Anomalies and WZW-term of two-flavour QCD

The U(2)_R x U(2)_L symmetry of QCD with two massless flavours is subject to anomalies which affect correlation functions involving the singlet currents A^0_\mu or V^0_\mu. These are relevant for pion-photon interactions, because - for two flavours - the electromagnetic current contains a singlet piece. We give the effective Lagrangian required for the corresponding low energy analysis to next-to-leading order, without invoking an expansion in the mass of the strange quark. In particular, the Wess-Zumino-Witten term that accounts for the two-flavour anomalies within the effective theory is written down in closed form.Comment: 17 pages, 1 figur

A model of a transition neutral pion formfactor measured in annihilation and scattering channels

We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and annihilation channels are considered including the relevant experiments with lepton-proton scattering.Comment: 5 pages, 4 figur

Rare decay \pi^0 \to e^+e^- as a Test of Standard Model

Experimental and theoretical progress concerning the rare decay \pi^0 \to e^+e^- is briefly reviewed. It includes the latest data from KTeV and a new model independent estimate of the decay branching which show the deviation between experiment and theory at the level of $3.3\sigma$. The predictions for \eta and \eta' decays into lepton pair are presented. We also comment on the impact on the pion rare decay estimate of the BABAR collaboration on the pion transition form factor at large momentum transfer.Comment: 11 pages, 2 figures, extended version of the talk given at "New Physics and Quantum Chromodynamics at External Conditions" conference, May 3-6, 2009, Dnipropetrovsk, Ukrain

Two- and Three-Point Functions in the Extended NJL Model

The two-point functions in generalized Nambu--Jona-Lasinio models are calculated to all orders in momenta and quark masses to leading order in $1/N_c$. The use of Ward identities and the heat-kernel expansion allows for a large degree of regularization independence. We also show how this approach works to the same order for three-point functions on the example of the vector-pseudoscalar-pseudoscalar three-point function. The inclusion of the chiral anomaly effects at this level is shown by calculating the pseudoscalar-vector-vector three-point function to the same order. Finally we comment on how (vector-)meson-dominance comes out in the presence of explicit chiral symmetry breaking in both the anomalous and the non-anomalous sectors.Comment: Latex, 42 pages, 3 latex figures, 7 postscript figures included, NORDITA 94/11 N,P. Improvement in the regularization procedure for the PVV three point functio

Radiative decays of heavy and light mesons in a quark triangle approach

The radiative meson decays $V\to P\gamma$ and $P\to \gamma\gamma$ are analyzed using the quark triangle diagram. Experimental data yield well determined estimates of the universal quark-antiquark-meson couplings $g_{Vq\bar{q}'}$ and $g_{Pq\bar{q}'}$ for the light meson sector. Also predictions for the ratios of neutral to charged heavy meson decay coupling constants are given and await experimental confirmation.Comment: 31 pages of RevTex, 5 figures, Postscript version available at http://info.utas.edu.au/docs/physics/theory/Publications/9548.html, scheduled to appear in Phys. Rev. D, vol 53, issue 11, 199

Z' Decays into Four Fermions

If a new $Z'$ is discovered with a mass $\sim 1 \ TeV$ at LHC/SSC, its (rare) decays into two charged leptons plus missing transverse energy will probe the $Z'$ coupling to the lepton doublet $(\nu,e)_L$ and to $W^+W^-$, allowing further discrimination among extended electroweak models.Comment: 9 pages plus 1 figure (not included but available), UG-FT-22/9

Strong UA(1)U_A(1) breaking in radiative η\eta decays

We study the \egg, \egm and \epg decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. We find that the $\eta$-meson mass, the \egg, \egm and \epg decay widths are in good agreement with the experimental values when the $U_{A}(1)$ breaking is strong and the flavor $SU(3)$ singlet-octet mixing angle $\theta$ is about zero. The calculated $\eta \gamma \gamma^\ast$ transition form factor has somewhat weaker dependence on the squared four-momentum of the virtual photon. The effects of the $U_A(1)$ anomaly on the scalar quark contents in the nucleon, the $\Sigma_{\pi N}$ and $\Sigma_{KN}$ terms and the baryon number one and two systems are also studied.Comment: 41 pages, LaTeX, 17 eps figures, uses epsf.sty and cite.st

How the recent BABAR data for P to \gamma\gamma* affect the Standard Model predictions for the rare decays P to l+l-

Measuring the lepton anomalous magnetic moments $(g-2)$ and the rare decays of light pseudoscalar mesons into lepton pairs $P\to l^{+}l^{-}$, serve as important tests of the Standard Model. To reduce the theoretical uncertainty in the standard model predictions, the data on the charge and transition form factors of the light pseudoscalar mesons play a significant role. Recently, new data on the behavior of the transition form factors $P\to\gamma\gamma*$ at large momentum transfer were supplied by the BABAR collaboration. There are several problems with the theoretical interpretation of these data: 1) An unexpectedly slow decrease of the pion transition form factor at high momenta, 2) the qualitative difference in the behavior of the pion form factor and the $\eta$ and $\eta^\prime$ form factors at high momenta, 3) the inconsistency of the measured ratio of the $\eta$ and $\eta^\prime$ form factors with the predicted one. We comment on the influence of the new BABAR data on the rare decay branchings.Comment: 11 pages, 3 figure

The π0→e+e−\pi^0\to e^+e^- and η→μ+μ−\eta\to \mu^+ \mu^- Decays Revisited

The rare $\pi^0 \to e^+e^-$ and $\eta \to \mu^+\mu^-$ decays are calculated in different schemes, which are seen to be essentially equivalent to and produce the same results as conventional Vector-Meson Dominance. We obtain the theoretical predictions $B(\pi^0 \to e^+e^-) = (6.41 \pm 0.19)\times 10^{-8}$ and $B(\eta \to \mu^+\mu^-) = (1.14 +0.06 -0.03) \times 10^{-5}$ in agreement with recent experimental data.Comment: 10 pages, LATEX (revised version for recent experimental data

Hadronic light-by-light scattering contribution to the muon g-2: an effective field theory approach

The hadronic light-by-light contribution to a_{mu}, the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a_{mu}, and to a sizeable reduction of the discrepancy between the present experimental value of a_{mu} and its theoretical counterpart in the standard model.Comment: 4 pages, 1 figure. v2: published versio