An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of \(F_{\pi }\) and \(M_{\pi }^2\) in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.     

Comparison of \pi K scattering in SU(3) chiral perturbation theory and dispersion relations

We establish the framework for the comparison of scattering amplitudes from SU(3) chiral perturbation theory with suitable dispersive representations which result from the combination of certain fixed-t dispersion relations with dispersion relations on hyperbolic curves. This allows for predictions for some combinations of low energy constants appearing in higher order calculations of chiral perturbation theory. Using a simple parametrization for the lowest partial waves, first estimates for some combinations are presented. Received: 6 December 2000 / Revised version: 13 February 2001 / Published online: 23 March 2001     

A dispersive approach to pion photo- and electroproduction

The relativistic amplitudes of pion photo- and electroproduction are calculated by dispersion relations at constant t. Several sum rules and low-energy theorems for the threshold amplitudes are investigated within this technique. The continuation of the amplitudes to sub-threshold kinematics is shown to provide a unique framework to derive the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.     

Spin polarizability of hyperons

We review the recent progress of the theoretical understanding of spin polarizabilities of the hyperon in the framework of SU(3) heavy baryon chiral perturbation theory (HBChPT). We present the results of a systematic leading-order calculation of hyperon Compton scattering and extract the forward spin polarizability (γ ₀) of hyperons. The results obtained for γ ₀ in the case of nucleons agree with the known results of SU(2) HBChPT when kaon loops are not considered.     

Predictive powers of chiral perturbation theory in Compton scattering off protons

We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (BχPT) with pion, nucleon, and Δ(1232) degrees of freedom, up to and including the next-to-next-to-leading order (NNLO). We include the effects of order p ², p ³, and p ⁴/Δ, with Δ≈300 MeV the Δ-resonance excitation energy. These are all “predictive” powers in the sense that no unknown low-energy constants enter until at least one order higher (i.e., p ⁴). Estimating the theoretical uncertainty on the basis of natural size for p ⁴ effects, we find that uncertainty of such a NNLO result is comparable to the uncertainty of the present experimental data for low-energy Compton scattering. We find an excellent agreement with the experimental cross-section data up to at least the pion-production threshold. Nevertheless, for the proton’s magnetic polarizability we obtain a value of (4.0±0.7)×10^?4 fm³, in significant disagreement with the current PDG value. Unlike the previous χPT studies of Compton scattering, we perform the calculations in a manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB) expansion. The difference between the lowest order HBχPT and BχPT results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HBχPT and BχPT with the hope to confront it with lattice QCD calculations in a near future. In studying some of the polarized observables we identify the regime where their naive low-energy expansion begins to break down, thus addressing the forthcoming precision measurements at the HIGS facility.     

The Fubini-Furlan-Rosetti sum rule and related aspects in light of covariant baryon chiral perturbation theory<Superscript>⋆</Superscript>

We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading-order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E₀₊.     

Quark Mass Dependence of the Ground-State Octet Baryons in Next-to-Next-to-Next-to-Leading Order Covariant Baryon Chiral Perturbation Theory

We report on a recent study of the ground-state octet baryon masses using the covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-next-to-leading order. By adjusting the available 19 low-energy constants, a good fit of the n _f  = 2 + 1 lattice quantum chromodynamics results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved.     

Non-leptonic hyperon decays in chiral perturbation theory

The non-leptonic hyperon decays are analyzed up to one-loop order including all counterterms in the framework of heavy baryon chiral perturbation theory. We use the exchange of the spin- decuplet resonances as an indication of which low-energy constants contribute significantly to these investigated processes. We choose four independent decay amplitudes that are not related by isospin relations in order to perform a fit for the pertinent low-energy constants and find a satisfactory fit both for s- and p-waves. The chiral corrections to the lowest order forms for the s-waves are moderate whereas there are significant modifications of the p-wave amplitudes. Received: 16 December 1997 / Revised version: 18 February 1998 / Published online: 15 June 1998     

Decuplet contribution to the meson–baryon scattering lengths

We calculate decuplet contributions to the s-wave pseudoscalar meson octet–baryon scattering lengths to the third order in heavy baryon chiral perturbation theory (HBχPT). Using experimental pion–nucleon and kaon–nucleon scattering lengths as inputs, we determine low-energy constants and predict other meson–baryon scattering lengths. Numerically we consider three cases: (1) the case with only baryon octet contributions; (2) with decuplet contributions and (3) in the large N_c limit. Hopefully, the analytical expressions and the predictions are helpful to future investigations of the meson–baryon scattering lengths. PACS 13.75.Gx; 13.75.Jz     

Lattice simulations for light nuclei: Chiral effective field theory at leading order

We discuss lattice simulations of light nuclei at leading order in the chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.     

Threshold neutral pion photoproduction off the tri-nucleon to O(q4)

We calculate the electromagnetic neutral pion production off tri-nucleon bound states (³H, ³He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth-order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off ³He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole $E_{0+}^{\pi^0 n}$ .     

Extracting information on renormalized coupling constants of contact interactions of the chiral perturbation theory lagrangian from the phase-shift analysis of π<Emphasis Type="Italic">N</Emphasis> scattering

The analytic approach to the construction of the effective theory of strong interactions in the low-energy range is developed and its application to pion-nucleon scattering is considered. A model-independent definition of renormalized coupling constants of contact interactions of the effective chiral perturbation theory Lagrangian is proposed. With the help of the available data of pion-nucleon phase-shift analysis the information on these constants is extracted.     

Electromagnetic properties of theZ boson

Direct (nonresonant) 3-body decays of charmed mesons are calculated in chiral perturbation theory. The magnitudes of the 20 and 84 representations of the effective chiralSU(4)×SU(4) Lagrangian are determined from the measured 2-bodyD→Kπ rate. For decay modes which do not contain nonspectator contributions, the agreement of theoretical predictions with the data is satisfactory. Nevertheless, the large discrepancy between theory and experiment for decays which can proceed through theW-exchange orW-annihilation might imply the importance of nonperturbative corrections to the nonspectator diagram and the existence of final-state interactions.     

Aspects of near-threshold neutral pion photoproduction off protons

We investigate near-threshold neutral pion photoproduction off protons to fourth order in heavy-baryon chiral perturbation theory in the light of the new data from MAMI. We show that the unitarity cusp at the secondary π⁺ n threshold is in agreement with expectations from the final-state theorem. We also analyze the fourth-order corrections to the P-wave low-energy theorems and show that potentially large Δ isobar contributions are cancelled by sizeable pion loop effects. This solidifies the parameter-free third-order predictions, which are in good agreement with the data. Received: 25 May 2001 / Accepted: 21 June 2001     

Radiative corrections to low-energy ππ scattering

Radiative corrections to low-energy ππ scattering are calculated. A chiral SU(2) × SU(2) Lagrangian is used to describe low-energy scattering. This strong interaction Lagrangian is modified in the presence of the electromagnetic field in a gauge invariant way. It is found that photons do not probe the strong vertex. Corrections to the cross sections are calculated to O(α). All the ultra-violet divergences cancel, and the results are independent of cut-off parameters. Corrections to the Weinberg scattering lengths of the order of 1% are defined by removal of the Coulomb pole terms. The field theoretic calculation is compared with a potential theory approach. It is argued that the potential theory calculation of radiative corrections is more reliable.     

Isomeric yield ratios of 87m,gY from different nuclear reactions

We investigate the parity-violating nucleon-nucleon potential as obtained in chiral effective field theory. By using resonance saturation we compare the chiral potential to the more traditional one-meson-exchange potential. In particular, we show how parameters appearing in the different approaches can be compared with each other and demonstrate that analyses of parity violation in proton-proton scattering within the different approaches are in good agreement. In the second part of this work, we extend the parity-violating potential to next-to-next-to-leading order. We show that generally it includes both one-pion- and two-pion-exchange corrections, but the former play no significant role. The two-pion-exchange corrections depend on five new low-energy constants which only become important if the leading-order weak pion-nucleon constant h _π turns out to be very small.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.