Search for Top Quark and a Test of Models without Top Quark up to 38.54 GeV at PETRA

With a PETRA energy scan in ≤30-MeV steps, the continuum production of open top quark up to 38.54 GeV is excluded. Over regions of energy scan from 29.90 to 38.63 GeV limits are set on the product of hadronic branching ratio and electronic width $B_h{\Gamma }_{\mathrm{ee}}$ for toponium to be less than 2.0 keV at the 95% confidence level. By a search for flavor-changing neutral currents in $b$ decay, models without a top quark are excluded.