An upper limit for the mass of upsi;e from tritium β-decay

Volume 173, number 4

PHYSICS LETTERS B

19 June 1986

AN UPPER LIMIT FOR THE MASS OF 6 e FROM TRITIUM ~I-DECAY M. FRITSCHI, E. HOLZSCHUH, W. KONDIG, J.W. PETERSEN 1, R.E. PIXLEY and H. STI]SSI Physics Institute, University of Ziirich, CH-8001 Zurich, Switserland and Swiss Institute for Nuclear Research, SIN, CH-5234 Villigen, Switzerland

Received 12 May 1986 The endpoint region of the tritium H-spectrum has been measured with 27 eV resolution, using a magnetic spectrometer. The tritium activity was implanted into a thin layer of carbon. The ~e mass determined is consistent with zero with an upper limit of 18 eV, which includes instrumental and statistical uncertainties as well as uncertainties due to the energy loss in the source and the final electronic states.

Since 1980 a group at ITEP (Institute for Theoretical and Experimental Physics, Moscow) has been publishing a series of papers [ 1], claiming evidence for a nonzero mass o f the electron antineutrino as determined from the spectrum of the tritium 13-decay. The experiment has been improved continuously, the latest result being 20 eV <~ m v ~< 45 eV with a central value of 35 eV. However, this result has been subject to some criticism [2,3]. Up to now no other experiment has reached a sufficient sensitivity to be a true, independent test. Here we report first results o f our measurement of the endpoint region at the tritium 13-spectrum. The instrument employed in the present investigation consists of a toroidal field, magnetic spectrometer of the Tretyakov type [4] with 2662 mm source-detector distance, modified with a radial, electrostatic retarding field around the source. At the exit of the spectrometer, the ~.-particles are reaccelerated by a voltage o f 15 kV before entering a proportional counter (diameter 5 cm, length 10 Cm) with a resistive anode wire. Pulse height and position, determined by charge division, are recorded. The source assembly consists o f 10 rings, each with 5 cm diameter and 1 cm width, i.e. the total active source surface is 157 cm 2. To compensate for the source length a gradient voltage, proportional to the spectrometer dispersion, 1 Present address: CERN, CH-1211 Geneva 23, Switzerland.

is applied along the rings. Spectra are recorded by stepping the retarding voltage while keeping the analyzing energy o f the magnetic spectrometer constant at 2.2 keV. More details may be found in ref. [5]. With a set-up as described above, the spectrometer has the following basic properties: 0.6% transmission, 1.1 eV/mm dispersion, and 27 eV resolution (full width at half maximum, FWHM). The spectrometer resolution function (SR) has been calculated by Monte Carlo simulation. Due to the simple, almost cylindrical geometry, the electric and magnetic fields o f the spectrometer are known analytically. Sufficient mechanical precision is assured by the modest, relative resolution (~1%) in the magnetic part of the spectrometer. Detailed conversion electron measurements [5] have confirmed the calculated shape of the SR (see fig. 1) and the agreement between the calculated and measured resolution width was found to be better then 10%. However, the determination of the SR from the measured conversion lines is complicated by shake-off effects and the calculated SR is believed to be more reliable. Three sources were prepared by implantation of T~ ions into carbon, evaporated onto an aluminium backing. The implantation energies were in the range 1 0 0 - 2 0 0 eV per tritium atom giving typically an activity of 0.3 mCi/cm 2. To avoid excessive contamination of the spectrometer, weakly bound tritium on the surface of the sources was removed by bombarding 485

Volume 173, number 4 I

PHYSICS LETTERS B I

I

25tl 2O EL+SR t~~///l/,/SR tZ

w t0 Z

5 I 0 5O

-100 -50 0 ENERGY LOSS (eV)

50

Fig. 1. Spectrometer resolution function (SR), energy loss spectrum (EL) in source T3 convoluted with SR, and the sum of both.

with tow energy ( ~ 1 0 eV) H~ ions. This process removed about 15% of the total activity. The depth profiles of the tritium concentration were then measured with 50 A resolution (FWHM) using a nuclear recoil technique similar to that described in ref. [6]. Experimental values for the mean free path k and the single interaction energy loss spectrum for electrons in carbon [7] were used in conjection with the profiles to determine the energy loss spectrum (EL) for each source. The result for source T3, already convoluted with the SR function, is displayed in fig. 1. Important uncertainties, which enter the calculation of EL, are due to the d E / d x values used in the profile measurement, the density of the carbon substrate, and X. All of these have equivalent effects on EL, i.e. there is only one effective length scale, which we choose to be the mean source thickness d and which should be accurate to better than 15%. Independently the spectrum of various conversion electron sources covered with evaporated carbon have been measured with the spectrometer. This test confirmed the validity of the procedure described above. The sum of the SR and EL spectra is the effective resolution function (ER) of our measurements and is also shown in fig. 1. Backscattering in the source substrate was investigated by MC simulation [8]. It was found that this effect can be adequately represented by a constant distribution below the no-loss line. Its intensity, how486

19 June 1986

ever, could not be calculated with sufficient accuracy and was therefore treated as a free parameter in the data analysis (see below). The data reported here were taken in four runs wiff three sources ( T 1 - T 3 ) , totalling 27 days of effective measuring time. Event data, consisting of pulse height and position along the detector, were recorded and binned into spectra for 20 detector positions. These were then energy shifted and added to obtain a single spectrum for each run. A small correction (less than 1% at high count rates) for detection dead time was applied. Data were taken in the energy range 1 7 . 7 19.3 keV. Fig. 2 shows a section of the spectra around the endpoint in the form of Kurie plots. The t3-spectrum was assumed to have the form N ( E ) = A F ( E ) P E t ( 1 + aeO)

-,,,vl~ iy

i

(1)

-BG,

where e i = Eoi - E. F ( E ) is the Fermi function, and p, E, and E t are momentum, kinetic and total energy, respectively. The sum runs over all electronic final states (FS) with branching fractions Wi and endpoints Eoi. Each term in the sum is set to zero for E above the point where the term reaches zero. The E o i are defined by Eoi = EO0 - Eex,i , where E00 corresponds to the electronic ground state and is, for m v = 0, the

18.4

I

I

I

I

18.5 18.6 ENERGY (keV)

I

18.7

Fig. 2. Section of the data (points) from runs 1-4 in the form of a Kurie plot and the corresponding best fits (solid lines) assuming CHaT ES and with fitted parameters as listed in table 1.

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PHYSICS LETTERS B

true endpoint o f the spectrum, and the Eex,i are excitation energies measured from the ground state. Backscattering in the source substrate is taken into account by the parameter ~ and enters in this approximate form by a convolution of the backscattering distribution with a t3-spectrum proportional to e 2. The fit function is obtained by convoluting eq. (1) with the ER function (see fig. 1), and by including a correction factor for the varying spectrometer acceptance with changing retarding voltage. The free parameters are a, E00 , an overall normalization A , background BG, and the neutrino mass squared m 2. The latter was allowed to take on nonphysical, negative values, in which case the square root in eq. (1) was replaced by its first-order expansion [ 1 - m 2 / ( 2 e i l e i [ ) [ . This gave symmetric, parabola-like curves for X2 versus m 2. Our final result does not depend on this assumption. The measured t3-spectra were fitted using the FS distributions o f the bare nucleus (T +, one level), the free atom (T), molecular tritium [9] (T2), and the methane molecule [10] (CH3T). In addition all four spectra were fitted simultaneously, with m 2v being the only common parameter. The results are shown in fig. 3 in the form of X2 versus m2v curves, all other parameters being fitted for each value ofm2v . The number of degrees o f freedom (DOF) for these fits is 1370. Obviously, the best value for m 2 depends on the assumed FS. However, at our present level of precision

-30

NEUTRINO MASS (eV) -20 -10 0 10

1420

20

T-

1410 .~ 1400

8

1390

o~ 1380

this dependence is only critically determined by three averaged properties of the FS. These are the ground state fraction W0, the mean energy Eex and the mean width 2~Eex of the excited states (the ground states excluded from the means). This dependence was confirmed by fitting our data using a variety o f FS distributions. It may also be justified analytically [ 11 ]. Concerning the FS for our sources we argue as follows. The extremely small diffusion rate o f hydrogen isotopes implanted in carbon [12] and the stability o f our sources strongly suggest that C - T bonds are formed. Kaplan et al. [10,13] calculated the FS for a variety o f molecules with C - T bonds and found very little variation in terms o f their averaged properties. Moreover, W0 and Eex can simply be calculated using ground state wave functions alone and are thus more reliable than any particular feature in the excited state distribution. We thus take CH3T , the simplest case, as an adequate representation for the FS of our sources. The corresponding fit results for the four spectra and the combined set of data are listed in table 1. Also shown here is F N L, the probability of no-energy loss in each source. As can be seen in fig. 2 and table 1, good fits were obtained and m 2v is compatible with zero within one sigma. Statistical upper limits UL for rn~ at the 95% confidence level are also shown. Due to calibration problems the E00 values show some non-statistical variation and may be subject to 10 eV systematic bias. It may be conceivable that some small fraction o f tritium in our sources is in the form of T 2 molecules. It can be seen in fig. 3 that this would make m 2 only smaller and thus does not invalidate any UL. The m v = 35 eV hypothesis was tested by fitting all data with fixed values m v = 0 and m v = 35 eV, giving X2 = 1370.2 and X2 = 1773.2, respectively, with DOF = 1370. In fig. 4 the normalized deviations for spectrum 4 are plotted for the two cases. It is seen that the m v = 35 eV hypothesis gives a very poor fit, whereas no systematic deviations are discernible for mv=O.

1370

136°-8bo

19 June 1986

' -46o

'

6

'

4do

MASS SQUARED (eV 2)

Fig. 3. Plot of x2 versus m2ufor the combined set of data, with all other free parameters being fitted. Assumed are the final states of the bare nucleus T÷, the atom T, the tritium molecule [9] T2, and methane [10l CH3T.

Systematic errors for m 2 were investigated by fitting our data with changed input parameters o f the fitted function. These are the width of the SR function and the effective mean source thickness d, and the FS parameters W0, Eex , 2~Eex. The uncertainties for the latter were taken to be the maximum variation in the results for all molecules involving C - T bonds reported in refs. [10,13] and increased generously to 487

Volume 173, number 4

PHYSICS LETTERS B

19 June 1986

Table 1 Fit results for four runs with three different sources and the combined set of data, using CH3T final states. Errors indicated are one standard deviation. Data set 1 2 3 4 all

Source TI T2 T2 T3 -

FNL

×2

0.573 0.589 0.589 0.662

328.8 345.6 349.9 343.7 1370.2

DOF 337 356 356 317 1369

E00 - 18500 (eV)

c~ (keV- 1)

m 2 v

(eV 2)

UL(95%) (eV 2)

82.6 -+ 0.3 84.5 +- 0.2 84.4 -+ 0.2 77.6+-0.2 -

0.018 -+ 0.004 0.020 -+ 0.002 0.022 -+ 0.002 0.021+-0.002 -

140 +- 130 9 -+ 140 - 2 2 +- 140 -85-+ 93 -11 + 63

356 218 202 70 95

t h a t m v2 was increased. N o t e t h a t X2 stays e i t h e r cons t a n t or is increased in all cases. M a k i n g all c h a n g e s in table 2 s i m u l t a n e o u s l y shifts m v2 up to 398 eV 2 b u t also increases X2 b y 28 u n i t s a n d is t h u s n o t a c c e p t a b l e T h e r e f o r e we t r e a t t h e shifts o f m 2 in table 2 as indep e n d e n t errors a n d add t h e m in q u a d r a t u r e . This gives 2 0 4 e V 2 as s y s t e m a t i c e r r o r for r n 2v . A s s u m i n g the best fitted value for m 2 v w o u l d be e x a c t l y zero ( a n d n o t - 1 1 e V 2) a statistical U L o f 106 eV 2 for m 2 at 9 5 % c o n f i d e n c e level was calculated. A d d i n g b o t h n u m b e r s linearly ( r a t h e r t h a n q u a d r a t i c a l l y ) we arrive at o u r final result, m 2v < 3 1 0 e V 2, or

5 0

5 0 -5

17.8

18.2

t8.6

19.0

m v

< 18 e V .

ENERGY (keV) Fig. 4. Plot of the difference between the fitted function and the data, divided by the standard deviation, for spectrum 4 with two fixed values of my, all other tree parameters being fitted. FS of CH3T were used.

In c o n c l u s i o n we find n o i n d i c a t i o n o f a n o n z e r o mass for the e l e c t r o n a n t i n e u t r i n o , w h i c h is in strong cont r a d i c t i o n to t h e results o f ref. [ 1 ]. We see n o possible source o f error in o u r e x p e r i m e n t large e n o u g h t o acc o u n t for this d i s c r e p a n c y .

a c c o u n t for c a l c u l a t i o n a l u n c e r t a i n t i e s , T h e effects o f varying e a c h i n p u t p a r a m e t e r separately are listed in t a b l e 2. T h e d i r e c t i o n o f t h e c h a n g e s was c h o s e n such

We gratefully a c k n o w l e d g e a grant f r o m t h e Swiss N a t i o n a l Science F o u n d a t i o n and the c o n t i n u o u s supp o r t f r o m SIN. We are p a r t i c u l a r l y i n d e b t e d to the

Table 2 Fitted values of m~ and the corresponding shift 2xm u when the input parameters ot the fitted function are changed. Shown are only changes which increase m2u. The complete set of data was fitted, with DOF = 1369. 2

488

•

-

Input parameter

Relative change (%)

x2

m2u(eV2)

Am2u(eV2)

best set spectrometer-resolution mean source thickness ground state fraction mean excitation energy width of excited states

+ 10 +15 -2.5 +6 +30

1370.2 1370.2 1373.8 1370.5 1373.2 1386.3

-11 52 120 30 111 52

63 131 41 122 63

Volume 173, number 4

PHYSICS LETTERS B

s t a f f o f t h e Physics I n s t i t u t e m a c h i n e s h o p for very close c o o p e r a t i o n d u r i n g t h e c o u r s e o f this e x p e r i m e n t .

References [1 ] V.A. Lubimov et al., Phys. Lett. B 94 (1980) 266; Sov. Phys. JETP 54 (1981) 616 [Zh. Eksp. Theor. Fiz. 81 (1981) 1158]; Phys. Lett. B 159 (1985) 217. [2] J.J. Simpson, Phys. Rev. D 30 (1984) 1110. [3] K.E. Bergkvist, Phys. Lett. B 154 (1985) 224; B 159 (1985) 408. [4] E.F. Tretyakov, Izv. Akad. Nauk SSSR Ser. Fiz. 39 (1975) 583. [5] W. Ktindig et al., Proc. Fourth Moriond Workshop (La Plagne, Savoie, France, 1984), ed. J. Tran Thanh Van (Editions Fronti6res, Paris, 1984)p. 261. [6] G.G. Ross, B. Tcrreault, G. Gobeil, G. Abel, C. Boucher and G. Veilleux, J. Nucl. Mat. 128 (1984) 730.

19 June 1986

[7] R.E. Burge and D.L. Misell, Phi]. Mag. 18 (1968) 251. [8] R. Shimizu, Y. Kataoka, T. Ikuta, T. Koshikawa and H. Hashimoto, J. Phys. D. 9 (1976) 10t. [9] O. Fackler, B. Jeriorski, W. Kolos, H.J. Monkhorst and K. Szalewicz, Phys. Rev. Lctt. 55 (1985) 1388. [10] I.G. Kaplan, G.V. Smelov and V.N. Smutnyi, Dokl. Akad. Nauk SSSR 279 (1984) 1110. [ 11 ] Chin Cheng-rui and Ho Tso-hsiu, Phys. Rep. 112 (1984) 1. [12] B.L. Doyle, W.R. Wampler and D.K. Brice, J. Nucl. Mat. 103 (1981) 513; V. Malka, H.D. R6hrig and R. Hecker, Proc. Tritium technology in fission, fusion, and isotopic applications, American Nuclear Society National Topical Meeting (Dayton, OH, 1980) p. 102. [13] I.G. Kaplan, V.N. Smutnyi and G.V. Smelov, Phys. Lett B 112 (1982)417.

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