introduction-weak-interaction-volume-one

implying that the constants GV and GA were relatively real . Defining
R =
we may writ e
GV/GA ,
(3 .7 .11a)
A = -2 (1 + R)/(l + 3R2 ) (3 .7 . 11b )
B = -2 (1 — R)/(l + 3R 2 ) . (3 .7 .11c)
Our experimental results for A and B are consistent with A = 0, B = 1 ,
and substituting these values in the relations (3 .7 .11) we obtai n
GA - 1 .25 GV , (3 .7 . 1 2 )
and thus we have demonstrated that the interaction occuring in beta deca y
has the form V — A. This is attractive, since the combination V — A i s
invariant under Fierz reordering (3 .3.17a) .
We now investigate our second P pseudoscalar (3 .7 .lb), which
corresponds to the longitudinal polarization of electrons emitted fro m
nonoriented nuclei . Since we now do not sum over electron polarizatio n
directions, the relations (3 .5 .7) become (51), assuming a V — A interaction ,
I(q) = 1/(2 n) 5 q 2 (E - E) 2 dlle fX dily , (3 .7 .13a )
max
X = - 1/(2Ev)
i , 3
(Mi i~~
)po~l
e(+)(r)(Ae) Fi 3
Yn
1v(n)
X
X Y4 Fj* Y4 ue(+)(r)(ae) , (i,J = V, A) (3 .7 .13b )
where r denotes the decay electron polarization index . Since integration
over all possible neutrino momenta must evidently yield zero, only term s
involving
Y 4 and Ev survive, and, using properties of the gamma matrice s
and of the spinors u, we find that (3 .7 .10b) may be written explicitly :
1X
2n(~N
v
' dS2 F
~2 G2 + 1M GT 2 2 + u
*(t)(r)(1e) Y5 ue(+)(r)(ae )
G GT e
X
X (IMr,I2 Re(CV C V ) + I MGT' 2 Re(CA C A)) ) . (3 .7 .14 )
The remaining variable term in this expression may be evaluated using th e
standard formul a
u (+)(r) (fl) Y5 u(+)(r) (s) _ - (1/E) (
!!(r) I
4a I ~(r) > ,
(3 .7 .15a)