- Email: [email protected]
A precision measurement of direct CP violation in the decay of neutral kaons into two pions
Nuclear Physics B (Proc. Suppl.) 120 (2003) 277-282
ELSEVIER
A Precision Measurement of Direct CP Violation Kaons into Two Pions. Dmitry
www.clscvier.com/locatclnpc
in the Decay of Neutral
Madigozhin
Joint Institute
for Nuclear Research, 141980 Dubna, Russia.
For the NA48 Collaboration The direct CP violation parameter Re(e’/e) has been measured from the decay rates of neutral kaons into two pions using the NA48 detector at the CERN SPS. The 2001 running period data was collected under varied conditions compared to earlier years (1997-99). The new data result is Re(e’/e) = (13.7 f 3.1) x 10e4. The overall value of Re(e’/e) = (14.7 f 2.2) x 10e4 is obtained from the complete NA48 data set.
1. Introduction
2. The
CP violation in kaon decays can occur via the mixing of CP eigenstates. It is called indirect CP violation and represented by the mixing parameter E. The interference of amplitudes with different isospins in the decay process leads to the another kind of CP violation. It is represented by the amplitude asymmetry parameter E’and is called direct CP violation. It is convenient to measure the double ratio R of decay widths, which is related to E’as follows:
The four decay modes are collected simultaneously and in the same decay region, which minimizes the sensitivity of the measurement to the variations in beam intensity and detection efficiency. K,O and K,O decays are provided by two almost collinear beams with similar momentum spectra, converging to the centre of the main detector. KE decays are weighted by the function of their proper lifetime, such that the Kz decay distribution becomes similar to that of Kg. To be insensitive to the small beam momentum spectra differences, the analysis is performed in bins of kaon energy. In this way, the acceptances almost cancel in the double ratio R, and only small remaining effects of the beam geometries need to be corrected using Monte Carlo simulation. K,O decays are distinguished from K,” ones by a coincidence between the decay time and the time of protons producing the K,O beam. The measured double ratio is sensitive only to the differences in misidentification probabilities between the two decay modes. A high-resolution detectors are used to detect the decay final states to minimize residual backgrounds which do not cancel in the double ratio and are taken into account by the corrections.
R = IyK,O -+ 7r07r0)IyK,O -+ 7r+7r-) IyK,o + 7+w) I l-yK,o + 7r+7r-) w 1- 6
x
Re(d/c)
(1)
Recently, NA48 published a result of Re(d/e) = (15.3 f 2.6) x 10v4, based on the data collected in 1997-99 [l], and KTeV presented a preliminary result of Re(d/e) = (20.7 f 2.8) x 1O-4 on data accumulated in 199697 [2]. These results confirmed the existence of a direct CP-violation component. This presentation reports a measurement of Re(d/E) performed using the 2001 data sample, recorded in somewhat changed conditions in the NA48 experiment. The drift chambers have been rebuilt after the damage in 1999, and the data in 2001 have been taken at a 30% lower beam intensity to check an intensity-related effects.
method
0920-5632/03/$- see front matter 0 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(03)01915-7
278
3. Beams
D. Mdgozhin/Nucleur
Physics B (Proc. Suppl.) 120 (2003) 277-282
and detectors
The K,” and K,Obeams are produced in two different targets by protons from the same CERN SPS beam. In the 2001 run the SPS had a cycle time of 16.8 s (14.4 s in 1998-99) with a spill length of 5.2 s (2.38 s in 1998-99) and a proton momentum of 400 GeV (450 GeV in 199899). KF/Kz intensity ratio is maintained stable to within &lo%. The primary proton beam (z 2.4 x 1012 protons per pulse) impinges on the KE target with an incidence angle of 2.4 mrad relative to the K,Obeam axes. Then charged particles are swept away from the outgoing beam by bending magnets. The fiducial region for the neutral beam starts 126 m downstream of the target. Here the beam is dominated by long-lived kaons, neutrons and photons. The primary protons not interacting in the K,” target are directed onto the bent mono-crystal of silicon [3]. A small fraction of them is deviated to produce a collimated beam x 5 x lo7 ppp, which is then directed to the K,O target, located 72 mm above the K,” beam axis and only 6 m upstream of the fiducial region. Two-pion decays from this beam come almost exclusively from K,O decays. The tagging station (Tagger) is located on the KS0 proton beam after the bent crystal. It consists of two ladders of 12 scintillator strips each, covering the beam horizontally and vertically. Two pulses 4-5 ns apart can be resolved. The beginning of the Kz decay region is defined by an anticounter (AKS), located at the exit of the K!j! collimator. Charged particles are measured by a magnetic spectrometer [4] composed of 4 drift chambers with a dipole magnet inducing a transverse momentum-kick of 265 MeV/c. The average efficiency per plane is 99.5 %, with a radial uniformity better than 0.2%. The spatial resolution is 96 pm, and momentum one is a(p)/p = 0.48% f 0.009% x p, where momentum p is in GeV/c The spectrometer is followed by a scintillator hodoscope. Fast logic combines the strip signals for use in the @n- trigger. A liquid Krypton calorimeter (LKr) [5] is
placed downstream of the hodoscope. It is 27 radiation length long and fully contain electromagnetic showers with energies up to 100 GeV. The energy resolution of the calorimeter is o(E)/E = (3.2 f 0.2)%/fiE) + (9 f 1)%/E + (0.42 f 0.05)%, with E in GeV. LKr is segmented on 13000 cells (each with 2 cm x 2cm cross-section) and is used to reconstruct K -+ 27r” decays. It is also used, together with an ironscintillator hadron calorimeter, to measure the total deposited energy for triggering purposes. Muon veto counters (used to identify KcLs background decays) are placed at the end of the beam line. Two beam intensities are measured by the beam counters: one is located at the extreme end of the Kz beam line (KE monitor) and the other (Kz monitor) views the Kz target station. For 2001 year data taking, another K,” monitor with a higher counting rate was added and a KS0 beam monitor near the tagging station was installed. These allow better measurements of the beam structures to be made down to a time scale of x 200ns. 4. Event
reconstruction
and selection
K + rr”7ro decays are triggered requiring LKr energy deposit > 50 GeV, a centre of energy to the beam axis distance smaller than 25 cm, and a decay vertex less than 5 K,” lifetimes from the beginning of the decay volume. Photon showers in the range 3-100 GeV are used. The shower position should be more than 15 cm away from the beam axis, more than 11 cm away from the outer edges of the calorimeter and more than 2 cm away from a defective calorimeter channel (a 0.4% of the channels). Four showers from the non0 decay have to be within f5 ns of their average time. Event is rejected if it has an additional cluster of energy above 1.5 GeV and within f3 ns of the kaon decay candidate (to reduce the background from K,” -+ 37~~ decays). The distance D from the decay vertex to LKr is computed as follows:
Here Ei, xi, yi are the energy and position
of
D. Mudigozhin/Nuclear Physics B (Proc. Suppl.) 120 (2003) 277-282
279
-114m
-126m
Figure 1. A schematic view of the beam line (not to scale). the i - th cluster. The average resolution on D is about 55 cm, and the resolution on the kaon energy is x 0.5%. The invariant masses ml and m2 of the two photon pairs are computed using D and then compared to the nominal x0 mass (m,o) using the following variable: x2 =
[
(ml +
m2)/2
g+
[(m l -
m2)P12
cl-
- m,o
I” + (3)
cr+ and U- are the corresponding resolutions parametrized from the data as a function of the lowest photon energy. The minimal x2 photons pairing is kept for each candidate and a cut x2 < 13.5 is applied. The r+riT- decays are triggered with a twolevel trigger system. First level trigger requires an opposite quadrant coincidence in the scintillator hodoscope, hits in the first drift chamber, and the total calorimetric energy above 35 GeV. The second level trigger, consisting of hardware coordinate builders and a farm of asynchronous microprocessors, reconstructs tracks using data from the drift chambers and applies a loose cuts to select the K -+ 7riT+r- candidates.
A vertex position is calculated offline for each pair of tracks with opposite charge. The longitudinal vertex position resolution is about 50 cm, whereas the transverse position resolution is around 2 mm. Since the beams are separated vertically by about 6 cm, a clean identification of the beam by the vertex position is applicable for the 7r+r- decays, that is impossible for the r”7ro ones. The tracks with momenta > lOGeV/c and not closer than 12 cm to the centre of each chamber are accepted. The tracks closest approach for the vertex is required to be less than 3 cm. The tracks are required to be within the acceptance of the LKr calorimeter and of the muon veto system, in order to ensure proper electron and muon identification. The kaon energy is computed from the opening angle 0 of the two tracks and from the ratio of their momenta pl and ~2, assuming K -+ r+rTTdecay: EK =
-pm9
where p = E + .E + 2. This measurement of the kaon energy 1s independent of the absolute magnetic field and relies mostly on the knowledge of the geometry of the detector.
280
D. Madigozhin /Nuclear
Physics B (Pmt.
A cut is applied to the asymmetry A = Ipl p21/(p1 +p21: A < min(0.62,1.08-0.0052 x EK), where EK is in GeV. It is intended to remove the A + p7r- decays and asymmetric kaon decays for which the Monte Carlo simulation is more critical. To reject background from semileptonic K,” decays, events with a muon veto hits near the track impact point as well as events with ELK~/~DC~ > 0.8 (for one of the tracks) are rejected. Here pDCh is a momentum of a track, and ELKS is the energy of the LKr cluster, associated with the track. The reconstructed kaon mass m,, resolution is typically 2.5 MeV/c2. An energy-dependent cut at f3a, is applied at the mass. The variable pk is defined as the kaon momentum component orthogonal to the line joining the production target and the impact point of the kaon on the first drift chamber plane. It is used to reduct further semileptonic decays background by the cut pb < 2 x 10m4 GeV2/c2. A decay is labelled K,O if a coincidence is found (within a f2 ns interval) between the event time and a proton time measured by the Tagger. The tagging inefficiency (1.12 f 0.03) x low4 as well as the accidental mistagging probability (8.115 f 0.010) x 10m2 are directly measured in the r+w- mode. The difference of these probabilities between the 7r”ro and 7rIr+7r-cases is calculated using the 3n0 decays coming almost entirely from the K,” beam, alongside with the side tagging windows technique. The mistagging probability difference is caused by the higher nIr+revents losses due to the accidental activity. It leads to the bias of the beam intensity seen by registered ~+7r- events. 5. Corrections ties
and
systematic
uncertain-
A small inefficiency of the TOTO trigger is found to be KZ-KZ symmetric and no correction to R need to be applied. For the rIT+r- case the correction is (5.2 f 3.6) x 10e4. The kaon proper time used to count events is chosen to be 0 < r < 3.5rs, where r = 0 is defined at the position of the AKS counter and 17-s is Kg mean lifetime. For K,” events, the proper time cut is applied on reconstructed r, while for
Suppl.) 120 (2003) 277-282
K,” events the cut at r = 0 is applied using the AKS. The veto inefficiency is 0.36% for 7r07roand 0.22% for T+T- events. The correction to be applied to the double ratio is (1.2 f 0.3) x 10m4. The background to the 7r”ro mode comes uniquely from K,” + 3n0 decays. It is estimated from the K,” and K,O distributions of x2 using the Monte Carlo to take into account the nonGaussian tails in the calorimeter resolution. The nor0 background correction is (-5.6f2.0) x 10W4. The residual Ke3 and KP3 backgrounds in 7r+r- mode are estimated by defining two control regions in the rnrrX - pT’ plane, populated by the two kinds of nfrbackground events with a different ratio. The resulting correction on the double ratio is (14.2 f 3.0) x 10m4 In the Kz beam the ph cut (applied only in the ~+7r- mode) is stronger than the extrapolated kaon impact point radius cut (the last one is almost symmetrical between the 7r+r- and n”rro modes). It leads to the excess of the collimator scattered events in the r”7ro mode. The correction to R needed is (-8.8 f 2.0) x 10m4. The K,” and K,O acceptances are made very similar in both modes by weighting K,” events according to their proper decay time. A small difference remains due to the differences in the beam sizes and directions. This residual correction is computed using a large-statistics Monte Carlo simulation (4 x lo* decays per mode). The correction to R for the acceptance is (21.9 f 3.5(MC stat) f 4.0(syst)) x 1o-4 The kaon energy and proper time in r”7ro mode rely on the measurements of the photon energies and positions. The absolute energy scale is set such that the average Z position of the reconstructed K!j’ + K’~FO decays around the AKS matches the value found in a Monte Carlo simulation. The scale is checked using the data taken during special runs with a r- beam striking two thin targets located near the beginning and the end of the fiducial decay region, producing 7~’ and q with known decay positions. The uncertainty on the double ratio due to the energy scale is f2 x 10m4. Non-linearities in the energy response are studied using special runs data and Ke3 decays, where the electron energy is measured in calorimeter as
D. Madigozhin/Nuclear
Physics B (Proc. Suppl.) 120 (2003) 277-282
well as in the drift chamber. Taking into account larger deviation from linearity observed for the photon energies < 6 GeV, the resulting uncertainty on the double ratio is f3.8 x 10e4. The uniformity of the calorimeter response over its surface is optimized using Ke3 decays and data from special runs. The corresponding systematic uncertainty on the double ratio is f1.6 x 10P4. The uncertainties due to the photons positions error and non-Gaussian tails in the energy response are also taken into account. Adding them in quadrature, the systematic error on the double ratio from the photon reconstruction is found to be f5.3 x 10P4. The uncertainty from the 7riT+7r-decays reconstruction takes into account the possible detector geometry deviations. Its value is f2.8 x 10e4. 6. Intensity
effects
The overlap of accidental activity with a good event in the detectors may result in the net event loss effect in the reconstruction or the selection. This effect is cancel with a good precision in double ratio R due to the simultaneous collection of data in the four channels and due to the very similar illumination of the detector by the K’jJ and K,O beams. The possible residual effect can be separated into two components. The first one (intensity difference effect) is given by: AR = Ax x AI/I
281
intensity difference is 1.1 x low4 The second component of the accidental effect (illumination difference) has been estimated from the overlay samples, computing separately the losses for K,O and K,” events. It has been performed using both data and Monte Carlo origIn the first case, the value obinal events. tained is 0.9 f 3.5 x 10e4, in the second it is (1.4 f 2.8) x 10d4. As expected, there is no evidence of a significant effect, and we use as uncertainty on the double ratio f3.0 x low4 . Combining the two above uncertainties in quadrature, the total uncertainty on R from accidental effects is f3.1 x 10U4. It is dominated by the statistical error of the overlay procedure. Studies of the additional detector activity generated by the same proton which produced the good event (in-time activity) allow an upper bound on the effect on R of 1 x 10e4 to be set. 7. Result The measured R in kaon energy bins is shown on the Fig. 2. The extreme bins (outside the region 70-170 GeV) are not used for the final calculation. They are plotted to check the absence of the energy dependence.
(5)
where Ax is the difference between the mean losses in r+w- and 7r07romodes, and AI/I is the difference in the mean K: beam (the main source of accidental decays) intensity as seen by Kz and K: events. AI/I have been measured from the activity in the main detectors as well as from the beam monitors data and is consistent with Of 1%. Ax is estimated by overlaying data and Monte Carlo events with the beam monitor (random) triggers taken in proportion to the beam intensity. It is measured also from the comparison of the normal Kz + Kz beam runs with pure Kz runs, in which the accidental activity is much smaller. The resulting estimate of Ax is (1.0 f 0.5)% So the uncertainty on the double ratio related to the
095
Figure 2. Measured double ratio R in kaon energy bins
282
D. Mudigozhin/Nuclear Physics B (Proc. Suppl.) 120 (2003) 277-282
The final result for the double ratio from 2001 data set is R = 0.99181 f 0.00147 f 0.00065 f 0.00110, where the first error is the statistical error for the 2n samples, second is the systematic error coming from the statistics of the control samples, and the third is the contribution of the other systematic uncertainties. The corresponding value of the direct @ -violation parameter is Re(d/e)
= (13.7 f 2.5 f 1.1 f 1.5) x low4 = (13.7 f 3.1) x 1o-4
(6)
It is in good agreement with the published value from the 1997-99 data: Re(d/c) = (15.3 f 2.6) x 10-4. Taking into account the partially correlated systematic uncertainty, the combined, final result from the NA48 experiment is: Re(d/c)
= (14.7 f 2.2) x lop4
(7)
REFERENCES 1. A. Lai et al., Eur. Phys. Jour. C 22 (2001) 231. 2. A. [KTeV Collaboration] in Glazov F.Costantini et al.(ed), Proc. of Int. Conference on Kaon Physics, Frascati Physics Serie 26, 2001, p.115. 3. N. Doble, L.Gatignon, P.Grafstrom, Nucl. Instr. and Meth. B 119 (1996) 181. 4. D. Bederede et. al., Nucl. Instr. and Meth. A 367 (1995) 88. 5. G. Unal [NA48 Collaboration] B. Aubert (ed), Proc. IX Int. Conf. on Calorimetry in HEP, Frascati Physics Serie 21, 2001 p.361.
ELSEVIER
A Precision Measurement of Direct CP Violation Kaons into Two Pions. Dmitry
www.clscvier.com/locatclnpc
in the Decay of Neutral
Madigozhin
Joint Institute
for Nuclear Research, 141980 Dubna, Russia.
For the NA48 Collaboration The direct CP violation parameter Re(e’/e) has been measured from the decay rates of neutral kaons into two pions using the NA48 detector at the CERN SPS. The 2001 running period data was collected under varied conditions compared to earlier years (1997-99). The new data result is Re(e’/e) = (13.7 f 3.1) x 10e4. The overall value of Re(e’/e) = (14.7 f 2.2) x 10e4 is obtained from the complete NA48 data set.
1. Introduction
2. The
CP violation in kaon decays can occur via the mixing of CP eigenstates. It is called indirect CP violation and represented by the mixing parameter E. The interference of amplitudes with different isospins in the decay process leads to the another kind of CP violation. It is represented by the amplitude asymmetry parameter E’and is called direct CP violation. It is convenient to measure the double ratio R of decay widths, which is related to E’as follows:
The four decay modes are collected simultaneously and in the same decay region, which minimizes the sensitivity of the measurement to the variations in beam intensity and detection efficiency. K,O and K,O decays are provided by two almost collinear beams with similar momentum spectra, converging to the centre of the main detector. KE decays are weighted by the function of their proper lifetime, such that the Kz decay distribution becomes similar to that of Kg. To be insensitive to the small beam momentum spectra differences, the analysis is performed in bins of kaon energy. In this way, the acceptances almost cancel in the double ratio R, and only small remaining effects of the beam geometries need to be corrected using Monte Carlo simulation. K,O decays are distinguished from K,” ones by a coincidence between the decay time and the time of protons producing the K,O beam. The measured double ratio is sensitive only to the differences in misidentification probabilities between the two decay modes. A high-resolution detectors are used to detect the decay final states to minimize residual backgrounds which do not cancel in the double ratio and are taken into account by the corrections.
R = IyK,O -+ 7r07r0)IyK,O -+ 7r+7r-) IyK,o + 7+w) I l-yK,o + 7r+7r-) w 1- 6
x
Re(d/c)
(1)
Recently, NA48 published a result of Re(d/e) = (15.3 f 2.6) x 10v4, based on the data collected in 1997-99 [l], and KTeV presented a preliminary result of Re(d/e) = (20.7 f 2.8) x 1O-4 on data accumulated in 199697 [2]. These results confirmed the existence of a direct CP-violation component. This presentation reports a measurement of Re(d/E) performed using the 2001 data sample, recorded in somewhat changed conditions in the NA48 experiment. The drift chambers have been rebuilt after the damage in 1999, and the data in 2001 have been taken at a 30% lower beam intensity to check an intensity-related effects.
method
0920-5632/03/$- see front matter 0 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(03)01915-7
278
3. Beams
D. Mdgozhin/Nucleur
Physics B (Proc. Suppl.) 120 (2003) 277-282
and detectors
The K,” and K,Obeams are produced in two different targets by protons from the same CERN SPS beam. In the 2001 run the SPS had a cycle time of 16.8 s (14.4 s in 1998-99) with a spill length of 5.2 s (2.38 s in 1998-99) and a proton momentum of 400 GeV (450 GeV in 199899). KF/Kz intensity ratio is maintained stable to within &lo%. The primary proton beam (z 2.4 x 1012 protons per pulse) impinges on the KE target with an incidence angle of 2.4 mrad relative to the K,Obeam axes. Then charged particles are swept away from the outgoing beam by bending magnets. The fiducial region for the neutral beam starts 126 m downstream of the target. Here the beam is dominated by long-lived kaons, neutrons and photons. The primary protons not interacting in the K,” target are directed onto the bent mono-crystal of silicon [3]. A small fraction of them is deviated to produce a collimated beam x 5 x lo7 ppp, which is then directed to the K,O target, located 72 mm above the K,” beam axis and only 6 m upstream of the fiducial region. Two-pion decays from this beam come almost exclusively from K,O decays. The tagging station (Tagger) is located on the KS0 proton beam after the bent crystal. It consists of two ladders of 12 scintillator strips each, covering the beam horizontally and vertically. Two pulses 4-5 ns apart can be resolved. The beginning of the Kz decay region is defined by an anticounter (AKS), located at the exit of the K!j! collimator. Charged particles are measured by a magnetic spectrometer [4] composed of 4 drift chambers with a dipole magnet inducing a transverse momentum-kick of 265 MeV/c. The average efficiency per plane is 99.5 %, with a radial uniformity better than 0.2%. The spatial resolution is 96 pm, and momentum one is a(p)/p = 0.48% f 0.009% x p, where momentum p is in GeV/c The spectrometer is followed by a scintillator hodoscope. Fast logic combines the strip signals for use in the @n- trigger. A liquid Krypton calorimeter (LKr) [5] is
placed downstream of the hodoscope. It is 27 radiation length long and fully contain electromagnetic showers with energies up to 100 GeV. The energy resolution of the calorimeter is o(E)/E = (3.2 f 0.2)%/fiE) + (9 f 1)%/E + (0.42 f 0.05)%, with E in GeV. LKr is segmented on 13000 cells (each with 2 cm x 2cm cross-section) and is used to reconstruct K -+ 27r” decays. It is also used, together with an ironscintillator hadron calorimeter, to measure the total deposited energy for triggering purposes. Muon veto counters (used to identify KcLs background decays) are placed at the end of the beam line. Two beam intensities are measured by the beam counters: one is located at the extreme end of the Kz beam line (KE monitor) and the other (Kz monitor) views the Kz target station. For 2001 year data taking, another K,” monitor with a higher counting rate was added and a KS0 beam monitor near the tagging station was installed. These allow better measurements of the beam structures to be made down to a time scale of x 200ns. 4. Event
reconstruction
and selection
K + rr”7ro decays are triggered requiring LKr energy deposit > 50 GeV, a centre of energy to the beam axis distance smaller than 25 cm, and a decay vertex less than 5 K,” lifetimes from the beginning of the decay volume. Photon showers in the range 3-100 GeV are used. The shower position should be more than 15 cm away from the beam axis, more than 11 cm away from the outer edges of the calorimeter and more than 2 cm away from a defective calorimeter channel (a 0.4% of the channels). Four showers from the non0 decay have to be within f5 ns of their average time. Event is rejected if it has an additional cluster of energy above 1.5 GeV and within f3 ns of the kaon decay candidate (to reduce the background from K,” -+ 37~~ decays). The distance D from the decay vertex to LKr is computed as follows:
Here Ei, xi, yi are the energy and position
of
D. Mudigozhin/Nuclear Physics B (Proc. Suppl.) 120 (2003) 277-282
279
-114m
-126m
Figure 1. A schematic view of the beam line (not to scale). the i - th cluster. The average resolution on D is about 55 cm, and the resolution on the kaon energy is x 0.5%. The invariant masses ml and m2 of the two photon pairs are computed using D and then compared to the nominal x0 mass (m,o) using the following variable: x2 =
[
(ml +
m2)/2
g+
[(m l -
m2)P12
cl-
- m,o
I” + (3)
cr+ and U- are the corresponding resolutions parametrized from the data as a function of the lowest photon energy. The minimal x2 photons pairing is kept for each candidate and a cut x2 < 13.5 is applied. The r+riT- decays are triggered with a twolevel trigger system. First level trigger requires an opposite quadrant coincidence in the scintillator hodoscope, hits in the first drift chamber, and the total calorimetric energy above 35 GeV. The second level trigger, consisting of hardware coordinate builders and a farm of asynchronous microprocessors, reconstructs tracks using data from the drift chambers and applies a loose cuts to select the K -+ 7riT+r- candidates.
A vertex position is calculated offline for each pair of tracks with opposite charge. The longitudinal vertex position resolution is about 50 cm, whereas the transverse position resolution is around 2 mm. Since the beams are separated vertically by about 6 cm, a clean identification of the beam by the vertex position is applicable for the 7r+r- decays, that is impossible for the r”7ro ones. The tracks with momenta > lOGeV/c and not closer than 12 cm to the centre of each chamber are accepted. The tracks closest approach for the vertex is required to be less than 3 cm. The tracks are required to be within the acceptance of the LKr calorimeter and of the muon veto system, in order to ensure proper electron and muon identification. The kaon energy is computed from the opening angle 0 of the two tracks and from the ratio of their momenta pl and ~2, assuming K -+ r+rTTdecay: EK =
-pm9
where p = E + .E + 2. This measurement of the kaon energy 1s independent of the absolute magnetic field and relies mostly on the knowledge of the geometry of the detector.
280
D. Madigozhin /Nuclear
Physics B (Pmt.
A cut is applied to the asymmetry A = Ipl p21/(p1 +p21: A < min(0.62,1.08-0.0052 x EK), where EK is in GeV. It is intended to remove the A + p7r- decays and asymmetric kaon decays for which the Monte Carlo simulation is more critical. To reject background from semileptonic K,” decays, events with a muon veto hits near the track impact point as well as events with ELK~/~DC~ > 0.8 (for one of the tracks) are rejected. Here pDCh is a momentum of a track, and ELKS is the energy of the LKr cluster, associated with the track. The reconstructed kaon mass m,, resolution is typically 2.5 MeV/c2. An energy-dependent cut at f3a, is applied at the mass. The variable pk is defined as the kaon momentum component orthogonal to the line joining the production target and the impact point of the kaon on the first drift chamber plane. It is used to reduct further semileptonic decays background by the cut pb < 2 x 10m4 GeV2/c2. A decay is labelled K,O if a coincidence is found (within a f2 ns interval) between the event time and a proton time measured by the Tagger. The tagging inefficiency (1.12 f 0.03) x low4 as well as the accidental mistagging probability (8.115 f 0.010) x 10m2 are directly measured in the r+w- mode. The difference of these probabilities between the 7r”ro and 7rIr+7r-cases is calculated using the 3n0 decays coming almost entirely from the K,” beam, alongside with the side tagging windows technique. The mistagging probability difference is caused by the higher nIr+revents losses due to the accidental activity. It leads to the bias of the beam intensity seen by registered ~+7r- events. 5. Corrections ties
and
systematic
uncertain-
A small inefficiency of the TOTO trigger is found to be KZ-KZ symmetric and no correction to R need to be applied. For the rIT+r- case the correction is (5.2 f 3.6) x 10e4. The kaon proper time used to count events is chosen to be 0 < r < 3.5rs, where r = 0 is defined at the position of the AKS counter and 17-s is Kg mean lifetime. For K,” events, the proper time cut is applied on reconstructed r, while for
Suppl.) 120 (2003) 277-282
K,” events the cut at r = 0 is applied using the AKS. The veto inefficiency is 0.36% for 7r07roand 0.22% for T+T- events. The correction to be applied to the double ratio is (1.2 f 0.3) x 10m4. The background to the 7r”ro mode comes uniquely from K,” + 3n0 decays. It is estimated from the K,” and K,O distributions of x2 using the Monte Carlo to take into account the nonGaussian tails in the calorimeter resolution. The nor0 background correction is (-5.6f2.0) x 10W4. The residual Ke3 and KP3 backgrounds in 7r+r- mode are estimated by defining two control regions in the rnrrX - pT’ plane, populated by the two kinds of nfrbackground events with a different ratio. The resulting correction on the double ratio is (14.2 f 3.0) x 10m4 In the Kz beam the ph cut (applied only in the ~+7r- mode) is stronger than the extrapolated kaon impact point radius cut (the last one is almost symmetrical between the 7r+r- and n”rro modes). It leads to the excess of the collimator scattered events in the r”7ro mode. The correction to R needed is (-8.8 f 2.0) x 10m4. The K,” and K,O acceptances are made very similar in both modes by weighting K,” events according to their proper decay time. A small difference remains due to the differences in the beam sizes and directions. This residual correction is computed using a large-statistics Monte Carlo simulation (4 x lo* decays per mode). The correction to R for the acceptance is (21.9 f 3.5(MC stat) f 4.0(syst)) x 1o-4 The kaon energy and proper time in r”7ro mode rely on the measurements of the photon energies and positions. The absolute energy scale is set such that the average Z position of the reconstructed K!j’ + K’~FO decays around the AKS matches the value found in a Monte Carlo simulation. The scale is checked using the data taken during special runs with a r- beam striking two thin targets located near the beginning and the end of the fiducial decay region, producing 7~’ and q with known decay positions. The uncertainty on the double ratio due to the energy scale is f2 x 10m4. Non-linearities in the energy response are studied using special runs data and Ke3 decays, where the electron energy is measured in calorimeter as
D. Madigozhin/Nuclear
Physics B (Proc. Suppl.) 120 (2003) 277-282
well as in the drift chamber. Taking into account larger deviation from linearity observed for the photon energies < 6 GeV, the resulting uncertainty on the double ratio is f3.8 x 10e4. The uniformity of the calorimeter response over its surface is optimized using Ke3 decays and data from special runs. The corresponding systematic uncertainty on the double ratio is f1.6 x 10P4. The uncertainties due to the photons positions error and non-Gaussian tails in the energy response are also taken into account. Adding them in quadrature, the systematic error on the double ratio from the photon reconstruction is found to be f5.3 x 10P4. The uncertainty from the 7riT+7r-decays reconstruction takes into account the possible detector geometry deviations. Its value is f2.8 x 10e4. 6. Intensity
effects
The overlap of accidental activity with a good event in the detectors may result in the net event loss effect in the reconstruction or the selection. This effect is cancel with a good precision in double ratio R due to the simultaneous collection of data in the four channels and due to the very similar illumination of the detector by the K’jJ and K,O beams. The possible residual effect can be separated into two components. The first one (intensity difference effect) is given by: AR = Ax x AI/I
281
intensity difference is 1.1 x low4 The second component of the accidental effect (illumination difference) has been estimated from the overlay samples, computing separately the losses for K,O and K,” events. It has been performed using both data and Monte Carlo origIn the first case, the value obinal events. tained is 0.9 f 3.5 x 10e4, in the second it is (1.4 f 2.8) x 10d4. As expected, there is no evidence of a significant effect, and we use as uncertainty on the double ratio f3.0 x low4 . Combining the two above uncertainties in quadrature, the total uncertainty on R from accidental effects is f3.1 x 10U4. It is dominated by the statistical error of the overlay procedure. Studies of the additional detector activity generated by the same proton which produced the good event (in-time activity) allow an upper bound on the effect on R of 1 x 10e4 to be set. 7. Result The measured R in kaon energy bins is shown on the Fig. 2. The extreme bins (outside the region 70-170 GeV) are not used for the final calculation. They are plotted to check the absence of the energy dependence.
(5)
where Ax is the difference between the mean losses in r+w- and 7r07romodes, and AI/I is the difference in the mean K: beam (the main source of accidental decays) intensity as seen by Kz and K: events. AI/I have been measured from the activity in the main detectors as well as from the beam monitors data and is consistent with Of 1%. Ax is estimated by overlaying data and Monte Carlo events with the beam monitor (random) triggers taken in proportion to the beam intensity. It is measured also from the comparison of the normal Kz + Kz beam runs with pure Kz runs, in which the accidental activity is much smaller. The resulting estimate of Ax is (1.0 f 0.5)% So the uncertainty on the double ratio related to the
095
Figure 2. Measured double ratio R in kaon energy bins
282
D. Mudigozhin/Nuclear Physics B (Proc. Suppl.) 120 (2003) 277-282
The final result for the double ratio from 2001 data set is R = 0.99181 f 0.00147 f 0.00065 f 0.00110, where the first error is the statistical error for the 2n samples, second is the systematic error coming from the statistics of the control samples, and the third is the contribution of the other systematic uncertainties. The corresponding value of the direct @ -violation parameter is Re(d/e)
= (13.7 f 2.5 f 1.1 f 1.5) x low4 = (13.7 f 3.1) x 1o-4
(6)
It is in good agreement with the published value from the 1997-99 data: Re(d/c) = (15.3 f 2.6) x 10-4. Taking into account the partially correlated systematic uncertainty, the combined, final result from the NA48 experiment is: Re(d/c)
= (14.7 f 2.2) x lop4
(7)
REFERENCES 1. A. Lai et al., Eur. Phys. Jour. C 22 (2001) 231. 2. A. [KTeV Collaboration] in Glazov F.Costantini et al.(ed), Proc. of Int. Conference on Kaon Physics, Frascati Physics Serie 26, 2001, p.115. 3. N. Doble, L.Gatignon, P.Grafstrom, Nucl. Instr. and Meth. B 119 (1996) 181. 4. D. Bederede et. al., Nucl. Instr. and Meth. A 367 (1995) 88. 5. G. Unal [NA48 Collaboration] B. Aubert (ed), Proc. IX Int. Conf. on Calorimetry in HEP, Frascati Physics Serie 21, 2001 p.361.