  The total cross section of the $pp\to pp\pi^0$ reaction near threshold is
calculated in pionless effective field theory with a di-baryon and external
pions. The amplitudes for a leading one-body and subleading contact neutral
pion production vertex are obtained including the initial and final state
interactions. After estimating a low-energy constant in the contact vertex, we
compare our results for the total cross section with the experimental data.
