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Michael Gronau

Publications and source records attributed to Michael Gronau.

At least 73 records · Page 4Linked to original sources
arXiv2006

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four $B\to Kπ$ decays, where isospin breaking is shown to be negligible. (2) An SU(3) sum rule for pairs of $B\to Kπ$ and $B\to Kη_8$, generalized to pairs of $B\to Kπ, B\to Kη$ and $B\to Kη'$.

hep-ph↗
arXiv2005

Symmetry relations in charmless B->PPP decays

Strangeness-changing decays of $B$ mesons to three-body final states of pions and kaons are studied, assuming that they are dominated by a $ΔI=0$ penguin amplitude with flavor structure $\bar b \to \bar s$. Numerous isospin relations for $B\to Kππ$ and for underlying quasi-two-body decays are compared successfully with experiment, in some cases resolving ambiguities in fitting resonance parameters. The only exception is a somewhat small branching ratio noted in $B^0\to K^{*0}π^0$, interpreted in terms of destructive interference between a penguin amplitude and an enhanced electroweak penguin contribution. Relations for B decays into three kaons are derived in terms of final states involving $K_S$ or $K_L$, assuming that $ϕK$-subtracted decay amplitudes are symmetric in $K$ and $\bar K$, as has been observed experimentally. Rates due to nonresonant backgrounds are studied using a simple model, which may reduce discrete ambiguities in Dalitz plot analyses.

hep-ph↗
arXiv2005

Weak Phases and CP Violation

Time-dependent CP asymmetries in $B^0$ decays from interference of $B^0$-$\bar B^0$ mixing and $b\to c\bar cs, u\bar ud, sq\bar q$, and direct asymmetries from interference of $b\to c\bar us$ and $b\to u\bar cs$ are studied, improving errors in the weak phases $β$ and $γ$ to $\pm 1^\circ$ and $\pm 7^\circ$, respectively. Two kinds of tests for New Physics are discussed: 1. Deviations of asymmetries in $b\to sq\bar q$ decays from $\sin 2β\sinΔmt$. 2. Violation of a sum rule for direct asymmetries in $B\to Kπ$.

hep-ph↗
arXiv2005

A precise sum rule among four B -> Kpi CP asymmetries

A sum rule relation is proposed for direct CP asymmetries in $B\to Kπ$ decays. Leading terms are identical in the isospin symmetry limit, while subleading terms are equal in the flavor SU(3) and heavy quark limits. The sum rule predicts $A_{\rm CP}(B^0\to K^0π^0)=-0.17 \pm 0.06$ using current asymmetry measurements for the other three $B\to Kπ$ decays. A violation of the sum rule would be evidence for New Physics in $b\to s\bar qq$ transitions.

hep-ph↗
arXiv2005

The $b \to s$ penguin amplitude in charmless $B \to PP$ decays

The $b \to s$ penguin amplitude affects a number of $B$ meson decays to two pseudoscalar ($P$) mesons in which potential anomalies are being watched carefully, though none has yet reached a statistically compelling level. These include (a) a rate for $B^0 \to K^0 π^0$ which is slightly enhanced with respect to expectations; (b) a time-dependent CP asymmetry parameter $S$ for $B^0 \to K^0 π^0$ which is low in comparison with the expected value of $\sin 2 β\simeq 0.73$, and (c) a similar deviation in the parameter $S$ for $B^0 \to η' K_S$. These and related phenomena involving vector mesons in the final state are discussed in a unified way in and beyond the Standard Model. Future experiments which would conclusively indicate the presence of new physics are identified. Several of these involve decays of the strange $B$ meson $B_s$. In the Standard Model we note an approximate sum rule for CP rate differences in $B^0\to K^+π^-, B^+\to K^+π^0$ and $B^0\to K^0π^0$, predicting a negative sign for the latter asymmetry.

hep-ph↗
arXiv2004

CP violation in B meson decays

Recent CP asymmetry measurements in tree-dominated processes, $B^0\to π^+π^-, ρ^+ρ^-, ρ^{\pm}π^{\mp}, B^+\to DK^+$, and in penguin-dominated decays, $B \to π^0 K_S, η' K_S, ϕK_S$, are interpreted in the framework of the Kobayashi-Maskawa (KM) mechanism of CP violation. The KM phase emerges as the dominant source of CP violation in tree-dominated decays, which are beginning to constrain the unitarity triangle beyond other constraints. Improving precision of CP asymmetry measurements in penguin-dominated decays may indicate the need for new physics.

hep-ph↗
arXiv2004

Correlated bounds on CP asymmetries in $B^0 \to η' K_S$

Flavor SU(3) is used to constrain the coefficients of $\sinΔmt$ and $\cosΔmt$ in the time-dependent CP asymmetry of $B^0 \to η' K_S$. Correlated bounds in the $(S_{η' K}, C_{η' K})$ plane are derived, by using recent rate measurements of $B^0$ decays into $K^+ K^-, π^0π^0, π^0η, π^0η', ηη, ηη', η'η'$. Stringent bounds are obtained when assuming a single SU(3) singlet amplitude and when neglecting annihilation-type amplitudes.

hep-ph↗
arXiv2004

Implications of CP Asymmetries in $B \to π^+ π^-$

CP asymmetries in $B^0(t)\to π^+ π^-$ are studied by relating this process in broken flavor SU(3) with $B^+\to K^0π^+$ and $B^0\to K^+π^-$. Using two different scenarios for SU(3) breaking, we show that the range of values of the weak phase $α$ permitted by the measured asymmetries overlaps with that obtained from other CKM constraints, supporting the KM origin of the asymmetries. We evaluate the potential precision of this method to improve the determination of $α$.

hep-ph↗
arXiv2004

Charmless $B \to PP$ decays using flavor SU(3) symmetry

The decays of $B$ mesons to a pair of charmless pseudoscalar ($P$) mesons are analyzed within a framework of flavor SU(3). Symmetry breaking is taken into account in tree ($T$) amplitudes through ratios of decay constants; exact SU(3) is assumed elsewhere. Acceptable fits to $B \to ππ$ and $B \to K π$ branching ratios and CP asymmetries are obtained with tree, color-suppressed ($C$), penguin ($P$), and electroweak penguin ($P_{EW}$) amplitudes. Crucial additional terms for describing processes involving $η$ and $η'$ include a large flavor-singlet penguin amplitude ($S$) as proposed earlier and a penguin amplitude $P_{tu}$ associated with intermediate $t$ and $u$ quarks. For the $B^+ \to π^+ η'$ mode a term $S_{tu}$ associated with intermediate $t$ and $u$ quarks also may be needed. Values of the weak phase $γ$ are obtained consistent with an earlier analysis of $B \to VP$ decays, where $V$ denotes a vector meson, and with other analyses of CKM parameters.

hep-ph↗
arXiv2003

Interpreting the time-dependent CP asymmetry in $B^0 \to π^0 K_S$

Flavor SU(3) is used for studying the time-dependent CP asymmetry in $B^0 \to π^0 K_S$ by relating this process to $B^0\to π^0π^0$ and $B^0 \to K^+K^-$. We calculate correlated bounds on $S_{πK} - \sin 2β$ and $C_{πK}$, with maximal magnitudes of 0.2 and 0.3, where $S_{πK}$ and $C_{πK}$ are coefficients of $\sinΔmt$ and $\cosΔmt$ in the asymmetry. Stronger upper limits on $B^0 \to K^+K^-$ are expected to reduce these bounds and to imply nonzero lower limits on these observables. The asymmetry is studied as a function of a strong phase and the weak phase $γ$.

hep-ph↗
arXiv2003

Charmless $B \to VP$ Decays Using Flavor SU(3) Symmetry

The decays of $B$ mesons to a charmless vector ($V$) and pseudoscalar ($P$) meson are analyzed within a framework of flavor SU(3) in which symmetry breaking is taken into account through ratios of decay constants in tree ($T$) amplitudes. The magnitudes and relative phases of tree and penguin amplitudes are extracted from data; the symmetry assumption is tested; and predictions are made for rates and CP asymmetries in as-yet-unseen decay modes. A key assumption for which we perform some tests and suggest others is a relation between penguin amplitudes in which the spectator quark is incorporated into either a pseudoscalar meson or a vector meson. Values of $γ$ slightly restricting the range currently allowed by fits to other data are favored, but outside this range there remain acceptable solutions which cannot be excluded solely on the basis of present $B \to VP$ experiments.

hep-ph↗
arXiv2003

Rates and Asymmetries in $B \to K π$ Decays

We discuss a potential discrepancy in an approximate relation among $B \to K π$ rates which, with increased statistical significance, would imply new physics in $ΔI=1$ transitions. An approximate relation between CP-violating rate differences in $B^0/\bar{B}^0 \to K^{\pm}π^{\mp}$ and $B^{\pm} \to K^{\pm}π^0$ is used to combine these rate differences to reduce upper limits on the two CP asymmetries. These rates and asymmetries are used to update bounds on the CKM phase $γ$.

hep-ph↗
arXiv2003

Two-Body Charmless B Decays Involving eta and eta'

We discuss implications of recent experimental data for B decays into two pseudoscalar mesons, with emphasis on those with $η$ and $η'$ in the final states. Applying a U-spin argument, we show that tree and penguin amplitudes, both in $B^+ \to π^+ η$ and in $B^+ \to π^+ η'$, are of comparable magnitudes. Nontrivial relative weak and strong phases between the tree-level amplitudes and penguin-loop amplitudes in the $B^{\pm} \to π^{\pm} η$ modes are extracted. We predict possible values for the averaged branching ratio and CP asymmetry of the $B^{\pm} \to π^{\pm} η'$ modes. We test the assumption of a singlet-penguin amplitude with the same weak and strong phases as the QCD penguin in explaining the large branching ratios of $η' K$ modes, and show that it is consistent with current branching ratio and CP asymmetry data of the $B^+ \to (π^0, η, η') K^+$ modes. We also show that the strong phases of the singlet-penguin and tree-level amplitudes can be extracted with further input of electroweak penguin contributions and a sufficiently well-known branching ratio of the $ηK^+$ mode. Using SU(3) flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.

hep-ph↗
arXiv2003

Phenomenological methods for unitarity triangle angles

I review several methods for determining the CKM phases $α\equiv ϕ_2$ and $γ\equiv ϕ_3$ through CP asymmetry measurements in hadronic B decays. The current status of these measurements and the near future feasibility of the methods are discussed.

hep-ph↗
arXiv2003

I-spin, U-spin, and penguin dominance in $B \to K K \bar K$

Isospin and U-spin symmetries are useful approximations for studying penguin dominance in $B$ meson decays to three kaons, $B\to KK\bar K$. We point out certain subtleties in treating these decays in these approximations. Resulting uncertainties are discussed in determining the CP content of the final state in $B \to K^+K^-K_S$, and in relating the CP asymmetry in this process to the value of $\sin 2β$.

hep-ph↗
arXiv2003

P and CP violation in B Decays

While the Kobayashi--Maskawa model of CP violation passed its first crucial precision test in $B\to J/ψK_S$, other CP asymmetries in $B$ and $B_s$ decays will have to be measured in order to critically test and overconstrain the model in an unambiguous way. On another front, the chirality of weak $b$-quark couplings has not yet been carefully tested. We discuss recent proposals for studying both the chiral and CP-violating phase structures of these couplings in $B\to D^*ρ$ and $B\to D^*a_1$.

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