Revisiting the annihilation corrections in nonleptonicB¯s0decays within QCD factorization

Abstract

Motivated by the recent measurements of non-leptonicB 0 s decays by CDF and LHCb collaborations, especially the large B(B 0 s → π + π − ), we revisit the hard spectator and annihilation corrections inB 0 s decays within QCD factorization approach with two schemes for the possible parameters for the known end-point divergence appeared in the estimation of the hard spectator and annihilation diagrams. The first one is to conservatively estimate the possible contributions by parameterization (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 measuredB 0 s → P P (V V ) decays, two (four) restricted solutions of the parameters spaces are found. In scheme II, we find that most of the theoretical predictions agree well with the experimental data with single parameter m g ∼ 0.5GeV. However, within both schemes, B(B 0 s → φφ) are always much larger than B(B 0 s → K * 0K * 0 ) in contrast to the experimental results B(B 0 s → φφ) ≃ B(B 0 s → K * 0K * 0 ). It is noted that the pattern B(B 0 s → φφ) > B(B 0 s → K * 0K * 0 ) also persists in other theoretical framework, thus the present experimental result B(B 0 s → φφ) ≃ B(B 0 s → K * 0K * 0 ) rises a challenge to theoretical approaches for B non-leptonic decays. Further refined measurements and theoretical studies are called for to resolve such a possible anomaly.

Spectator scattering and annihilation contributions as a solution to theπKandππpuzzles within QCD factorization approach

“…As to the first issue, there is no an imperative reason for the annihilation parameters ρ A and φ A to be the same for different B u,d,s decays, even for different annihilation topologies, although they were usually taken to be universal in the previous numerical calculation for simplicity [10,11]. Phenomenologically, it is almost impossible to account for all of the well-measured two-body charmless B decays with the universal values of ρ A and φ A based on the QCDF approach [5,6,11,13]. In addition, the pQCD study on B meson decays also indicate that the annihilation parameters ρ A and φ A should be process-dependent.…”

“…• are acceptable, even necessary, to reproduce the data for some two-body nonleptonic B u,d,s decay modes [5,6]. In this paper, we will perform a fitting on the parameters ρ A and φ A by considering B → ππ, πK and KK decay modes, on one hand, to investigate the strength of annihilation contribution, on the other hand, to study their effects on the anomalies in B physics, such as the well-known πK and ππ puzzles.…”

“…In addition, the pQCD study on B meson decays also indicate that the annihilation parameters ρ A and φ A should be process-dependent. In fact, in the practical QCDF application to the B → P P , P V decays (where P and V denote the light pseudoscalar and vector SU (3) meson nonet, respectively), the non-universal values of annihilation phase φ A with respect to PP and PV final states are favored (scenario S4) [11]; the process-dependent values of ρ A and φ A are given based on an educated guess [13,14] or the comparison with the updated measurements [6]; the flavour-dependent values of ρ A and φ A are suggested recently in the nonfactorizable annihilation contributions [5]. In principle the value of ρ A and φ A should differ from each other for different topologies with different flavours, but we hope that the QCDF approach can accommodate and predict much more hadronic B decays with less input parameters.…”

Light-front holographic distribution amplitudes of pseudoscalar mesons and their application to B -meson decays

“…As a result, a complex parameter X A has been introduced in the traditional parameterization scheme within the framework of QCDF [38]. By using the dynamical gluon mass m g (q 2 ) in QCDF approach [41] or by introducing transverse momentum k T degree in pQCD approach [30,31,42], a large imaginary part in the annihilation amplitudes is also obtained because the singularities exist in the integral over momentum fractions.…”

“…In the QCDF approach, the end-point divergent integrals are treated as signals of infrared-sensitive contributions which can be regularized by introducing a complex quantity X A [38,39]. Alternatively, one can introduce an infrared-finite dynamical gluon propagator which moves the end-point singularity into an integral over the time-like gluon momentum; the divergence then vanishes, and a large strong phase is predicted [40,41]. In the pQCD approach, the end-point singularity is avoided by introducing parton transverse momentum k T , but at the expense of having to model the additional k T dependence of the meson distributions; this again predicts a large complex annihilation correction [30,31,42].…”