Revisiting the annihilation corrections in nonleptonic (B)over-bars0 decays within QCD factorization

Motivated by the recent measurements of nonleptonic (B) over bar (0)(s) decays by the CDF and LHCb collaborations, especially the large B((B) over bar (0)(s) -> pi(+)pi(-)), we revisit the hard spectator and annihilation corrections in (B) over bar (0)(s) decays within a QCD factorization approach, with two schemes for the possible parameters for the known end-point divergence appearing in the estimation of the hard spectator and annihilation diagrams. The first one is to conservatively estimate the possible contributions by parametrization (scheme I); another one uses an infrared finite gluon propagator (scheme II) to regulate the end-point singularity. In scheme I, with the constraints from the measured (B) over bar (0)(s) -> PP(VV) decays, two (four) restricted solutions of the parameter spaces are found. In scheme II, we find that most of the theoretical predictions agree well with the experimental data with a single parameter m(g) similar to 0.5 GeV. However, within both schemes, B((B) over bar (0)(s) -> phi phi) are always much larger than B((B) over bar (0)(s) -> K-*0(K) over bar (*0)), in contrast to the experimental results B((B) over bar (0)(s) -> phi phi) similar or equal to B((B) over bar (0)(s) -> K-*0(K) over bar (*0)). It is noted that the pattern B((B) over bar (0)(s) -> phi phi) > B((B) over bar (0)(s) -> K-*0(K) over bar (*0)) also persists in other theoretical frameworks; thus, the present experimental result B((B) over bar (0)(s) -> phi phi) similar or equal to B((B) over bar (0)(s) -> K-*0(K) over bar (*0)) raises a challenge to theoretical approaches for B nonleptonic decays. Further refined measurements and theoretical studies are called for to resolve such a possible anomaly.