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
decay amplitudes (43-45)neglecting the a 1and ρwidths.The resulting decay distributions for longitudinal and transverse a 1are given by
1
d cos θa d cos θρdφρ
= m 2a +m 2ρ8πm a m ρ 2+8 (46)
1
d cos θa d cos θρdφρ
= m 2a +m 2ρ16πm a m ρ
2+8 .(47)In the a ±1→ρ±π0decay θa is the angle of ρin the a 1rest frame measured relative to the a 1line of ?ight in the laboratory (z -axis),while the plane con-taining these two vectors de?nes the x ?z plane.Similarly in the ρ±→π0decay θρand φρare the polar and azimuthal angles of the charged pion in the ρrest frame,measured relative to the above ρline of ?ight (z ′-axis)and the above plane respectively.In terms of these angles,the fraction of a 1laboratory energy-momentum carried by the charged pion is given by
x ′=E π±
m a m ρ
2m a m ρ
+m ρ2m a m ρcos θa +q m 2a ?m 2ρ2m a m ρcos θρcos θa ?q sin θρcos φρsin θa ,
(48)q =1m 2ρ?4m 2π?1