Baryon chiral perturbation theory in manifestly Lorentz invariant form
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We show that in the presence of massive particles, such as nucleons, the standard low-energy expansion, in powers of meson momenta and light-quark masses, in general converges in only part of the low-energy region. The expansion of the scalar form factor \(\sigma(t)\), for instance, breaks down in the vicinity of \(t=4M_\pi^2\). In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region results only if the multiple internal-line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low-energy region, while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order \(p^4\).
KeywordsPerturbation Theory Massive Particle Invariant Form Chiral Perturbation Theory Threshold Region
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