We explore the prospect of charged Higgs boson search in top quark decay at the Tevatron collider upgrade, taking advantage of the opposite states of $\tau$ polarization resulting from the $H^\pm$ and $W^\pm$ decays. Methods of distinguishing the two contr
Γt→bW=
g2
2 1,m2b m2t
m2W(m2t+m2b)+(m2t?m2b)2?2m4W (9)
Γt→bH=
g2
2 1,m2b m2t
(m2t cot2β+m2b tan2β)(m2t+m2b?m2H)?4m2t m2b (10)
ΓH→τν=
g2m H
32πm2W m2c cot2β+m2s tan2β .(12) From these one can construct the relevant branching fractions
B t→bH=Γt→bH/(Γt→bH+Γt→bW)(13)
B H→τν=ΓH→τν/(ΓH→τν+ΓH→c¯s).(14) It is the product of these two branching fractions that controls the size of the observable charged Higgs signal.The t→bH branching fraction has a pronounced dip at
tanβ=(m t/m b)1