Determining the sign of theZ-penguin amplitude

Abstract

We point out that the precision measurements of the pseudo observables ${R}_{b}^{0}$, ${\mathcal{A}}_{b}$, and ${A}_{\mathrm{FB}}^{0,b}$ performed at the CERN LEP and the Stanford Linear Collider suggest that in models with minimal-flavor violation the sign of the $Z$-penguin amplitude is identical to the one present in the standard model. We determine the allowed range for the nonstandard contribution to the Inami-Lim function $C$ and show, by analyzing possible scenarios with positive and negative interference of standard model and new physics contributions, that the derived bound holds in each given case. Finally, we derive lower and upper limits for the branching ratios of ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, $\overline{B}\ensuremath{\rightarrow}{X}_{d,s}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and ${B}_{d,s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ within constrained minimal-flavor violation, making use of the wealth of available data collected at the $Z$ pole.