Abstract:
The baryon masses are examined in SU(3) chiral perturbation theory to third order using the recently proposed infrared regularization scheme. Fourth order is estimated by evaluating the dominant diagram. With this regularization the magnitude of the loop integrals is reduced so that the convergence of the series appears to be better than in the heavy baryon approach.

Abstract:
We investigate the use of long distance regularization in SU(3) baryon chiral perturbation theory with decuplet fields. The one-loop decuplet contributions to the octet baryon masses, axial couplings, S-wave nonleptonic hyperon decays and magnetic moments are evaluated in a chirally consistent fashion by employing a cutoff to implement long distance regularization. The convergence of the chiral expansions of these quantities is improved compared to the dimensionally regularized version which indicates that the propagation of Goldstone bosons over distances smaller than a typical hadronic size, which is beyond the regime of chiral perturbation theory but included by dimensional regularization, is removed by use of a cutoff.

Abstract:
We include the eta-prime in chiral perturbation theory without employing 1/N_c counting rules. The method is illustrated by calculating the masses and decay constants of the Goldstone boson octet (pions, kaons, eta) and the singlet eta-prime up to one-loop order. The effective Lagrangian describing the interactions of the eta-prime with the Goldstone boson octet is presented up to fourth chiral order and the loop integrals are evaluated using infrared regularization, which preserves Lorentz and chiral symmetry.

Abstract:
The SU(3) chiral lagrangian for the lightest octets of mesons and baryons is constructed on a spacetime lattice. The lattice spacing acts as an ultraviolet momentum cutoff which appears directly in the Lagrangian so chiral symmetry remains explicit. As the lattice spacing vanishes, Feynman loop diagrams typically become divergent due to inverse powers of the lattice spacing, and these divergences get absorbed into counterterms such that the standard results of dimensional regularization are obtained. One advantage of lattice regularization is that power divergences are seen explicitly. In the present work, the octet meson masses, the octet baryon masses and the pion-nucleon sigma term are all computed explicitly to one loop order.

Abstract:
We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied straightforwardly to multi-loop diagrams with an arbitrary number of particles with arbitrary masses.

Abstract:
This article provides a pedagogical introduction to the basic concepts of chiral perturbation theory and is designed as a text for a two-semester course on that topic. Chapter 1 serves as a general introduction to the empirical and theoretical foundations which led to the development of chiral perturbation theory. Chapter 2 deals with QCD and its global symmetries in the chiral limit; the concept of Green functions and Ward identities reflecting the underlying chiral symmetry is elaborated. In Chap. 3 the idea of a spontaneous breakdown of a global symmetry is discussed and its consequences in terms of the Goldstone theorem are demonstrated. Chapter 4 deals with mesonic chiral perturbation theory and the principles entering the construction of the chiral Lagrangian are outlined. Various examples with increasing chiral orders and complexity are given. Finally, in Chap. 5 the methods are extended to include the interaction between Goldstone bosons and baryons in the single-baryon sector, with the main emphasis put on the heavy-baryon formulation. At the end, the method of infrared regularization in the relativistic framework is discussed.

Abstract:
The use of SU(3) chiral perturbation theory in the analysis of low energy meson-baryon interactions is discussed. It is emphasized that short distance effects, arising from propagation of Goldstone bosons over distances smaller than a typical hadronic size, are model-dependent and can lead to a lack of convergence in the SU(3) chiral expansion if they are included in loop diagrams. In this paper we demonstrate how to remove such effects in a chirally consistent fashion by use of a cutoff and demonstrate that such removal ameliorates problems which have arisen in previous calculations due to large loop effects.

Abstract:
In the framework of perturbation theory, it is possible to put chiral gauge theories on the lattice without violating the gauge symmetry or other fundamental principles, provided the fermion representation of the gauge group is anomaly-free. The basic elements of this construction (which starts from the Ginsparg-Wilson relation) are briefly recalled and the exact cancellation of the gauge anomaly, at any fixed value of the lattice spacing and for any compact gauge group, is then proved rigorously through a recursive procedure.

Abstract:
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical evaluation of lattice Feynman diagrams. The automated method significantly simplifies working with improved or extended actions. Some applications to the study of finite-volume effects will be presented.

Abstract:
We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. Contrary to other claims in the literature we show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone Boson masses. We also discuss in detail the prize, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization, which is usually not paid attention to. We also compare the fourth order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.