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Charmless hadronic two-body decays of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>mesons
Two-body charmless nonleptonic decays of ${B}_{u}$ and ${B}_{d}$ mesons are studied within the framework of generalized factorization in which the effective Wilson coefficients ${c}_{i}^{\mathrm{eff}}$ are renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Contrary to previous studies, our ${c}_{i}^{\mathrm{eff}}$ do not suffer from gauge …