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

Weak Phase γ\gamma From Ratio of B→KπB \to K \pi Rates

The ratio of partial decay rates for charged and neutral $B$ mesons to $K \pi$ final states provides information on the weak phase $\gamma \equiv {\rm Arg} (V_{ub}^*)$ when augmented with information on the CP-violating asymmetry in the $K^\pm \pi^\mp$ mode. The requirements for a useful determination of $\gamma$ are examined in the light of present information about the decays $B^0 \to K^+ \pi^-$, $B^+ \to K^0 \pi^+$, and the corresponding charge-conjugate modes. The effects of electroweak penguins and rescattering corrections are noted, and proposals are made for estimating and measuring their importance.Comment: 16 pages, latex, 3 figures, revised version sent to Phys. Rev.

Rescattering Information from B→KKˉB \to K \bar K Decays

Rescattering effects can modify the dependence on the weak phase $\gamma = -{\rm Arg}(V^*_{ub}V_{ud}/V^*_{cb} V_{cd})$ of the ratio of rates for $B^{\pm} \to K \pi^\pm$ and $B \to K^\pm \pi^\mp$. A test for these effects based on the processes $B^\pm \to K^\pm K$ has been suggested. It is pointed out that the rates for the processes $B \to K^+ K^-$, which are expected to be {\it dominated} by rescattering and for which considerably better experimental bounds exist, are likely to provide a more stringent constraint on these effects.Comment: 22 pages, latex, 7 figures, to be published in Phys. Rev. D. Minor corrections and addition

In Pursuit of New Physics with B_s Decays

The presence of a sizeable CP-violating phase in B_s^0-B_s^0-bar mixing would be an unambiguous signal of physics beyond the Standard Model. We analyse various possibilities to detect such a new phase considering both tagged and untagged decays. The effects of a sizeable width difference Delta Gamma between the B_s mass eigenstates, on which the untagged analyses rely, are included in all formulae. A novel method to find this phase from simple measurements of lifetimes and branching ratios in untagged decays is proposed. This method does not involve two-exponential fits, which require much larger statistics. For the tagged decays, an outstanding role is played by the observables of the time-dependent angular distribution of the B_s -> J/psi [-> l^+ l^-] \phi [-> K^+K^-] decay products. We list the formulae needed for the angular analysis in the presence of both a new CP-violating phase and a sizeable Delta Gamma, and propose methods to remove a remaining discrete ambiguity in the new phase. This phase can therefore be determined in an unambiguous way.Comment: minor changes, lattice prediction of Delta Gamma updated, appears in PR

Exploring CP Violation with BcB_c Decays

We point out that the pure ``tree'' decays $B_c^\pm\to D^\pm_s D$ are particularly well suited to extract the CKM angle $\gamma$ through amplitude relations. In contrast to conceptually similar strategies using $B^\pm\to K^\pm D$ or $B_d\to K^{\ast0} D$ decays, the advantage of the $B_c$ approach is that the corresponding triangles have three sides of comparable length and do not involve small amplitudes. Decays of the type $B_c^\pm\to D^\pm D$ -- the $U$-spin counterparts of $B_c^\pm\to D^\pm_s D$ -- can be added to the analysis, as well as channels, where the $D^\pm_s$- and $D^\pm$-mesons are replaced by higher resonances.Comment: 9 pages, LaTeX, 3 figures, reference adde

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

CP Asymmetry in B_d --> phi K_S: Standard Model Pollution

The difference in the time dependent CP asymmetries between the modes $B --> psi K_S$ and $B --> phi K_S$ is a clean signal for physics beyond the Standard Model. This interpretation could fail if there is a large enhancement of the matrix element of the $b --> u ubar s$ operator between the $B_d$ initial state and the $phi K_S$ final state. We argue against this possibility and propose some experimental tests that could shed light on the situation.Comment: 9 pages, Revte

CP violation and CKM phases from angular distributions for BsB_s decays into admixtures of CP eigenstates

We investigate the time-evolutions of angular distributions for $B_s$ decays into final states that are admixtures of CP-even and CP-odd configurations. A sizable lifetime difference between the $B_s$ mass eigenstates allows a probe of CP violation in time-dependent untagged angular distributions. Interference effects between different final state configurations of $B_s\to D^{*+}_s D^{*-}_s$, $J/\psi \phi$ determine the Wolfenstein parameter $\eta$ from untagged data samples, or -- if one uses $|V_{ub}|/|V_{cb}|$ as an additional input -- the notoriously difficult to measure CKM angle $\gamma$. Another determination of $\gamma$ is possible by using isospin symmetry of strong interactions to relate untagged data samples of $B_s\to K^{\ast+} K^{\ast-}$ and $B_s\to K^{\ast0} \overline{K^{\ast0}}$. We note that the untagged angular distribution for $B_s\to\rho^0 \phi$ provides interesting information about electroweak penguins.Comment: 19 pages, LaTeX, no figure

Bs,d→ππ,πK,KKB_{s,d} \to \pi\pi,\pi K, KK: Status and Prospects

Several years ago, it was pointed out that the U-spin-related decays $B_d\to\pi^+\pi^-$, $B_s\to K^+K^-$ and $B_d\to\pi^\mp K^\pm$, $B_s\to \pi^\pm K^\mp$ offer interesting strategies for the extraction of the angle gamma of the unitarity triangle. Using the first results from the Tevatron on the $B_s$ decays and the B-factory data on $B_{u,d}$ modes, we compare the determinations of gamma from both strategies, study the sensitivity on U-spin-breaking effects, discuss the resolution of discrete ambiguities, predict observables that were not yet measured but will be accessible at LHCb, explore the extraction of the width difference $\Delta\Gamma_s$ from untagged $B_s\to K^+K^-$ rates, and address the impact of new physics. The data for the $B_d\to\pi^+\pi^-$, $B_s\to K^+K^-$ system favour the BaBar measurement of direct CP violation in $B_d\to\pi^+\pi^-$, which will be used in the numerical analysis, and result in a fortunate situation, yielding $\gamma=(66.6^{+4.3+4.0}_{-5.0-3.0})^\circ$, where the latter errors correspond to a generous estimate of U-spin-breaking effects. On the other hand, the $B_d\to\pi^\mp K^\pm$, $B_s\to \pi^\pm K^\mp$ analysis leaves us with $26^\circ\leq\gamma\leq70^\circ$, and points to a value of the $B_s\to \pi^\pm K^\mp$ branching ratio that is larger than the current Tevatron result. An important further step will be the measurement of mixing-induced CP violation in $B_s\to K^+K^-$, which will also allow us to extract the $B^0_s$--$\bar B^0_s$ mixing phase unambiguously with the help of $B_s\to J/\psi \phi$ at the LHC. Finally, the measurement of direct CP violation in $B_s\to K^+K^-$ will make the full exploitation of the physics potential of the $B_{s,d}\to \pi\pi, \pi K, KK$ modes possible.Comment: 28 pages, 10 figure

Taming the Penguin in the B0(t) -> Pi+Pi- CP-asymmetry: Observables and Minimal Theoretical Input

Penguin contributions, being not negligible in general, can hide the information on the CKM angle alpha coming from the measurement of the time-dependent B0(t) -> pi+pi- CP-asymmetry. Nevertheless, we show that this information can be summarized in a set of simple equations, expressing alpha as a multi-valued function of a single theoretically unknown parameter, which conveniently can be chosen as a well-defined ratio of penguin to tree amplitudes. Using these exact analytic expressions, free of any assumption besides the Standard Model, and some reasonable hypotheses to constrain the modulus of the penguin amplitude, we derive several new upper bounds on the penguin-induced shift |2alpha-2alpha_eff|, generalizing the recent result of Grossman and Quinn. These bounds depend on the averaged branching ratios of some decays (pi0pi0, K0K0bar, K+-pi-+) particularly sensitive to the penguin. On the other hand, with further and less conservative approximations, we show that the knowledge of the B+- -> Kpi+- branching ratio alone gives sufficient information to extract the free parameter without the need of other measurements, and without knowing |V_td| or |V_ub|. More generally, knowing the modulus of the penguin amplitude with an accuracy of ~30% might result in an extraction of alpha competitive with the experimentally more difficult isospin analysis. We also show that our framework allows to recover most of the previous approaches in a transparent and simple way, and in some cases to improve them. In addition we discuss in detail the problem of the various kinds of discrete ambiguities.Comment: LaTeX2e, 44 pages, 9 figures (from 18 postscript files) included with epsf. Minor changes, references updated. New CLEO results from ICHEP'98 are taken into account. To appear in Phys. Rev.