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The charged kaon mass measurement
Nuclear Physics B148 (1979) 53-60 © North-Holland Publishing Company
THE CHARGED KAON MASS MEASUREMENT L.M. BARKOV, I.B. VASSERMAN, M.S. ZOLOTOREV, N.I. KRUPIN, S.I. SEREDNYAKOV, A.N. SKRINSKY, V.P. SMAKHTIN, E.P. SOLODOV, G.M. TUMAIKIN and Yu.M. SHATUNOV Institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences, USSR
L.A. M A K A R I N A , A.P. MISHAKOVA and V.V. OGURTZOV Institute Atomnoi Energii of L V. Kurchatov, USSR
Received 16 February 1978 (Revised 28 August 1978)
The average mass of the K+ and K - was measured in the reaction e+e- ~ ~ ~ K+Kat the VEPP 2M storage ring as the difference of the energy of the colliding beam and the kaon kinetic energy and was found to be 493.670 +_0.029 MeV. The energy of the colliding beams was determined by the resonance depolarization method. The kaon kinetic energy was found from range measurements in nuclear emulsion.
At present there are a number of measurements o f the charged kaon mass [ 1 - 6 ] and one measurement o f the charged kaon mass difference [7]. In early works [ 1 - 3 ] , the K + and K - masses were measured with the help o f nuclear emulsion. The next measurements [ 4 - 6 ] were performed b y studying X-ray transitions o f kaonic atoms. This m e t h o d allows one to measure the negative kaon mass with a high accuracy, presently limited mainly by the uncertainty of the radiative correction calculation. So in ref. [6] the authors noted that two different methods o f radiative correction calculations led to the different values o f the kaon mass M R_ = 493.657 + 0.020 MeV and M K_ = 493.696 + 0.025 MeV. Therefore, it is very desirable to perform measurements o f the kaon mass with the same accuracy b y using other methods. In this experiment the average mass o f positive and negative charge kaons produced in the reaction e+e - -~ K+K - at the energy of the ~b-meson m a x i m u m has been measured at the VEPP 2M storage ring as the difference o f the colliding beam energy and the kaon kinetic energy. The absolute value o f particle energy in the electron-positron storage ring was determined b y measuring the spin precession frequency with the help o f the resonance beam depolarization b y a high-frequency longitudinal magnetic field (LMF). The development of this m e t h o d [ 8 - 1 0 ] made 53
L.M. Barkov et al. / Charged kaon mass measurement
54
r * """'""
T
40*
2_
¸~
U
v
',
% /
,
I
cm i
Fig. 1. T h e e m u l s i o n c h a m b e r scheme: 1, the storage ring v a c u u m tube; 2, the emulsion pel-
licles; 3, the interaction region.
it possible to determine in this experiment the absolute particle energy with an accuracy of 10 keV (z~E/E ~ 2 × 10-s). The kinetic energies of slow kaons were found from their ranges in nuclear emulsion. The geometry of an emulsion chamber placed in one of the straight sections of the storage ring is given in fig. 1. Kaons came from the interaction region mainly in the perpendicular direction to beam axis, passed through the stainless steel vacuum tube 36 mm in diameter and stopped in the emulsion chamber. The emulsion cham. ber consisted of two symmetrically placed stacks. Each stack was collected from five 86 × 46 mm 2 peUicles of ~400 microns nuclear emulsion BR-2. In such a geometry about 75% of produced kaons stopped in the emulsion stacks. Two runs were made in this experiment. Every run was conducted in the following way. The positron beam, with initial current about 30 mA, was polarized for two hours at 650 MeV energy, which is close to maximum energy of the storage ring. The polarization time of the beam is proportional to E - s and is equal to about one hour at this energy. Then the energy of the polarized beam was decreased to that corresponding to the 0-meson maximum. After some time necessary for relaxation of the storage ring systems, the LMF was switched on and the spin precession frequency of the beam was measured. After that, the electron beam was injected into the storage ring and the emulsion chamber was put on. The guiding magnetic field was kept at a constant value with an accuracy 2 X 10 -s. The first emulsion
L.M. Barkov et at / Charged kaon mass measurement
55
chamber was exposed with currents 3 × 3 mA 2 for 50 minutes and the second one was exposed with currents 5 × 5 mA for 30 minutes. To f'md the spin precession frequency, the LMF frequency was varied with the constant rate 6.5 sec -2 in the first run and 12.5 sec -2 in the second. The counting rate N of particles which escaped from the beam due to elastic scattering within a bunch, depends upon the beam polarization and was measured by scintillation counters. When the LMF frequency becomes divisible by the spin precession frequency, resonance spin depolarization takes place. The value o f N/I2+, where I+ is the positron current, is given in fig. 2 as a function of LMF frequency for two runs. The frequency of spin precession was determined by the jump in the counting rate. The average energy of the beam in the storage ring can be calculated [8] by the formula F~ = m c 2 ( 2
- A/fo)
~o/~' ,
where fs is the average frequency of spin precession, fo = 16.76664 -+ 0.00001 MHz is the particle revolution frequency,/l' and/10 are the anomalous and normal parts of the magnetic moment of electron. The values of beam energy were 509.345 + 0.010 MeV in the first run and 509.331 +- 0.010 MeV in the second run. In this experiment the magnetic moments of electron and positron were assumed to be the same. The first pellicle of each stack was scanned with a microscope. The tracks of high grain density which stopped inside the stacks and traversed more then one peUicle were registered. The latter condition allowed almost complete exclusion of tracks of cosmic particles as the emulsion pellicles were collected together only for a short time of the exposure. The coordinates and the angles of these tracks at the point of the particle entrance in the emulsion stack were measured. The charge sign identification was carried out by studying interactions and decays of the particles at the end of the range. All the registered events were divided into three groups. The first group contained r-decay events and events having only one track at the end of the range with grain density g < 1.5 go, where go was the grain density of a relativistic particle. This group contained K + with about 10% K - . Events with severn tracks at the end of the range or with one track havingg > 1.5 go were included in the second group. This group contained K - with about 3% K +. Events with no tracks at the end of the range were included in the third group. This group contained negative kaons, which had no tracks in the interaction point, positive kaons, whose relativistic track had not been found, and protons produced in the vacuum tube of the storage ring. To reduce the number of background events in each group, particles coming only from the interaction region of the beams and with angles between their trajectories and the beam axis lying in the interval from 45 ° to 135 ° were selected. The numbers of the registered and selected events are given in table 1. The selected particles stopped mainly in the third emulsion pellicle. The range measurement in the emulsion was carried out by breaking up the tra-
56
L.M. Barkov et al. / Charged kaon mass measurement
37
NIl 2 , Hz/mA 2
36
I
35
I
I I I I
34
33
32
31
I I I I
30
I
t
I
t
t
I
14.150
37
If
,,,,~.,.z,,.,,
I
b
t
34
33
MHz
II
36
35
I
fd,
14.155
IIIII
t I
32
31
30
I
14.150
z
I
14.155
I
fd,MHz
Fig. 2. The counting rate divided by the positron current squared as a function of LMF frequency, (a) for the f'trst run, (b) for the second run.
jectory into a number o f segments. Each segment was approximated b y a straight line. The projections o f the track to the emulsion surface were measured with an eyepiece reticle. The depth measurements were made b y a micrometer f l i e d on the microscope. The track o f the particle in the stainless steel was not visible and was approximated b y a straight line tangential to the initial part of emulsion trajectory.
57
L.M. Barkov et aL / Charged kaon mass measurement
Table 1 Group registered events selected events
First run 1 2 71 82 53 63
3 102 36
Second run 1 2 88 112 68 89
3 130 44
As the angles between the selected tracks and the pellicles perpendicular to the emulsion and between the selected tracks and the stainless steel foil were small, the accuracy of the range measurements in the present experiment depended mainly on the accuracy of the thickness measurements. The thickness of each unprocessed pellicle was measured at four points by the micrometer with an accuracy of one micron. But the precision of this method of thickness determination was not sufficient for our experiment and we used another in which the average thickness of each pellicle was measured in g/cm 2 by weighing with an accuracy of 0.03%. The dispersion in thickness of each emulsion pellicle was less than 1%. All measurements were made at constant humidity and temperature. During the exposure the stacks were placed in a stainless steel, hermetic container. The average thicknesses of the vacuum tube and container wall were found to be 0.10697 +- 0.00005 g/cm 2 and 0.07184 --- 0.00003 g/cm 2, respectively. So it was important that in this work the ranges of the particles were measured in g/cm 2 because the thickness determination was made with more precision in g/cm ~ than in microns. Tracks that showed evidence of inelastic scattering and those that passed near the edge of the stack were discarded. A small correction due to the bend of emulsion pellicles was made, but no other distortion effects were found that could significantly affect the range. The difference due to multiple scattering between the true trajectory and the tangential line in the stainless steel was calculated and this correction was made. The energy losses in the emulsion and then in the stainless steel were determined for each particle according to their range-energy relation. The range-energy relations for BR-2 emulsion and for stainless steel were obtained from the results of calibration and from the semi-empirical range-energy relation in Ilford G-5 emulsion [11, 12] with small corrections for different composition structure of the emulsions and water contents. For calibration we used monoenergetic protons with an energy 40.01 +- 0.04 MeV from the NAP-M storage ring [13]. The proton ranges in the sandwiches from the emulsion and stainless steel were measured by the same method as the kaon ranges. As a result, the accuracy achieved in range-energy relation for positive kaons in the energy region of this experiment was 0.1% (+ 16 keV in energy). We found that the average range for the events of the second group was longer than that of the first group. The range difference was 6 + 2 mg/cm 2 and showed that the ionization losses for negative kaons were lower than those for positive kaons. This effect was first described in [2] and studied in detail in [14]. As the calibration of the range-energy relation was made only with positive-charged parti-
58
L.M. Barkov et al. / Charged kaon mass measurement
cles, only the events o f the first group were used for determination o f the kaon kinetic energy with a correction for the 10% admixture o f K - in this group. The width of the kaonic energy distribution depended on the energy spread of particles in the storage ring, the fluctuation o f kaonic energy losses and the dispersion in the thickness o f emulsion pellicles. The experimental width was consistent
dN/dTK
10
0 14.5
I
15,0
15.5
| TR, MeV
!
16.0
16.5
dN / d T K
o
b
o~ 14.5
15.0
,
15.5
~
16.0
.
16.5
[-'] T=,., M e /
Fig. 3. The energy distributions of kaons from the f'trst group and the best fitted theoretical curves with small background level: (a) for the first run, (b) for the second run.
59
L.M. Barkov et al. / Charged kaon mass measurement
with the expected value. The radiative effects caused an asymmetry of kaonic energy distribution and were calculated according to [15] with the mass and width of the ~-meson equal to 1019.7 -+ 0.3 MeV and 4.1 -+ 0.2 MeV, respectively. The uncertainty in the value of the ~-meson parameters led to an uncertainty 0.006 MeV in the value of charged kaon mass. The energy distributions of kaons from the first group for two runs and the best fitted theoretical curves with a small background level are given in fig. 3. As a result of likelihood-function calculations, the values of the charged kaon mass have been obtained in the two runs. They differed by 0.010 MeV. The averaged value for the two runs was: MK+_ = 493.670 + 0.029 MeV. The limited number of events and the accuracy of the range-energy relation gave approximately the same contributions to the charged kaon mass error. Consequently, for further improvement of the accuracy in this method it requires not only more events but also a more precise range-energy relation. It should be emphasized once more that just the average value of K÷ and K -
M K ' , MeV MK +
493.0
493.8
I 493.6
-7" ' ~ - 7 " r ~
~,
493.4
./'V" / .J"
493.2
./ I 493.2
!
I 493.4
I
I 493.6
I
I 493.8
I
I /+93.0
I MK + , MeV
Fig. 4. The graphic illustration of experimental values for positive kaon mass [ 1,3 ], negative kaon mass [2,4-6], charged kaon mass difference [7] and average charged kaon mass (this work).
60
L.M. Barkov et al. / Charged kaon mass measurement
masses has been measured in this experiment. Actually, as the average m o m e n t a o f positive and negative kaons were equal and the charged kaon mass difference did not exceed 0.I MeV [7], the average kinetic energies o f positive and negative kaons differed by less than 2 keV. In this case, the average value of the charged kaon mass was found from energy conservation: ~(MK+ + M K - ) = ~(2ff -- TK + - T K_ - f f . r ) - . ~ E - TK+ -- 1E-7, where E. r ~ 0.1 MeV is the average energy o f 3,-rays due to the radiation effects. The illustration o f experimental values for the positive and negative kaon masses, their difference and the average charged kaon mass is given in fig. 4. Two values o f the negative kaon mass correspond to two possible calculations of the radiative corrections [6]. The dashed-point line shows the C P T prediction. F r o m the results o f the works [ 1 - 7 ] and the present experiment, one can draw the conclusion that the K + and K - masses are equal with an accuracy "~10 -4. It is consistent with the C P T theorem prediction. On the other hand, the absence of the discrepancy between kaon masses can be interpreted as p r o o f o f the validity o f the energy calculation formulae for particles in the storage ring and consequently of relativity theory with an accuracy o f 10 - 4 at E / r n e 2 = 10 3 for particles in the noninertial system o f reference. We would like to thank Professor G.I. Budker and Professor I.I. Gurevitch for their support and interest, N.S. Dikansky and V.V. Parkhomchuk for help in the calibration, S.I. Eidelman for help in computing and all the team o f the VEPP 2M storage ring for their sustained effort.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
G. Cohen et al., Fund. Cons. Phys. (1957). W.H. Barkas et al., Phys. Rev. Lett. 11 (1963) 26. W.T. Greiner, Ann. Rev. Nucl. Sci. 15 (1965) 67. G. Backenstoss et al., Phys. Lett. 43B (1973) 431. R. Kunselman, Phys. Rev. C9 (1974) 2469. S.C. Cheng et al., Nucl. Phys. A254 (1975) 381. W.T. Ford et al., Phys. Lett. 38B (1972) 335. A.D. Bukin et al., Proc. 5th Int. Symp. on high-energy and elementary particle physics, Warsaw (1975) 138. L.M. Kurdadze et al., Proc. 5th Int. Symp. on high-energy and elementary particle physics, Warsaw (1975) 148. S.I. Serednyakov et al., Phys. Lett. 66B (1977) 102. W.H. Barkas et al., Nuovo Cim. 8 (1958) 186. W.H. Barkas, Nuovo Cim. 8 (1958) 201. G.I. Budker et al., Proc. 4th All-Union Meeting on charged particle accelerators, Nauka 2 (1975) 102. H.H. Heckman et aL, Phys. Rev. Lett. 22 (1969) 871. Y.I. Azimov et al., ZhETF Pisma 21 (1975) 378.
THE CHARGED KAON MASS MEASUREMENT L.M. BARKOV, I.B. VASSERMAN, M.S. ZOLOTOREV, N.I. KRUPIN, S.I. SEREDNYAKOV, A.N. SKRINSKY, V.P. SMAKHTIN, E.P. SOLODOV, G.M. TUMAIKIN and Yu.M. SHATUNOV Institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences, USSR
L.A. M A K A R I N A , A.P. MISHAKOVA and V.V. OGURTZOV Institute Atomnoi Energii of L V. Kurchatov, USSR
Received 16 February 1978 (Revised 28 August 1978)
The average mass of the K+ and K - was measured in the reaction e+e- ~ ~ ~ K+Kat the VEPP 2M storage ring as the difference of the energy of the colliding beam and the kaon kinetic energy and was found to be 493.670 +_0.029 MeV. The energy of the colliding beams was determined by the resonance depolarization method. The kaon kinetic energy was found from range measurements in nuclear emulsion.
At present there are a number of measurements o f the charged kaon mass [ 1 - 6 ] and one measurement o f the charged kaon mass difference [7]. In early works [ 1 - 3 ] , the K + and K - masses were measured with the help o f nuclear emulsion. The next measurements [ 4 - 6 ] were performed b y studying X-ray transitions o f kaonic atoms. This m e t h o d allows one to measure the negative kaon mass with a high accuracy, presently limited mainly by the uncertainty of the radiative correction calculation. So in ref. [6] the authors noted that two different methods o f radiative correction calculations led to the different values o f the kaon mass M R_ = 493.657 + 0.020 MeV and M K_ = 493.696 + 0.025 MeV. Therefore, it is very desirable to perform measurements o f the kaon mass with the same accuracy b y using other methods. In this experiment the average mass o f positive and negative charge kaons produced in the reaction e+e - -~ K+K - at the energy of the ~b-meson m a x i m u m has been measured at the VEPP 2M storage ring as the difference o f the colliding beam energy and the kaon kinetic energy. The absolute value o f particle energy in the electron-positron storage ring was determined b y measuring the spin precession frequency with the help o f the resonance beam depolarization b y a high-frequency longitudinal magnetic field (LMF). The development of this m e t h o d [ 8 - 1 0 ] made 53
L.M. Barkov et al. / Charged kaon mass measurement
54
r * """'""
T
40*
2_
¸~
U
v
',
% /
,
I
cm i
Fig. 1. T h e e m u l s i o n c h a m b e r scheme: 1, the storage ring v a c u u m tube; 2, the emulsion pel-
licles; 3, the interaction region.
it possible to determine in this experiment the absolute particle energy with an accuracy of 10 keV (z~E/E ~ 2 × 10-s). The kinetic energies of slow kaons were found from their ranges in nuclear emulsion. The geometry of an emulsion chamber placed in one of the straight sections of the storage ring is given in fig. 1. Kaons came from the interaction region mainly in the perpendicular direction to beam axis, passed through the stainless steel vacuum tube 36 mm in diameter and stopped in the emulsion chamber. The emulsion cham. ber consisted of two symmetrically placed stacks. Each stack was collected from five 86 × 46 mm 2 peUicles of ~400 microns nuclear emulsion BR-2. In such a geometry about 75% of produced kaons stopped in the emulsion stacks. Two runs were made in this experiment. Every run was conducted in the following way. The positron beam, with initial current about 30 mA, was polarized for two hours at 650 MeV energy, which is close to maximum energy of the storage ring. The polarization time of the beam is proportional to E - s and is equal to about one hour at this energy. Then the energy of the polarized beam was decreased to that corresponding to the 0-meson maximum. After some time necessary for relaxation of the storage ring systems, the LMF was switched on and the spin precession frequency of the beam was measured. After that, the electron beam was injected into the storage ring and the emulsion chamber was put on. The guiding magnetic field was kept at a constant value with an accuracy 2 X 10 -s. The first emulsion
L.M. Barkov et at / Charged kaon mass measurement
55
chamber was exposed with currents 3 × 3 mA 2 for 50 minutes and the second one was exposed with currents 5 × 5 mA for 30 minutes. To f'md the spin precession frequency, the LMF frequency was varied with the constant rate 6.5 sec -2 in the first run and 12.5 sec -2 in the second. The counting rate N of particles which escaped from the beam due to elastic scattering within a bunch, depends upon the beam polarization and was measured by scintillation counters. When the LMF frequency becomes divisible by the spin precession frequency, resonance spin depolarization takes place. The value o f N/I2+, where I+ is the positron current, is given in fig. 2 as a function of LMF frequency for two runs. The frequency of spin precession was determined by the jump in the counting rate. The average energy of the beam in the storage ring can be calculated [8] by the formula F~ = m c 2 ( 2
- A/fo)
~o/~' ,
where fs is the average frequency of spin precession, fo = 16.76664 -+ 0.00001 MHz is the particle revolution frequency,/l' and/10 are the anomalous and normal parts of the magnetic moment of electron. The values of beam energy were 509.345 + 0.010 MeV in the first run and 509.331 +- 0.010 MeV in the second run. In this experiment the magnetic moments of electron and positron were assumed to be the same. The first pellicle of each stack was scanned with a microscope. The tracks of high grain density which stopped inside the stacks and traversed more then one peUicle were registered. The latter condition allowed almost complete exclusion of tracks of cosmic particles as the emulsion pellicles were collected together only for a short time of the exposure. The coordinates and the angles of these tracks at the point of the particle entrance in the emulsion stack were measured. The charge sign identification was carried out by studying interactions and decays of the particles at the end of the range. All the registered events were divided into three groups. The first group contained r-decay events and events having only one track at the end of the range with grain density g < 1.5 go, where go was the grain density of a relativistic particle. This group contained K + with about 10% K - . Events with severn tracks at the end of the range or with one track havingg > 1.5 go were included in the second group. This group contained K - with about 3% K +. Events with no tracks at the end of the range were included in the third group. This group contained negative kaons, which had no tracks in the interaction point, positive kaons, whose relativistic track had not been found, and protons produced in the vacuum tube of the storage ring. To reduce the number of background events in each group, particles coming only from the interaction region of the beams and with angles between their trajectories and the beam axis lying in the interval from 45 ° to 135 ° were selected. The numbers of the registered and selected events are given in table 1. The selected particles stopped mainly in the third emulsion pellicle. The range measurement in the emulsion was carried out by breaking up the tra-
56
L.M. Barkov et al. / Charged kaon mass measurement
37
NIl 2 , Hz/mA 2
36
I
35
I
I I I I
34
33
32
31
I I I I
30
I
t
I
t
t
I
14.150
37
If
,,,,~.,.z,,.,,
I
b
t
34
33
MHz
II
36
35
I
fd,
14.155
IIIII
t I
32
31
30
I
14.150
z
I
14.155
I
fd,MHz
Fig. 2. The counting rate divided by the positron current squared as a function of LMF frequency, (a) for the f'trst run, (b) for the second run.
jectory into a number o f segments. Each segment was approximated b y a straight line. The projections o f the track to the emulsion surface were measured with an eyepiece reticle. The depth measurements were made b y a micrometer f l i e d on the microscope. The track o f the particle in the stainless steel was not visible and was approximated b y a straight line tangential to the initial part of emulsion trajectory.
57
L.M. Barkov et aL / Charged kaon mass measurement
Table 1 Group registered events selected events
First run 1 2 71 82 53 63
3 102 36
Second run 1 2 88 112 68 89
3 130 44
As the angles between the selected tracks and the pellicles perpendicular to the emulsion and between the selected tracks and the stainless steel foil were small, the accuracy of the range measurements in the present experiment depended mainly on the accuracy of the thickness measurements. The thickness of each unprocessed pellicle was measured at four points by the micrometer with an accuracy of one micron. But the precision of this method of thickness determination was not sufficient for our experiment and we used another in which the average thickness of each pellicle was measured in g/cm 2 by weighing with an accuracy of 0.03%. The dispersion in thickness of each emulsion pellicle was less than 1%. All measurements were made at constant humidity and temperature. During the exposure the stacks were placed in a stainless steel, hermetic container. The average thicknesses of the vacuum tube and container wall were found to be 0.10697 +- 0.00005 g/cm 2 and 0.07184 --- 0.00003 g/cm 2, respectively. So it was important that in this work the ranges of the particles were measured in g/cm 2 because the thickness determination was made with more precision in g/cm ~ than in microns. Tracks that showed evidence of inelastic scattering and those that passed near the edge of the stack were discarded. A small correction due to the bend of emulsion pellicles was made, but no other distortion effects were found that could significantly affect the range. The difference due to multiple scattering between the true trajectory and the tangential line in the stainless steel was calculated and this correction was made. The energy losses in the emulsion and then in the stainless steel were determined for each particle according to their range-energy relation. The range-energy relations for BR-2 emulsion and for stainless steel were obtained from the results of calibration and from the semi-empirical range-energy relation in Ilford G-5 emulsion [11, 12] with small corrections for different composition structure of the emulsions and water contents. For calibration we used monoenergetic protons with an energy 40.01 +- 0.04 MeV from the NAP-M storage ring [13]. The proton ranges in the sandwiches from the emulsion and stainless steel were measured by the same method as the kaon ranges. As a result, the accuracy achieved in range-energy relation for positive kaons in the energy region of this experiment was 0.1% (+ 16 keV in energy). We found that the average range for the events of the second group was longer than that of the first group. The range difference was 6 + 2 mg/cm 2 and showed that the ionization losses for negative kaons were lower than those for positive kaons. This effect was first described in [2] and studied in detail in [14]. As the calibration of the range-energy relation was made only with positive-charged parti-
58
L.M. Barkov et al. / Charged kaon mass measurement
cles, only the events o f the first group were used for determination o f the kaon kinetic energy with a correction for the 10% admixture o f K - in this group. The width of the kaonic energy distribution depended on the energy spread of particles in the storage ring, the fluctuation o f kaonic energy losses and the dispersion in the thickness o f emulsion pellicles. The experimental width was consistent
dN/dTK
10
0 14.5
I
15,0
15.5
| TR, MeV
!
16.0
16.5
dN / d T K
o
b
o~ 14.5
15.0
,
15.5
~
16.0
.
16.5
[-'] T=,., M e /
Fig. 3. The energy distributions of kaons from the f'trst group and the best fitted theoretical curves with small background level: (a) for the first run, (b) for the second run.
59
L.M. Barkov et al. / Charged kaon mass measurement
with the expected value. The radiative effects caused an asymmetry of kaonic energy distribution and were calculated according to [15] with the mass and width of the ~-meson equal to 1019.7 -+ 0.3 MeV and 4.1 -+ 0.2 MeV, respectively. The uncertainty in the value of the ~-meson parameters led to an uncertainty 0.006 MeV in the value of charged kaon mass. The energy distributions of kaons from the first group for two runs and the best fitted theoretical curves with a small background level are given in fig. 3. As a result of likelihood-function calculations, the values of the charged kaon mass have been obtained in the two runs. They differed by 0.010 MeV. The averaged value for the two runs was: MK+_ = 493.670 + 0.029 MeV. The limited number of events and the accuracy of the range-energy relation gave approximately the same contributions to the charged kaon mass error. Consequently, for further improvement of the accuracy in this method it requires not only more events but also a more precise range-energy relation. It should be emphasized once more that just the average value of K÷ and K -
M K ' , MeV MK +
493.0
493.8
I 493.6
-7" ' ~ - 7 " r ~
~,
493.4
./'V" / .J"
493.2
./ I 493.2
!
I 493.4
I
I 493.6
I
I 493.8
I
I /+93.0
I MK + , MeV
Fig. 4. The graphic illustration of experimental values for positive kaon mass [ 1,3 ], negative kaon mass [2,4-6], charged kaon mass difference [7] and average charged kaon mass (this work).
60
L.M. Barkov et al. / Charged kaon mass measurement
masses has been measured in this experiment. Actually, as the average m o m e n t a o f positive and negative kaons were equal and the charged kaon mass difference did not exceed 0.I MeV [7], the average kinetic energies o f positive and negative kaons differed by less than 2 keV. In this case, the average value of the charged kaon mass was found from energy conservation: ~(MK+ + M K - ) = ~(2ff -- TK + - T K_ - f f . r ) - . ~ E - TK+ -- 1E-7, where E. r ~ 0.1 MeV is the average energy o f 3,-rays due to the radiation effects. The illustration o f experimental values for the positive and negative kaon masses, their difference and the average charged kaon mass is given in fig. 4. Two values o f the negative kaon mass correspond to two possible calculations of the radiative corrections [6]. The dashed-point line shows the C P T prediction. F r o m the results o f the works [ 1 - 7 ] and the present experiment, one can draw the conclusion that the K + and K - masses are equal with an accuracy "~10 -4. It is consistent with the C P T theorem prediction. On the other hand, the absence of the discrepancy between kaon masses can be interpreted as p r o o f o f the validity o f the energy calculation formulae for particles in the storage ring and consequently of relativity theory with an accuracy o f 10 - 4 at E / r n e 2 = 10 3 for particles in the noninertial system o f reference. We would like to thank Professor G.I. Budker and Professor I.I. Gurevitch for their support and interest, N.S. Dikansky and V.V. Parkhomchuk for help in the calibration, S.I. Eidelman for help in computing and all the team o f the VEPP 2M storage ring for their sustained effort.
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