introduction-weak-interaction-volume-one

3r = a o J + a, Jr . (5 .3 .20 )
There exist two further
r
important selection rules for semileptonic reactions :
the p I = 3 and L I . 1 rules . The = 1 rule states that in any
pY = G semileptonic process, the change in total isospin must satisf y
LSI = 1 . (5 .3 .21 )
In hypercharge-changing reactions, total isospin cannot be conserved becaus e
of the Gell-Hann - Nishijima - Nakano (9) (GNN) relatio n
Q = 1 3 t Y/2 . (5 .3 .22 )
In fact, in g = 1 processes, it is found that
pI = . (5 .3 .23)
Both (5 .3 .21) and (5 .3 .23) appear to be obeyed to a high degree of accuracy
in the weak interaction .
We now consider the symmetry properties of the AY = 0 hadroni c
current . Since the latter has
AQ = 1, (5 .3 .22) implies
tiI 3 =1 . (5 .3 .24 )
Similarly, the current z
corresponds to PY = 0, pQ = -1, so tha t
A.1 3 = -1 . (5 .3 .25 )
In terms of isospin, the C operator may be considered as an operator which
reverses the sign of the third component of isospin of a particle, i .e . i t
reflects it in the plane 1 3
C = e j'7 12 ,
— 0 . Alternatively, we may say that
(5 .3 .26 )
where 1 2 is the generator of rotations about the I 2 axis in isospace . Using th e
perator (5 .3 .26) we may decompose the currents Jr and T
with AY = 0 :
Jr (0) i(Jd(0) e j'cI 2 JH(0) e jr12 ) +
-E(o )
r
+ L( JF.(0) - e jn1 2 J :(0) ej't12) ~
i(J'ri(0)
so that
ej-rcl 2 JH(0) e-J,,12
r
-}-
ej'cI 2 JI~'.(o) ei,71 2) +
+ ( (0) - e j'rtI2 J;3(o) e j7s'1 2 )
r r '
=
(Jii(0) + -j'TI 2 Jii(o) ej-r I 2
r
)
- 1 (JH(0) - e '2 Jh(o) e 3,cI2 )
(5 .3 .27 )
(5 .3 .28 )
(5 .3 .29 )
From (5 .3 .29) we see that, in general, JJ(0) need not necessarily be the charge
conjugate of Js-(0) . However, if either term on the right-hand side of (5 .3 .27 )