Radiative η′\eta' Decays, the Topological Susceptibility and the Witten-Veneziano Mass Formula

The formulae describing the radiative decays \eta'(\eta)\rta\c\c in QCD beyond the chiral limit are derived. The modifications of the conventional PCAC formulae due to the gluonic contribution to the axial anomaly in the flavour singlet channel are precisely described. The decay constants are found to satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. Combining these results, it is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of \eta'(\eta)\rta\c\c.Comment: TeX, 21 pages, no figures, uses harvma

Phenomenological evidence for the energy dependence of the η−η′\eta-\eta' mixing angle

A phenomenological analysis on various decay processes is performed using an energy-dependent $\eta-\eta'$ mixing angle scheme. Special attention is given to the radiative couplings between lowest-lying vector and pseudoscalar mesons. The agreement between our predictions and the experimental values is remarkable. This analysis opens a connection to two-angle fits in the $\eta-\eta'$ sector.Comment: 13 pages. Introduction slightly modified. A second Table added. Conclusions remain unchange

The number of colors in the decays pi^0, eta, eta-prime -> gamma gamma

The decays pi^0, eta, eta-prime -> gamma gamma are investigated up to next-to-next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Without mixing of the pseudoscalar mesons the N_c independence of the pi^0 and eta decay amplitudes is shown to persist at the one-loop level, although the contribution of the Wess-Zumino-Witten term to the pertinent vertices is not canceled by the N_c dependent part of a Goldstone-Wilczek term. The decay amplitude of the singlet field, on the other hand, depends strongly on N_c and yields under the inclusion of mixing also a strong N_c dependence for the eta decay. Both the eta and eta-prime decay are suited to confirm the number of colors to be N_c=3.Comment: 18 pages, 1 figur

Matching of U_L(3) x U_R(3) and SU_L(3) x SU_R(3) Chiral Perturbation Theories

The heavy singlet field is integrated out from the U_L(3) x U_R(3) Chiral Perturbation Theory and it is shown how its effects on the low-energy dynamics are reduced to effective vertices for the light mesons. The results are matched against the standard SU_L(3) x SU_R(3) Chiral Perturbation Theory in order to establish the relations between the coupling constants from both theories to one-loop level accuracy.Comment: 10 pages, 1 eps figure. Some comments rephrase

The electric dipole moment of the neutron in chiral perturbation theory

We calculate the electric dipole moments of the neutron and the Lambda within the framework of heavy baryon chiral perturbation theory. They are induced by strong CP-violating terms of the effective Lagrangian in the presence of the vacuum angle theta_0. The construction of such a Lagrangian is outlined and we are able to give an estimate for theta_0.Comment: 17 pages, 2 figure

Short- and long-distance contributions to the rare decay K_L-->mu+ mu-

The interplay between short- and long-distance contributions to the K_L-->mu+ mu- decay amplitude is analyzed. The long-distance piece is estimated using chiral perturbation theory techniques and large-N_C considerations, leading to a consistent description of the pi^0-->e+ e-, eta-->mu+ mu- and K_L-->mu+ mu- branching ratios.Comment: 4 pages, 1 figure, talk given at the Euroconference QCD 98, Montpellier, France, July 199

The eta' in baryon chiral perturbation theory

We include in a systematic way the eta' in baryon chiral perturbation theory. The most general relativistic effective Lagrangian describing the interaction of the lowest lying baryon octet with the Goldstone boson octet and the eta' is presented up to linear order in the derivative expansion and its heavy baryon limit is obtained. As explicit examples, we calculate the baryon masses and the pi N sigma-term up to one-loop order in the heavy baryon formulation. A systematic expansion in the meson masses is possible, and appearing divergences are renormalized.Comment: 16 pages, 2 figure

Hadronic eta and eta-prime decays

The hadronic decays eta, eta-prime -> 3 pi and eta-prime -> eta pi pi are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall agreement with currently available data on decay widths and spectral shapes is achieved.Comment: 28 pages, 5 figures, 8 table