- Email: [email protected]
Search for exotic K X-rays from neutral iodine atoms and limits on charge non-conservation
Physics Letters B 282 (1992) 281-287 North-Holland
P H YSI C S I_ETT ER$ B
Search for exotic K X-rays from neutral iodine atoms and limits on charge non-conservation H . Ejiri, H . K i n o s h i t a , H. S a n o a n d H. O h s u m i Department of Physics, Osaka University, Toyonaka, Osaka 560, Japan Received 19 February 1992
Exotic K X-ray emission from neutral iodine atoms was searched for by using a large volume NaI detector. The most stringent upper limit on the K X-ray emission rate was obtained as 8.3 × 10-~4 yr- ~. It leads to the most stringent upper limits ~v < 3.0× 10- 30, ~2 < 1.5 × 10-45 and fi2p < 1.1 × 10 -46 for the relative strengths of the charge non-conserving (CNC) weak process, the CNC electromagnetic process, and of the non-paulian K X-ray emission, respectively.
This letter reports the most stringent limit on exotic K X-ray emission from neutral iodine atoms, and accordingly the most stringent limits on the relevant charge non-conservation. On the basis o f the stand a r d m o d e l o f the electron, the K X-ray emission is forbidden in stable atoms, where the K-shell is filled by two electrons. Searches for such forbidden K Xrays, however, have recently attracted strong interest as the most sensitive test for the stability o f electrons in atoms, and for the charge conservation ( C C ) law. The possible process relevant to exotic K X-ray emission is the X-ray transition to the K-electron hole p r o d u c e d by the spontaneous d i s a p p e a r a n c e ( d e c a y ) o f the K-electron ( e ~ ) . In the framework o f the stand a r d model the electron is the charged particle with the lowest mass and the CC law is valid. Consequently a disappearance (decay) o f the electron must be associated with the C N C processes, which is a process b e y o n d the s t a n d a r d model. The K-electron decay and the C N C can be studied by investigating the following three modes: e3v mode:
e ~ ---~Ve -1- Vi -1- Vi ,
(1)
~ mode:
e - (v) + A - - , e - (v) + B ,
(2)
ev mode:
e v N N ' : eff~ + A - - , v + A * ,
(3)
evNN: ey. + A ~ v + A ,
(4)
where A and B are atomic nuclei, and A* is an excited state o f A. The F e y n m a n diagrams are shown in fig. 1. The gauge bosons (B °-+ ) m e d i a t i n g the C N C process are the weak bosons (Z °, W ÷ ) in case o f the weak process a n d the p h o t o n ('/) in case o f the electromagnetic process. The C N C process must involve either e*--,v or u,--~d conversions (see fig. 1 ) which violate the CC law at either the lepton or quark sector, respectively. The CC law is considered to be valid under the framework o f the gauge-invariance o f the Q E D field theory with the massless gauge boson ( p h o t o n ) . Experimentally, the CC law, however, has not been checked with an accuracy c o m p a r a b l e to other conservation laws. Thus it is o f great importance to search for a possible violation o f the CC law and to i m p r o v e the experimental limit on the validity o f the CC law. Experimental studies o f the e3v m o d e (eq. ( 1 ) ) have been m a d e by searching for K X-rays [ l - 7 ] and those o f the ££ m o d e (eq. ( 2 ) ) by searching for the forbidden beta decays [ 8 - 1 0 ] as shown in fig. 1 (12t~np). Recently the ev m o d e has been studied by investigating `/-rays following nuclear C N C excitation [ 11,t2], as shown in fig. 1 ( e v N N ' ) . Small volume g e r m a n i u m detectors have been used for most o f the K X-ray studies o f the germanium isotopes with the atomic n u m b e r Z = 32 and the neutron n u m b e r N = 38-42. Recently large volume N a I detectors have been used for studying "/-rays following inelastic excitation o f 127I with Z = 5 3 and N = 7 4 . The experi-
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
281
Volume 282, number 3,4 (I)e3k
mode
e
(2) [ [ mode
PHYSICS LETTERS B ;TB °
e (~)..
1,)
e
• i B +-
e(z,)
e (z/) , ,
u(d,)
d (u
e(h) :B o i. u (d.)
q
II. np
d
(u). i
B+ -
e
(l,)~, .
e(/,,)
n A -
z,)
O~c
,
IB °*>,, p, ~/ B "
0 ..'"'" ---~--
- ~
e
QEe-me B
(3) ez, mode ?
~
u(d):, i:B° u ( c ~ ) eK
e ~ NN'
; ;
Ea
/~
eK
A
eK/
A~
> :
~,7" A
Ea
I, ~
T.
~- A*
0 A/
i B°+- / ~I ~ A -~.} '
--
" ~'--~i.
"
e/~NN
u(d); ii B-+ u((~)
! B°±
N A
~
K e 0
A
~ A
Fig. 1. The CNC (charge non-conserving) diagrams for ( 1) the e3v mode of e----+Ve'~Vi-'l-Q i (2) J~ mode of A--*B +e-(v)+e+(9) and (3) ev mode o f e - + A ~ v + A (B or A*). £~np, evNN' and evNN stand for the CNC process relevant to the IS-decay (n,-,p), the inelastic process (A-*A*) and to the elastic process (A--,A), respectively. The bosons mediating these processes are given by B°x. They are the weak bosons (Z, W ± ) in the weak process and the photon (7) in the electromagnetic process. QEc, me and Ea are the electron capture Q value, the electron rest mass energy and the K-electron binding energy, respectively. ments and theories o f the C N C processes are discussed in refs. [13,14]. The possible C N C and electron decay processes have been discussed also from a cosmological point of view [ 15,16 ]. In the present work we studied for the first time the elastic mode o f e v N N by searching for the K X-ray o f iodine. The CNC process mediated by the neutral weak boson (Z °) and by the p h o t o n ( 7 ) are concerned with the CNC at the lepton sector ( e - v conversion), while the process mediated by the charged weak bosons (W ± ) are with the C N C at the quark 282
28 May 1992
sector. Then both the lepton and quark sectors are studied by the evNN mode as in the case of the evNN' mode [ 12 ]. The unique and the crucial points of the present work are threefold: (i) study of the elastic mode, (ii) search for the K X-ray from iodine with its large Z and N, and (iii) use o f a large volume low background NaI detector. The nuclear matrix element, Me, = 5~N=~( N i IIHIIN~), for the elastic mode is the coherent sum of all amplitudes of all neutrons in the nucleus. On the other hand the matrix elements for the ££np([~-decay) and e v N N ' (inelastic excitation) modes are the transition (non-diagonal) ones, Ma=
Volume 282, number 3,4
PHYSICS LETTERS B
Pb PM
28 May 1992
Shield
Cu S h i e l d i
,, ~'S
,,
e
D
~
Pb 0 ....
0;5 . . . .
Fig. 2. Schematic drawing of the side view of ELEGANTS-V used for 1313decays. CD: Cable drain, DC: Drift chamber, NaI: Nal scintillator, PI: Plastic scintillator, PM: photomultiplier, Q: Quartz light guide and S: source. The 17 modules of the NaI detectors among the 20 modules, 10 above and 10 below DC, were used for the present K X-ray search. Thus the data were taken in a c o i n c i d e n c e - a n t i c o i n cidence m o d e o f EiXi ~j~i XjFIkPk, where Xi is a signal from the ith N a I scintillator, and Xi and Pk stand for anticoincidence with signals from t h e j t h N a I a n d kth P L modules, respectively. The m e a s u r e d energy spectrum in the K X-ray region is shown in fig. 3. The total measuring time was 2823 h. Unfortunately, each N a I crystal turned out to contain more or less 2~°Pb isotopes with a Q value Q~=63.0 keV. It decays 19% to the ground state o f 2t°Bi and 81% to the 46.5 keV excited state. The 46.5 keV T-ray peak c o m b i n e d with the c o n t i n u u m ~-ray spectrum is clearly seen. In the analysis we selected 17 NaI crystals out o f 20 modules since the other three modules contained much more 2~°pb than the average content o f the selected ones. The K X-ray emission is followed by successive L, M, ... X-rays or Auger electrons in the same detector. Thus the K Xray signature is expected at the b i n d i n g energy at E a = 3 3 . 2 keV, corresponding to the energy sum o f these X-rays. The observed spectrum shows no distinct peak at this energy o f EB. In order to obtain the u p p e r limit on the K X-ray yield, the spectrum in the energy interval between Ex = 20 keV and 120 keV was analyzed by a least-square fit with the following five components: ( i ) F e r m i function o f the 13-ray spect r u m corresponding to a transition from 2~°pb to the 2'°Bi ground state, (ii) F e r m i function o f the fl-ray spectrum corresponding to a transition from 2~°pb to the 2~°Bi first excited state c o m b i n e d with the following 46.5 keV transition to the ground state, ( i i i ) two
gaussian peaks corresponding to the b r o a d b u m p o f the K X-rays a r o u n d 80 keV from U-chain a n d Thchain isotopes, ( i v ) a c o n t i n u u m b a c k g r o u n d given by a trigonal function o f the energy, a n d ( v ) the possible X-ray peak at Ex = 33.2 keV o f present interest. The energy resolution A E ( F W H M ) was taken as a function o f the energy E as A E = aE-I-b, where the parameters a = 0.085 and b = 7.8 keV were derived from the observed peaks for the T-rays and X-rays from 241Am, 133Ba, 137Cs a n d 2~°pb sources. It is A E = 10 keV at E a = 33.2 keV. The observed spectrum is well reproduced by the fit as shown in the subtraction spectrum (fig. 3). The upper limit on the K X-ray emission rate is o b t a i n e d from the fit as T(KX)=8.3×
10 -24 yr -1 ,
(5)
with 68% confidence level ( C L ) . The limit is mainly due to the fitting (systematic) error, which is larger by one order o f magnitude than the statistical fluct u a t i o n ( e r r o r ) o f the background. The upper limit on the K X-ray emission rate can be converted to a lower limit o f the K-electron m e a n life o f Zm= 1.2 × 1023 yr with 68% CL. The present value is comp a r e d with other data in table 1. This limit is improved by one o r d e r o f magnitude over the previous one for the K-electron in 127I, a n d it is the same as the most stringent value for the K-electron in german i u m isotopes [ 7 ]. The present result gives a limit on the possible decay ( d i s a p p e a r a n c e ) rate o f e~. --*Ve'JrVi "]-Vi, prov i d e d that the decays are followed by successive X283
Volume 282, number 3,4
PHYSICS LETTERS B
Zl°Pb '
~> @
40
-
30
_
'
'
I
/7
+
. . . .
zl°Bi I
28 May 1992
3'
. . . .
I
'
'
'
I
I
I
I
,
,
o
1
\
20
2 o
10
ill
0
0.15
I
llil
I
. . . .
I :~::
Il i l l
~X
0.10 a~
0.05
o o
0.00
-0.05 N
,
,
,
40
I
,
,,
60 Energy (keV)
,
I
80
, , ,
,
I
100
Fig. 3. The energy spectrum measured by the 17 module Nal detectors. Top: the singles spectrum with the solid line being the best fit. The statistical errors are much smaller than the points. Bottom: the energy spectrum after subtraction of the best fit function (see text). The arrow at E= 33.2 keV indicates the binding energy of the K-electron in iodine. The possible X-ray peak, corresponding to 68% CL, is drawn as a solid line. ray ( a n d A u g e r e l e c t r o n ) e m i s s i o n w i t h a s u m m e d energy o f EB. I f the e l e c t r o n d e c a y is a c c o m p a n i e d by m a n y soft p h o t o n s as discussed by O k u n [ 13 ], t h e o b s e r v e d energy m a y n o t be the b i n d i n g energy EB
284
a n d thus the o b s e r v e d l i m i t is n o t necessarily related to the e l e c t r o n d e c a y rate. T h e i n v a r i a n t a m p l i t u d e o f the C N C process o f e+A-,v+A t h r o u g h the neutral w e a k b o s o n Z ° is
Volume 282, number 3,4
PHYSICS LETTERS B
28 May 1992
Table 1 Lower limits on the K X-ray emission (electron decay) mean lives (zm(yr)), upper limits on relative strength (~2w)for the CNC to CC weak processes and upper limits on the branching ratio (82p) for the non-paulian K X-ray, all with 68% CL. The left column contains: (a) Bellotti et al. [ 15 ], (b) Reusser et al. [ 7 ], (c) Kovalchuk et al. [4 ]. (d) Ejiri et al. [ 12 ], K X-rays following the CNC excitation of the first excitation state of ~27I. Element
Detector
Tm(yr)
E2w
Oe Ge I 1 I
Ge Ge Nal NaI NaI
2.0x 1.9X 2.0X 5.8 X 1.2X
1.5X 1.6x 1.8X 1.1 X 3.0x
10 22 1023 1022 1022 1023
~ 2w __
(6) where the vector coupling constant is given by Cv = l for the neutron and Cv = 14-4 sinE0w for the proton, and the axial vector coupling constant is given by CA= 1.25 for all nucleons in the naive quark model. The transition probability is written as (7)
where M w is the matrix element a n d f t h e phase space factor. In the present case o f the elastic weak process M w is given by the coherent sum o f the Cv7u and the CAYu)'5 terms over all nucleons in eq. ( 6 ) . Then one gets a large value o f I M w 12=Nn - (1 - 4 sin20w)Np,
(8)
where Nn is the n u m b e r o f neutrons and N o is the n u m b e r o f protons in ~27I. Since the second term in eq. ( 8 ) almost vanishes because o f sin20w-~ ~, IM ~ 12 is a p p r o x i m a t e l y given by the square o f the neutron n u m b e r as I M w 1 2 = N 2 = 5 X 103. Here we have neglected the small c o m p o n e n t o f the CATu75 term. It should be noticed that IM W l 2 is by four to five orders o f m a g n i t u d e larger than the value o f w IMinet [ 2 -~ 0.1 for the inelastic process as m e n t i o n e d earlier [ 12]. The phase space factor f is given in a similar way as for K-electron capture as
f = ½.27r( o:Z)3E 2 .
4.8X 5.1 X 6.4X 1.1 X
(9)
The u p p e r limit on the C N C strength G2NC is de-
10 -45
(a) (b) (c) (d) present
10 - 4 6
10 .46 10 -46
,
N
T c N c = G2NC I M ~ IZf, 2/z 3
10 -2s 10 -29 10 .29 10 .24 10 -3°
Comments
d u c e d from the upper limit on the transition rate (eq. ( 5 ) ). The strength relative to the corresponding CC strength o f G2c is derived as
written in analogy to the neutral current process o f e + N - ~ e + N ( N = p or n ) mCNCac ~ GCNC[/J~U( 1 - - 7 s ) e ] [Nyu(Cv - C A ~ s ) N ]
C~hp
= G c2N c / G F2 < 3 . 0 X
10-3o
,
(10)
where GF is the F e r m i coupling constant. Here we used the relation G c c = p G F ~ GF for the neutral current CC coupling constant G c o where p = M w2 / M z 2 cos20w with Mz, M w and 0w being the W boson mass, the Z boson mass and the Weinberg angle, respectively. The C N C process through the charged boson ( W e ) m a y be analyzed by a similar way as the C N C process through Z °, a n d the same value for the limit on the C N C strength is derived. Consequently one can get an upper limit o f 3 X 10- 30 on the relative strengths for both C N C weak processes at the lepton a n d quark sectors. The relative C N C strength, e2, for the p h o t o n mediating process m a y be o b t a i n e d by c o m p a r i n g the 2 C N C rate with the analogous CC rate as Ey = TyCNC/TIC, where T CNC is the C N C transition rate with eK~V, and T IC is the corresponding CC internal conversion rate with e K ~ e . Here we used such internal conversion electron processes that have the same m o m e n t u m as the neutrino and the same matrix element as the elastic one. Then the following upper limit on the relative C N C strength for the p h o t o n - m e d i a t ing process is o b t a i n e d with 68% CL: ~2 ~ 1.5X 10 -45 .
(11)
The o b t a i n e d values are c o m p a r e d with other d a t a in table 1. The present data give the most stringent limit on the C N C weak process, almost six orders o f m a g n i t u d e smaller than the values o b t a i n e d from the 285
Volume 282, number 3,4
PHYSICS LETTERS B
inelastic ( e v N N ' ) process of 127I. The CNC limit can be derived as 1.6X 10 -29 from the limit on the Kelectron life-time of germanium [7]. The present value is one order of magnitude smaller than the value for germanium. The limit on the CNC process for the £~np mode is EZw< 9 X 10- 24 [ 9,18 ]. This is six orders of magnitude less stringent than the present limit. The CNC limit on the lepton sector e3v process (see fig. 1 (e3v)) can be deduced from the K X-ray limit as done in ref. [ 12]. The limit obtained from the present life-time limit o n 127I is E2w< 2.2 × 10-25 and the value obtained from the limit on germanium [ 7 ] is eZw< l A X 10 -zS. These are less stringent than the present limit given in eq. (10). The CNC process through the photon-mediating process is studied by observing the electron decay e-~ve+7. This process, however, may be followed by many soft photons, and the observation of the single "/-ray ofEv = meC2/2 does not necessarily prove this process as discussed in ref. [13]. The present K X-ray search in the neutral iodine atom with the electron-filled K-shell can be related also to the incomplete Pauli-blocking effect associated with the admixture of the symmetric wave function q/s (Bose statisitics). Then such non-paulian K X-ray emission rate T ( K X) is compared with the normal transition rate T O(K X ) for the ionized atom with one electron-hole in the K-shell, as T ( K X) =62NpT°(K X), where 62p is the probability of the admixed symmetric components. Since T O(K X ) is proportional to the fourth power of the atomic number Z, the very stringent limit on the ratio 6~p can be obtained by studying K X-rays of atoms with large Z. T ° ( K X) for 127I with Z = 5 3 is derived as T ° ( K X ) = 0 . 7 8 × 10 -23 yr -~. Then the upper limit is deduced as
62p < T ( K X ) / T ° ( K X )= l.l × lO -46 .
(12)
The non-paulian X-ray transition is shown to be forbidden between states with different symmetries [ 13,14]. Recently the admixture of the symmetric component has been discussed in terms of the possible electron structure (size) in the framework of the composite models for quark and leptons [ 19 ]. Then the Pauli forbidden K X-ray emission rate is related simply to the electron size parameter ro provided that the final state is lower in energy so that the K X-ray 286
28 May 1992
emission is energetically allowed. The K X-ray emission rate is written in terms of ro as
T(KX)=4~rr3(2/ao)31(~slHEMI~2p)I 2,
(13)
where ao is the Bohr radius and (~u~slHEMI~U2p) is the matrix element of the transition between 2p (L) and ls(K)-shells. Then the upper limit on the electron size parameter is obtained from the present K X-ray limit as ro< 1.1 × 10 -17 c m . This value, corresponding to the energy scale of E > 2 TeV, is more stringent than the value obtained from an electron collider experiment [20 ]. In short, the present work gives the most stringent limit on the possible K X-ray emission in a neutral atom with a filled K-electron shell. The use of a large volume low-background Nal detector with large Z(Z:53) 127I has made it possible to get a more stringent value, relative to the normal K X-ray emission rate, by one order of magnitude, than the previous value on germanium. It should be emphasized here that the present K X-ray search associated with the elastic (evNN) CNC process o n 127I with its large neutron number of Am=74 gives a more stringent CNC limit than the values derived from the inelastic ( e v N N ' ) process and from the 13-decay (££np) process by six orders of magnitude. The K X-ray limit is used to deduce the upper limit on any possible Kelectron stability followed by the K X-ray transition and on the possible non-paulian K X-ray transition rate. The authors thank Professor E. Takasugi, Professor A. Hosoya, Professor K. Okada and Professor T. Kishimoto for valuable discussions, Dr. T. Watanabe and Dr. T. Shima for collaboration in this experiment, and the Mitsui Metal Ltd. for the support at the Kamioka mine. This work is supported in part by the Grant in Aid of Scientific Research, the Ministry of Education, Science and Culture, Japan.
References [ 1 ] G. Feinberg and M. Goldhaber, Proc. Nat. Acad. Sci. USA 45 (1959) 1301; A.W. Sunyar and M. Goldhaber, Phys. Rev. 120 (1960) 871. [2] M.K. Moe and F. Reines, Phys. Rev. 140 (1965) 992; F. Reines et al., Phys. Rev. Lett. 32 (1974) 954. [3] R.I. Steinberg et al., Phys. Rev. D 12 (1975) 2582.
Volume 282, number 3,4
PHYSICS LETTERS B
[4] E.L. Kovalchuk, A.A. Pomansky and A.A. Smolnikov, Pis'ma Zh. Eksp. Teor. Fiz. 29 (1979) 163 [JETP Lett. 29 (1979) 145]. [5] E. Bellotti et al., Phys. Lett. B 124 (1983) 435. [ 6 ] E.T. Avignone III et al., Phys. Rev. D 34 ( 1986 ) 97. [7] D. Reusser et al., Phys. Lett. B 255 ( 1991 ) 143. [ 8 ] B.E. Normal and A.G. Seamster, Phys. Rev. Lett. 43 ( 1979 ) 1226. [9] S.C. Vaidya et al., Phys. Rev. D 27 (1983) 486. [ 10] A. Roy et al., Phys. Rev. D 28 (1983) 1770. [ 11 ] S. Holjevic, B.A. Logan and A. Ljubici, Phys. Rev. C 35 (1987) 341. [ 12] H. Eijiri et al., Phys. Rev. C 44 ( 1991 ) 502. [ 13 ] L.B. Okun and Ya.B. Zeldovich, Phys. Lett. B 78 (1978 ) 78; L.B. Okun, Comm. Nucl. Part. Phys. 19 (1989) 99;
28 May 1992
Particle Data Group, J.J. Hermtndez et al., Review of particle properties, Phys. Lett. B 239 (1990) VI.5, and references therein. [14] R.D. Amado and H. Primakoff, Phys. Rev. C 22 (1980) 1388. [15] S. Orito and M. Yoshimura, Phys. Rev. Lett. 54 (1985) 2457. [ 16] A.A. Pomansky, Proc. 1976 Intern. Neutrino Conf., eds. H. Faissner, H. Reithler and P. Zerwas (Aachen, June 1976) p. 671. [ 17 ] H. Ejiri et al., Nucl. Instrum. Methods A 302 ( 1991 ) 304. [18]J.N. Bahcall, Neutrino astrophysics (Cambridge U.P., Cambridge, 1989) p. 361, and references therein. [19]H. Terasawa and M. Yasue, INS report INS-Rep-873 ( 1991 ), unpublished. [20] B. Naroska, Phys. Rev. 148 (1987) 67.
287
P H YSI C S I_ETT ER$ B
Search for exotic K X-rays from neutral iodine atoms and limits on charge non-conservation H . Ejiri, H . K i n o s h i t a , H. S a n o a n d H. O h s u m i Department of Physics, Osaka University, Toyonaka, Osaka 560, Japan Received 19 February 1992
Exotic K X-ray emission from neutral iodine atoms was searched for by using a large volume NaI detector. The most stringent upper limit on the K X-ray emission rate was obtained as 8.3 × 10-~4 yr- ~. It leads to the most stringent upper limits ~v < 3.0× 10- 30, ~2 < 1.5 × 10-45 and fi2p < 1.1 × 10 -46 for the relative strengths of the charge non-conserving (CNC) weak process, the CNC electromagnetic process, and of the non-paulian K X-ray emission, respectively.
This letter reports the most stringent limit on exotic K X-ray emission from neutral iodine atoms, and accordingly the most stringent limits on the relevant charge non-conservation. On the basis o f the stand a r d m o d e l o f the electron, the K X-ray emission is forbidden in stable atoms, where the K-shell is filled by two electrons. Searches for such forbidden K Xrays, however, have recently attracted strong interest as the most sensitive test for the stability o f electrons in atoms, and for the charge conservation ( C C ) law. The possible process relevant to exotic K X-ray emission is the X-ray transition to the K-electron hole p r o d u c e d by the spontaneous d i s a p p e a r a n c e ( d e c a y ) o f the K-electron ( e ~ ) . In the framework o f the stand a r d model the electron is the charged particle with the lowest mass and the CC law is valid. Consequently a disappearance (decay) o f the electron must be associated with the C N C processes, which is a process b e y o n d the s t a n d a r d model. The K-electron decay and the C N C can be studied by investigating the following three modes: e3v mode:
e ~ ---~Ve -1- Vi -1- Vi ,
(1)
~ mode:
e - (v) + A - - , e - (v) + B ,
(2)
ev mode:
e v N N ' : eff~ + A - - , v + A * ,
(3)
evNN: ey. + A ~ v + A ,
(4)
where A and B are atomic nuclei, and A* is an excited state o f A. The F e y n m a n diagrams are shown in fig. 1. The gauge bosons (B °-+ ) m e d i a t i n g the C N C process are the weak bosons (Z °, W ÷ ) in case o f the weak process a n d the p h o t o n ('/) in case o f the electromagnetic process. The C N C process must involve either e*--,v or u,--~d conversions (see fig. 1 ) which violate the CC law at either the lepton or quark sector, respectively. The CC law is considered to be valid under the framework o f the gauge-invariance o f the Q E D field theory with the massless gauge boson ( p h o t o n ) . Experimentally, the CC law, however, has not been checked with an accuracy c o m p a r a b l e to other conservation laws. Thus it is o f great importance to search for a possible violation o f the CC law and to i m p r o v e the experimental limit on the validity o f the CC law. Experimental studies o f the e3v m o d e (eq. ( 1 ) ) have been m a d e by searching for K X-rays [ l - 7 ] and those o f the ££ m o d e (eq. ( 2 ) ) by searching for the forbidden beta decays [ 8 - 1 0 ] as shown in fig. 1 (12t~np). Recently the ev m o d e has been studied by investigating `/-rays following nuclear C N C excitation [ 11,t2], as shown in fig. 1 ( e v N N ' ) . Small volume g e r m a n i u m detectors have been used for most o f the K X-ray studies o f the germanium isotopes with the atomic n u m b e r Z = 32 and the neutron n u m b e r N = 38-42. Recently large volume N a I detectors have been used for studying "/-rays following inelastic excitation o f 127I with Z = 5 3 and N = 7 4 . The experi-
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
281
Volume 282, number 3,4 (I)e3k
mode
e
(2) [ [ mode
PHYSICS LETTERS B ;TB °
e (~)..
1,)
e
• i B +-
e(z,)
e (z/) , ,
u(d,)
d (u
e(h) :B o i. u (d.)
q
II. np
d
(u). i
B+ -
e
(l,)~, .
e(/,,)
n A -
z,)
O~c
,
IB °*>,, p, ~/ B "
0 ..'"'" ---~--
- ~
e
QEe-me B
(3) ez, mode ?
~
u(d):, i:B° u ( c ~ ) eK
e ~ NN'
; ;
Ea
/~
eK
A
eK/
A~
> :
~,7" A
Ea
I, ~
T.
~- A*
0 A/
i B°+- / ~I ~ A -~.} '
--
" ~'--~i.
"
e/~NN
u(d); ii B-+ u((~)
! B°±
N A
~
K e 0
A
~ A
Fig. 1. The CNC (charge non-conserving) diagrams for ( 1) the e3v mode of e----+Ve'~Vi-'l-Q i (2) J~ mode of A--*B +e-(v)+e+(9) and (3) ev mode o f e - + A ~ v + A (B or A*). £~np, evNN' and evNN stand for the CNC process relevant to the IS-decay (n,-,p), the inelastic process (A-*A*) and to the elastic process (A--,A), respectively. The bosons mediating these processes are given by B°x. They are the weak bosons (Z, W ± ) in the weak process and the photon (7) in the electromagnetic process. QEc, me and Ea are the electron capture Q value, the electron rest mass energy and the K-electron binding energy, respectively. ments and theories o f the C N C processes are discussed in refs. [13,14]. The possible C N C and electron decay processes have been discussed also from a cosmological point of view [ 15,16 ]. In the present work we studied for the first time the elastic mode o f e v N N by searching for the K X-ray o f iodine. The CNC process mediated by the neutral weak boson (Z °) and by the p h o t o n ( 7 ) are concerned with the CNC at the lepton sector ( e - v conversion), while the process mediated by the charged weak bosons (W ± ) are with the C N C at the quark 282
28 May 1992
sector. Then both the lepton and quark sectors are studied by the evNN mode as in the case of the evNN' mode [ 12 ]. The unique and the crucial points of the present work are threefold: (i) study of the elastic mode, (ii) search for the K X-ray from iodine with its large Z and N, and (iii) use o f a large volume low background NaI detector. The nuclear matrix element, Me, = 5~N=~( N i IIHIIN~), for the elastic mode is the coherent sum of all amplitudes of all neutrons in the nucleus. On the other hand the matrix elements for the ££np([~-decay) and e v N N ' (inelastic excitation) modes are the transition (non-diagonal) ones, Ma=
Volume 282, number 3,4
PHYSICS LETTERS B
Pb PM
28 May 1992
Shield
Cu S h i e l d i
,, ~'S
,,
e
D
~
Pb 0 ....
0;5 . . . .
Fig. 2. Schematic drawing of the side view of ELEGANTS-V used for 1313decays. CD: Cable drain, DC: Drift chamber, NaI: Nal scintillator, PI: Plastic scintillator, PM: photomultiplier, Q: Quartz light guide and S: source. The 17 modules of the NaI detectors among the 20 modules, 10 above and 10 below DC, were used for the present K X-ray search. Thus the data were taken in a c o i n c i d e n c e - a n t i c o i n cidence m o d e o f EiXi ~j~i XjFIkPk, where Xi is a signal from the ith N a I scintillator, and Xi and Pk stand for anticoincidence with signals from t h e j t h N a I a n d kth P L modules, respectively. The m e a s u r e d energy spectrum in the K X-ray region is shown in fig. 3. The total measuring time was 2823 h. Unfortunately, each N a I crystal turned out to contain more or less 2~°Pb isotopes with a Q value Q~=63.0 keV. It decays 19% to the ground state o f 2t°Bi and 81% to the 46.5 keV excited state. The 46.5 keV T-ray peak c o m b i n e d with the c o n t i n u u m ~-ray spectrum is clearly seen. In the analysis we selected 17 NaI crystals out o f 20 modules since the other three modules contained much more 2~°pb than the average content o f the selected ones. The K X-ray emission is followed by successive L, M, ... X-rays or Auger electrons in the same detector. Thus the K Xray signature is expected at the b i n d i n g energy at E a = 3 3 . 2 keV, corresponding to the energy sum o f these X-rays. The observed spectrum shows no distinct peak at this energy o f EB. In order to obtain the u p p e r limit on the K X-ray yield, the spectrum in the energy interval between Ex = 20 keV and 120 keV was analyzed by a least-square fit with the following five components: ( i ) F e r m i function o f the 13-ray spect r u m corresponding to a transition from 2~°pb to the 2'°Bi ground state, (ii) F e r m i function o f the fl-ray spectrum corresponding to a transition from 2~°pb to the 2~°Bi first excited state c o m b i n e d with the following 46.5 keV transition to the ground state, ( i i i ) two
gaussian peaks corresponding to the b r o a d b u m p o f the K X-rays a r o u n d 80 keV from U-chain a n d Thchain isotopes, ( i v ) a c o n t i n u u m b a c k g r o u n d given by a trigonal function o f the energy, a n d ( v ) the possible X-ray peak at Ex = 33.2 keV o f present interest. The energy resolution A E ( F W H M ) was taken as a function o f the energy E as A E = aE-I-b, where the parameters a = 0.085 and b = 7.8 keV were derived from the observed peaks for the T-rays and X-rays from 241Am, 133Ba, 137Cs a n d 2~°pb sources. It is A E = 10 keV at E a = 33.2 keV. The observed spectrum is well reproduced by the fit as shown in the subtraction spectrum (fig. 3). The upper limit on the K X-ray emission rate is o b t a i n e d from the fit as T(KX)=8.3×
10 -24 yr -1 ,
(5)
with 68% confidence level ( C L ) . The limit is mainly due to the fitting (systematic) error, which is larger by one order o f magnitude than the statistical fluct u a t i o n ( e r r o r ) o f the background. The upper limit on the K X-ray emission rate can be converted to a lower limit o f the K-electron m e a n life o f Zm= 1.2 × 1023 yr with 68% CL. The present value is comp a r e d with other data in table 1. This limit is improved by one o r d e r o f magnitude over the previous one for the K-electron in 127I, a n d it is the same as the most stringent value for the K-electron in german i u m isotopes [ 7 ]. The present result gives a limit on the possible decay ( d i s a p p e a r a n c e ) rate o f e~. --*Ve'JrVi "]-Vi, prov i d e d that the decays are followed by successive X283
Volume 282, number 3,4
PHYSICS LETTERS B
Zl°Pb '
~> @
40
-
30
_
'
'
I
/7
+
. . . .
zl°Bi I
28 May 1992
3'
. . . .
I
'
'
'
I
I
I
I
,
,
o
1
\
20
2 o
10
ill
0
0.15
I
llil
I
. . . .
I :~::
Il i l l
~X
0.10 a~
0.05
o o
0.00
-0.05 N
,
,
,
40
I
,
,,
60 Energy (keV)
,
I
80
, , ,
,
I
100
Fig. 3. The energy spectrum measured by the 17 module Nal detectors. Top: the singles spectrum with the solid line being the best fit. The statistical errors are much smaller than the points. Bottom: the energy spectrum after subtraction of the best fit function (see text). The arrow at E= 33.2 keV indicates the binding energy of the K-electron in iodine. The possible X-ray peak, corresponding to 68% CL, is drawn as a solid line. ray ( a n d A u g e r e l e c t r o n ) e m i s s i o n w i t h a s u m m e d energy o f EB. I f the e l e c t r o n d e c a y is a c c o m p a n i e d by m a n y soft p h o t o n s as discussed by O k u n [ 13 ], t h e o b s e r v e d energy m a y n o t be the b i n d i n g energy EB
284
a n d thus the o b s e r v e d l i m i t is n o t necessarily related to the e l e c t r o n d e c a y rate. T h e i n v a r i a n t a m p l i t u d e o f the C N C process o f e+A-,v+A t h r o u g h the neutral w e a k b o s o n Z ° is
Volume 282, number 3,4
PHYSICS LETTERS B
28 May 1992
Table 1 Lower limits on the K X-ray emission (electron decay) mean lives (zm(yr)), upper limits on relative strength (~2w)for the CNC to CC weak processes and upper limits on the branching ratio (82p) for the non-paulian K X-ray, all with 68% CL. The left column contains: (a) Bellotti et al. [ 15 ], (b) Reusser et al. [ 7 ], (c) Kovalchuk et al. [4 ]. (d) Ejiri et al. [ 12 ], K X-rays following the CNC excitation of the first excitation state of ~27I. Element
Detector
Tm(yr)
E2w
Oe Ge I 1 I
Ge Ge Nal NaI NaI
2.0x 1.9X 2.0X 5.8 X 1.2X
1.5X 1.6x 1.8X 1.1 X 3.0x
10 22 1023 1022 1022 1023
~ 2w __
(6) where the vector coupling constant is given by Cv = l for the neutron and Cv = 14-4 sinE0w for the proton, and the axial vector coupling constant is given by CA= 1.25 for all nucleons in the naive quark model. The transition probability is written as (7)
where M w is the matrix element a n d f t h e phase space factor. In the present case o f the elastic weak process M w is given by the coherent sum o f the Cv7u and the CAYu)'5 terms over all nucleons in eq. ( 6 ) . Then one gets a large value o f I M w 12=Nn - (1 - 4 sin20w)Np,
(8)
where Nn is the n u m b e r o f neutrons and N o is the n u m b e r o f protons in ~27I. Since the second term in eq. ( 8 ) almost vanishes because o f sin20w-~ ~, IM ~ 12 is a p p r o x i m a t e l y given by the square o f the neutron n u m b e r as I M w 1 2 = N 2 = 5 X 103. Here we have neglected the small c o m p o n e n t o f the CATu75 term. It should be noticed that IM W l 2 is by four to five orders o f m a g n i t u d e larger than the value o f w IMinet [ 2 -~ 0.1 for the inelastic process as m e n t i o n e d earlier [ 12]. The phase space factor f is given in a similar way as for K-electron capture as
f = ½.27r( o:Z)3E 2 .
4.8X 5.1 X 6.4X 1.1 X
(9)
The u p p e r limit on the C N C strength G2NC is de-
10 -45
(a) (b) (c) (d) present
10 - 4 6
10 .46 10 -46
,
N
T c N c = G2NC I M ~ IZf, 2/z 3
10 -2s 10 -29 10 .29 10 .24 10 -3°
Comments
d u c e d from the upper limit on the transition rate (eq. ( 5 ) ). The strength relative to the corresponding CC strength o f G2c is derived as
written in analogy to the neutral current process o f e + N - ~ e + N ( N = p or n ) mCNCac ~ GCNC[/J~U( 1 - - 7 s ) e ] [Nyu(Cv - C A ~ s ) N ]
C~hp
= G c2N c / G F2 < 3 . 0 X
10-3o
,
(10)
where GF is the F e r m i coupling constant. Here we used the relation G c c = p G F ~ GF for the neutral current CC coupling constant G c o where p = M w2 / M z 2 cos20w with Mz, M w and 0w being the W boson mass, the Z boson mass and the Weinberg angle, respectively. The C N C process through the charged boson ( W e ) m a y be analyzed by a similar way as the C N C process through Z °, a n d the same value for the limit on the C N C strength is derived. Consequently one can get an upper limit o f 3 X 10- 30 on the relative strengths for both C N C weak processes at the lepton a n d quark sectors. The relative C N C strength, e2, for the p h o t o n mediating process m a y be o b t a i n e d by c o m p a r i n g the 2 C N C rate with the analogous CC rate as Ey = TyCNC/TIC, where T CNC is the C N C transition rate with eK~V, and T IC is the corresponding CC internal conversion rate with e K ~ e . Here we used such internal conversion electron processes that have the same m o m e n t u m as the neutrino and the same matrix element as the elastic one. Then the following upper limit on the relative C N C strength for the p h o t o n - m e d i a t ing process is o b t a i n e d with 68% CL: ~2 ~ 1.5X 10 -45 .
(11)
The o b t a i n e d values are c o m p a r e d with other d a t a in table 1. The present data give the most stringent limit on the C N C weak process, almost six orders o f m a g n i t u d e smaller than the values o b t a i n e d from the 285
Volume 282, number 3,4
PHYSICS LETTERS B
inelastic ( e v N N ' ) process of 127I. The CNC limit can be derived as 1.6X 10 -29 from the limit on the Kelectron life-time of germanium [7]. The present value is one order of magnitude smaller than the value for germanium. The limit on the CNC process for the £~np mode is EZw< 9 X 10- 24 [ 9,18 ]. This is six orders of magnitude less stringent than the present limit. The CNC limit on the lepton sector e3v process (see fig. 1 (e3v)) can be deduced from the K X-ray limit as done in ref. [ 12]. The limit obtained from the present life-time limit o n 127I is E2w< 2.2 × 10-25 and the value obtained from the limit on germanium [ 7 ] is eZw< l A X 10 -zS. These are less stringent than the present limit given in eq. (10). The CNC process through the photon-mediating process is studied by observing the electron decay e-~ve+7. This process, however, may be followed by many soft photons, and the observation of the single "/-ray ofEv = meC2/2 does not necessarily prove this process as discussed in ref. [13]. The present K X-ray search in the neutral iodine atom with the electron-filled K-shell can be related also to the incomplete Pauli-blocking effect associated with the admixture of the symmetric wave function q/s (Bose statisitics). Then such non-paulian K X-ray emission rate T ( K X) is compared with the normal transition rate T O(K X ) for the ionized atom with one electron-hole in the K-shell, as T ( K X) =62NpT°(K X), where 62p is the probability of the admixed symmetric components. Since T O(K X ) is proportional to the fourth power of the atomic number Z, the very stringent limit on the ratio 6~p can be obtained by studying K X-rays of atoms with large Z. T ° ( K X) for 127I with Z = 5 3 is derived as T ° ( K X ) = 0 . 7 8 × 10 -23 yr -~. Then the upper limit is deduced as
62p < T ( K X ) / T ° ( K X )= l.l × lO -46 .
(12)
The non-paulian X-ray transition is shown to be forbidden between states with different symmetries [ 13,14]. Recently the admixture of the symmetric component has been discussed in terms of the possible electron structure (size) in the framework of the composite models for quark and leptons [ 19 ]. Then the Pauli forbidden K X-ray emission rate is related simply to the electron size parameter ro provided that the final state is lower in energy so that the K X-ray 286
28 May 1992
emission is energetically allowed. The K X-ray emission rate is written in terms of ro as
T(KX)=4~rr3(2/ao)31(~slHEMI~2p)I 2,
(13)
where ao is the Bohr radius and (~u~slHEMI~U2p) is the matrix element of the transition between 2p (L) and ls(K)-shells. Then the upper limit on the electron size parameter is obtained from the present K X-ray limit as ro< 1.1 × 10 -17 c m . This value, corresponding to the energy scale of E > 2 TeV, is more stringent than the value obtained from an electron collider experiment [20 ]. In short, the present work gives the most stringent limit on the possible K X-ray emission in a neutral atom with a filled K-electron shell. The use of a large volume low-background Nal detector with large Z(Z:53) 127I has made it possible to get a more stringent value, relative to the normal K X-ray emission rate, by one order of magnitude, than the previous value on germanium. It should be emphasized here that the present K X-ray search associated with the elastic (evNN) CNC process o n 127I with its large neutron number of Am=74 gives a more stringent CNC limit than the values derived from the inelastic ( e v N N ' ) process and from the 13-decay (££np) process by six orders of magnitude. The K X-ray limit is used to deduce the upper limit on any possible Kelectron stability followed by the K X-ray transition and on the possible non-paulian K X-ray transition rate. The authors thank Professor E. Takasugi, Professor A. Hosoya, Professor K. Okada and Professor T. Kishimoto for valuable discussions, Dr. T. Watanabe and Dr. T. Shima for collaboration in this experiment, and the Mitsui Metal Ltd. for the support at the Kamioka mine. This work is supported in part by the Grant in Aid of Scientific Research, the Ministry of Education, Science and Culture, Japan.
References [ 1 ] G. Feinberg and M. Goldhaber, Proc. Nat. Acad. Sci. USA 45 (1959) 1301; A.W. Sunyar and M. Goldhaber, Phys. Rev. 120 (1960) 871. [2] M.K. Moe and F. Reines, Phys. Rev. 140 (1965) 992; F. Reines et al., Phys. Rev. Lett. 32 (1974) 954. [3] R.I. Steinberg et al., Phys. Rev. D 12 (1975) 2582.
Volume 282, number 3,4
PHYSICS LETTERS B
[4] E.L. Kovalchuk, A.A. Pomansky and A.A. Smolnikov, Pis'ma Zh. Eksp. Teor. Fiz. 29 (1979) 163 [JETP Lett. 29 (1979) 145]. [5] E. Bellotti et al., Phys. Lett. B 124 (1983) 435. [ 6 ] E.T. Avignone III et al., Phys. Rev. D 34 ( 1986 ) 97. [7] D. Reusser et al., Phys. Lett. B 255 ( 1991 ) 143. [ 8 ] B.E. Normal and A.G. Seamster, Phys. Rev. Lett. 43 ( 1979 ) 1226. [9] S.C. Vaidya et al., Phys. Rev. D 27 (1983) 486. [ 10] A. Roy et al., Phys. Rev. D 28 (1983) 1770. [ 11 ] S. Holjevic, B.A. Logan and A. Ljubici, Phys. Rev. C 35 (1987) 341. [ 12] H. Eijiri et al., Phys. Rev. C 44 ( 1991 ) 502. [ 13 ] L.B. Okun and Ya.B. Zeldovich, Phys. Lett. B 78 (1978 ) 78; L.B. Okun, Comm. Nucl. Part. Phys. 19 (1989) 99;
28 May 1992
Particle Data Group, J.J. Hermtndez et al., Review of particle properties, Phys. Lett. B 239 (1990) VI.5, and references therein. [14] R.D. Amado and H. Primakoff, Phys. Rev. C 22 (1980) 1388. [15] S. Orito and M. Yoshimura, Phys. Rev. Lett. 54 (1985) 2457. [ 16] A.A. Pomansky, Proc. 1976 Intern. Neutrino Conf., eds. H. Faissner, H. Reithler and P. Zerwas (Aachen, June 1976) p. 671. [ 17 ] H. Ejiri et al., Nucl. Instrum. Methods A 302 ( 1991 ) 304. [18]J.N. Bahcall, Neutrino astrophysics (Cambridge U.P., Cambridge, 1989) p. 361, and references therein. [19]H. Terasawa and M. Yasue, INS report INS-Rep-873 ( 1991 ), unpublished. [20] B. Naroska, Phys. Rev. 148 (1987) 67.
287