Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2003-01-10
Phys.Rev. C67 (2003) 027002
Physics
Nuclear Physics
Nuclear Theory
6 pages, 2 figures, accepted for publication in Physical Review C
Scientific paper
10.1103/PhysRevC.67.027002
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 $\mu^-p\to \nu_\mu n$ 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 $g_{\pi N}= 13.2\pm 0.2$. 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: $G_P(t) = 4g_{\pi N} M f_\pi/ (m_\pi^2 -t)- 2g_A M^2 < r_A^2 >/3$, with $
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