introduction-weak-interaction-volume-one

where
rl 1 1 1 1 ;
4 -2 0 2 -4 I
)■ = 'a 6 0 -2 0 6 1 (3 .3 .15 )
(._41
2 0 -2 -4
-1 1 -1 1j
Denoting the five coupling constants by S, V, T, A and P when they occu r
in the order (1 2 3 4) and by 5', V', T', A' and P' when they occur
(3 2 1 4), we have
S' ( S + V + T + A + P) , (3 .3 .16a )
V' _ -4 (4S - 2V + 2A - 4P) , (3 .3 .16b )
T' _ - (6s - 2T + 6P) , (3 .3 .16c )
A' = 4 (4s 2V - 2A - 4P) , (3 .3 .16d )
P' = - y ( S- V + T - A P) . (3 .3 .16e )
From the relations (3 .3 .16) we may deduce tha t
V' - A' = V - A ,
S' - + P' S - T P ,
and hence these combinations are invariant under Fierz reordering .
We now consider the properties of the neutron decay Hamiltonia n
under the P, C and T operators . In 2 .7, we showed that any interaction ,
such as our neutron decay Hamiltonian, constructed from Dirac (J = i- )
fields must be invariant under the combined transformation CPT (Ldders-
Pauli Theorem), but not necessarily under the separated operators . For
the space reflection operator, P, we hav
(3 .3 .17a )
(3 .3 .17b)
e
P ( H I (x, x o ) - E' P i S (
7 ,rp (-x, x o ) 0 i l i n (-x, xo ) ) X
x (-x, xo ) O i (C i - Cl y5 ) y v xo ) )
t
+ Hem . conj . ,
(3 .3 .18 )
where the intrinsic parity factor E P is given by
E P = E; ( p ) • g (n) . Ep (e) • e p ( v ) . (3 .3 .19 )
Thus P invariance would requir e
Ci = 0 (i = 1, 5) ,
(3 .3 .20 )
and for this reason, the Ci are known as the parity-violating couplin g