Chiral Perturbation Theory With Nucleons

Abstract

I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external momenta and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward–identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the method. Some processes which are discussed are threshold photopion production, low-energy Compton scattering off nucleons, πN scattering and the σ–term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

Nucleon form factors in dispersion theory

“…where i = E, M . In fact, precisely the same effect is obtained at leading one-loop accuracy in relativistic chiral perturbation theory [44,45]. This topic was also discussed in heavy baryon ChPT [25,27] and in a covariant calculation based on infrared regularization [26].…”

Dispersion analysis of the nucleon form factors including meson continua

“…If one were to neglect this important unitarity correction, one would severely underestimate the nucleon isovector radii [43]. In fact, precisely the same effect is obtained at leading one-loop accuracy in relativistic chiral perturbation theory [44,45]. This topic was also discussed in heavy baryon chiral perturbation theory (ChPT) [46,47] and in a covariant calculation based on infrared regularization [48,49].…”

Novel evaluation of the two-pion contribution to the nucleon isovector form factors

“…If one were to neglect this important unitarity correction, one would severely underestimate the nucleon isovector radii [10]. In fact, precisely the same effect is obtained at leading one-loop accuracy in relativistic chiral perturbation theory [36,37]. This topic was further elaborated on in the framework of heavy baryon CHPT [17,20] and in a covariant calculation based on infrared regularization [18].…”