Detecting and Studying the Lightest Pseudo-Goldstone Boson at Future $pp$, $e^+e^-$ and $\mu^+\mu^-$ Colliders

For an attractive class of dynamical symmetry breaking (technicolor) models, the lightest neutral pseudo-Nambu-Goldstone boson ($\pzero$) contains only down-type techniquarks and charged technileptons. We discuss the prospects for discovering and studying the $\pzero$ of such models at the Tevatron and the LHC and at future $\epem$ and $\mupmum$ colliders. Depending upon the number of technicolors, $\ntc$, discovery of the $\pzero$ at the Tevatron and the LHC in the $gg\to\pzero\to\gam\gam$ mode could be possible over a wide range of mass. For $\ntc=4$, discovery of the $\pzero$ at an $\epem$ collider via the reaction $\epem\to\gam \pzero$ should be possible as long as $\mpzero$ is not near $\mz$. In the $\gam\gam$ collider mode of operation at an $\epem$ collider, the $\gam\gam\to\pzero\to b\anti b$ signal should be very robust if $\ntc=4$. For the minimal $\ntc=1$ case, detection of the $\pzero$ at the Tevatron and in $\epem$ collisions will be very difficult, and the precision of measurements at the LHC and the $\gam\gam$ collider decline markedly. A $\mupmum$ collider yields a $\pzero$ production rate that does not depend markedly upon $\ntc$. At a $\mupmum$ collider discovery of the $\pzero$ as an $s$-channel resonance should prove possible via scanning, even if it has not already been detected elsewhere. Once $\mpzero$ is precisely known, operation of the $\mupmum$ collider as a $\pzero$ factory will allow precision measurements of enough observables to determine the number of technicolors of the theory and (up to a discrete set of ambiguities) the fundamental parameters of the low-energy effective Lagrangian describing the Yukawa couplings of the $\pzero$.