Appendix B: ``Scalar QCD''

In assessing to what extent various measurements constitute tests of QCD, it is convenient to compare QCD predictions for them with results obtained from other theories. In this appendix, we give the forms for some of the results discussed in this paper which would follow from a theory in which the gluons () are colored scalars (see also [12]). This theory has many fundamental differences from QCD. In particular, the effective coupling does not tend logarithmically to zero as increases but rather goes to a constant value as a power of Nevertheless, this behavior is not yet ruled out by deep inelastic scattering measurements. The differential cross-section is

Note that this exhibits collinear but not combined collinear and soft infrared divergences. Adding in the one-loop corrections to one finds that for scalar QCD, the total cross-section is (11)

From (B.1) one finds that for :

while for [1]:

For :

The corresponding results for are given in Sect.2.2. Equations (B.3) through (B.8) indicate that, for a given value of the coupling constant, scalar QCD predicts that continuum annihilation events should be closer to the two-jet limit than is expected from QCD.

Near the given in (B.7) becomes

while around the regular part goes like

Note the absence of a double logarithmic divergence in the integral of close to This implies [2] that the for depend on for large rather than as in QCD. The at large for the process behave like when summed to all orders in in contrast to the result found in QCD.

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