Virtual contributions from D⁎(2007)0 and D⁎(2010)± in the B → Dπh decays

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We study the quasi-two-body decays B→D⁎h→Dπh with h=(π,K) in the perturbative QCD approach and focus on the virtual contributions from the off-shell D⁎(2007)0 and D⁎(2010)± in the four measured decays B¯0→D0π+π−, B¯0→D0π+K−, B−→D+π−π− and B−→D+π−K−. For the B¯0→D⁎+π−→D0π+π− and B¯0→D⁎+K−→D0π+K− decays, their branching fractions concentrate in a very small region of mD0π+ near D⁎+ pole mass, and the virtual contributions from D⁎+, in the region mD0π+>2.1 GeV, are about 5% of the corresponding quasi-two-body results. We define two ratios RD⁎+ and RD⁎0, from which we conclude that the flavor-SU(3) symmetry will be maintained for the B→D⁎h→Dπh decays with very small breaking at any physical value of the mDπ. The B−→D⁎0π−→D0π0π− and B−→D⁎0K−→D0π0K− decays can be employed as a constraint for the D⁎0 decay width, with preferred values consistent with previous theoretical predictions for this quantity.