Different approaches to calculate the K^{\pm }\rightarrow \pi ^{\pm }\pi ^0e^+e^- decay width

The rare $K^\pm \rightarrow \pi ^\pm \pi ^0 e^+e^-$ decay, currently under analysis by the NA62 Collaboration, is considered. We have followed two theoretical approaches to calculate the differential decay width—in the kaon rest frame, where we use Cabibbo–Maksymowicz variables, and in the center-of-mass system of the lepton pair. The latter essentially simplifies the computations. A comparison between the two approaches has been performed. We have also found the dependencies of the differential decay rate as a function of the virtual photon and dipion system masses.     

K\rightarrow \pi\pi e^+e^- decays and chiral low-energy constants

The branching ratios of the measured decay and of the still unmeasured decay are calculated to next-to-leading order in chiral perturbation theory (CHPT). Recent experimental results are used to determine two possible values of the combination of weak low-energy couplings (LECs) from the chiral Lagrangian. The values obtained are compared to the predictions of theoretical approaches to weak counterterm couplings to distinguish between the two values. Using the favoured value of the combination and taking into account additional assumptions suggested by the considered models, one obtains the branching ratio of the second decay as a function of the unknown combination of weak low-energy couplings. Finally, using values of the individual LECs derived from a particular model, one predicts the branching ratio of the decay. Received: 27 February 2001 / Published online: 11 May 2001     

The reaction e^ + e^ - \to \gamma \pi ^0 \to \gamma v\overline v as a probe of neutrino mass

The reaction $e^ + e^ - \to \gamma \pi ^0 \to \gamma v\overline v $ is considered. It is shown that this reaction possesses a clear signature, producing in the resonance region practically monochromatic photons, which can easily be distinguished from background bremsstrahlung photons. Since the cross section of the reaction is proportional to the square of the neutrino mass, such a reaction can be used as a probe for neutrino mass.     

Dipole moments of the tau neutrino via the process {e^{+}e^{-}\rightarrow \nu\bar\nu \gamma} in a 331 model

The limits on the anomalous magnetic and electric dipole moments of the ?? _?? through the reaction $e^{+}e^{-}\rightarrow \nu \bar \nu \gamma$ at the Z ₁-pole, and in the framework of a 331 model are obtained. The results are based on the data reported by the L3 Collaboration at LEP. We find that the bounds are almost independent of the mixing angle ? of the model in the allowed range for this parameter.     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .