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

Abstract

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 $<r_A^2>=(0.44\pm 0.02)$ fm${}^2$ the axial mean square radius of the nucleon.

6 pages, 2 figures, accepted for publication in Physical Review C

References in corpus (2)

• Induced pseudoscalar coupling of the proton weak interaction
• Chiral 3$\pi$-exchange NN-potentials: Results for dominant next-to-leading order contributions

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