slac-pub-2605 - SLAC - Stanford University

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The second rule is easily derived from the first in the Breit frame. There
the net change in the hadron's angular momentum along the direction of motion
is Nz = -hf -hi = -2h, because the helicity is unchanged while the momentum
is reversed. As the photon has spin 1, only lhl I l/2 is permitted, up to
corrections of O(m/Q).
Applying these selection rules to e+e- collisions beyond the resonance
region, for example, we find that the final states np, PLPJ. ’ PlPL are
suppressed by yn2/Q2 (in the cross section) relative to xx, KK and pLpL final
states.
The selection rules are direct consequences of the vector nature of the
gluon. In contrast, e+e- + plpl is not suppressed in a theory with scalar
-
gluons. Furthermore while each of the 'allowed' form factors is positive
at large Q2 in QCD, they are negative in scalar gluon theories, and then must
vanish at some finite Q2 (since F(0) = 1). Scalar theories are probably
already ruled out by existing data.
In the case of baryons, the evolution equation to leading order in as(Q2)
has a general solution of the form
jhl = l/2
Ihj = 3/2
(3.8)
where the leading zr.,, y", are given in Ref. 121, and h is the total quark
helicity (= hadron's helicity since L =O).
2
However in practice it is
generally more efficient to integrate the evolution equation numberically
rather than expanding @ as in (3.8).
Convoluting the hard-scattering amplitude TR (see Fig. 2) with @(xi,Q)
then gives the QCD prediction El,21