The decay $b\to s\gamma$ in the 3-3-1 model

The 3-3-1 model, based on the gauge group $SU(3)_c\times SU(3)_L\times U(1)_X$, makes a natural prediction of three generations based on anomaly cancellation. Since this is accomplished by incorporating the third family of quarks differently from the other two, it leads to potentially large flavor changing neutral currents. A sensitive place to look for such effects is the flavor changing $b\to s\gamma$ decay, which has recently been measured at CLEO. We compute this decay rate in the 3-3-1 model and compare it with that of the two-Higgs-doublet model, a subset of the full 3-3-1 model. We find that the additional 3-3-1 physics weakens the bound on the charged Higgs mass from $M_{H^+}>290$~GeV to $M_{H^+}\agt120$~GeV.