  The couplings and decay widths of the proceses (1^+,2^+)->(0^-,1^-)+rho are
studied with ligh-cone QCD sum rules in the leading order of heavy quark
effective theory. These processes are employed to estimate the two pion
transition widths of the (1^+,2^+) doublet through the low mass tail of the rho
resonance. Our calculation shows that the two pion decay widths are much
smaller than the single pion decay widths. However, B_1 and B_2^* mesons should
also have significant two pion decay widths around 1.5 MeV.
