Subatomic Physics

360 The Weak Interaction
be innocent. We now have GF ,Vud,GV F Vud, and|GA F /GVF |, given in Eqs. (11.55),
(11.60), (11.70), and (11.71). Within the given limits of error, the following relations
hold:
G V F = GF , G A F �= GF . (11.72)
What do these relations tell us about the weak interaction? At first sight it appears
that the equal coupling constants for the vector current (GV F ) and for the purely
leptonic current (GF )simplyexpresstheuniversality of the weak interaction and
that GA F �= GF requires an explanation. However, the situation is not so straightforward.
A proton, for instance, is not just a simple point particle. At small distance
it is made up of three quarks confined by gluons, and at distances �1 fmitisaptly
described as clothed by a meson cloud (Fig. 6.8). Why should the physical proton
have the same vector current as a point lepton? There is no a priori reason why GV F
and GF should be identical. The result GA F �= GF appears to be more in agreement
with intuitive arguments, and the primary puzzle is the explanation of GV F = GF .
The solution to the puzzle is the conserved vector current hypothesis (CVC). It was
first proposed in a tentative way by Gershtein and Zeldovich (23) and put into a
powerful form by Feynman and Gell-Mann. (5) To explain CVC, consider first the
electromagnetic case. In Section 7.2, it was pointed out that the electromagnetic
charge is conserved. The positron and proton have the same electric charge despite
the structure of the proton. In other words, the coupling constant e, which characterizes
the interaction with the electromagnetic field, is the same for particles of
the same charge regardless of their structural properties. The hadronic force responsible
for the confinement of the quarks does not change the coupling constant
e. The classical expression for this fact is current conservation, Eq. (10.51). The
CVC hypothesis postulates that the weak vector current is also conserved:
1 ∂V0
+ ∇·V =0. (11.73)
c ∂t
The equality of the coupling constants G V F and GF then follows: whenever a hadron
virtually decomposes into another set of hadrons (for instance, a proton into a
neutron and a negative pion), the weak vector current is conserved. The equality of
G V F and GF is not the only evidence for CVC; many additional experiments support
Eq. (11.73). (24,20)
An example is the comparison of the beta decay rates for 14 Oandπ + . The
systems are quite different; however, they have some common features. Both are
decays from and to states of spin zero and isospin 1. Since the final and initial
hadronic states are within an isospin multiplet, the decays are superallowed with
matrix elements given by Eq. (11.66). The ft 1/2 for both 14 Oandπ + should thus
be identical. Tables 11.1 and 11.2 show that they are almost identical; indeed, they
23S. S. Gershtein and Y. B. Zeldovich ZhETF 29, 698(1955) [Transl. Sov. Phys. JETP 2, 576
(1957)].
24L. Grenacs, Annu. Rev. Nucl. Part. Sci. 35, 455 (1985) and references therein.