The B -> pi K Puzzle and its Relation to Rare B and K Decays

The Standard-Model interpretation of the ratios of charged and neutral B-> pi K rates, R_c and R_n, respectively, points towards a puzzling picture. Since these observables are affected significantly by colour-allowed electroweak (EW) penguins, this ``B -> pi K puzzle'' could be a manifestation of new physics in the EW penguin sector. Performing the analysis in the R_n-R_c plane, which is very suitable for monitoring various effects, we demonstrate that we may, in fact, move straightforwardly to the experimental region in this plane through an enhancement of the relevant EW penguin parameter q. We derive analytical bounds for q in terms of a quantity L, that measures the violation of the Lipkin sum rule, and point out that strong phases around 90 deg are favoured by the data, in contrast to QCD factorisation. The B -> pi K modes imply a correlation between q and the angle gamma that in the limit of negligible rescattering effects and colour suppressed EW penguins depends only on the value of L. Concentrating on a minimal flavour-violating new-physics scenario with enhanced Z^0 penguins, we find that the current experimental values on B -> X_s mu^+ mu^- require roughly L pi K data give L = 5.7 +- 2.4, L has either to move to smaller values once the B -> pi K data improve or new sources of flavour and CP violation are needed. In turn, the enhanced values of L seen in the B -> pi K data could be accompanied by enhanced branching ratios for rare decays. Most interesting turns out to be the correlation between the B -> pi K modes and BR(K^+ -> pi^+ nu nu), with the latter depending approximately on a single ``scaling'' variable \bar L= L (|V_{ub}/V_{cb}|/0.086)^2.3.Comment: 19 pages, 7 figures, a few typos corrected and two references adde

The B -> pi pi, pi K Puzzles: Implications for Hadron Physics, New Physics and Rare Decays

The B-meson system is an interesting probe for the exploration of strong interactions, the quark-flavour sector of the Standard Model, and the search for new physics. In this programme, non-leptonic B decays, which are particularly challenging from the point of view of QCD, play a key role. After discussing strategies to deal with the corresponding hadronic matrix elements of four-quark operators and popular avenues for new physics to manifest itself in B decays, we focus on puzzling patterns in the B-factory data for B -> pi pi, pi K decays; we explore their implications for hadron physics, new physics and rare K and B decays.Comment: 10 pages, 2 figures, plenary talk at the International Conference on QCD and Hadronic Physics, Peking University, Beijing, China, 16-20 June 2005, to appear in the Proceeding

New Aspects of B -> pi pi, pi K and their Implications for Rare Decays

We analyse the B -> pi pi, pi K modes in the light of the most recent B-factory data, and obtain the following new results: (i) the B0 -> pi+ pi-, pi- K+ modes prefer gamma=(74+-6)deg, which - together with |V_ub/V_cb| - allows us to determine the ``true'' unitarity triangle and to search for CP-violating new-physics contributions to B0_d-\bar B0_d mixing; (ii) the B -> pi K puzzle reflected in particular by the low experimental value of the ratio R_n of the neutral B -> pi K rates persists and still favours new physics in the electroweak penguin sector with a new CP-violating phase phi ~ -90deg, although now also phi ~ +90deg can bring us rather close to the data; (iii) the mixing-induced B0 -> pi0 K_S CP asymmetry is a sensitive probe of the sign of this phase, and would currently favour phi ~ +90deg, as well as the direct CP asymmetry of B+- -> pi0 K+-, which suffers, however, from large hadronic uncertainties; (iv) we investigate the sensitivity of our B -> pi K analysis to large non-factorizable SU(3)-breaking effects and find that their impact is surprisingly small so that it is indeed exciting to speculate on new physics; (v) assuming that new physics enters through Z0 penguins, we study the interplay between B -> pi K and rare B, K decays and point out that the most recent B-factory constraints for the latter have interesting implications, bringing us to a few scenarios for the future evolution of the data, where also the mixing-induced CP violation in B0 -> pi0 K_S plays a prominent role.Comment: Two references added, to appear in the European Physical Journal

Waiting for Clear Signals of New Physics in B and K Decays

We classify the extensions of the Standard Model (SM) according to the structure of local operators in the weak effective Hamiltonian and the presence or absence of new flavour and CP-violating interactions beyond those represented by the CKM matrix. In particular we review characteristic properties of models with minimal flavour violation (MFV), models with significant contributions from Higgs penguins and models with enhanced Z^0 penguins carrying a large new CP-violating phase. Within the latter models, the anomalous behaviour of certain B\to\pi K observables implies large departures from the SM predictions for rare and CP-violating K and B decays. Most spectacular is the enhancement of Br(K_L->pi^0 nu nubar) by one order of magnitude and a strong violation of the MFV relation (\sin2\beta)_{\pi\nu\bar\nu}=(\sin2\beta)_{\psi K_S}. On the other hand our prediction for (\sin2\beta)_{\phi K_S}\approx 0.9 differs from the Belle result by the sign but is consistent with the BaBar value. We give a personal shopping list for the coming years.Comment: Main latex-file, 4 figures, 22 page

Limitations in Measuring the Angle β\beta by Using SU(3)SU(3) Relations for BB-Meson Decay-Amplitudes

Flavour $SU(3)$ symmetry of strong interactions and certain dynamical assumptions have been used in a series of recent publications to extract weak CKM phases from $B$-decays into $\{\pi\pi,\pi K, K\bar K\}$ final states. We point out that irrespectively of $SU(3)$-breaking effects the presence of QCD-penguin contributions with internal $u$- and $c$-quarks precludes a clean determination of the angle $\beta$ in the unitarity triangle by using the branching ratios only. This difficulty can be overcome by measuring in addition the ratio $x_d/x_s$ of $B^0_d-\bar B^0_d$ to $B^0_s-\bar B^0_s$ mixings. The measurement of the angle $\gamma$ is unaffected by these new contributions. Some specific uncertainties related to $SU(3)$-breaking effects and electroweak penguin contributions are briefly discussed.Comment: 15 pages (LaTeX) + 5 figures included, Munich Technical University preprint TUM-T31-69/9

Flavour constraints on multi-Higgs-doublet models: Yukawa alignment

In multi-Higgs-doublet models, the alignment in flavour space of all Yukawa matrices coupling to a given right-handed fermion guarantees the absence of tree-level flavour-changing neutral couplings, while introducing new sources of CP violation. With N Higgs doublets (and no right-handed neutrinos) the Yukawa Lagrangian is characterized by the fermion masses, the CKM quark mixing matrix and 3(N-1) complex couplings. Quantum corrections break the alignment, generating a minimal-flavour-violation structure with flavour-blind phases. The aligned multi-Higgs-doublet models lead to a rich and viable phenomenology with an interesting hierarchy of flavour-changing neutral current effects, suppressing them in light-quark systems while allowing potentially relevant signals in heavy-quark transitions.Comment: 6 pages, 5 figures. Talk given in the "Third Workshop on Theory, Phenomenology and Experiments in Heavy Flavour Physics" (Capri, 5-7 July 2010

CP Violation in B -> pi+ pi- and the Unitarity Triangle

We analyze the extraction of weak phases from CP violation in $B\to\pi^+\pi^-$ decays. We propose to determine the unitarity triangle $(\bar\rho,\bar\eta)$ by combining the information on mixing induced CP violation in $B\to\pi^+\pi^-$, $S$, with the precision observable $\sin 2\beta$ obtained from the CP asymmetry in $B\to\psi K_S$. It is then possible to write down exact analytical expressions for $\bar\rho$ and $\bar\eta$ as simple functions of the observables $S$ and $\sin 2\beta$, and of the penguin parameters $r$ and $\phi$. As an application clean lower bounds on $\bar\eta$ and $1-\bar\rho$ can be derived as functions of $S$ and $\sin 2\beta$, essentially without hadronic uncertainty. Computing $r$ and $\phi$ within QCD factorization yields precise determinations of $\bar\rho$ and $\bar\eta$ since the dependence on $r$ and $\phi$ is rather weak. It is emphasized that the sensitivity to the phase $\phi$ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter $C$ of direct CP violation in $B\to\pi^+\pi^-$. We also discuss alternative ways to analyze $S$ and $C$ that can be useful if new physics affects $B_d$--$\bar B_d$ mixing. Predictions and uncertainties for $r$ and $\phi$ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in $1/m_b$ and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.Comment: 26 pages, 7 figure

On fermion masses and mixing in a model with A4A_4 symmetry

In a recently proposed multi-Higgs extension of the standard model in which discrete symmetries, $A_4$ and $Z_3$ are imposed we show that, after accommodating the fermion masses and the mixing matrices in the charged currents, the mixing matrices in the neutral currents induced by neutral scalars are numerically obtained. However, the flavor changing neutral currents are under control mainly by mixing and/or mass suppressions in the neutral scalar sector.Comment: Version accepted for publication in International Journal of Modern Physics A. In this version we added a discussion on the charged lepton and neutrino masses. The title has been changed. Other minor changes do not modify the conclusion