VACUUM POLARIZATION BUBBLE EFFECTS ON THE TRIANGLE RELATIONS FOR B-MESON CHARMLESS DECAY AMPLITUDES

Assuming that factorization is valid and that contributions of the exc hange, annihilation, and penguin-annihilation diagrams are negligible, we study the effects of the QCD vacuum polarization bubbles on the de cay amplitudes of some B meson charmless decays into two light pseudos calars. The bubbles have much less effects on B-0 --> pi(+)pi(-), pi(- )K(+), pi(0)K(0) than on B-0 --> pi(0) pi(0), thus the triangle relati on root 2A(B+ --> pi(+)pi(0)) = A(B-0 --> pi(-)K(+))/R-u + root 2A(B-0 --> pi(0)K(0))/R-u is changed slightly while root 2A(B+ --> pi(+)pi(0 )) = root 2A(B-0 --> pi(0) pi(0)) + A(B-0 --> pi(+)pi(-)) is altered s ignificantly. This may indicate that in order to test or use these tri angle relations other higher order QCD corrections should also be care fully taken into consideration.