  We apply here a recently developed approach to compute the short distance
corrections to scaling for the correlators of all primary operators of the
critical two dimensional Ising model in a magnetic field. The essence of the
method is the fact that if one deals with O.P.E. Wilson coefficients instead of
correlators, all order I.R. safe formulas can be obtained for the perturbative
expansion with respect to magnetic field. This approach yields in a natural way
the expected fractional powers of the magnetic field, that are clearly absent
in the naive perturbative expression for correlators. The technique of the
Mellin transform have been used to compute the I.R. behavior of the regularized
integrals. As a corollary of our results, by comparing the existing numerical
data for the lattice model we give an estimate of the Vacuum Expectation Value
of the energy operator, left unfixed by usual nonperturbative approaches
(Thermodynamic Bethe Ansatz).
