introduction-weak-interaction-volume-one

vanishes, the n
e jn I 2 JH(o)
e O"I2 = ± aii(o) (5 .3 .30 )
(5 .3 .30) is known as the charge symmetry condition (10) . Those terms in th e
hadronic current which yield a positive right-hand side of (5 .3 .30)
are sai d
to be first-class terms, and those which make it negative are called second -
class (11) . We find that if both T invariance and (5 .3 .30) hold, then secondclass
terms must be absent . However, if both first- and second-class, terms ar e
present in the hadronic current, then this implies T violation . If CPT holds ,
then T violation implies C violation . If T invariance does hold, then th e
current must not obey (5 .3 .30) . An operator related to the charge symmetry on e
(5 .3 .26) is the G parity operator defined
G = C ej7'12 , (5 .3 .31 )
where C is the standard charge conjugation operator, which, unlike (5 .3 .26) ,
reverses the sense of a figure in isospace . A possible G parity scheme fo r
the J H0) current i s
r
-
G V r G 1 = V , (5 .3 .32 )
G Ar G
I
= - A , (5 .3 .33)
where V and A are the vector and axial vector terms in the current Jn(0 )
r
respectively. We shall not enter into a verification of (5 .3 .32) here, bu t
this may be found inharshak, Piazuddin, Ryan :
Theory of Weak Interaction i n
Particle Physics, Fraley-Interscience, 1969, pp . 108-109 . (5 .3 .32) and (5 .3 .33 )
may be shown to imply that only first-class terms appear in the matri x
elements of JH(0) .
r
We now consider the current JK(1) with
r
PQ = Y = 1 • (5 .3 .34 )
From (5 .3 .34) and (5 .3 .22), we see immediately that
AI 3 (5 .3 .35 )
(5 .3 .35) is not the only possible 1 3 assignment for J (1) , but it has ber n
found to be the only one occuling in nature T
Jx(0 )
. We find that, unlike the
r
current, the vector component of the Jr(1 ~ current is not precisely conserve d
under the effect of the strong interaction, unless two particles can have th e
same spin, parity and mass while having charges and hypercharges differing b y
one unit . This situation is not found in nature, and hence we are forced to conclud e
that the vector term in 4(1) is not conserved .