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Register a new userPossible resolution of the B -> pi pi, pi K puzzles
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We show that there exist uncanceled soft divergences in the k_T factorization for nonfactorizable amplitudes of two-body nonleptonic B meson decays, similar to those identified in hadron hadroproduction. These divergences can be grouped into a soft factor using the eikonal approximation, which is then treated as an additional nonperturbative input in the perturbative QCD formalism. Viewing the special role of the pion as a q-qbar bound state and as a pseudo Nambu-Goldstone boson, we postulate that the soft effect associated with it is significant. This soft factor enhances the nonfactorizable color-suppressed tree amplitudes, such that the branching ratios B(pi^0 pi^0) and B(pi^0 rho^0) are increased under the constraint of the B(rho^0 rho^0) data, the difference between the direct CP asymmetries A_{CP}(pi^mp K^pm) and A_{CP}(pi^0 K^pm) is enlarged, and the mixing-induced CP asymmetry S_{pi^0 K_S} is reduced. Namely, the known pi pi and pi K puzzles can be resolved simultaneously.
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Recently, we have seen interesting progress in the exploration of CP violation in B^0_d -> pi^+ pi^-: the measurements of mixing-induced CP violation by the BaBar and Belle collaborations are now in good agreement with each other, whereas the picture of direct CP violation is still unclear. Using the branching ratio and direct CP asymmetry of B^0_d -> pi^- K^+, this situation can be clarified. We predict A_CP^dir(B_d -> pi^+ pi^-) = -0.24+-0.04, which favours the BaBar result, and extract gamma=(70.0^{+3.8}_{-4.3})deg, which agrees with the unitarity triangle fits. Extending our analysis to other B -> pi K modes and B^0_s -> K^+ K^- with the help of the SU(3) flavour symmetry and plausible dynamical assumptions, we find that all observables with colour-suppressed electroweak penguin contributions are measured in excellent agreement with the Standard Model. As far as the ratios R_{c,n} of the charged and neutral B -> pi K branching ratios are concerned, which are sizeably affected by electroweak penguin contributions, our Standard-Model predictions have almost unchanged central values, but significantly reduced errors. Since the new data have moved quite a bit towards these results, the B -> pi K puzzle for the CP-conserving quantities has been significantly reduced. However, the mixing-induced CP violation of B^0_d -> pi^0 K_S does look puzzling; if confirmed by future measurements, this effect could be accommodated through a modified electroweak penguin sector with a large CP-violating new-physics phase. Finally, we point out that the established difference between the direct CP asymmetries of B^+- -> pi^0 K^+- and B_d -> pi^-+ K^+- appears to be generated by hadronic and not by new physics.
We summarize a recent strategy for a global analysis of the B -> pi pi, pi K systems and rare decays. We find that the present B -> pi pi and B -> pi K data cannot be simultaneously described in the Standard Model. In a simple extension in which new physics enters dominantly through Z^0 penguins with a CP-violating phase, only certain B -> pi K modes are affected by new physics. The B -> pi pi data can then be described entirely within the Standard Model but with values of hadronic parameters that reflect large non-factorizable contributions. Using the SU(3) flavour symmetry and plausible dynamical assumptions, we can then use the B -> pi pi decays to fix the hadronic part of the B -> pi K system and make predictions for various observables in the B_d -> pi^-+ K^+- and B^+- -> pi^+- K decays that are practically unaffected by electroweak penguins. The data on the B^+- -> pi^0 K^+- and B_d -> pi^0 K modes allow us then to determine the electroweak penguin component which differs from the Standard Model one, in particular through a large additional CP-violating phase. The implications for rare K and B decays are spectacular. In particular, the rate for K_L -> pi^0 nu bar nu is enhanced by one order of magnitude, the branching ratios for B_{d,s} -> mu^+ mu^- by a factor of five, and BR(K_L -> pi^0 e^+ e^-, pi^0 mu^+ mu^-) by factors of three.
Within the quasi-two-body decay model, we study the localized $CP$ violation and branching fraction of the four-body decay $bar{B}^0rightarrow [K^-pi^+]_{S/V}[pi^+pi^-]_{V/S} rightarrow K^-pi^+pi^-pi^+$ when $K^-pi^+$ and $pi^-pi^+$ pair invariant masses are $0.35<m_{K^-pi^+}<2.04 , mathrm{GeV}$ and $0<m_{pi^-pi^+}<1.06, mathrm{GeV}$, with the pairs being dominated by the $bar{K}^*_0(700)^0$, $bar{K}^*(892)^0$, $bar{K}^*(1410)^0$, $bar{K}^*_0(1430)$ and $bar{K}^*(1680)^0$, and $f_0(500)$, $rho^0(770)$ , $omega(782)$ and $f_0(980)$ resonances, respectively. When dealing with the dynamical functions of these resonances, $f_0(500)$, $rho^0(770)$, $f_0(980)$ and $bar{K}^*_0(1430)$ are modeled with the Bugg model, Gounaris-Sakurai function, Flatt$acute{mathrm{e}}$ formalism and LASS lineshape, respectively, while others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters $rho_Ain[0,0.5]$ and $phi_Ain[0,2pi]$, our predicted results are $mathcal{A_{CP}}(bar{B}^0rightarrow K^-pi^+pi^+pi^-)in[-0.383,0.421]$ and $mathcal{B}(bar{B}^0rightarrow K^-pi^+pi^+pi^-)in[7.36,199.69]times10^{-8}$ based on the hypothetical $qbar{q}$ structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the $CP$ violating asymmetries and branching fractions of the two-body decays $bar{B}^0rightarrow SV(VS)$ and all the individual four-body decays $bar{B}^0rightarrow SV(VS) rightarrow K^-pi^+pi^-pi^+$, respectively. Our theoretical results for the two-body decays $bar{B}^0rightarrow bar{K}^*(892)^0$$f_0(980)$, $bar{B}^0rightarrow bar{K}^*_0(1430)^0$$omega(782)$, $bar{B}^0rightarrow bar{K}^*(892)^0f_0(980)$, $bar{B}^0rightarrowbar{K}^*_0(1430)^0rho$,
First observations of the Cabibbo suppressed decays B0bar -->D+ K- pi+ pi- and B- --> D0 K- pi+ pi- are reported using 35 pb^{-1} of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo favored decays, from which we obtain B(B0bar --> D+ K- pi+ pi-)/B(B0bar --> D+ pi- pi+ pi-)=(5.9pm1.1pm0.5) x 10^{-2} and B(B- --> D0 K- pi+ pi-)/B(B- --> D0 pi- pi+ pi-)=(9.4pm1.3pm0.9) x 10^{-2}, where the uncertainties are statistical and systematic, respectively. The B- --> D0 K- pi+ pi- decay is particularly interesting, as it can be used in a similar way to B- --> D0 K- to measure the CKM phase gamma.
A search is made for the highly-suppressed B meson decays $B^{+}rightarrow K^{+}K^{+}pi^{-}$ and $B^{+}rightarrow pi^{+}pi^{+}K^{-}$ using a data sample corresponding to an integrated luminosity of 3.0 $fb^{-1}$ collected by the LHCb experiment in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. No evidence is found for the decays, and upper limits at 90% confidence level are determined to be $mathcal{B}(B^{+}rightarrow K^{+}K^{+}pi^{-}) < 1.1times 10^{-8}$ and $mathcal{B}(B^{+}rightarrow pi^{+}pi^{+}K^{-}) < 4.6times 10^{-8}$.
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