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Register a new userSplitting Strong and Electromagnetic Interactions in K(L4) Decays
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A. Nehme
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We recently considered $K_{ell 4}$ decays in the framework of chiral perturbation theory based on the effective Lagrangian including mesons, photons, and leptons. There, we published analytic one-loop-level expressions for form factors $f$ and $g$ corresponding to the mixed process, $K^0topi^0pi^-ell^+ u_{ell}$. We propose here a possible splitting between strong and electromagnetic parts allowing analytic (and numerical) evaluation of Isospin breaking corrections. The latter are sensitive to the infrared divergence subtraction scheme and are sizeable near the $pipi$ production threshold. Our results should be used for the extraction of the $P$-wave iso-vector $pipi$ phase shift from the outgoing data of the currently running KTeV experiment at FNAL.
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We evaluate the size of isospin breaking corrections to form factors $f$ and $g$ of the $K_{ell 4}$ decay process $K^+topi^+pi^-ell^+ u_{ell}$ which is actually measured by the extended NA48 setup at CERN. We found that, keeping apart the effect of Coulomb interaction, isospin breaking does not affect modules. This is due to the cancelation between corrections of electromagnetic origin and those generated by the difference between up and down quark masses. On the other hand, electromagnetism affects considerably phases if the infrared divergence is dropped out using a minimal subtraction scheme. Consequently, the greatest care must be taken in the extraction of $pipi$ phase shifts from experiment.
We present a model for the decay $D^+to K^-pi^+pi^+$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the $Kpi$ scalar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. Allowing for a global phase difference between the $S$ and $P$ waves of $-65^circ$, the Dalitz plot of the $D^+to K^-pi^+pi^+$ decay, the $Kpi$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.
The strong, electromagnetic and mixed strong-electromagnetic amplitudes of the $psi(2S)$ decays into baryon-anti-baryon pairs have been obtained by exploiting all available data sets in the framework of an effective Lagrangian model. We observed that at the $psi(2S)$ mass the QCD regime is not completely perturbative, as can be inferred by the relative strength of the strong and the mixed strong-electromagnetic amplitudes. Recently a similar conclusion has been reached also for the $J/psi$ decays. The relative phase between the strong and the electromagnetic amplitudes is $varphi = (58pm 8)^circ$, to be compared with $varphi = (73pm 8)^circ$ obtained for the $J/psi$. On the other hand, in the case of the $psi(2S)$ meson, different values of the ratio between strong and mixed strong-electromagnetic amplitudes are phenomenologically required, while for the $J/psi$ meson only one ratio was enough to describe the data. Finally, we also observed a peculiar behavior of the mixed strong-electromagnetic amplitudes of the decays $psi(2S)toSigma^+ overline Sigma{}^-$ and $psi(2S)toSigma^- overline Sigma{}^+$.
We present a model for the decay D+ --> K- pi+ pi+. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the Kpi scalar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the S wave thus obtained agree nicely with experiment up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the S and P waves of -65 degrees, the Dalitz plot of the D+ --> K- pi+ pi+ decay, the Kpi invariant mass spectra and the total branching ratio due to S-wave interactions are well reproduced.
We study the radiative corrections to all Kl3 decay modes to leading non-trivial order in the chiral effective field theory, working with a fully inclusive prescription on real photon emission. We present new results for Kmu3 modes and update previous results on Ke3 modes. Our analysis provides important theoretical input for the extraction of the CKM element Vus from Kl3 decays.
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