  The $pp\to pp\pi^0$ cross section near threshold is computed up to one-loop
order including the initial and final state interactions using the hybrid heavy
baryon chiral perturbation theory and the counting rule a la Weinberg. With the
counter terms whose coefficients are fixed by the resonance-saturation
assumption, we find that the one-loop contributions are as important as the
tree-order contribution and bring the present theoretical estimation of the
total cross section close to the experimental data. The short-ranged
contributions are controlled by means of a cutoff, and a mild cutoff dependence
is observed when all diagrams of the given chiral order are summed. To the
order treated, however, the expansion is found to converge rather slowly,
calling for further studies of the process.
