introduction-weak-interaction-volume-one

changing semileptonic reactions occur in nature, terms of each type must b e
included in JH . Let LAY be the difference between the hypercharges of th e
r
initial and final states in a reaction . Theoretically ,
,l = a0 a r + al Jr + a2 Jr + a-1 Jr + a 2 Jr2 . . . .(5 .3 .11 )
where the numbers 0, 1, 2, -1, -2, . . . . associated with each term correspon d
to the value of ,AY for those terms . a is a parameter which allows the variou s
terms in the current .1t r` to be coupled with different strengths to the leptonic
current . Thus the semileptonic interaction Hamiltonian become s
0 1
22
,T-L
Hl
J Or Jr
+ G2 Jr
Without a selection rule for aY, the hadronic current could contai n
(5 .3 .12 )
all the terms on the right-hand side of (5 .3 .11), including an infinite numbe r
of coupling constants . However, it is found that the partial conservation la w
IA Yl < 1 (5 .3 .13 )
is obeyed in all reactions, so that only the terms corresponding to n ,y =
0, 1 and -1 remain on the right-hand side of (5 .3 .11) . There is little evidence
fir ( Yi 2 reactions, although the deca y
—) p e v , (5 .3 .14 )
which has 411=2, has only been shown to have a branching ratio of under (7 )
1.3 x 10- 3 , (5 .3 .15 )
which nevertheless sets a small maximum
current . We usually assume that no 'AY\ ..
rule which appears to apply to all I
4 .1''t'e.2 amplitude for the hadroni c
2 transitions occur . Another selectio n
Yl= 1 semileptonic processes i s
L1Y = AQ (5 .3 .16 )
implying that the change in hypercharge in an interacting system of hadrons
is equal in sign to the change in their total charge . Processes of the for m
dY/LiQ = -1 (5 .3 .17 )
almost certainly do not occur, although the upper limit on the branching rati o
for decays of the typ e
KO >17 TT + 1-1 r 1 - + v l
where 1 is either an electron or a muon, is (8) onl y
10 2,
however, on the assumption that
hadronic current becomes :
(5 .3 .16) always holds true, our
(5 .3 .18)
(5 .3 .19 )