slac-pub-2605 - SLAC - Stanford University

-25-
where, because of the large ms/md ratio, Y Ko need not be symmetric in
xs-Hx
d'
The transition form factor FK OK (Q2) at large
s L
Q2 can then be
written in the form of Eq. (1.12) with
and thus
TH(Xi’Yi’Q) =
16xes(Q2)CF e-
Q2
[j& + i&l ' (3.4)
F K~+\(Q~) =(i)siras~~2)cF[n(~en) mFdd) azarn (gn $,'nm'm + h.c]
x [l + o(us(Q2)dQ)] (3.5)
Thus the form factor requires the odd (asymmetric under x = xd-% + -x)
Gegenbauer components of the K" distribution amplitude. Asymptotically,
the transition form factor vanishes with an extra anomalous dimensions:
F~s + +Q2)
2 Q 2 SW ($)Re(z)(log $)"
FK+(Q )
where y1 = (8/3)(CF/i3) ("0.4 for nf=3). If this ratio of form factors is
indeed appreciable [i.e., of order 11, then the odd, asymmetric components
play a major role in the structure of the kaon wavefunction. This would also
imply a strong violation of the relation F r+(Q2) /F+(Q2) z f;/f; at sub-
asymptotic QL. All of these results can, of course, be extended to mesons
containing heavy quarks.
Since quark helicity is conserved at each vertex in TH, it is diagonal
in hadronic helicity up to corrections of order m/Q. Further, to leading
order in l/Q2 only terms with csi
i
= Ss contribute in $(xi,Q). Consequently
there are two selection rules restricting the helicities of initial (hi) and
final (hf) hadrons C1,2,271:
(a) Ah = hf-hi = 0 (for timelike photon: h1 = -h2)
6) Ihl = Ihi,f] s l/2 .
(3.6)
(3.7)