qcd factorization in hadronic b  j/ ( ,k) decays*

using qcd factorization for the hadronic matrix elements, we show that existing data, inparticular the branching ratios br ( b →j/ψk) and br ( b →j/ψπ), can be accounted for in this approach.we analyze the decay b j /k( ) within the framework of qcd factorization. the calculation of therelevant hard-scattering kernels for twist-2 and twist-3 is completed. we calculate this decay in a special scale(  mb ) and in two schemes for wilson coefficients in nlo. we consider three functions for j / . thetwist-3 contribution involves the logarithmically divergent integral, we consider  h  0 the cancelingdivergent. the obtained results are in agreement with available experimental data.