arXiv subjects
Publications and source records attributed to G. Ecker.
We calculate the leading isospin-violating and electromagnetic corrections for the decay tau --> pi^0 pi nu_tau at low energies. The corrections are small but relevant for the inclusion of tau decay data in the determination of hadronic vacuum polarization especially for the anomalous magnetic moment of the muon.
A brief survey of applications of chiral perturbation theory to both semileptonic and nonleptonic kaon decays is presented. Special emphasis is given to recent theoretical advances related to semileptonic decays, in particular pion pion scattering and Ke4 decays. The systematic approach for including isospin violation and electromagnetic corrections in semileptonic decays is discussed for Kl3 decays.
We calculate the leading isospin-violating and electromagnetic corrections for the decay tau -> pi^0 pi nu_tau at low energies. The corrections are small but relevant for the inclusion of tau decay data in the determination of hadronic vacuum polarization especially for the anomalous magnetic moment of the muon. We show that part of the systematic differences between the measured form factors in tau -> pi^0 pi nu_tau and e^+ e^- -> pi^+ pi^- is due to isospin violation .
We update the theoretical analysis of the CP-violating asymmetry in the decay K_L -> pi+ pi- e+ e-, relying on chiral perturbation theory and on the most recent phenomenological information. With the experimentally determined magnetic amplitude and branching ratio as input, the asymmetry can be calculated with good accuracy. The theoretical interpretation of the sign of the asymmetry is discussed.
After an introduction to chiral perturbation theory, the effective field theory of the standard model at low energies, a brief overview is given of applications to light-flavour physics. Three topics in the strong interactions of pseudoscalar mesons are then discussed in some detail: loops and chiral logs, pion-pion scattering and isospin violation.
We construct a low-energy effective field theory that permits the complete treatment of isospin-breaking effects in nonleptonic weak interactions to next-to-leading order. To this end, we enlarge the chiral Lagrangian describing strong and Delta S=1 weak interactions by including electromagnetic terms with the photon as additional dynamical degree of freedom. The complete and minimal list of local terms at next-to-leading order is given. We perform the one-loop renormalization at the level of the generating functional and specialize to K -> pi pi decays.
We discuss $π^0$ -$η$ mixing and its implication for $ε'/ ε$ to next-to-leading order in the low-energy expansion. The big effect due to $η$-$η'$ mixing is shown to be largely cancelled by other contributions occurring at the same order in the chiral expansion.
The renormalization of chiral perturbation theory is carried out to next-to-next-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p^6) for chiral SU(n), involving one- and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p^6) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.
We analyse the radiative decay $η\to π^+π^- π^0γ$ in the low--energy expansion of the Standard Model. We employ the notion of ``generalized bremsstrahlung'' to take full advantage of the theoretical and experimental information on the corresponding non-radiative $η\to 3 π$ decay. The direct emission amplitude of ${\cal O}(p^4)$ is due to one-loop diagrams with intermediate pions (isospin violating) and kaons (isospin conserving). The isospin conserving contributions to direct emission, including vector meson exchange appearing at ${\cal O}(p^6)$, are suppressed.
We determine the full structure of the leading (double-pole) divergences of O(p^6) in the meson sector of chiral perturbation theory. The field theoretic basis for this calculation is described. We then use an extension of this result to determine the p^6 contributions containing double chiral logarithms (L^2), single logarithms times p^4 constants (L x L_i^r) and products of two p^4 constants (L_i^r x L_j^r) for F_π, F_K/F_π, K_{l3} and K_{e4} form factors. Numerical results are presented for these quantities.
We present a model-independent analysis of $K^+\toπ^+\ell^+\ell^-$ and $K_S\toπ^0\ell^+\ell^-$ decays, including $K\to 3 π$ unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on $K^+\toπ^+ e^+ e^-$ we predict the ratio $R= B(K^+\toπ^+μ^+μ^-)/B(K^+\toπ^+ e^+ e^-)$ to be larger than 0.23, in slight disagreement with the recent measurement $R = 0.167 \pm 0.036$. Consequences for the $K^\pm \toπ^\pm e^+ e^-$ charge asymmetries and for the $K_L\toπ^0 e^+ e^-$ mode are also discussed.
We employ notions familiar from supersymmetry for constructing the one-loop functional of general quantum field theories with bosons and fermions (spin < 1). To demonstrate the advantages of such an approach for calculating one-loop divergences, we analyse a simple Yukawa theory with two different versions of a super-heat-kernel expansion. These methods also simplify the calculation of one-loop divergences for non-renormalizable meson--baryon Lagrangians occurring in chiral perturbation theory.
We establish exact relations between relativistic form factors and amplitudes for single-baryon processes and the corresponding quantities calculated in the framework of heavy baryon chiral perturbation theory. A crucial ingredient for the proper matching is the first complete treatment of baryon wave function renormalization in heavy baryon chiral perturbation theory.
We present technical details of the evaluation of the elastic pi-pi scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions. For the sake of clarity, we discuss these matters both in the N-component $ϕ^4$ theory (in its symmetric phase) and in chiral perturbation theory. Estimates for the relevant low-energy constants of $O(p^6)$ are presented. Threshold parameters and phase shifts are then calculated for two sets of $O(p^4)$ coupling constants and compared with experiment. We comment on the extraction of threshold parameters from phase shift data.
We present a complete analysis of K -> 3 pi gamma decays to O(p^4) in the low-energy expansion of the Standard Model. We employ the notion of "generalized bremsstrahlung" to take full advantage of experimental information on the corresponding non-radiative K -> 3 pi decays.
We present a general discussion of radiative four--meson processes to $O(p^4)$ in chiral perturbation theory. We propose a definition of ``generalized bremsstrahlung'' that takes full advantage of experimental information on the corresponding non--radiative process. We also derive general formulae for one--loop amplitudes which can be applied, for instance, to $η\ra 3πγ$, $ππ\ra ππγ$ and $K \ra 3πγ$.
We evaluate analytically the elastic $ππ$ scattering amplitude to two loops in chiral perturbation theory and give numerical values for the two $S$--wave scattering lengths and for the phase shift difference $δ_0^0-δ_1^1$.
We investigate to what extent DA$Φ$NE will be able to test the Standard Model in the confinement regime with radiative kaon decays. We concentrate on processes which can be detected at DA$Φ$NE and we review briefly those decays where only upper limits can be expected. The Standard Model predictions for these decays are analyzed in the framework of chiral perturbation theory.