Induced pseudoscalar form factor of the nucleon at two-loop order in chiral perturbation theory

We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon G(P)(t) in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant g(P)=(m(mu)/2M)G(P)(t=-0.877m(mu)(2)), measurable in ordinary muon capture mu(-)p-->nu(mu)n, turns out to be negligibly small. Possible contributions from counterterms at two-loop order are numerically smaller than the uncertainty of the dominant pion-pole term proportional to the pion-nucleon coupling constant g(piN)=13.2+/-0.2. We conclude that a sufficiently accurate representation of the induced pseudoscalar form factor of the nucleon at low momentum transfers t is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: G(P)(t)=4g(piN)Mf(pi)/(m(pi)(2)-t)-2g(A)M(2)/3, with =(0.44+/-0.02) fm(2) the axial mean square radius of the nucleon.