Abstract
We estimate the potential size of the weak annihilation amplitudes in QCD factorization as allowed by experimental data. To achieve this goal, we establish a connection between the amplitudes in the QCD factorization and the so-called topological and SU(3)-invariant descriptions. Our approach is based purely on the analysis of the tensor structure of the decay amplitudes. By focusing on the processes Brightarrow P P and considering data from CP asymmetries and branching fractions, we perform a global fit to the SU(3)-irreducible quantities assuming minimal theoretical bias. Subsequently we translate the outcome to the QCD factorization decomposition, and find that the most constrained weak annihilation amplitudes are below 0.04. However, in view of the large uncertainties in several of the experimental input parameters, values up to sim 0.3 are allowed in certain cases.
Highlights
Charmless non-leptonic B(s)-meson decays play a prominent role in testing the CKM mechanism of quark flavour mixing, in determining the angles of the unitarity triangle and – closely related – in quantifying the amount of CP violation in the quark flavour sector of the Standard Model (SM), which represents the only established source of CP violation to date
On the theoretical side the phenomenology of charmless non-leptonic B(s)-decays is governed by the interplay between CKM factors, Wilson coefficients, and non-perturbative hadronic matrix elements, where the computation of the latter has been the bottleneck to precision predictions for quite some time due to the appearance of QCD effects from many different scales that arise in the purely hadronic initial and final states, and due to the fact that these matrix elements cannot be directly computed with non-perturbative methods such as lattice QCD at present
We start with the best-fit point of the SU (3)-irreducible amplitudes in polar coordinates, Tables 4 and 5
Summary
Charmless non-leptonic B(s)-meson decays play a prominent role in testing the CKM mechanism of quark flavour mixing, in determining the angles of the unitarity triangle and – closely related – in quantifying the amount of CP violation in the quark flavour sector of the Standard Model (SM), which represents the only established source of CP violation to date. One of the shortcomings of the QCDF approach in its present use is the failure to compute subleading power corrections in the heavy-quark expansion from first field-theoretical principles (see [33] for a determination of annihilation topologies for B → π π using QCD-sum rules) This results in sizeable uncertainties that in many observables spoil the precision achieved at leading power Flavour symmetries based on the approximate SU (3) invariance in the (u, d, s) flavour space or one of its SU(2) subgroups isospin, U-spin and V-spin have been used extensively in the Literature and have been applied both to nonleptonic bottom [9,10,40–50] and charm decays [51–58] The advantages of this approach are the fact that hardly any assumption about the scales of QCD effects are needed, and that it relates different decay channels, thereby reducing the number of parameters, for instance in a global analysis.
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