Exploring CP Violation through B Decays

The B-meson system provides many strategies to perform stringent tests of the Standard-Model description of CP violation. In this brief review, we discuss implications of the currently available B-factory data on the angles alpha, beta and gamma of the unitarity triangle, emphasize the importance of Bs studies at hadronic B experiments, and discuss new, theoretically clean strategies to determine gamma.Comment: 22 pages, 4 figures, invited brief review for Modern Physics Letters

B -> pi pi, New Physics in B -> pi K and Implications for Rare K and B Decays

The measured B -> pi pi, pi K branching ratios exhibit puzzling patterns. We point out that the B -> pi pi hierarchy can be nicely accommodated in the Standard Model (SM) through non-factorizable hadronic interference effects, whereas the B -> pi K system may indicate new physics (NP) in the electroweak (EW) penguin sector. Using the B -> pi pi data and the SU(3) flavour symmetry, we may fix the hadronic B -> pi K parameters, which allows us to show that any currently observed feature of the B -> pi K system can be easily explained through enhanced EW penguins with a large CP-violating NP phase. Restricting ourselves to a specific scenario, where NP enters only through Z^0 penguins, we derive links to rare K and B decays, where an enhancement of the K_L-> pi^0 nu nu_bar rate by one order of magnitude, with BR(K_L -> pi^0 nu nu_bar) > BR(K^+ -> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+ e^-)=O(10^{-10}), (\sin2\beta)_{pi nu nu_bar} K* mu^+ mu^-, are the most spectacular effects. We address also other rare K and B decays, epsilon'/epsilon and B_d -> phi K_S.Comment: 6 pages, LaTeX, reference added and a few typos correced, to appear in Physical Review Letter

In Pursuit of New Physics in the B System

The B-meson system offers interesting probes for the search of physics beyond the Standard Model. After addressing possible signals of new-physics contributions to the B -> phi K and B -> pi K decay amplitudes, we focus on the data for B^0_q-\bar B^0_q mixing (q = d, s), giving a critical discussion of their interpretation in terms of model-independent new-physics parameters. We address, in particular, the impact of the uncertainties of the relevant input parameters, discuss benchmarks for future precision measurements at the LHC, and explore the prospects for new CP-violating effects in the B_s-meson system, which could be detected at the LHC.Comment: 8 pages, 7 figures, invited talk at the 1st Workshop on Theory, Phenomenology and Experiments in Heavy Flavour Physics, Anacapri, Capri, Italy, 29-31 May 2006, 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

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

Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

Model Independent Bound on the Unitarity Triangle from CP Violation in B-> pi+ pi- and B-> psi K_S

We derive model independent lower bounds on the CKM parameters (1-rhobar) and etabar as functions of the mixing-induced CP asymmetry S in B-> pi+ pi- and sin(2 beta) from B->psi K_S. The bounds do not depend on specific results of theoretical calculations for the penguin contribution to B-> pi+ pi-. They require only the very conservative condition that a hadronic phase, which vanishes in the heavy-quark limit, does not exceed 90 degrees in magnitude. The bounds are effective if -sin(2 beta) < S < 1. Dynamical calculations indicate that the limits on rhobar and etabar are close to their actual values.Comment: 5 pages, 2 figure

Angles from B Decays with Charm: Summary of Working Group 5 of the CKM Workshop 2006

We summarize the results presented in Working Group 5 (WG5) of the CKM 2006 Workshop in Nagoya. The charge of WG5 was to discuss the measurements of unitarity triangle angles $\beta/\phi_1$ and $\gamma/\phi_3$ from $B$-meson decays containing charm quark(s) in the final states.Comment: 9 pages, 8 postscript figures, to appear in the proceedings of 4th International Workshop on the CKM Unitarity Triangle (CKM 2006), Nagoya, Japan, 12-16 Dec 200

Extracting gamma and Penguin Topologies through CP Violation in B_s^0 -> J/psi K_S

The B_s^0 -> J/psi K_S decay has recently been observed by the CDF collaboration and will be of interest for the LHCb experiment. This channel will offer a new tool to extract the angle gamma of the unitarity triangle and to control doubly Cabibbo-suppressed penguin corrections to the determination of sin(2beta) from the well-known B_d^0 -> J/psi K_S mode with the help of the U-spin symmetry of strong interactions. While any competitive determination of gamma is interesting, the latter aspect is particularly relevant as LHCb will enter a territory of precision which makes the control of doubly Cabibbo-suppressed Standard-Model corrections mandatory. Using the data from CDF and the e^+e^- B factories as a guideline, we explore the sensitivity for gamma and the penguin parameters and point out that the B_s^0-\bar B_s^0 mixing phase phi_s, which is only about -2 deg in the Standard Model but may be enhanced through new physics, is a key parameter for these analyses. We find that the mixing-induced CP violation S(B_s^0 -> J/psi K_S) shows an interesting correlation with sin(phi_s), which serves as a target region for the first measurement of this observable at LHCb.Comment: 20 pages, 8 figure