B→M1M2: Factorization, charming penguins, strong phases, and polarization

Abstract

Using the soft-collinear effective theory we derive the factorization theorem for the decays B ! M 1 M 2 with M 1;2 ; K; ; K , at leading order in =E M and =m b . The results derived here apply even if s E M is not perturbative, and we prove that the physics sensitive to the E scale is the same in B ! M 1 M 2 and B ! M form factors. We argue that c c penguins could give long-distance effects at leading order. Decays to two transversely polarized vector mesons are discussed. Analyzing B ! we find predictions for B 0 ! 0 0 and jV ub jf B! 0 as a function of .Decays of B mesons to two light mesons are important for the study of CP violation in the standard model. In [1] it was suggested that since m b ; E M ; m M the amplitudes should factorize into simpler nonperturbative objects, and the proposed factorization theorem was checked at one-loop. This approach is often referred to as ''QCD factorization'' (QCDF). Factorization has also been considered in the ''perturbative QCD'' (pQCD) approach [3]. These approaches rely on a perturbative expansion in s E M . The results obtained from factorization are quite predictive and may allow us to answer fundamental questions about the standard model. At the current time several important issues remain to be answered. These include (i) the extent to which the results are model-independent consequences of QCD (since QCD is a predictive theory any model-independent limit must give the same answer in different approaches). A complete proof of a factorization theorem will answer this question. (ii) Unambiguous definitions of any nonperturbative hadronic parameters which appear are required. This allows the universality of parameters to be understood, as well as making clear the extent to which predictions rely on model dependent assumptions about parameter values. (iii) Does the power expansion converge? If power suppressed contributions really compete with leading order contributions as some studies [4,5] suggest then the expansion cannot be trusted. In this case the only hope is a systematic modification of the power counting to promote these effects to leading order, or an identification of certain observables that are free from this problem.The soft collinear effective theory (SCET) [6,7] provides the necessary tools to address these issues. A first study of SCET factorization for B ! has been made in [8]. In this paper we go beyond Refs. [1,3,8] in several ways. We first reduce the SCET operator basis to its minimal form and extend it to allow for all B ! M 1 M 2 decays (including two vectors). Our results show that all of the so-called ''hard spectator'' contributions are already present in the form factors, just with different hard Wilson coefficients. We also derive a form of the factorization theorem which does not rely on a perturbative expansion in s E M , and show that the nonperturbative parameters are still the same as those in the B ! M form factors. In our analysis long distance c c penguins [9,10] are investigated, but are left unfactorized. For the values of m b ...

Extracting|Vub|fromB→πlνdecays using a multiply-subtracted Omnès dispersion relation

“…Applying soft collinear effective theory (SCET) to B → ππ decays allows a factorisation result to be derived which leads to a model-independent extraction of the form factor (multiplied by |V ub |) at q 2 = 0 [39]. We quote the result from our fit:…”

“…|V ub | f + (0) = (8.7 ± 1.0) × 10 −4 (13) to be compared to |V ub | f + (0) = (7.2 ± 1.8) × 10 −4 in [39]. In view of this, we have tried replacing the LCSR input at q 2 = 0 with the |V ub | f + (0) constraint from SCET.…”

Improved method for CKM constraints in charmless three-bodyBandBsdecays

“…This expression can be simplified by neglecting the ∆S = 0 QCD penguin amplitude given by the second term in the numerator, and by assuming that the strong phase difference between the two amplitudes in the remaining term is small, as this phase is expected to be suppressed by 1/m b and α s (m b ) [18,19,20]. This is supported by studies of QCD penguin amplitudes (including charming penguins) in B → ρπ which have been found to be small, with a penguin-to-tree ratio of about 0.2 [21].…”

Diagnostic for new physics in B→πK decays

“…Assuming values for the weak phases β and γ as determined in a global CKM fit [5], these observables can be expressed in terms of nine parameters: the magnitude of the five independent amplitudes, P tc , P uc , T , C, A, and their four [7], one may perform a best fit with two degrees of freedom. Such a fit was made about two years ago [8] with data available in early 2007.…”

“…[12], and the central value |C/T | = 0.58 account well for the difference between the two asymmetries. While this magnitude of C/T can be accounted for in QCD calculations, its large negative phase seems a problem for certain QCD calculations [7,9] but not for others [10].…”