I [8]. The determination on whether a bunch crossing is empty or not depends on the CLC selection criteria. For a coincidence of two CLC modules the experimental probability to see empty crossings is PEW ðmÞ ¼ ð2ee1 m 1Þeð1e0 Þm
ð4Þ
where e0 is the probability to detect no hits in both CLC modules, and e1 is the probability to detect at least one hit exclusively in one module.3 In the low luminosity approximation, when m-0; we obtain PEW ðmÞ-eeEW m ; where eEW ; is the probability of a coincidence of two CLC modules. The advantage of this method is its weak dependence on the amplitude threshold. The disadvantage is a very small probability of empty crossings at high luminosity, which becomes difficult to measure with precision due to pile-up of multiple pp% interactions and beam losses. At low luminosity the systematic uncertainty is dominated by the uncertainty on the acceptance eEW ðB2%Þ and this 3
Assuming the CLC modules are identical.
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
method is equivalent to other methods discussed below. 5.2. Counting of hits For a specific selection criteria a; which defines a collision and threshold on the amplitude of the CLC hits, the average number of pp% interactions per bunch crossing can be estimated as ma ¼ N% a =N% sa ; where N% a is the measured average number of hits per bunch crossing and N% sa is the average number of hits from a single pp% collision, which can be measured at low luminosity when m51: The CLC occupancy grows with luminosity and eventually saturates due to the finite number of counters. Therefore, an accurate measurement of the ma non-linearity is required. In order to construct bunch crossings with large m we have superimposed the counters response from many bunch crossings recorded at low luminosity. Fig. 5 shows the saturation of the number of hits for
61
increasing m; calculated for a coincidence of two CLC modules and an amplitude threshold of 0.5 SPP. We observe an excellent agreement between the data and simulation. At m ¼ 5 a correction of about 40% is needed to compensate for the nonlinearity. This could contribute a systematic uncertainty of a few percent in the luminosity measurement. At low luminosity, the hit counting method is equivalent to particle counting. In this case the systematic error of ma is dominated by variations of the CLC amplitude and by the contribution from beam losses. Since the amplitude variations are corrected with the measurements of the SPP, and since we suppress losses with the time of flight cut, we expect to reduce this systematic error down to the 1% level. During the first part of Run II we have used both the counting of empty crossings and hits for real-time luminosity measurements. Fig. 6 shows the luminosity measured in real-time by the counting of hits for one of the Tevatron stores.
Fig. 6. Real-time pp% luminosity for one of the Tevatron stores.
62
D. Acosta et al. / Nuclear Instruments and Methods in Physics Research A 494 (2002) 57–62
5.3. Counting of particles By dividing a counter’s amplitude by its SPP mean value, we can calibrate it in units of the effective number of particles crossing the counter. Then the total normalized amplitude Ap of the counters, which passed the selection criteria, is proportional to the actual number of particles detected by CLC and therefore, to the luminosity. We expect that the Ap does not saturate at high luminosity as it happens for hits. However, it may not be a linear function of m as well. Fig. 5 shows the total amplitude Ap (‘‘particles’’) as a function of m: Bunch crossings with large m were constructed from collisions recorded at low luminosity. Approximately a 7% correction needs to be applied to the luminosity (for mE5), which is much smaller than the equivalent correction for hit counting. This method is thus suitable for use at very high luminosities. The systematic uncertainty arising from the Ap non-linearity is expected to be less than 2%.
6. Conclusion The CDF luminosity monitor is a novel detector, based on gas Cherenkov counters, capable of an accurate measurement of the Tevatron luminosity in Run II by detecting inelastic pp% collisions. It allows instantaneous amplitude calibration to track detector gain drifts
and provides several methods suitable for measurements both at low and high luminosity. The detector has performed very well during the first part of Run II and the feasibility of these measurements has been demonstrated. The systematic error of the luminosity measurement is dominated by the uncertainties of the inelastic pp% cross-section ðB3%Þ; the CLC acceptance ea ðB2%Þ and the non-linearity of the CLC acceptance da ðo2%Þ: The total systematic error is expected to be below the 5% level. Work remains to be done to more accurately estimate these uncertainties. Although we did not discuss it in this paper, the process of W -boson production, with W decaying leptonically, will be used for an independent cross-check of the absolute normalization of the luminosity measured with the CLC.
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