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

Jan, 2003
6 pages
Published in:
  • Phys.Rev.C 67 (2003) 027002
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Abstract:
We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon GP(t)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 gP=(mμ/2M)GP(t=−0.877mμ2)g_P = (m_\mu/2M) G_P(t=-0.877m_\mu^2) measurable in ordinary muon capture μ−p→νμn\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 gπN=13.2±0.2g_{\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 tt is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: GP(t)=4gπNMfπ/(mπ2−t)−2gAM2<rA2>/3G_P(t) = 4g_{\pi N} M f_\pi/ (m_\pi^2 -t)- 2g_A M^2 < r_A^2 >/3, with <rA2>=(0.44±0.02)<r_A^2> = (0.44 \pm 0.02) fm2^2 the axial mean square radius of the nucleon.
  • 12.38.Bx
  • 11.30.Rd
  • 12.39.Fe
  • 12.20.Ds
  • muon- p: capture
  • charged current
  • nucleon: form factor
  • form factor: pseudoscalar
  • perturbation theory: chiral
  • Feynman graph: higher-order