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Register a new userThe electromagnetic effects in $K_{e4}$ decay
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The final state interaction of pions in $K_{e4}$ decay allows one to obtain the value of the isospin and angular momentum zero $pipi$ 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.
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The final state interaction of pions in the decay $K^pmto pi^+pi^-e^pm u$ allows to obtain the value of the isospin and angular momentum zero pion-pion scattering length $a_0^0$. To extract this quantity from experimental data the radiative corrections (RC) have to be taken into account. Basing on the lowest order results and the factorization hypothesis, we get the expressions for RC in the leading and next-to leading logarithmical approximation. It is shown that the decay width dependence on the lepton mass $m_e$ through the parameter $sigma=frac{alpha}{2pi}br{lnfrac{M^2}{m_e^2}-1}$ has a standard form of the Drell-Yan process and is proportional to the Sommerfeld-Sakharov factor. The numerical estimations are presented.
The $K^+ to pi^0 pi^0 e^+ u$ ($K_{e4}^{00}$) decay has been measured with stopped positive kaons for a data sample of 216 events. A comparison of the observed spectra with a Monte Carlo simulation determined the $K_{e4}^{00}$ form factor. The results are compatible with the $K^+ to pi^+ pi^- e^+ u$ data, as estimated from the $Delta I=1/2$ rule. We also established that the $K_{e4}^{00}$ channel can be used to determine the $pi$-$pi$ scattering lengths.
Recent results from OKA setup concerning form factor studies in $K_{e3}$ decay are presented. About 5.25M events are selected for the analysis. The linear and quadratic slopes for the decay formfactor $f_{+}(t)$ are measured: $lambda_{+}=(26.1 pm 0.35 pm 0.28 )times 10^{-3}$, $lambda_{+}=(1.91 pm 0.19 pm 0.14)times 10^{-3}$. The scalar and tensor contributions are compatible with zero. Several alternative parametrizations are tried: the Pole fit parameter is found to be $M_V = 891 pm 2.0$ MeV ; the parameter of the Dispersive parametrization is measured to be $Lambda_+ =(24.58 pm 0.18) times 10^{-3}$. The presented results are considered as preliminary.
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.
The measurements of $V_{us}$ in leptonic $(K_{mu 2})$ and semileptonic $(K_{l3})$ kaon decays exhibit a $3sigma$ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the $K_{e3}$ decay rates that achieves an unprecedented level of precision of $10^{-4}$, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the ``list of culprits responsible for the $K_{mu 2}$--$K_{l3}$ discrepancy.
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