What do we count in the e+e--->Z neutrino counting experiment?

Abstract

We find that the difference between ${N}_{\ensuremath{\nu}}=\frac{{\ensuremath{\Gamma}}_{\mathrm{inv}}}{{\ensuremath{\Gamma}}_{\overline{\ensuremath{\nu}}\ensuremath{\nu}}^{\mathrm{SM}}}$ and ${\overline{N}}_{\ensuremath{\nu}}=\frac{{\ensuremath{\Gamma}}_{\mathrm{inv}}}{{\ensuremath{\Gamma}}_{\overline{l}l}}\frac{{\ensuremath{\Gamma}}_{\overline{l}l}^{\mathrm{SM}}}{{\ensuremath{\Gamma}}_{\overline{\ensuremath{\nu}}\ensuremath{\nu}}^{\mathrm{SM}}}$ can be used as an indicator of possible extensions of the standard model. This test will be possible, however, only after the top-quark mass measurement. We illustrate our point by an example of a left-right symmetric model with the Higgs sector containing one bidoublet and two triplets and the additional assumption that there is no fine-tuning in neutrino Yukawa couplings. If this is the case, the difference between ${N}_{\ensuremath{\nu}}$ and ${\overline{N}}_{\ensuremath{\nu}}$ could be a test for the bidoublet contents, assuming that nonstandard radiative corrections are negligible.