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 GP (t) in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant gP = (mμ/2M)GP (t = −0.877mμ) measurable in ordinary muon capture μp → νμn 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 gπN = 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: GP (t) = 4gπNMfπ/(m 2 π − t)− 2gAM〈r A〉/3, with 〈r2 A〉 = (0.44± 0.02) fm2 the axial mean square radius of the nucleon. PACS: 11.30.Rd, 12.20.Ds, 12.38.Bx, 12.39.Fe, 14.20.Dh. To be published in: The Physical Review C (2003), Brief Report The structure of the nucleon as probed by charged weak currents is encoded in two form factors, the axial and the pseudoscalar ones. To be specific consider the matrix element of the isovector axial current between nucleon states: 〈N(p + k)|q̄γγ5τaq|N(p)〉 = ū(p+ k) [ γGA(t) + k 2M GP (t) ]