QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters

TL;DR

Beneke, Buchalla, Neubert, and Sachrajda develop a QCD factorization framework for B→πK and B→ππ decays in the heavy-quark limit, deriving a factorization formula where short-distance kernels and long-distance hadronic inputs (form factors, light-cone DAs) separate cleanly. They compute amplitude parameters a_i and b_i at NLO, incorporating electroweak penguins, asymmetric distribution amplitudes, and chirally enhanced twist-3 power corrections, while modeling power-suppressed annihilation effects with endpoint-divergent parameters X_H and X_A. The analysis yields predictions for branching fractions and CP asymmetries, reduces hadronic uncertainties in weak-phase extractions, and enables a global fit to constrain the Wolfenstein parameters (ρ̄,η̄), showing compatibility with the standard CKM picture and providing a framework for future experimental tests. The work also contrasts this approach with PQCD and sum-rule methods, arguing for the robustness of factorization in the heavy-quark limit and highlighting areas where power corrections remain the dominant theoretical uncertainties.

Abstract

In the heavy-quark limit, the hadronic matrix elements entering nonleptonic $B$-meson decays into two light mesons can be calculated from first principles including ``nonfactorizable'' strong-interaction corrections. The $B\toπK,ππ$ decay amplitudes are computed including electroweak penguin contributions, SU(3) violation in the light-cone distribution amplitudes, and an estimate of power corrections from chirally-enhanced terms and annihilation graphs. The results are then used to reduce the theoretical uncertainties in determinations of the weak phases $γ$ and $α$. In that way, new constraints in the $(\barρ,\barη)$ plane are derived. Predictions for the $B\toπK, ππ$ branching ratios and CP asymmetries are also presented. A good global fit to the (in part preliminary) experimental data on the branching fractions is obtained without taking recourse to phenomenological models.

Figures (19)

• Figure 1: Graphical representation of the factorization formula. Only one of the two form-factor terms in (\ref{['fact']}) is shown for simplicity.
• Figure 2: Order $\alpha_s$ corrections to the hard-scattering kernels $T_{M,i}^{\rm I}$ (first two rows) and $T_i^{\rm II}$ (last row). In the case of $T_{M,i}^{\rm I}$, the spectator quark does not participate in the hard interaction and is not drawn. The two lines directed upwards represent the quarks that make up one of the light mesons (the emission particle) in the final state.
• Figure 3: The two different penguin contractions.
• Figure 4: Annihilation diagrams.
• Figure 5: Ranges for the complex parameter $H_{\pi K}$. The dot shows the default value used in obtaining the results in Table \ref{['tab:aiII']}.