  The WMAP results on the scalar spectral index n and its running with scale,
though preliminary, open a very interesting window to physics at very high
energies. We address the problem of finding inflaton potentials well motivated
by particle physics which can accomodate WMAP data. We make a model independent
analysis of a large class of models: those with flat tree-level potential
lifted by radiative corrections, which cause the slow rolling of the inflaton
and the running of n. This includes typical hybrid inflation models. In the
small-coupling regime the predictions for the size and running of n are
remarkably neat, e.g. -dn/dln k=(n-1)^2 << 1, and n does not cross n=1,
contrary to WMAP indications. On the other hand, n can run significantly if the
couplings are stronger but at the price of having a small number of e-folds,
Ne. We also examine the effect of mass thresholds crossed during inflation.
Finally, we show that the presence of non-renormalizable operators for the
inflaton, suppressed by a mass scale above the inflationary range, is able to
give both dn/dln k ~ O(-0.05) and Ne ~ 50.
