introduction-weak-interaction-volume-one

We see that the first term in (5 .2 .13) is simply the weak vector nucleon ,
current (5 .2 .9) . However, we have not yet proved that the latter is conserve d
on its own . Setting
J W' ( x ) _ (J g/ e ) J 2 ( JJ (+) (x) (+) (x) ) , (5 .2 .14 )
we find that
JW' (x) = -Tip (x) Y r 7 r ( x) - g,. 2(, o (x) (a4t (x)/ x r ) -
q { ( x ) (a 0 ( x )/ 3 xr) ) (5 .2 .15 )
where ce p , ( and are defined in (5 .1 .21), (5 .1 .22) and (5 .1 .23) respectively .
From (5 .2 .15), it is easy to deduce tha t
( JW' (x)/ 2 xr) = 0 (5 .2 .16 )
so tha t
(' JW ( x )/ xr ) = 0 (5 .2 .17)
Thus the weak vector current in neutron decay is unaffected by the stron g
pion current, which explains the near equality of the true vector couplin g
constants in muon and neutron decay . (5 .2 .17) is known as the conserved vecto r
current or CVC hypothesis . It is natural to ask whether a similar relation t o
(5 .2 .17) might hold for the axial vector current in neutron decay . However ,
as we saw above, the axial vector coupling constant in muon decay is abou t
20 5 more than that in neutron decay, and thus it seems likely that axia l
vector current is not conserved . In fact, by similar reasoning as tha t
employed above for the vector current, we may show tha t
( a Jr ( x )/a xr) = f0 m 2,, ep( x ) , (5 end .2 .18 f )
where is the axial vector current, 0 (x) was defined in (5 .1 .22)
is a constant dependent on the strength of the strong interaction . (5 .2 .18 )
is known as the partial conservation of axial vector current or PCAC .
n
5 .3 The Structure of the Weak Hadronic Current .
There exist in nature three different types of weak reaction . Th e
first type are termed leptonic, and contain only leptons . The second type, th e
so—called semileptonic reactions, involve both leptons and hadrons, and th e
third type, which are called hadronic reactions, consist purely of hadrons, whic h
also react via the strong interaction . We denote the weak hadronic current