- Email: [email protected]
Neutrino rest mass and anomaly in the tritium beta-spectrum
L-
|
PROCEEDINGS SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190
NEUTRINO REST MASS AND ANOMALY IN THE TRITIUM BETA-SPECTRUM V.M.Lobashev ~, A.I.Belesev ~, A.I.Berlev ~, E.V.Geraskin ~, A.A.Golubev ~, N.A.Golubev ~, O.V.Kazachenko ~, Yu.E.Kuznetsov ~, L.A.Ryvkis a, B.E.Stern, a N.A.Titov a, I.E.Yarykin a, S.V.Zadorozhny a, Yu.I.Zakharov a
Presented by V.M.Lobashev aInstitute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect, 7a, 117312 Moscow, Russia The end point region of the tritium beta-spectrum has been studied on the "Troitsk u -mass" set-up during 1993-1997. Fits to the data give evidence for the existence of a bump-like structure placed 5-12 eV below end point with a relative intensity about 10-1°. The comparison of the anomaly region of the spectrum measured at different time reveals a movment of the bump position back and forth with respect to end point energy. After accounting for the bump and a correction for effect of electron trapping in the source the shape of all the measured part of the beta spectrum agree with m ,2 about zero thus eliminating the problem of "negative m,2 . . An upper limit for the neutrino mass including only data of 1994-1996 runs is : m~ < 3, 8 eV/c ~ at 95 % C.L.
1. I n t r o d u c t i o n
2. M e a s u r e m e n t s
The problem of neutrino rest mass remains to be one of the most important in Elementary Particle Physics and Cosmology. One of the methods which are based on the study of decay kinematics is a measurement of the shape of the beta spectrum near its end-point. The decay of tritium is a unique opportunity for such experiments due to the low end-point energy, high specific activity, the lowest Z and possibility to calculate most of the corrections for its superallowed spectrum. The latter includes also calculation of molecular effects in the final state spectrum. This report reviews the results of the experiment carried out on the set-up "Troitsk v-mass" at the Institute for Nuclear Research of the Russian Academy of Sciences (Troitsk). The set-up includes an integral electrostatic spectrometer with strong nonuniform magnetic field providing guiding and collimation of the electrons. Spectrometer of such type is specially aimed to study the very end of beta-spectrum to search for the neutrino rest mass. The main features of the set-up, procedure of the measurement, data analysis and fitting are described in [1-3].
The spectrometer resolution function is described by the step function with almost linear slope from 0 to 1. In most of the measurements the width of the slope was adjusted to be 3.7 - 4.7 eV (FW) at 18.6 keV by proper choice of the magnetic fields in the spectrometer. The measurements were made in the range of spectrometer potential from 17800 to 18770 V . The background was measured up to 19700 V.The direction of scanning of the spectrometer potential was reversed each cycle.
0920-5632/98/$19.00 © 1998 Elsevier Science B.V. All fights reserved. PII S0920-5632(98)00032-2
3. Data analysis The fitting procedure of the 94 data was done with variation of 4 parameters: the spectrum normalization factor, the background value, the end-point energy and m~2 It resulted in the value m ~2 -~- - 2 2 ± 5 eV2/c 4 for the truncated spectrum with the truncation energy (further it is referred as Elow) 18300 to 18450eV. At lower truncation energy (down to 18000eV) the m~ value increased and was accompanied by a strong increase in X2 Ill.It was found that the part of the spectrum with Elo~, > 18300 eV may be well fit
188
V.M. Lobashev et al./Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190
taking into account an excess of counts observed from about 7 e V below the end point and described as a step-like function with two parameters (step size and step energy) corresponding to a spike- or bump-like structure in the differential spectrum.A fit with these new parameters resulted in m~ about zero for Eto~ > 18300. Lowenergy increase of the negative value of m,2 was found to be due to rise in the counting rate when Elow < 18300 V. The results of the measurements of the 96 run revealed for the first look the similar feature as in the 1994 run. The fit with 4 parameters resulted in m v2 = -(15 - 20) e V 2 / c 4 for Elo~ > 18200 eV and in some rise for smaller values of Ezow. The negative value of m~ at Etow > 18300 e V disappeared as well as in the previous run when introducing the step-like function. The main distinction from the 1994 run proved to be a shift of the step energy towards lower energies by 4.7 eV, keeping the magnitude of the step about the same as in the 94 run, that is 6.6 :t: 1.8.10 -11. The shift was definitely seen when the spectra of 1994 and 1996 runs were superposed being reduced to the same end-point energy and normalization factor. The difference between spectra proved to be the bump-like shaped with a width nearly corresponding to energy resolution. It excludes any description of the step as some smooth local enhancement produced by final state spectrum distortion or improper account for energy loss or other similar phenomena. Being very strange by itself this shift gave nevertheless an sufficient evidence in favor of small width of the spike-like structure producing the step in the integral spectrum. In the first report of our group [1] a low-energy anomaly was described as a rise of the spectrum intensity below 18300 eV with respect to theoretical spectrum. It is worth mentioning that the rise of the intensity at low energy was earlier observed in the experiment of the Mainz group [4] and this effect was considered as a source of the rise of the negative m 2 when decreasing Elow. Further analysis of possible systematics revealed considerable underestimation of the effect connected with the trapping of electrons in the tritium source. Such trapping has happened in
> 12 i,i
I
lO
t2 B
¢
2
01~
19'94
19195
19196
19197
1998 year
Figure 1. Evolution of step position with calendar time. Crossed point is an average of Run 94. E0 is the fitted end-point energy.
the tritium tube due to the bottle-like configuration of magnetic field in the source. The majority of trapped electrons is slowed down or escaping by multiple scattering to rear side of the source but small part of them may be scattered from the trapping momentum space into the solid angle of the momentum space which corresponds to the acceptance of the spectrometer.Such scattering takes place after some slowing down of the electrons in the magnetic trap so the scattered electrons will enrich the low-energy part of the measured spectrum. Calculation of trapping effect was made by means of the Monte-Carlo method. Unfortunately accuracy of calculations is limited by uncertainty of stopping power cross section amounting to 18%. After correction for trapping effect the low energy anomaly in the spectrum disappeared within errors. Accounting for both the step and trapping effect provided description of all the measured part of the spectrum with m v2 about zero within fit errors [2,3] thus eliminating 2 the problem of the negative m~. 4. R u n 97 results. The last long run was carried out in FebruaryMarch 1997.There were no significant changes of the set-up besides some upgrading of tritium and
V.M. Lobashev et aL/Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190 data acquisition systems. The fit results are given in table 1.As well as in the Run96 the 4 parameter fit with correction for the trapping effect gives negative m ,2 but smaller then in previous runs.The introduction of step makes fit result unstable and increase fit error for m~2 more then two times.The size of step fluctuate around value which is a few times smaller then in previous measurement and its position is found to be shifted from the 96 run by about 7 eV toward end point as shown in Fig.1 .This step position is obtained in the fit with fixing m ,2 = 0.The results shown in table 1 were obtained by fixing this step position leaving m v2 free. Thus we face very strange behaviour of bump effect which , if to accept that it belongs to tritium decay , should correspond to very exotic physics. In Fig.1 the positions of bump found in different runs are plotted with respect to the calendar time of the measurement.The first three point are obtained from subsection of data of 1994 in three subruns with maximum difference in time approaching half a year.The error of these points are not small enough to make decisive conclusion but their position spread hints to possibility of regular movement of the bump. At the moment we do not see any possibility for an instrumental artefact causing the bump effect. The last attempt to fix the part of the set-up possibly responsible for the effect was performed during run 97,when the tritium source was isolated from the spectrometer and potential+15V was applied to it. The fit of the partial run data after correction to 15 V showed good accordance with data without shift.Unfortunately this test cannot be quite decisive due to small size of the step in this run mentioned above.Other tests were considered in [1]. 5, T h e n e u t r i n o m a s s u p p e r l i m i t The shape of the difference spectrum of the 96 and 94 runs near end point indicate that accounting for the step-like distortion is necessary for adequate description of the experimental spectrum. Of course the size of the step being introduced as free parameter correlate with my2 and increase the final error of neutrino mass thus acting as a kind
189
of systematic error. Absence of dependence of mv2 on Eloto permit to assume that the step-like structure near the end point is the only visible anomaly in the spectrum.Its uncertainty increases the uncertainty of the fitted neutrino mass due to correlations and together with uncertaintties of corrections used before fitting form a systematic error. To deduce the neutrino mass effect one must select the interval of the spectrum which provides minimum total error of m~2 including statistical and systematical one . Most important of the uncertainties of parameters of correction factors come from the following: 1.Density of the source. 2.The shape of the energy loss spectrum. 3.Trapping effect in the source. 4.Final states spectrum (FSS) uncertainty. Regression dependence of the fitted m~2 on the variation of the parameters of the above mentioned corrections was given in Table 2. of [2]. These values can be considered as estimates of systematical errors. The fit errors of m v2 decrease with rise of Etow while the systematic error increase. For this reason one may select optimal Elow when the total error taken as the quadrature of the fit and systematic error has minimum. With these assumptions one may select Elo,,, 18400eV for estimation of the neutrino mass limit from the data of the 96 run. 2
7Tt v -----
3, 8 4- 7.4/it + 2, 98yat, e V 2 / c 4
(1)
In Run 94 Etow = 18300 e V corresponds to minimum of full error so we have - 2 , 7 -t- 10.1/it 4- 4.9svst, e V 2 / c 4
m b,
(2)
It is possible to combine results of both runs into one because each of them is statistically independent. We sum figures with statistical errors as usual but make weighted average of systematical errors using o'stat -2 as weights. A combined value was given in [2,3]: rn,2 = 1.5 4- 5.91it 4- 3.6,y,t, e V 2 / c 4
(3)
From here one may deduce:
m,, < 3, 8 e V / c 2, 95% C.L.
(4)
In Run 97 the minimum error corresponds to Elo,~ = 18400eV, rn~
2
:
- 8 . 6 4- 7.6/it 4- 2, 9,v,t, e V 2 / c 4
(5)
I(.M. Lobashev et al./Nuclear Physics B (Proc. SuppL) 66 (1998) 187-190
190
Table 1 Fit results for the run 97 data spectrum.
EIo w
m2
Step(B.R.)
eV
eV2/c 4
10-11
E0 eV
18000 18100 18200 18300 18350 18400 18450
-5.7 4, 6.8 -6.3 q- 4.7 -2.1 4- 5.6 -7.7 q- 6.2 -10.1 4, 6.5 -8.6 4, 7.6 3.5 -4- 11.1
0.64-1.1 0.64-0.9 1.14-1.1 0.44.1.0 0.24-1.0 0.34-1.1 1.64,1.6
18575.30 18575.23 18575.30 18575.20 18575.15 18575.18 18573.46
Combining all the data one could deduce : my < 3, 2 eV/c 2, at 95% C.L. but large spread of fit results in run 97 make it reasonable to use only previous limit. 6. C o n c l u s i o n
New measurements of the tritium betaspectrum on the "TROITSK v -MASS" set-up and new analysis of systematic effects explained one of the earlier reported anomalies in the spectrum [1], that is a rise of intensity of experimental spectrum toward lower energy thus reducing so called "negative m v2, effect to problem of existing a narrow bump in the vicinity of end point. The position of the bump with respect to the fitted end point energy is found to move within the range 5 - 12eV belowE0 with some hint of periodic character of this movement.The origin of this bump remains puzzling, but if its existence is confirmed in further experiments as a tritium decay branching process, it will be necessary to consider very exotic possibilities such as were considered in [5,6],for example. This work was partially supported by the Russian Foundation for Basic Research (grants 3903 and 18633a), by Program for Fundamental Nuclear Physics and by INTAS-RFBR (grant 96-02819).
Step -- 0
x2/
m y2
d.o.f.
eV2/c 4
59.7/59 58.1/55 53.2/51
-9.2 4- 3.3 -8.6 4- 2.6 -7.34-2.8 -9.8+3.1 -10.9 4- 3.5 -10.5 4- 3.8 -7.3 4- 4.3
47.3/47 41.5/45 43.4/43
39.9/41
d.o.f.
60.0/60 58.43/56
53. /52 47.4/48 43.8/46 43.5/44 41.1/42
REFERENCES
1. A.I.Belesev et al., Physics Letters B 350
(1995) 263. 2. V.M.Lobashev et al., Proceedings of the International Conference "NEUTRINO-96" Helsinki,Finland; June 13-19, 1996,World Scientific P.264-277. 3. V.M.Lobashev , Conference Proceedings Vol.57," Frontier Objects in Astrophysics and Particle Physics", F.Giovannelli and Mannocci(Eds),SIF,Bologna, 1997, p.511. 4. Ch.Weinheimer et al., Physics Letter B 300 (1993)210. 5. R.N.Mohapatra, S.Nussinov, Physics Letter B 395(1997),63-68. 6. J.Ciborowski, J.Rembielinski, Proc.28th Int.Conf.on High Energy Physics, IHEP-96, vol II ,p.1274.
|
PROCEEDINGS SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190
NEUTRINO REST MASS AND ANOMALY IN THE TRITIUM BETA-SPECTRUM V.M.Lobashev ~, A.I.Belesev ~, A.I.Berlev ~, E.V.Geraskin ~, A.A.Golubev ~, N.A.Golubev ~, O.V.Kazachenko ~, Yu.E.Kuznetsov ~, L.A.Ryvkis a, B.E.Stern, a N.A.Titov a, I.E.Yarykin a, S.V.Zadorozhny a, Yu.I.Zakharov a
Presented by V.M.Lobashev aInstitute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect, 7a, 117312 Moscow, Russia The end point region of the tritium beta-spectrum has been studied on the "Troitsk u -mass" set-up during 1993-1997. Fits to the data give evidence for the existence of a bump-like structure placed 5-12 eV below end point with a relative intensity about 10-1°. The comparison of the anomaly region of the spectrum measured at different time reveals a movment of the bump position back and forth with respect to end point energy. After accounting for the bump and a correction for effect of electron trapping in the source the shape of all the measured part of the beta spectrum agree with m ,2 about zero thus eliminating the problem of "negative m,2 . . An upper limit for the neutrino mass including only data of 1994-1996 runs is : m~ < 3, 8 eV/c ~ at 95 % C.L.
1. I n t r o d u c t i o n
2. M e a s u r e m e n t s
The problem of neutrino rest mass remains to be one of the most important in Elementary Particle Physics and Cosmology. One of the methods which are based on the study of decay kinematics is a measurement of the shape of the beta spectrum near its end-point. The decay of tritium is a unique opportunity for such experiments due to the low end-point energy, high specific activity, the lowest Z and possibility to calculate most of the corrections for its superallowed spectrum. The latter includes also calculation of molecular effects in the final state spectrum. This report reviews the results of the experiment carried out on the set-up "Troitsk v-mass" at the Institute for Nuclear Research of the Russian Academy of Sciences (Troitsk). The set-up includes an integral electrostatic spectrometer with strong nonuniform magnetic field providing guiding and collimation of the electrons. Spectrometer of such type is specially aimed to study the very end of beta-spectrum to search for the neutrino rest mass. The main features of the set-up, procedure of the measurement, data analysis and fitting are described in [1-3].
The spectrometer resolution function is described by the step function with almost linear slope from 0 to 1. In most of the measurements the width of the slope was adjusted to be 3.7 - 4.7 eV (FW) at 18.6 keV by proper choice of the magnetic fields in the spectrometer. The measurements were made in the range of spectrometer potential from 17800 to 18770 V . The background was measured up to 19700 V.The direction of scanning of the spectrometer potential was reversed each cycle.
0920-5632/98/$19.00 © 1998 Elsevier Science B.V. All fights reserved. PII S0920-5632(98)00032-2
3. Data analysis The fitting procedure of the 94 data was done with variation of 4 parameters: the spectrum normalization factor, the background value, the end-point energy and m~2 It resulted in the value m ~2 -~- - 2 2 ± 5 eV2/c 4 for the truncated spectrum with the truncation energy (further it is referred as Elow) 18300 to 18450eV. At lower truncation energy (down to 18000eV) the m~ value increased and was accompanied by a strong increase in X2 Ill.It was found that the part of the spectrum with Elo~, > 18300 eV may be well fit
188
V.M. Lobashev et al./Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190
taking into account an excess of counts observed from about 7 e V below the end point and described as a step-like function with two parameters (step size and step energy) corresponding to a spike- or bump-like structure in the differential spectrum.A fit with these new parameters resulted in m~ about zero for Eto~ > 18300. Lowenergy increase of the negative value of m,2 was found to be due to rise in the counting rate when Elow < 18300 V. The results of the measurements of the 96 run revealed for the first look the similar feature as in the 1994 run. The fit with 4 parameters resulted in m v2 = -(15 - 20) e V 2 / c 4 for Elo~ > 18200 eV and in some rise for smaller values of Ezow. The negative value of m~ at Etow > 18300 e V disappeared as well as in the previous run when introducing the step-like function. The main distinction from the 1994 run proved to be a shift of the step energy towards lower energies by 4.7 eV, keeping the magnitude of the step about the same as in the 94 run, that is 6.6 :t: 1.8.10 -11. The shift was definitely seen when the spectra of 1994 and 1996 runs were superposed being reduced to the same end-point energy and normalization factor. The difference between spectra proved to be the bump-like shaped with a width nearly corresponding to energy resolution. It excludes any description of the step as some smooth local enhancement produced by final state spectrum distortion or improper account for energy loss or other similar phenomena. Being very strange by itself this shift gave nevertheless an sufficient evidence in favor of small width of the spike-like structure producing the step in the integral spectrum. In the first report of our group [1] a low-energy anomaly was described as a rise of the spectrum intensity below 18300 eV with respect to theoretical spectrum. It is worth mentioning that the rise of the intensity at low energy was earlier observed in the experiment of the Mainz group [4] and this effect was considered as a source of the rise of the negative m 2 when decreasing Elow. Further analysis of possible systematics revealed considerable underestimation of the effect connected with the trapping of electrons in the tritium source. Such trapping has happened in
> 12 i,i
I
lO
t2 B
¢
2
01~
19'94
19195
19196
19197
1998 year
Figure 1. Evolution of step position with calendar time. Crossed point is an average of Run 94. E0 is the fitted end-point energy.
the tritium tube due to the bottle-like configuration of magnetic field in the source. The majority of trapped electrons is slowed down or escaping by multiple scattering to rear side of the source but small part of them may be scattered from the trapping momentum space into the solid angle of the momentum space which corresponds to the acceptance of the spectrometer.Such scattering takes place after some slowing down of the electrons in the magnetic trap so the scattered electrons will enrich the low-energy part of the measured spectrum. Calculation of trapping effect was made by means of the Monte-Carlo method. Unfortunately accuracy of calculations is limited by uncertainty of stopping power cross section amounting to 18%. After correction for trapping effect the low energy anomaly in the spectrum disappeared within errors. Accounting for both the step and trapping effect provided description of all the measured part of the spectrum with m v2 about zero within fit errors [2,3] thus eliminating 2 the problem of the negative m~. 4. R u n 97 results. The last long run was carried out in FebruaryMarch 1997.There were no significant changes of the set-up besides some upgrading of tritium and
V.M. Lobashev et aL/Nuclear Physics B (Proc. Suppl.) 66 (1998) 187-190 data acquisition systems. The fit results are given in table 1.As well as in the Run96 the 4 parameter fit with correction for the trapping effect gives negative m ,2 but smaller then in previous runs.The introduction of step makes fit result unstable and increase fit error for m~2 more then two times.The size of step fluctuate around value which is a few times smaller then in previous measurement and its position is found to be shifted from the 96 run by about 7 eV toward end point as shown in Fig.1 .This step position is obtained in the fit with fixing m ,2 = 0.The results shown in table 1 were obtained by fixing this step position leaving m v2 free. Thus we face very strange behaviour of bump effect which , if to accept that it belongs to tritium decay , should correspond to very exotic physics. In Fig.1 the positions of bump found in different runs are plotted with respect to the calendar time of the measurement.The first three point are obtained from subsection of data of 1994 in three subruns with maximum difference in time approaching half a year.The error of these points are not small enough to make decisive conclusion but their position spread hints to possibility of regular movement of the bump. At the moment we do not see any possibility for an instrumental artefact causing the bump effect. The last attempt to fix the part of the set-up possibly responsible for the effect was performed during run 97,when the tritium source was isolated from the spectrometer and potential+15V was applied to it. The fit of the partial run data after correction to 15 V showed good accordance with data without shift.Unfortunately this test cannot be quite decisive due to small size of the step in this run mentioned above.Other tests were considered in [1]. 5, T h e n e u t r i n o m a s s u p p e r l i m i t The shape of the difference spectrum of the 96 and 94 runs near end point indicate that accounting for the step-like distortion is necessary for adequate description of the experimental spectrum. Of course the size of the step being introduced as free parameter correlate with my2 and increase the final error of neutrino mass thus acting as a kind
189
of systematic error. Absence of dependence of mv2 on Eloto permit to assume that the step-like structure near the end point is the only visible anomaly in the spectrum.Its uncertainty increases the uncertainty of the fitted neutrino mass due to correlations and together with uncertaintties of corrections used before fitting form a systematic error. To deduce the neutrino mass effect one must select the interval of the spectrum which provides minimum total error of m~2 including statistical and systematical one . Most important of the uncertainties of parameters of correction factors come from the following: 1.Density of the source. 2.The shape of the energy loss spectrum. 3.Trapping effect in the source. 4.Final states spectrum (FSS) uncertainty. Regression dependence of the fitted m~2 on the variation of the parameters of the above mentioned corrections was given in Table 2. of [2]. These values can be considered as estimates of systematical errors. The fit errors of m v2 decrease with rise of Etow while the systematic error increase. For this reason one may select optimal Elow when the total error taken as the quadrature of the fit and systematic error has minimum. With these assumptions one may select Elo,,, 18400eV for estimation of the neutrino mass limit from the data of the 96 run. 2
7Tt v -----
3, 8 4- 7.4/it + 2, 98yat, e V 2 / c 4
(1)
In Run 94 Etow = 18300 e V corresponds to minimum of full error so we have - 2 , 7 -t- 10.1/it 4- 4.9svst, e V 2 / c 4
m b,
(2)
It is possible to combine results of both runs into one because each of them is statistically independent. We sum figures with statistical errors as usual but make weighted average of systematical errors using o'stat -2 as weights. A combined value was given in [2,3]: rn,2 = 1.5 4- 5.91it 4- 3.6,y,t, e V 2 / c 4
(3)
From here one may deduce:
m,, < 3, 8 e V / c 2, 95% C.L.
(4)
In Run 97 the minimum error corresponds to Elo,~ = 18400eV, rn~
2
:
- 8 . 6 4- 7.6/it 4- 2, 9,v,t, e V 2 / c 4
(5)
I(.M. Lobashev et al./Nuclear Physics B (Proc. SuppL) 66 (1998) 187-190
190
Table 1 Fit results for the run 97 data spectrum.
EIo w
m2
Step(B.R.)
eV
eV2/c 4
10-11
E0 eV
18000 18100 18200 18300 18350 18400 18450
-5.7 4, 6.8 -6.3 q- 4.7 -2.1 4- 5.6 -7.7 q- 6.2 -10.1 4, 6.5 -8.6 4, 7.6 3.5 -4- 11.1
0.64-1.1 0.64-0.9 1.14-1.1 0.44.1.0 0.24-1.0 0.34-1.1 1.64,1.6
18575.30 18575.23 18575.30 18575.20 18575.15 18575.18 18573.46
Combining all the data one could deduce : my < 3, 2 eV/c 2, at 95% C.L. but large spread of fit results in run 97 make it reasonable to use only previous limit. 6. C o n c l u s i o n
New measurements of the tritium betaspectrum on the "TROITSK v -MASS" set-up and new analysis of systematic effects explained one of the earlier reported anomalies in the spectrum [1], that is a rise of intensity of experimental spectrum toward lower energy thus reducing so called "negative m v2, effect to problem of existing a narrow bump in the vicinity of end point. The position of the bump with respect to the fitted end point energy is found to move within the range 5 - 12eV belowE0 with some hint of periodic character of this movement.The origin of this bump remains puzzling, but if its existence is confirmed in further experiments as a tritium decay branching process, it will be necessary to consider very exotic possibilities such as were considered in [5,6],for example. This work was partially supported by the Russian Foundation for Basic Research (grants 3903 and 18633a), by Program for Fundamental Nuclear Physics and by INTAS-RFBR (grant 96-02819).
Step -- 0
x2/
m y2
d.o.f.
eV2/c 4
59.7/59 58.1/55 53.2/51
-9.2 4- 3.3 -8.6 4- 2.6 -7.34-2.8 -9.8+3.1 -10.9 4- 3.5 -10.5 4- 3.8 -7.3 4- 4.3
47.3/47 41.5/45 43.4/43
39.9/41
d.o.f.
60.0/60 58.43/56
53. /52 47.4/48 43.8/46 43.5/44 41.1/42
REFERENCES
1. A.I.Belesev et al., Physics Letters B 350
(1995) 263. 2. V.M.Lobashev et al., Proceedings of the International Conference "NEUTRINO-96" Helsinki,Finland; June 13-19, 1996,World Scientific P.264-277. 3. V.M.Lobashev , Conference Proceedings Vol.57," Frontier Objects in Astrophysics and Particle Physics", F.Giovannelli and Mannocci(Eds),SIF,Bologna, 1997, p.511. 4. Ch.Weinheimer et al., Physics Letter B 300 (1993)210. 5. R.N.Mohapatra, S.Nussinov, Physics Letter B 395(1997),63-68. 6. J.Ciborowski, J.Rembielinski, Proc.28th Int.Conf.on High Energy Physics, IHEP-96, vol II ,p.1274.