Vo]ame I, number 7
SMALL
PHYSICS LETTERS
PROBABILITY
AND
NEUTRAL
OF
THE
~ - e + ~ AND
CUItit~NTS
IN WEAK
1 July 1962
~ - e + e ~ e PROCESSES
INTERACTIONS
]3.P O N T E C O R V O
Joint L~filu+.~ for Nuclear Research, Laboratory
of Th~.~oretical Physics, Dubrm
Eeceived 14 June 1962
During the l a ~ fifteen y e a r s m a ~ y u n s u c c e s S ~ l
a t t e m p t s w e r e m a d e to obr, e r v e the ~ ~ + 7 decay ;.
The probability of thi~ p r o c e s s , according to the
most precise data, is less than 6 x I0 "8 ~ with a
90~ confidence level (a is the probability of the
-e+ v+~pr~eeuson). The~e+e+eprocess
h a s not yet been o b s e r v e d either ~), i t s probability
by the latsst data being l e s s thad 2,6 x 10-7 a 4).
The absence of t h e s e p r o c e s s e s ( U p r o c e s s e s ) m a y
be due to the existence of two types of neutrinos
(muor~ and electron) having different lepton charges.
The question a s to whether there a r e in nature
two types of neutrinos can be unambiguously solved
e~erL~a,.e~tally 5), and is likely to be answered
soon. H e r e we wish to point out that an e x t r e m e l y
s m a l l probability of the U p r o c e s s e s might be a c eonnted for even in the c a s e when there i s only one
type ~ n~utrinos in nature, if we a s s u m e that besides the well..known "char~,ed c u r r e n t s ~ c~), in weak
interactions there a r e also " n e u t r a l .~urr~~tr? ',
Consider the case when t h e fou=,-ferminn ~.~eraction i~ l o c a l (i.e., when t h e r e a r e no intermediate
boson~). A s an exs~nple, fig. 1 shows two typical
d i a g r a m s which can lead to the unobserved U p r o ce~se~. The di~z:~.ams involv~a~g baryons practically
do ,act coutribu~e tc tLe zate o: the U p r o c e s s e s b e e~us~ of ;he strong in~rac'A~n foru~actor e -'*~off.
2~,e U decay p~-ocesses a p p e a r L~ the secon( ~ r d e r
of pergwhation theory. They a r e due to the e::let~nce of the interactions of Lhe types [6~) (~e) an~
C~'~,,~ (V~), which is esseuO'~l in the Feynman and
G e L - M a n n theory 6). Accurdlng to loffe 7), the
u nper l i m i t s f o r the r ~ e of the U p r o c e s s e s r e q u i r e
surprlsingly small values of the eut-off parameter
(~ ~ 20 GeV). ~f t h ~ interactions of the type ( ~ ) (Ve)
a r e absent, the U p r o c e s s e s ~triee in the third o r -
(a)
Fig. i. Typical d i ~ a m s for the p r ~ 2 s e s
a~d (b) ~--e + e +e.
0~
(a) ~ -- e + y
der of the weak interaction con,s:at G (see, e,g.,
the diagram in fig. 2 for the ~ - e + e + e process}.
In this case the parameter h turns out to be substanflally greater so that the difficulties connected
with the small probability of the U processes are
o v e r c o m e , at least partially. Note, however, that
it i s highly unnatural that t h e "diagunal" t e r m s ef
type (gv) ('~e) a r e not p r e s e n t in the weak i n t e r a c tio~ Lagrongian. Such an assumption would lead to
a violation of the Feynman and Gell-Munn conception of the interaction bet~-eeu two currents as the
source of the four-ferrules weak interaction. It.is,
however, possible, to conserve this idea and to
forbid, at the s a m e time, the U processes. This
c o m e s cmt of a proposal m a d e in 1958 by Btudm a n 8). However, the significance of Bludman's
scheme of weak interactions in rek.tlon to t h e sm~.li
probabilities of the U p r o c e s s e s was not r e c o g nized 97.
Fig. 2. Third order tiag~'em for tl ~ ~ - e + e + e process.
According to the Btu, l m a u ' s theory, the w e a k
i n t e r a ~ i o n Lagrangian i s supposed to consist of
two r ~ r i s : the " c h a r g e d " one, connected with the
"charged currents" eu, ~ ~ pn, pA, and the'"neutral"
one, con~%ining "symmet~'ical neutral" eurren.'~ ~v,
ee, tt~, ~ n , pp, Ah.
In t h i s s c h e m e the v + e - v + e p r o c e s s d o e s net
exist because the t e r m ~ the " c h a r g e d " Lagrangian
('ev) ('~e) and that Of the "neutral" Lagrangiau (e'e)
~v) cancel oL~t.
It s h o u ~ be emphasized that the absence of the
processes of type K - ~; + e + e by no m e a n s argues
against the above s c h e m e , since the currents under
consideration m u s t b e s y m m e t r i c a l : both the c u r r e n t ~e and the c u r r e n t An a r e raled out. Note a l s o ,
that t h e n e u t r a l s y m m e t r i c a l c u r r e n t s we a r e c o n -
287
Vchtrae I, namber 7
PtIYSICS L E T T E R S
sidering have nothtag ~to do with the rul~ AT = ½ for
the non-leptonic p r o c e s s e s in strange particle decays.
T h e questinn may be asked as to whether the
introduction of Symmetrical neutral currents contradLct~ the available experimental data. The consequences of the scheme m~der study are the f o r
_~owlng:
L There must occur s o ~ e weak processes,
~Mr instance, electron scattering on protons 19) and
o:a e~ectr0as 11) without conservation of parity.
There are no experimental data on this problem,
~md ~..ti s e~ren~ely diff,.cult to obtain such cM~,
~. As a I r e ~ y mentioned, the p r o c e s s e s of the
first order in the weak :Interaeti,m constant of the
type v + e -- u + e must be absent. The related experiments have not yet heen attempted. Should it
turn out that there i s no such p r o c e s s , t h i s would
not n e c e s s a r i l y refute the conception of the i n t e r action betweem two currents in spite of frequent a s sertions to the contrary in the literature.
3. Excited nuclei must emit ~ p a i r s . Thi,'~
effect i s practically unobservabie in the laboratory
bee~ase o~ the "competition" of electromagnetic
processes. How~-ver, i t would undoubtedly have
~ p o r t a a t consequences h~ astrophys~cs~ since it
g i v e s a powerful meehani~un for energy l o s s e s in
stars. In this mechanism the emisstca of vVpairs
by stars i s characterized ~by a p r o c e s s of ~ e order
of G (not Ge2, like in the case when v - e s e a . c r a g
¢'2.kes place 12)),
4. In l,/gh energy neutrino experirneats there
must be observed events of neutrino~nucleon seatterhlg (told stars in complex nuclei ) no nceompan ied by charged leptons. A search for such processes~ with cross seetlons of the order of 10 -38 10-40 c m 2 per nucleon, mi~ht answsr ?.he question
on the presence of neutral curreats.
In eoneinsioa it should he noted tha~ ff the experLments indicate the existeace in nature of ouly
one type of neutriuo, then the small probability of
the U process would provide argnments in favour of
the existence of symmetrical n e u t r ~ currents in
weak interactions.
The s;a%hor t~kes the p~easure th thar&ing
V.N. Bayer, S.M. Biler~ki, ~. $.Gerstein, L.B.
Oic~_~' and R, M. i%,vndin for di~cusainnS,
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