Cusps in K --> 3 pi decays

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl

On the low energy end of the QCD spectrum

The energy gap of QCD is now understood very well. There is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of m_s, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the Okubo-Iizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on m_s can be determined, to next-to-next-to-leading order of the chiral expansion. The range of validity of ChPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KKbar threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances.Comment: Talks given at QCD08 and Confinement

Radiative corrections to neutral pion-pair production

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \to \pi^-\pi^0\pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $\pi^+\pi^-\to\pi^0\pi^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $R\sim \alpha/2\pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. The radiative corrections to the total cross section vary between $+2\%$ and $-2\%$ for center-of-mass energies from threshold up to $7m_\pi$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1\%$, however with a large uncertainty.Comment: 10 pages, 6 figures, submitted to Eur. Phys. J.

The electromagnetic effects in Ke4K_{e4} decay

The final state interaction of pions in $K_{e4}$ decay allows one to obtain the value of the isospin and angular momentum zero $\pi\pi$ scattering length $a_0^0$.We take into account the electromagnetic interaction of pions and isospin symmetry breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering length extraction from $K_{e4}$ decay.Comment: 8 pages,1 figur

The isospin symmetry breaking effects in Ke4K_{e4} decays

The Fermi-Watson theorem is generalized to the case of two coupled channels with different masses and applied to final state interaction in $K_{e4}$ decays. The impact of considered effect on the phase of the $\pi\pi$ scattering is estimated and shown that it can be crucial for scattering lengths extraction from experimental data on $K_{e4}$ decays

New, high statistics measurement of the K+ -> pi0 e+ nu (Ke3) branching ratio

E865 at the Brookhaven National Laboratory AGS collected about 70,000 K+(e3) events with the purpose of measuring the relative K+(e3) branching ratio. The pi0 in all the decays was detected using the e+e- pair from pi0 -> e+e-gamma decay and no photons were required. Using the Particle Data Group branching ratios for the normalization decays we obtain BR(K+(e3(gamma))=(5.13+/-0.02(stat)+/-0.09(sys)+/-0.04(norm))%, where $K+(e3(gamma)) includes the effect of virtual and real photons. This result is 2.3 sigma higher than the current Particle Data Group value. The implications of this result for the$V_{us}$ element of the CKM matrix, and the matrix's unitarity are discussed.Comment: 4 pages, 5 figures; final version accepted by PR

Radiative corrections in K --> 3 pi decays

We investigate radiative corrections to K --> 3 pi decays. In particular, we extend the non-relativistic framework developed recently to include real and virtual photons and show that, in a well-defined power counting scheme, the results reproduce corrections obtained in the relativistic calculation. Real photons are included exactly, beyond the soft-photon approximation, and we compare the result with the latter. The singularities generated by pionium near threshold are investigated, and a region is identified where standard perturbation theory in the fine structure constant alpha may be applied. We expect that the formulae provided allow one to extract S-wave pi pi scattering lengths from the cusp effect in these decays with high precision.Comment: 57 pages, 17 figure

T-odd correlations in charged Kl4 decays

We analyse the sensitivity to physics beyond the SM of T-odd correlations in $K_{\ell 4}$ decays, which do not involve the lepton polarization. We show that a combined analysis of $K^+_{\mu 4}$ and $K^-_{\mu 4}$ decays can lead to new constraints about CP violation in $\Delta S=1$ charged-current interactions, complementary to those obtained from the transverse muon polarization in $K_{\mu 3}$ and of comparable accuracy.Comment: 6 pages (LaTeX

Experimental Study of the Radiative Decays K+ -> mu+ nu e+e- and K+ -> e+ nu e+e-

Experiment 865 at the Brookhaven AGS obtained 410 K+ -> e+ nu e+e- and 2679 K+ -> mu+ nu e+e- events including 10% and 19% background. The branching ratios were measured to be (2.48+-0.14(stat.)+-0.14(syst.))x10^-8 (m_ee>150 MeV) and (7.06+-0.16+-0.26)x10^-8 (m_ee>145 MeV), respectively. Results for the decay form factors are presented.Comment: 4 pages, 3 figures, RevTeX

Chiral Perturbation Theory Beyond One Loop

The existing Chiral Perturbation Theory (ChPT) calculations at order $p^6$ are reviewed. The principles of ChPT and how they are used are introduced. The main part is a review of the two- and three-flavour full two-loop calculations and their comparison with experiment. We restrict the discussion to the mesonic purely strong and semileptonic sector. The review concludes by mentioning the existing results in finite volume, finite temperature and partially quenched ChPT.Comment: 66 pages, review article, some references added plus a few discussions extende