Isospin-breaking vector meson decay constants from continuous families of finite energy sum rules

The isospin-breaking vector meson decay constants are determined from a QCD sum rule analysis of the vector current correlator 〈O|T(Vμ³Vν⁸)|O〉, using a recently proposed implementation of the finite energy sum rule approach. The analysis employs the three-loop version of the OPE and two different families of weight functions. It is shown that the requirement of consistency between results obtained using these two different weight families leads to a rather good determination of the parameter describing the deviation of the D=6 condensate term in the OPE from its vacuum saturation value, and that the ability to determine this value has non-trivial numerical consequences on the analysis. The phenomenological relevance of the results to experimental extractions of the isoscalar and isovector spectral functions in e+e-→hadrons, the extraction of the strange quark mass and the determination of the 6th order chiral low energy constant, Q, is also briefly discussed.Kim Maltman and C. E. Wolf

Strong Isospin-Breaking Effects in K-->pi pi at Next-to-Leading Order in the Chiral Expansion

Strong isospin-breaking (IB) contributions to both the octet and 27-plet weak K-->2 pi transitions are evaluated at next-to-leading order (NLO) in the chiral expansion. NLO contributions are shown to significantly reduce the leading order result for the potentially large contribution to the $\Delta I=3/2$ amplitude resulting from strong isospin-breaking modifications to the weak Delta I=1/2 amplitude. The ratio of strong IB 27-plet to strong IB octet contributions is found to be small for all decay amplitudes. Combined with recent results on the corresponding electromagnetic contributions, we find that the ratio of the intrinsic strengths of octet and 27-plet effective weak operators can be taken to be that obtained from experimental data, analyzed ignoring isospin breaking, to an accuracy better than of order 10 percent.Comment: 10 pages, 1 figure. NLO determination of strong IB modification of weak 27-plet transitions now also included; modified phase discussio

Isospin Breaking in the Relation Between the tau-->nu_tau pi pi and e^+e^- -->pi^+ pi^- Versions of |F_\pi (s)|^2$ and Implications for (g-2)_mu

We investigate two points related to existing treatments of isospin-breaking corrections to the CVC relation between the e^+e^- --> pi^+ pi^- cross-section and dGamma[tau^- --> nu_tau pi^- pi^0]/ds. Implications for the value of the hadronic contribution to a_mu =(g-2)_mu /2 based on those analyses incorporating hadronic tau decay data are also considered. We conclude that the uncertainty on the isospin-breaking correction which must be applied to the tau decay data should be significantly increased, and that the central value of the rho-omega ``mixing'' contribution to this correction may be significantly smaller than indicated by the present standard determination. Such a shift would contribute to reducing the discrepancy between the tau- and electroproduction-based determinations of the leading order hadronic contribution to a_mu.Comment: 15 pages, 1 figur

Consequences of the BaBar e^+e^- --> pi^+pi^- Measurement for the Determination of Model-Dependent rho-omega Mixing Effects in Pi_{\rho\omega}(m_{\rho}^2) and (g-2)_mu

We update our analysis of rho-omega mixing effects in the pion form factor to incorporate the recently published BaBar e^+e^- --> pi^+\pi^- cross-sections. The implications for tau-decay-based Standard Model estimates of the leading order hadronic contribution [a_\mu]_{had}^{LO}, to the anomalous magnetic moment of the muon, and for the extraction of the off-diagonal vector meson self-energy matrix element, Pi_{\rho\omega}(m_\rho^2), are discussed.Comment: 7 pages, 2 figure

Models of Isospin Breaking in the Pion Form Factor: Consequences for the Determination of Pi_{\rho\omega}(m_rho^2) and (g-2)_mu/2

We study the implications of several recent high-precision measurements of the pion form factor in the region of the rho-omega interference "shoulder" for (i) the extraction of the rho-omega mixing matrix element, Pi_{\rho\omega}(m_rho^2), and (ii) the evaluation of the isospin-breaking (IB) correction needed to incorporate hadronic tau decay data into the determination of the Standard Model expectation for the leading order hadronic contribution, [a_mu]_{had}^{LO}, to the anomalous magnetic moment of the muon, focussing, in the latter case, on the model-dependence of the rho-omega mixing component of the IB correction. We consider a range of different models for the broad rho contribution to the e^+e^- --> \pi\pi amplitude, applying these models to each experimental data set, and find that the model dependence of the rho-omega mixing correction is significantly larger than the uncertainty induced by experimental errors for any individual model. We also find that, for each such model, the recent data allows one to separate rho-omega mixing and direct omega --> \pi\pi coupling contributions to the amplitude, and hence to obtain a reasonably precise extraction of Pi_{\rho\omega}(m_rho^2), uncontaminated by direct omega --> \pi\pi coupling effects, for use in meson exchange model calculations of charge symmetry breaking in NN scattering.Comment: 25 pages, 4 figures. Final published version. Main change is inclusion of a detailed discussion of the source of differences between the present work and M. Davier et al. (arXiv:0906.5443v3

Some New Results on the H Dibaryon in the Quark Cluster Model

The H dibaryon channel, (I=0,J=0,S=-2), is revisited in the non-relativistic quark cluster model (NRQCM) using a basis extended beyond the usual set of baryon cluster pairs to include an explicit spatially symmetric 6q state, analogous in structure to the MIT bag model H. We find that the binding predicted using the two-baryon basis alone is significantly deepened by the addition of the additional 6q configuration. The NRQCM thus appears, contrary to earlier findings, to be incompatible with the experimental information available for this channel.Comment: 11 pages, REVTE

Isospin-Breaking Vacuum-to-Pi^0,Eta Pseudoscalar Matrix Elements at Next-to-Leading Order in the Chiral Expansion

We employ Chiral Perturbation Theory (ChPT) to evaluate the complete set of pseudoscalar matrix elements, , with P_f any of the flavor-diagonal pseudoscalar currents (f=u,d,s), to order (m_d-m_u), and to next-to-leading order in the chiral expansion. These matrix elements represent the basic input to a QCD sum rule analysis of isospin breaking in the pi NN couplings using the three-point-function method. We discuss also how one could use the results to construct a one parameter family of interpolating fields for the $\pi^0$, all of whose members have zero vacuum-to-$\eta$ matrix element, and explain how this could in principle be used to provide non-trivial tests of the reliability of the assumptions underlying the use of the three-point-function method. It is shown that the isospin-breaking mixing parameters required for this construction receive significant corrections beyond leading order in the chiral expansion.Comment: 9 pages, 1 postscript figur

An 84 microGauss Magnetic Field in a Galaxy at Redshift z=0.692

The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars. The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ~ 3 microGauss. The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain. Here we report a measurement of a magnetic field of B ~ 84 microGauss in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 microGauss in the neutral interstellar gas of our Galaxy. This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past rather than stronger

Electromagnetic Corrections to Pi Pi Scattering: Some Lessons for the Implementation of Meson Exchange Models

The leading non-Coulombic electromagnetic contributions to pi pi s-wave scattering lengths are computed in Chiral Perturbation Theory. It is shown that these corrections are zeroth order in the chiral expansion and associated with electromagnetic contact terms in the effective Lagrangian, i.e. that they do not involve explicit photon fields in the low-energy effective theory. It is pointed out that, if one followed the standard meson-exchange-model ansatz for removing electromagnetic effects, i.e. of subtracting contributions associated with explicit photon exchange and radiative corrections, as determined by the photon coupling vertices of the effective hadronic theory, one would completely miss these contributions and arrive at the erroneous conclusion that the strong interactions exhibited very large isospin breaking in pi pi scattering. Implications for electromagnetic "subtraction" procedures in other hadronic systems and the utility of the effective Lagrangian method for avoiding such errors are obvious.Comment: 16 pages, REVTE

The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion

The strong isospin-breaking correction, Omega_{st}, which appears in estimates of the Standard Model value for the direct CP-violating ratio epsilon'/epsilon, is evaluated to next-to-leading order (NLO) in the chiral expansion using Chiral Perturbation Theory. The relevant linear combinations of the unknown NLO CP-odd weak low-energy constants (LEC's) which, in combination with 1-loop and strong LEC contributions, are required for a complete determination at this order, are estimated using two different models. It is found that, to NLO, Omega_{st}=0.08 +/- 0.05, significantly reduced from the ``standard'' value, 0.25 +/- 0.08, employed in recent analyses. The potentially significant numerical impact of this decrease on Standard Model predictions for epsilon'/epsilon, associated with the decreased cancellation between gluonic penguin and electroweak penguin contributions, is also discussed.Comment: 12 pages, 1 figur