- Email: [email protected]
Nonconservation of total lepton number with scalar bosons
Volume 70B, number 4
PHYSICS LETTERS
NONCONSERVATION
24 October 1977
OF TOTAL LEPTON NUMBER WITH SCALAR BOSONS W. KONETSCHNY and W. KUMMER
Institut fiir Theoretische Physik II, Technische Universitdt Wien, Vienna, Austria Received 27 July 1977 The role of scalar bosons is studied in connection with a violation of the number of fermions + antifermions. Some simple estimates of the transitions ~ --, e7 and ~ ~ 3e are based upon a minimal extension of the "standard" gauge model of weak and electromagnetic interactions.
The "standard" gauge model [ 1] of weak and electromagnetic interactions, while very successful in explaining the data, is known to imply rather severe restrictions: any SU(2) × U(1) gauge theory with an (arbitrary) number n of left-handed leptonic doublets L(0 = (L~0, L(0) and right-handed charged singlets R0) automatically exhibits n separately conserved lepton numbers, provided the L(0i) are mass-degenerate (or massless in the absence of R(0i)) and provided one single scalar doublet ~0= (~p+, ~00) is responsible for the symmetry breaking [2, 3]. On the other hand models with a larger number of scalar doublets show a violation of those n separate conservation laws [3]. The vast majority of models with such violations proposed so far, in fact, is based upon two other alternatives: removal of the degeneracy of Li(0i) [4] and/or introduction of larger gauge groups [5]. The purpose of this note is to regard the "standard" model from an even more general point of view: given the structure of multiplets described above, also the conservation of total lepton number may be viewed as an "accident", caused by the absence of certain scalar multiplets. This removes fermion number from its usual, aesthetically not very appealing position of an exact conservation law without related gauge group. Scalar singlets S+ and S~.+ and a triplet ¢0 = (qS++, q~+, 4~0) permit Yukawa couplings - £Yukawa = EGR~o + ~ ? H L S + RcH'RS '
+ Lc~TFxLdp+ h.c.
c~ = e , B F B T = 2 ~ [ ml m2
0 mN
0 in terms of the new fields 10. The neutral leptons in this theory are described by Majorana spinors N 0 = 10 + loc for m 4= 0 4-3. Note that no neutral singlets are necessary to render the neutral spinors massive. In terms of the physical fields ( L , lo) t h e Lagrangian (1) may be rewritten as:
,2 G, H, H' and F are assumed to be real, so that no CP viola(1)
which may lead to a violation of the total number of fermions plus antifermions 4-1. The matrices of the tl Our £Yukawa is more general than the one in ref. [6] where essentially only ~ appears.
coupling constants are G, H = - H T, H' = H 'T and F = FT 4-2 ; ~c = c~-T denotes the charge conjugate of and r/= (o -ol). The restrictive structure o f the model mentioned above enables us to take G diagonal, which can always be achieved by a unitary transformation of the lepton fields [2, 3] (plus a corresponding redefinition of the coupling matrices H, H', F). In this basis, spontaneous breaking of the symmetry (~p0) = e, (¢0) = e' provides masses for tile charged and neutral leptons. Whereas the charged mass matrix c ~ = eG is now diagonal, an orthogonal transformation B of the neutral lepton fields L 0 = BTl 0 yields the diagonalized neutral mass matrix
tion is caused by these interactions. ~3 Majorana neutrinos asa vehicle of nonconservation of (total) lepton number have a long history [7]; for a more recent use of Majorana spinors in vectorlike theories cf. [8]. We may add that these fields do not allow an arbilrary redefinition of the phase. Thus interesting possibilities arise from a complex G and/or F in connection with CP violation for leptons. 433
Volume 70B, number 4
-£y= ~~
PHYSICS LETTERS
C;~R- ~00+ 1-/0BC'~R_~0+ + 2
+ R_c f i R S + + + ~ -~'2
lo-c BHL_S+
Foc c'K10¢ 0
(3)
-cBTQ'LBL _ ¢++ - 2 loc9~BL _ ¢+ +h.c.
The matrix B is responsible for a possible violation o f usual lepton numbers via the charged currents ~v~gToBTtaL_. The assumptions IBll I ~ 1B221 ~ 1 and [B2112 ~< 2 X 10 --3 are in agreement with electronmuon universality (i = 1,2 for e, p) and the experimental upper limit on up + n --' e - + p [9]. For our estimates below we shall assume B31 , B32 to be of the same size as B21 , consistent with orthogonality, We note that schemes such as in [10] where IBlll IB221 is not necessarily near unity can also be combined with our mechanism. F r o m the nonobservation of neutrino-oscillations [7] an upper bound m 2 - m 2 25 (eV) 2 [11] is obtained. Massive Majorana neutrinos permit neutrinoless double/3-decay. The upper and lower limits for the neutrino masses deduced in ref. [12] do not directly apply here, since we are dealing with several Majorana neutrinos, one or more o f which can be heavy, with nonuniversal couplings. The suppression factors B2 i (in this case) weaken the bounds of ref. [121. Estimates o f experimental implications of the model (3) shall be based upon a consideration o f the decay p ~ e3' mediated by the diagrams in figs. 1 and 2 [3], if - in the spirit of our approach - we assume m (scalar) < m w as an alternative to the situation [6] where the usual W-loop is taken to dominate. We use a simple prescription similar to [3] for those estimates: ]el ~le'] ~ 6~F1/2 ~ e / r r ~ , Igl ~ Ig'l ~ muV~F ' g2/4~r a and a factor (8rr2) - 1 for each loop.
I
)
/~
I
"
p
f
?, •
\
) e
Fig. 1. One loop graphs contributing to p ~ e7. The dashed line represents any one of the charged scalar bosons in (3). Only one possible insertion of the photon ~, is indicated. We have p = U+R for S+ and O, u = ~+L for S++ and ~o+. 434
24 October 1977
,p.
e
~)
/,.
1
~)
Fig. 2. Two loop graphs. The double lines can be scalars, W, Z and % Closed lepton loops (C1 = C2 = lepton in 2a) yield another suppression factor m~eptons/rn2 w. ¢
For S+ and S++ only the one-loop graphs o f fig. 1 are relevant. With our (in this case somewhat arbitrary) assumption about the strength of H and H ' the ratio R = F (p --> e 3 ' ) / P ~ -+ ~uF) is of the order (a/n) X (mu/ms) 4 ,4 and thus m s ~ 10 GeV can be concluded from R ~ 10 . 9 i s . The radiative p-decay with S+ exchange is forbidden, if only two leptonic doublets are assumed and if there is no neutral mixing (B = 1). This follows from the antisymmetry o f H. The S+ behaves like a boson with well defined muon number (one) and electron number (one) [14]. Statements about R are less arbitrary for diagrams with ¢+, 4~+ and ~++. Those cases are summarized in table 1. Tiny results are obtained with two lepton types due to the appearance o f m 2 -- m 2. Two loop graphs such as in fig. 2 are enhanced for ¢ (compare [3] ; we assume m w > raN) , but still very small. For ~ o n e of the graphs of fig. 2a may become about as important as the one of fig. 1, ifmw/m ¢ ~ 10. In the "optical" case o f triplet exchange with three (or more) types of leptons, the present limit of R requires the triplet boson mass m e > 3raN, where N could be the neutral partner of the new heavy lepton ( r _ ) seen at SPEAR and DORIS [15]. The decay/2 ~ 3e either proceeds via a Dalitz pair in/2 -->e7 or by a tree graph with S'++ or ¢++-exchange. In the last case a factor ( m l m 2 ) 2 in the rate makes any hope for an observation unrealistic, whereas ,4 The Feynman amplitude ~(a + bTs) aU~/VeU~ implies a switch of helicity = chirality for massless leptons. Therefore a transition without change of chirality as in fig. 1 2 2 costs a f a c t o r m u ( ~ me) ina ~ b ,~ IHI2 emJmS(BTr ). This is used in F(~ ~ e~) = m~(~[ 2 + [b12)/2~,to be compared with r (p ~ cv~) = m~G~,[3(4~) 3 ] -I. :is The published value [13] is 2.2 × 10 -8. Experiments currently under way are expected to be sensitive d o w n to 10-9_10-Io.
Volume 70B, number 4
PHYSICS LETTERS
Table 1 Contribution of scalar bosons to R; 0 = EiBilBi2m~Jrn2w, 0 (2 doublets) = 2.10 -3 (m] - m22)/rn~v, o (3 doublets) -2.10-3m~q/m~v. In the third column other identifications of Cr yield at most contributions of the same size to R. Scalar boson
a (one loop)
a (two loops) a (one loop)
¢
e3 pints rn4 lr~mtFnem-~ ~(mume)_t,,@ rr mw
R (dominant loop) (;)3 p2
Fig. 2a:
4)
e 3 pm u rr2 m~
C1 = C2 = Ca = e) a__(mwl2 ~r \me)!
~ p2(mwl4 ~r \ me~]
Fig. 2b: C1 =e), C2 ='y 7T
for S++ - where the coupling H' is less well determ i n e d - R(/a ~ 3e)/(/2 ~ ev-ff) ~ ( m J m s ) 4 . This dominates the Dalitz-pair diagram and lies at the experimental limit 1.9 × 10 - 9 [16] again for rns>~ 1 0 G e V . Direct observation o f the new scalar bosons ¢++ ¢ and S++, e.g. as a " r e s o n a n c e " with lepton n u m b e r 2 in e - + e - - / 2 - + # - , for q~++ again is h a m p e r e d b y the e x t r e m e l y small coupling constants. The d o m i n a n t decay channel o f ~++ is the one into 2 r _ (Fe)__,2r <~me)G~m 2 ~ 100 k e V for me) -~ 10 GeV, m N ~ 1 GeV). S~.+-production is not restricted to the same extent. F r o m these crude estimates we c o n c l u d e that nonconservation o f l e p t o n n u m b e r may well proceed via singlets and triplets o f scalar particles w i t h fermionn u m b e r nonconserving coupling in a unified gauge theory. The range o f mass values as d e t e r m i n e d by present e x p e r i m e n t a l limits permits effects for quite " r e a s o n a b l e " choices of the masses involved (e.g. m (scalar) ~ 10 GeV, m (heavy neutral l e p t o n ) ~ 0 . 5 - 1 GeV).
24 October 1977
References [ l] A. Salam, in: Elementary particle theory, ed. N. Svartholm (Almqvist and Wiksell, Stockholm, 1968) p. 367; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264. [2] M.K. Gaillard, B.W. Lee and J.L. Rosner, Rev. Mod. Phys. 47 (1975) 277; B.W. Lee and R.E. Shrock, FNAL preprint FermilabPub-77/21-THY. [3] J.D. Bjorken and S. Weinberg, Phys. Rev. Lett. 38 (1977) 622. [4] We cannot possibly list all the old and recent literature. For a review cf. Ta-Pei Cheng and Ling-Fong Li, Invited talk at Orbis Scientiae, Univ. of Miami, Coral Gables, Florida (January 1977). [5] Cf. [4] and as examples of recent work with extensive references: P. Langacker and G. Segr~, Univ. of Pennsylvania report UPR-00732T (1977); B.W. Lee and S. Weinberg, Phys. Rev. Lett. 38 (1977) 1237. [6] P. Minkowski, Phys. Lett. 67B (1977) 421. [7] B. Pontecorvo, Soviet Phys. JETP 26 (1968) 984; V. Gribov and B. Pontecorvo, Phys. Lett. 28B (1969) 493. [8] H. Fritzsch, M. Gell-Mann and .P. Minkowski, Phys. Lett. 59B (1975) 256. [91 Numbers taken from G. Altarelli, L. Beaulieu, N. Cabibbo, L. Maiani and R. Petronzio, Paris preprint LPTENS 77/4 (March 1977). [10] V. Barger, D.V. Nanopoulos and R.J.N. Phillips, University of Wisconsin preprint C00-597, revised. [11] For a recent discussion see A.K. Mann and H. Primakoff, Phys. Rev. D15 (1977) 655. [12] A. Halprin, P. Minkowski, H. Primakoff and S.P. Rosen, Phys. Rev. D13 (1976) 2567. [13] S. Parker, H.L. Anderson and C. Rey, Phys. Rev. 133B (1964) 768. [14] Such bosons have been postulated a long time ago in a renormalizable theory of ~-decay: Y. Tanikawa, Phys. Rev. 108 (1957) 1615. [15] M.L. Perl et al., Phys. Rev. Lett. 35 (1975) 1489; M.L. Perl et al., Phys. Lett. 63B (1976) 466; J. Burmester et al., Phys. Lett. 68B (1977) 297,301. [16] S.M. Korencho et al., Soviet Phys. JETP 43 (1976) 1.
435
PHYSICS LETTERS
NONCONSERVATION
24 October 1977
OF TOTAL LEPTON NUMBER WITH SCALAR BOSONS W. KONETSCHNY and W. KUMMER
Institut fiir Theoretische Physik II, Technische Universitdt Wien, Vienna, Austria Received 27 July 1977 The role of scalar bosons is studied in connection with a violation of the number of fermions + antifermions. Some simple estimates of the transitions ~ --, e7 and ~ ~ 3e are based upon a minimal extension of the "standard" gauge model of weak and electromagnetic interactions.
The "standard" gauge model [ 1] of weak and electromagnetic interactions, while very successful in explaining the data, is known to imply rather severe restrictions: any SU(2) × U(1) gauge theory with an (arbitrary) number n of left-handed leptonic doublets L(0 = (L~0, L(0) and right-handed charged singlets R0) automatically exhibits n separately conserved lepton numbers, provided the L(0i) are mass-degenerate (or massless in the absence of R(0i)) and provided one single scalar doublet ~0= (~p+, ~00) is responsible for the symmetry breaking [2, 3]. On the other hand models with a larger number of scalar doublets show a violation of those n separate conservation laws [3]. The vast majority of models with such violations proposed so far, in fact, is based upon two other alternatives: removal of the degeneracy of Li(0i) [4] and/or introduction of larger gauge groups [5]. The purpose of this note is to regard the "standard" model from an even more general point of view: given the structure of multiplets described above, also the conservation of total lepton number may be viewed as an "accident", caused by the absence of certain scalar multiplets. This removes fermion number from its usual, aesthetically not very appealing position of an exact conservation law without related gauge group. Scalar singlets S+ and S~.+ and a triplet ¢0 = (qS++, q~+, 4~0) permit Yukawa couplings - £Yukawa = EGR~o + ~ ? H L S + RcH'RS '
+ Lc~TFxLdp+ h.c.
c~ = e , B F B T = 2 ~ [ ml m2
0 mN
0 in terms of the new fields 10. The neutral leptons in this theory are described by Majorana spinors N 0 = 10 + loc for m 4= 0 4-3. Note that no neutral singlets are necessary to render the neutral spinors massive. In terms of the physical fields ( L , lo) t h e Lagrangian (1) may be rewritten as:
,2 G, H, H' and F are assumed to be real, so that no CP viola(1)
which may lead to a violation of the total number of fermions plus antifermions 4-1. The matrices of the tl Our £Yukawa is more general than the one in ref. [6] where essentially only ~ appears.
coupling constants are G, H = - H T, H' = H 'T and F = FT 4-2 ; ~c = c~-T denotes the charge conjugate of and r/= (o -ol). The restrictive structure o f the model mentioned above enables us to take G diagonal, which can always be achieved by a unitary transformation of the lepton fields [2, 3] (plus a corresponding redefinition of the coupling matrices H, H', F). In this basis, spontaneous breaking of the symmetry (~p0) = e, (¢0) = e' provides masses for tile charged and neutral leptons. Whereas the charged mass matrix c ~ = eG is now diagonal, an orthogonal transformation B of the neutral lepton fields L 0 = BTl 0 yields the diagonalized neutral mass matrix
tion is caused by these interactions. ~3 Majorana neutrinos asa vehicle of nonconservation of (total) lepton number have a long history [7]; for a more recent use of Majorana spinors in vectorlike theories cf. [8]. We may add that these fields do not allow an arbilrary redefinition of the phase. Thus interesting possibilities arise from a complex G and/or F in connection with CP violation for leptons. 433
Volume 70B, number 4
-£y= ~~
PHYSICS LETTERS
C;~R- ~00+ 1-/0BC'~R_~0+ + 2
+ R_c f i R S + + + ~ -~'2
lo-c BHL_S+
Foc c'K10¢ 0
(3)
-cBTQ'LBL _ ¢++ - 2 loc9~BL _ ¢+ +h.c.
The matrix B is responsible for a possible violation o f usual lepton numbers via the charged currents ~v~gToBTtaL_. The assumptions IBll I ~ 1B221 ~ 1 and [B2112 ~< 2 X 10 --3 are in agreement with electronmuon universality (i = 1,2 for e, p) and the experimental upper limit on up + n --' e - + p [9]. For our estimates below we shall assume B31 , B32 to be of the same size as B21 , consistent with orthogonality, We note that schemes such as in [10] where IBlll IB221 is not necessarily near unity can also be combined with our mechanism. F r o m the nonobservation of neutrino-oscillations [7] an upper bound m 2 - m 2 25 (eV) 2 [11] is obtained. Massive Majorana neutrinos permit neutrinoless double/3-decay. The upper and lower limits for the neutrino masses deduced in ref. [12] do not directly apply here, since we are dealing with several Majorana neutrinos, one or more o f which can be heavy, with nonuniversal couplings. The suppression factors B2 i (in this case) weaken the bounds of ref. [121. Estimates o f experimental implications of the model (3) shall be based upon a consideration o f the decay p ~ e3' mediated by the diagrams in figs. 1 and 2 [3], if - in the spirit of our approach - we assume m (scalar) < m w as an alternative to the situation [6] where the usual W-loop is taken to dominate. We use a simple prescription similar to [3] for those estimates: ]el ~le'] ~ 6~F1/2 ~ e / r r ~ , Igl ~ Ig'l ~ muV~F ' g2/4~r a and a factor (8rr2) - 1 for each loop.
I
)
/~
I
"
p
f
?, •
\
) e
Fig. 1. One loop graphs contributing to p ~ e7. The dashed line represents any one of the charged scalar bosons in (3). Only one possible insertion of the photon ~, is indicated. We have p = U+R for S+ and O, u = ~+L for S++ and ~o+. 434
24 October 1977
,p.
e
~)
/,.
1
~)
Fig. 2. Two loop graphs. The double lines can be scalars, W, Z and % Closed lepton loops (C1 = C2 = lepton in 2a) yield another suppression factor m~eptons/rn2 w. ¢
For S+ and S++ only the one-loop graphs o f fig. 1 are relevant. With our (in this case somewhat arbitrary) assumption about the strength of H and H ' the ratio R = F (p --> e 3 ' ) / P ~ -+ ~uF) is of the order (a/n) X (mu/ms) 4 ,4 and thus m s ~ 10 GeV can be concluded from R ~ 10 . 9 i s . The radiative p-decay with S+ exchange is forbidden, if only two leptonic doublets are assumed and if there is no neutral mixing (B = 1). This follows from the antisymmetry o f H. The S+ behaves like a boson with well defined muon number (one) and electron number (one) [14]. Statements about R are less arbitrary for diagrams with ¢+, 4~+ and ~++. Those cases are summarized in table 1. Tiny results are obtained with two lepton types due to the appearance o f m 2 -- m 2. Two loop graphs such as in fig. 2 are enhanced for ¢ (compare [3] ; we assume m w > raN) , but still very small. For ~ o n e of the graphs of fig. 2a may become about as important as the one of fig. 1, ifmw/m ¢ ~ 10. In the "optical" case o f triplet exchange with three (or more) types of leptons, the present limit of R requires the triplet boson mass m e > 3raN, where N could be the neutral partner of the new heavy lepton ( r _ ) seen at SPEAR and DORIS [15]. The decay/2 ~ 3e either proceeds via a Dalitz pair in/2 -->e7 or by a tree graph with S'++ or ¢++-exchange. In the last case a factor ( m l m 2 ) 2 in the rate makes any hope for an observation unrealistic, whereas ,4 The Feynman amplitude ~(a + bTs) aU~/VeU~ implies a switch of helicity = chirality for massless leptons. Therefore a transition without change of chirality as in fig. 1 2 2 costs a f a c t o r m u ( ~ me) ina ~ b ,~ IHI2 emJmS(BTr ). This is used in F(~ ~ e~) = m~(~[ 2 + [b12)/2~,to be compared with r (p ~ cv~) = m~G~,[3(4~) 3 ] -I. :is The published value [13] is 2.2 × 10 -8. Experiments currently under way are expected to be sensitive d o w n to 10-9_10-Io.
Volume 70B, number 4
PHYSICS LETTERS
Table 1 Contribution of scalar bosons to R; 0 = EiBilBi2m~Jrn2w, 0 (2 doublets) = 2.10 -3 (m] - m22)/rn~v, o (3 doublets) -2.10-3m~q/m~v. In the third column other identifications of Cr yield at most contributions of the same size to R. Scalar boson
a (one loop)
a (two loops) a (one loop)
¢
e3 pints rn4 lr~mtFnem-~ ~(mume)_t,,@ rr mw
R (dominant loop) (;)3 p2
Fig. 2a:
4)
e 3 pm u rr2 m~
C1 = C2 = Ca = e) a__(mwl2 ~r \me)!
~ p2(mwl4 ~r \ me~]
Fig. 2b: C1 =e), C2 ='y 7T
for S++ - where the coupling H' is less well determ i n e d - R(/a ~ 3e)/(/2 ~ ev-ff) ~ ( m J m s ) 4 . This dominates the Dalitz-pair diagram and lies at the experimental limit 1.9 × 10 - 9 [16] again for rns>~ 1 0 G e V . Direct observation o f the new scalar bosons ¢++ ¢ and S++, e.g. as a " r e s o n a n c e " with lepton n u m b e r 2 in e - + e - - / 2 - + # - , for q~++ again is h a m p e r e d b y the e x t r e m e l y small coupling constants. The d o m i n a n t decay channel o f ~++ is the one into 2 r _ (Fe)__,2r <~me)G~m 2 ~ 100 k e V for me) -~ 10 GeV, m N ~ 1 GeV). S~.+-production is not restricted to the same extent. F r o m these crude estimates we c o n c l u d e that nonconservation o f l e p t o n n u m b e r may well proceed via singlets and triplets o f scalar particles w i t h fermionn u m b e r nonconserving coupling in a unified gauge theory. The range o f mass values as d e t e r m i n e d by present e x p e r i m e n t a l limits permits effects for quite " r e a s o n a b l e " choices of the masses involved (e.g. m (scalar) ~ 10 GeV, m (heavy neutral l e p t o n ) ~ 0 . 5 - 1 GeV).
24 October 1977
References [ l] A. Salam, in: Elementary particle theory, ed. N. Svartholm (Almqvist and Wiksell, Stockholm, 1968) p. 367; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264. [2] M.K. Gaillard, B.W. Lee and J.L. Rosner, Rev. Mod. Phys. 47 (1975) 277; B.W. Lee and R.E. Shrock, FNAL preprint FermilabPub-77/21-THY. [3] J.D. Bjorken and S. Weinberg, Phys. Rev. Lett. 38 (1977) 622. [4] We cannot possibly list all the old and recent literature. For a review cf. Ta-Pei Cheng and Ling-Fong Li, Invited talk at Orbis Scientiae, Univ. of Miami, Coral Gables, Florida (January 1977). [5] Cf. [4] and as examples of recent work with extensive references: P. Langacker and G. Segr~, Univ. of Pennsylvania report UPR-00732T (1977); B.W. Lee and S. Weinberg, Phys. Rev. Lett. 38 (1977) 1237. [6] P. Minkowski, Phys. Lett. 67B (1977) 421. [7] B. Pontecorvo, Soviet Phys. JETP 26 (1968) 984; V. Gribov and B. Pontecorvo, Phys. Lett. 28B (1969) 493. [8] H. Fritzsch, M. Gell-Mann and .P. Minkowski, Phys. Lett. 59B (1975) 256. [91 Numbers taken from G. Altarelli, L. Beaulieu, N. Cabibbo, L. Maiani and R. Petronzio, Paris preprint LPTENS 77/4 (March 1977). [10] V. Barger, D.V. Nanopoulos and R.J.N. Phillips, University of Wisconsin preprint C00-597, revised. [11] For a recent discussion see A.K. Mann and H. Primakoff, Phys. Rev. D15 (1977) 655. [12] A. Halprin, P. Minkowski, H. Primakoff and S.P. Rosen, Phys. Rev. D13 (1976) 2567. [13] S. Parker, H.L. Anderson and C. Rey, Phys. Rev. 133B (1964) 768. [14] Such bosons have been postulated a long time ago in a renormalizable theory of ~-decay: Y. Tanikawa, Phys. Rev. 108 (1957) 1615. [15] M.L. Perl et al., Phys. Rev. Lett. 35 (1975) 1489; M.L. Perl et al., Phys. Lett. 63B (1976) 466; J. Burmester et al., Phys. Lett. 68B (1977) 297,301. [16] S.M. Korencho et al., Soviet Phys. JETP 43 (1976) 1.
435