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Register a new userField Redefinitions and Wave Function Renormalization to $O(p^4)$ in Heavy Baryon Chiral Perturbation Theory
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Authors
Joachim Kambor
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Mass- and wave-function renormalization is calculated to order $p^4$ in heavy baryon chiral perturbation theory. Two different schemes used in the literature are considered. Several technical issues like field redefinitions, non-transformation of sources as well as subtleties related to the definition of the baryon propagator are discussed. The nucleon axial-vector coupling constant $g_A$ is calculated to order $p^4$ as an illustrative example.
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The complete renormalization of the weak Lagrangian to chiral order q^2 in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay Lambda -> p pi^- and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.
Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as sums of two-particle irreducible contributions of time-ordered diagrams and the scattering amplitudes are obtained as solutions of integral equations. Ultraviolet renormalizability is achieved by solving integral equations for the leading order amplitude and including higher order corrections perturbatively. As an application of the developed formalism, pion-nucleon scattering is considered.
Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms the order of the cubed pion mass, which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms the order of the squared lattice spacing. The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.
A brief introduction to chiral perturbation theory, the effective field theory of quantum chromodynamics at low energies, is given.
We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order (i.e., $mathcal{O}(p^4)$) in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite volume corrections. Up to $mathcal{O}(p^3)$ all relevant low energy constants can be well determined. As a consequence, we obtain the physical values for the masses of $Xi_{cc}$ and $Omega_{cc}$ baryons by extrapolating to the physical limit. Our determination of the $Xi_{cc}$ mass is consistent with the recent experimental value by LHCb collaboration, however, larger than the one by SELEX collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the $Xi_{cc}$ and $Omega_{cc}$ states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of $mathcal{O}(p^4)$ order, where more unknown constants are involved, when more data are available for unphysical pion masses.
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