Complete bremsstrahlung corrections to the forward-backward asymmetries in b→ Xₛℓ+ℓ-

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In a recent paper we presented a calculation of NNLL virtual corrections to the forward-backward asymmetries in b→ Xₛℓ+ℓ- decay. That result does not include bremsstrahlung corrections which are free from infrared and collinear singularities. In the present paper we include the remaining O(αₛ) bremsstrahlung corrections to the forward-backward asymmetries in b→ Xₛℓ+ℓ- decay. The numerical effect of the calculated contributions is found to be below 1%.