Waiting for the top quark mass,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>→<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>νν¯,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="italic">B</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>-<i>B</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">¯</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>mixing, and<i>CP</i>asymmetries in<i>B</i>decays

Abstract

Anticipating improved determinations of ${\mathit{m}}_{\mathit{t}}$, \ensuremath{\Vert}${\mathit{V}}_{\mathit{u}\mathit{b}}$/${\mathit{V}}_{\mathit{c}\mathit{b}}$\ensuremath{\Vert}, ${\mathit{B}}_{\mathit{K}}$, and ${\mathit{F}}_{\mathit{B}}$ \ensuremath{\surd}${\mathit{B}}_{\mathit{B}}$ in the next five years we make an excursion into the future in order to find a possible picture of the unitarity triangle, the quark mixing, and CP violation around the year 2000. We then analyze what impact on this pciture the measurements of the four possibly cleanest quantities will have: B(${\mathit{K}}^{+}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$\ensuremath{\nu}\ensuremath{\nu}\ifmmode\bar\else\textasciimacron\fi{}), ${\mathit{x}}_{\mathit{d}}$/${\mathit{s}}_{\mathit{x}}$, sin(2\ensuremath{\alpha}), and sin(2\ensuremath{\beta}). Our analysis shows very clearly that there is an exciting time ahead of us. In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in \ensuremath{\lambda} and we derive several useful analytic formulas for quantities of interest.