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.     

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 \(\sqrt s \approx 70 GeV\) .     

Angular asymmetries in the reactions \vec pp \to d\pi ^ + \eta and \vec pn \to d\pi ^0 \eta and a 0-f 0 mixing

The reactions pp → dπ ⁺ η and pn → dπ ⁰ η are of special interest for investigating the a ₀(980) (J ^P=0⁺) resonance in the process NN → da ₀ → dπη. We study some aspects of those reactions within a general formalism and also in a concrete phenomenological model. In particular, it is shown that the presence of nonresonant (i.e., without excitation of the a ₀ resonance) contributions to these reactions yields nonvanishing values for specific polarization observables, i.e., to effects like those generated by a ₀ ⁰ -f ₀ mixing. An experimental determination of these observables for the reaction $\vec pp \to d\pi ^ + \eta $ would provide concrete information on the magnitude of those nonresonant contributions to πη production. We also discuss the possibility of extracting information about a ₀ ⁰ -f ₀ mixing from the reaction $\vec pn \to d\pi ^0 \eta $ with a polarized proton beam.     

Results for all reactions e^+ e^- \rightarrow 4{\rm f}, 4{\rm f}\gamma with nonzero fermion masses

We accomplish our efforts to obtain predictions for all four–fermion final states of –annihilation and the corresponding bremsstrahlung reactions which are possible in the framework of the Standard Model. For this purpose we have developed a program ee4 . Our predictions are valid for fermions of arbitrary masses and we can obtain results for total cross sections without any collinear cut. Keeping exact fermion masses is of course required for top quark production. We give a detailed phenomenological analysis of fermion mass effects and real photon radiation for all channels of four–fermion production at LEP-II and next linear collider energies. Received: 2 October 2001 / Revised version: 2 January 2002 / Published online: 1 March 2002