arXiv subjects
Publications and source records attributed to Michael Gronau.
While the Kobayashi--Maskawa single phase origin of CP violation passed its first crucial precision test in $B\to J/ψK_S$, the chirality of weak $b$-quark couplings has not yet been carefully tested. We discuss recent proposals for studying the chiral and CP-violating structure of these couplings in radiative and in hadronic B decays.
In view of recent experimental progress in rate and CP asymmetry measurements in $B^{\pm} \to DK^{\pm}$, we reconsider information on the weak phase $γ$ which can be obtained from these processes. Model-independent inequalities are proven for $\sin^2γ$ in terms of two ratios of partial rates for $B^{\pm,0} \to D X_s^{\pm,0}$, where $X_s$ is any multiparticle charmless state carrying strangeness $\pm 1$. Good prospects are shown to exist for using these inequalities and CP asymmetry measurements in two body and multibody decays in order to improve present bounds on $γ$.
We point out that the decays of B mesons into a vector meson and an axial-vector meson can distinguish between left and right-handed polarized mesons, in contrast to decays into two vector mesons. Measurements in B0 -> D*-a1+ are proposed for testing factorization and the V-A structure of the weak b -> c current, and for resolving a discrete ambiguity in 2β+ γ.
We study decay distributions in B -> K pi pi gamma, combining contributions from several overlapping resonances in a K pi pi mass range near 1400 MeV, (1^+) K_1(1400), (2^+) K^*_2(1430) and (1^-) K^*(1410). A method is proposed for using these distributions to determine a photon polarization parameter in the effective radiative weak Hamiltonian. This parameter is measured through an up-down asymmetry of the photon direction relative to the K pi pi decay plane. We calculate a dominant up-down asymmetry of 0.33 +- 0.05 from the K1(1400) resonance, which can be measured with about 10^8 B B-bar pairs, thus providing a new test for the Standard Model and a probe for some of its extensions.
CP-violating asymmetries in the decay $B^0(t)\to π^+ π^-$ are a potentially rich source of information about both strong and weak phases. In a previous treatment by the present authors use was made of an assumption about the relative magnitude of tree and penguin amplitudes contributing to this process. This assumption involved an ambiguity in relating the tree amplitude to the amplitude for $B \to π\ell ν$. It is shown here that one can avoid this assumption, which adopted a particular convention for tree and penguin amplitudes, and that the results are convention-independent.
Time-dependence in $B^0(t) \to π^+ π^-$ and $\ob(t) \to π^+ π^-$ is utilized to obtain a maximal set of information on strong and weak phases. One can thereby check theoretical predictions of a small strong phase $δ$ between penguin and tree amplitudes. A discrete ambiguity between $δ\simeq 0$ and $δ\simeq π$ may be resolved by comparing the observed charge-averaged branching ratio predicted for the tree amplitude alone, using measurements of $B \to πl ν$ and factorization, or by direct comparison of parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix with those determined by other means. It is found that with 150 fb$^{-1}$ from BaBar and Belle, this ambiguity will be resolvable if no direct CP violation is found. In the presence of direct CP violation, the discrete ambiguity between $δ$ and $π- δ$ becomes less important, vanishing altogether as $|δ| \to π/2$. The role of measurements involving the lifetime difference between neutral $B$ eigenstates is mentioned briefly.
We re-examine the time-dependent rates of $\bs(t) \to K^+ K^-$ and $\obs(t) \to K^+ K^-$, including a lifetime difference between neutral $\bs$ mass eigenstates. The two rates, normalized by the rate of $\bs \to \ko \ok$, are used to obtain ambiguity-free information on a strong phase and on the weak phase $γ$. We discuss the sensitivity of extracting $γ$ to the measured quantities, and find that an error of $\pm 10^\circ$ in $γ$ is possible for a sample of several thousand $\bs(t) \to K^+ K^-$ decays. This study is complementary to a recent similar analysis of the U-spin related decays $\bo(t) \to π^+π^-$ and $\ob(t) \to π^+π^-$.
We report on recent progress in studying two aspects of $B$ physics, in which penguin amplitudes play an important role: (1) Bounds on penguin pollution in $B^0(t) \to π^+π^-$ constraining CKM parameters, and a lower bound on $B^0 \to π^0π^0$ improving precision in $\sin 2α$. (2) A suggestion for measuring the photon polarization in electroweak penguin decay, $B \to K_1(1400)γ$, providing a precision test of the Standard Model and a probe for new physics.
We propose a way of measuring the photon polarization in radiative B decays into K resonance states decaying to Kππ, which can test the Standard Model and probe new physics. The photon polarization is shown to be measured by the up-down asymmetry of the photon direction relative to the Kππdecay plane in the K resonance rest frame. The integrated asymmetry in K_1(1400)\to Kππ, calculated to be 0.34\pm 0.05 in the Standard Model, is measurable at currently operating B factories.
Recent experimental limits for the direct CP asymmetries in $B^0 \to K^+ π^-$, $B^+ \to K^+ π^0$, $B^+ \to K^0 π^+$, and $B^0 \to π^+ π^-$, and for the indirect CP asymmetry in $B^0 \to π^+ π^-$, are combined with information on CP-averaged branching ratios to shed light on weak and strong phases. At present such bounds favor $γ\ge 60^\circ$ at the $1 σ$ level. The prospects for further improvements are discussed.
In the presence of penguin contributions, the indirect CP asymmetry in B0(t) -> pi+ pi- measures sin(2α+ 2θ), where 2θparametrizes the size of the penguin ``pollution.'' We derive a new upper bound on |2θ|, requiring the measurement of of BR(B+ -> pi+ pi0) and an upper bound on B00 \equiv {1\over 2} [BR(B0 -> pi0 pi0) + BR(B0bar -> pi0 pi0)]. The new bound is stronger than those previously discussed in the literature. We also present a lower bound on B00. Current data may suggest that it is not very small, in which case θcan be determined using a complete isospin analysis.
We review recent suggestions for testing through B decays the flavor structure of CP violation in the Standard Model. Relative signs of CP asymmetries in U-spin related processes can by themselves test the Kobayashi-Maskawa mechanism in a crude manner. Ratios of charge-averaged decay rates and certain CP asymmetries may constrain tightly the weak phases $γ=ϕ_3$ and $α=ϕ_2$.
We propose a set of measurements at a charm factory to determine the $D^0-\bar D^0$ mixing parameters $ΔM$ and $ΔΓ$ and the strong phase difference $δ$ between doubly-Cabibbo-suppressed (DCS) and Cabibbo-favored (CF) neutral $D$ decays into $K^-π^+$. The method can also be used to measure strong phase differences between other corresponding DCS and CF amplitudes. These phase differences are important for studies of $D^0$--$\bar D^0$ mixing.
We prove a U-spin amplitude triangle relation among doubly Cabibbo-suppressed (DCS) charmed meson decays, $D^0\to K^+π^-, D^0 \to K^0π^0$ and $D^+_s \to K^0 K^+$, congruent to an isospin relation among corresponding Cabibbo-favored (CF) decays. U-spin breaking in relative phases between CF and DCS amplitudes affects time-dependent studies of $D^0-\od$ mixing. Comparison of final state phase patterns in DCS and CF amplitude triangles, which can shed some light on these phases, is carried out in a phenomenological framework incorporating resonance contributions.
Measuring phases in the Cabibbo-Kobayashi-Maskawa matrix through CP asymmetries in B decays is a major goal of current and future experiments. Methods based on charge-conjugation and isospin symmetries involve very little theoretical uncertainties, while schemes based on flavor SU(3) involve uncertainties due to SU(3) breaking. Resolving these uncertainties requires further studies involving a dialogue between theory and experiments.
A density-matrix method for the study of tagged states of neutral B mesons with arbitrary coherence properties is applied to several examples, including $e^+ e^-$ production both at and above the $Υ(4S)$ resonance, and hadronic production. In the absence of coherence the only term modulating the exponential decay of a neutral B meson behaves as $\cos Δm t$, while a $\sin Δm t$ modulation is a signal of partial or full coherence. Decays to CP eigenstates are needed to fully specify the density matrix. We relate these results to more familiar expressions for the cases of the $Υ(4S)$ and incoherent production.
We prove a general theorem about equal CP rate differences within pairs of U-spin related charmless $B$ and $B_s$ decays. Large deviations from equalities would be evidence for new physics. Six pairs of decays into two pseudoscalar mesons are identified where such relations hold. Ratios of corresponding rate differences and certain ratios of rates measure U-spin breaking. These processes provide useful information on the weak phase $γ={\rm Arg} V^*_{ub}$. Applications of U-spin symmetry to other decays are discussed.
We consider two SU(3) breaking parameters, $R_1(m_B)$ and $R_2(m_B)$, appearing in a relation between $B^+\to Kπ$ and $B^+\toππ$ amplitudes, which plays an important role in determining the weak phase $γ$. We identify an isospin-related quantity $R_2(m_D)$ measured in $D$ decays, exhibiting large SU(3) breaking which is likely due to nonfactorizable effects. With a cautious remark about possible nonfactorizable SU(3) breaking in $B$ decays, we proceed to calculate factorizable SU(3) breaking corrections. Applying heavy quark symmetry to semileptonic $D$ and B decay form factors, we find that SU(3) breaking in $R_2(m_B)/R_1(m_B)$ may be significantly larger than estimated from certain model calculations of form factors.