arXiv subjects

G. Ecker

Publications and source records attributed to G. Ecker.

At least 19 recordsLinked to original sources

arXiv2014

Approximating chiral SU(3) amplitudes

We construct large-N_c motivated approximate chiral SU(3) amplitudes of next-to-next-to-leading order. The amplitudes are independent of the renormalization scale. Fitting lattice data with those amplitudes allows for the extraction of chiral coupling constants with the correct scale dependence. The differences between approximate and full amplitudes are required to be at most of the order of N^3LO contributions numerically. Applying the approximate expressions to recent lattice data for meson decay constants, we determine several chiral couplings with good precision. In particular, we obtain a value for F_0, the meson decay constant in the chiral SU(3) limit, that is more precise than all presently available determinations.

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arXiv2012

Kaon Decays in the Standard Model

A comprehensive overview of kaon decays is presented. The Standard Model predictions are discussed in detail, covering both the underlying short-distance electroweak dynamics and the important interplay of QCD at long distances. Chiral perturbation theory provides a universal framework for treating leptonic, semileptonic and nonleptonic decays including rare and radiative modes. All allowed decay modes with branching ratios of at least 10^(-11) are analyzed. Some decays with even smaller rates are also included. Decays that are strictly forbidden in the Standard Model are not considered in this review. The present experimental status and the prospects for future improvements are reviewed.

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arXiv2009

Reanalysis of pion pion phase shifts from K -> pi pi decays

We re-investigate the impact of isospin violation for extracting the s-wave pion pion scattering phase shift difference delta_0(M_K) - delta_2(M_K) from K -> pi pi decays. Compared to our previous analysis in 2003, more precise experimental data and improved knowledge of low-energy constants are used. In addition, we employ a more robust data-driven method to obtain the phase shift difference delta_0(M_K) - delta_2(M_K) = (52.5 \pm 0.8_{exp} \pm 2.8_{theor}) degrees.

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arXiv2007

Tensor meson exchange at low energies

We complete the analysis of meson resonance contributions to chiral low-energy constants of O(p^4) by including all quark-antiquark bound states with orbital angular momentum less or equal to one. Different tensor meson Lagrangians used in previous work are shown to produce the same final results for the low-energy constants once QCD short-distance constraints are properly implemented. We also discuss the possible relevance of axial-vector mesons with odd C-parity.

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arXiv2006

Towards a consistent estimate of the chiral low-energy constants

Guided by the large-Nc limit of QCD, we construct the most general chiral resonance Lagrangian that can generate chiral low-energy constants up to O(p^6). By integrating out the resonance fields, the low-energy constants are parametrized in terms of resonance masses and couplings. Information on those couplings and on the low-energy constants can be extracted by analysing QCD Green functions of currents both for large and small momenta. The chiral resonance theory generates Green functions that interpolate between QCD and chiral perturbation theory. As specific examples we consider the VAP and SPP Green functions.

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arXiv2005

Progress in chiral perturbation theory

After a short status report on chiral perturbation theory, I review recent progress in determining some of the low-energy couplings by matching the effective theory to QCD. Consequences for K_{l3} decays and for the extraction of the CKM matrix element V_{us} are reported. Hadronic vacuum polarization at low energies and its impact on the anomalous magnetic moment of the muon are discussed.

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arXiv2005

Generating Functional for Strong and Nonleptonic Weak Interactions

The generating functional for Green functions of quark currents is given in closed form to next-to-leading order in the low-energy expansion for chiral SU(3), including one-loop amplitudes with up to three meson propagators. Matrix elements and form factors for strong and nonleptonic weak processes with at most six external states can be extracted from this functional by performing three-dimensional flavour traces. To implement this procedure, a Mathematica program is provided that evaluates amplitudes with at most six external mesons, photons (real or virtual) and virtual W (semileptonic form factors). The program is illustrated with several examples that can be compared with existing calculations.

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arXiv2005

Effective field theories

Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.

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arXiv2005

The < S P P > Green function and SU(3) breaking in K_{l3} decays

Using the 1/N_C expansion scheme and truncating the hadronic spectrum to the lowest-lying resonances, we match a meromorphic approximation to the < S P P > Green function onto QCD by imposing the correct large-momentum falloff, both off-shell and on the relevant hadron mass shells. In this way we determine a number of chiral low-energy constants of O(p^6), in particular the ones governing SU(3) breaking in the K_{l3} vector form factor at zero momentum transfer. The main result of our matching procedure is that the known loop contributions largely dominate the corrections of O(p^6) to f_{+}(0). We discuss the implications of our final value f_{+}^{K^0 π^-}(0)=0.984 \pm 0.012 for the extraction of V_{us} from K_{l3} decays.

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arXiv2004

Green Function in the Resonance Region

We analyse the three-point function of vector, axial-vector and pseudoscalar currents. In the spirit of large N_C, a resonance dominated Green function is confronted with the leading high-energy behaviour from the operator product expansion. The matching is shown to be fully compatible with a chiral resonance Lagrangian and it allows to determine some of the chiral low-energy constants of O(p^6).

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arXiv2004

Isospin Breaking in K -> Pi Pi Decays

We perform a complete analysis of isospin breaking in K -> Pi Pi amplitudes in chiral perturbation theory, including both strong isospin violation and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N_c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g_8 and g_27 from a fit to K -> Pi Pi branching ratios, finding small deviations from the isospin-limit case. The ratio Re(A_0)/Re(A_2) measuring the Delta I=1/2 enhancement is found to decrese from 22.1 +/- 0.1 in the isospin limit to 20.3 +/- 0.5 in the presence of isospin breaking. We also analyse the effect of isospin violation on the CP violation parameter epsilon-prime, finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for epsilon-prime is below 15%.

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arXiv2003

Isospin violation in epsilon'

On the basis of a next-to-leading-order calculation in chiral perturbation theory, the first complete analysis of isospin breaking for direct CP violation in K^0 -> 2 pi decays is performed. We find a destructive interference between three different sources of isospin violation in the CP violation parameter epsilon'. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for epsilon' is below 15 %.

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arXiv2003

Meson resonances, large N_c and chiral symmetry

We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.

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arXiv2002

Two-pion contribution to the muon magnetic moment

The two-pion contribution to hadronic vacuum polarization can be extracted from tau decay data when isospin violating and radiative corrections are taken into account. When the dominant corrections are applied to the photon-inclusive decay of the tau into two pions, one obtains a shift (-12.0 +/- 2.6).10^{-10} for the anomalous magnetic moment of the muon. The shift appears to be too small to reconcile the determinations of hadronic vacuum polarization from existing tau and e+ e- data. The reliability of electromagnetic corrections in the photon-inclusive tau decay is examined.

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arXiv2002

Spontaneously Broken Chiral Symmetry and Hard QCD Phenomena

These are the mini-proceedings of the workshop ``Spontaneously Broken Chiral Symmetry and Hard QCD Phenomena" held at the Physikzentrum Bad Honnef from July 15 to 19, 2002. Every author presents a summary of his talk. The transparencies of all speakers and further information on the workshop can be found on the website: http://www.tp2.ruhr-uni-bochum.de/hardreactions.html

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arXiv2002

Four-pion production

Starting from the low-energy structure derived from QCD, we extend the amplitudes for four-pion production in e+ e- annihilation and tau decays up to invariant four-pion masses of 1 GeV. Cross sections and branching ratios BR(rho^0 -> 4 pi) are compared with available data.

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arXiv2002

Radiative tau decay and the magnetic moment of the muon

We discuss the decay tau^- -> nu_tau pi^- pi^0 gamma in terms of a model with the correct low-energy structure and with the relevant resonance degress of freedom. The nontrivial radiative dynamics becomes visible for large photon momenta only. We use the model to calculate electromagnetic corrections for the two-pion contribution to hadronic vacuum polarization extracted from photon-inclusive two-pion decays. The corrections are insensitive to the details of the model and depend on the pion form factor only. Putting all relevant isospin violating corrections together, we obtain a shift Delta a_mu = (- 120 +/- 26 +/- 3) x 10^-11 to be applied to determinations of the anomalous magnetic moment of the muon from photon-inclusive tau data.

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arXiv2002

Four-pion production in e+ e- annihilation

We calculate the processes e+ e- -> 4 pions and tau -> nu_tau + 4 pions to O(p^4) in the low-energy expansion of the standard model. The chiral amplitudes of O(p^4) can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of omega, a_1 and double rho exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios BR(rho -> 4 pions) are in good agreement with available data.

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