introduction-weak-interaction-volume-one

form factors : an isoscalar fora factor :
G S - -}(Gp + G n ) , (5 .4 .10 )
and an isovector one :
i- ( Gp - Gn ) . (5 .4 .11 )
Gv =
From (5 .4 .10) and (5 .4 .11), we may deduce that
G
P
= GS + Gv , (5 .4 .12 )
G n = GS - Gv , (5 .4 .13 )
and similarly for the electric form factors . We see that G S has the same sign
for the proton and the neutron, whereas
Gv has opposite signs for the two
particles . Thus the meson responsible for G S will have zero isospin, and tha t
responsible for G v will have I = 1 . The mesons which fit these requirements
are the 6J (783) and the e°(770) respectively .
In the weak interaction, we may also define form factors . We use two
form factors, the vector one : Gv ( q2 ), and the axial vector one : GA ( q 2 ) .
In the matrix elements for hadronic weak processes, wo must include six for m
factors : fv(g2 ), gv( g2 ), hv( g2), fA(g2), gA(g 2 ), h A (g2 ), all of 'which ar e
scalar functions of
q 2 . These contain all possible information concernin g
the modifications to the basic weak interaction caused by the existence o f
virtual strong interactions . In order to produce a complete model for th e
weak interaction, we mast determine the nature and structure of these form
factors . The best method of so doing is to employ dispersion theory. However ,
this is beyond the scope of this book . A good introduction to dispersio n
theory is S .Landelstam : Dispersion Nelations in Strong-Coupling Physics ,
Rep . Frog . Phys ., , pp . 99-162 (1962), which is reproduced in ed . Fronsdnl :
Lecture Notes on Posh Interactions and Topics in Dispersion Physics from th e
Second Bergen International School of Physics - 1962, Benjamin 1963, pp . 26 9
et . seq. Using arguments in dispersion theory, we find tha t
gv(g 2) , (5 .4 .14 )
fv(g2 ) (5 .4 .15 )
receive contributions from states with r G of 1 +, of which the resonan t
pion states 2r and 4-T are the lowest mass examples . The former correspond s
to the (770) meson .
(gv(g 2)( mA - m ) + q2 hv (g 2)) (5 .4.16)