arXiv subjects
Publications and source records attributed to Michael Gronau.
An earlier analysis of observed and anticipated $Λ_c$ decays [M. Gronau and J. L. Rosner, Phys.\ Rev.\ D {\bf 97}, 116015 (2018)] is provided with a table of inputs and a figure denoting branching fractions. This addendum is based on the 2018 Particle Data Group compilation and employs a statistical isospin model to estimate branching fractions for as-yet-unseen decay modes.
The decays of the ground-state charmed baryon $Λ_c$ are now close to being completely mapped out. In this paper we discuss some remaining open questions, whose answers can help shed light on weak processes contributing to those decays, on calculations of such quantities as transition form factors in lattice QCD, and on missing decay modes such as $Λ_c \to Λ^* \ell^+ ν_\ell$, where $Λ^*$ is an excited resonance. The discussion is in part a counterpart to a previous analysis of inclusive $D_s$ decays.
We reexamine, update and extend a suggestion we made fifteen years ago for measuring the photon polarization in $b \to sγ$ by observing in $B \to Kππγ$ an asymmetry of the photon with respect to the $Kππ$ plane. Asymmetries are calculated for different charged final states due to intermediate $K_1(1400)$ and $K_1(1270)$ resonant states. Three distinct interference mechanisms are identified contributing to asymmetries at different levels for these two kaon resonances. For $K_1(1400)$ decays including a final state $π^0$ an asymmetry around $+30\%$ is calculated, dominated by interference of two intermediate $K^*π$ states, while an asymmetry around $+10\%$ in decays including final $π^+π^-$ is dominated by interference of $S$ and $D$ wave $K^*π$ amplitudes. In decays via $K_1(1270)$ to final states including a $π^0$ a negative asymmetry is favored up to $-10\%$ if one assumes $S$ wave dominance in decays to $K^*π$ and $Kρ$, while in decays involving $π^+π^-$ the asymmetry can vary anywhere in the range $-13\%$ to $+24\%$ depending on unknown phases. For more precise asymmetry predictions in the latter decays we propose studying phases in $K_1 \to K^*π, Kρ$ by performing dedicated amplitude analyses of $B\to J/ψ(ψ') Kππ$. In order to increase statistics in studies of $B\to Kππγ$ we suggest using isospin symmetry to combine in the same analysis samples of charged and neutral $B$ decays.
It has been pointed out that the currently most precise determination of the weak phase $ϕ_2 = α$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix achieved in $B \to ρρ$ decays is susceptible to a small correction at a level of $(Γ_ρ/m_ρ)^2$ due to an $I=1$ amplitude caused by the $ρ$ width. Using Breit-Wigner distributions for the two pairs of pions forming $ρ$ mesons, we study the $I=1$ contribution to $B\to ρρ$ decay rates as function of the width and location of the $ρ$ band. We find that in the absence of a particular enhancement of the $I=1$ amplitude reducing a single band to a width $Γ_ρ$ at SuperKEKB leads to results which are completely insensitive to the $ρ$ width. If the $I=1$ amplitude is dynamically enhanced relative to the $I=0,2$ amplitude one could subject its contribution to a "magnifying glass" measurement using two separated $ρ$ bands of width $Γ_ρ$. Subtraction of the $I=1$ contribution from the measured decay rate would lead to a very precise determination of the $I=0,2$ amplitude needed for performing the isospin analysis.
CP-violating asymmetries in $B \to ππ$ and $B \to ρρ$ decays can help specify the weak phase $ϕ_2 = α$ of the Cabibbo-Kobayashi-% Maskawa (CKM) matrix. We discuss the impact of improved measurements of these processes such as will be available in the near future, finding special value in better measurement of the time-dependent CP violation parameter $S_{00}$ in $B^0 \to π^0 π^0$ and $B^0 \to ρ^0 ρ^0$. Reducing the errors on $B \to ρρ$ measurements by a factor of two can potentially lead to an error in $ϕ_2 = α$ just above $2^\circ$, at which level isospin-breaking corrections must be considered.
Using a successful framework for describing S-wave hadronic decays of light hyperons induced by a subprocess $s \to u (\bar u d)$, we presented recently a model-independent calculation of the amplitude and branching ratio for $Ξ^-_b \to Λ_b π^-$ in agreement with a LHCb measurement. The same quark process contributes to $Ξ^0_c \to Λ_c π^-$, while a second term from the subprocess $cs \to cd$ has been related by Voloshin to differences among total decay rates of charmed baryons. We calculate this term and find it to have a magnitude approximately equal to the $s \to u (\bar u d)$ term. We argue for a negligible relative phase between these two contributions, potentially due to final state interactions. However, we do not know whether they interfere destructively or constructively. For constructive interference one predicts ${\cal B}(Ξ_c^0 \to Λ_c π^-) = (1.94 \pm 0.70)\times 10^{-3}$ and ${\cal B}(Ξ_c^+ \to Λ_c π^0) = (3.86 \pm 1.35)\times 10^{-3}$. For destructive interference, the respective branching fractions are expected to be less than about $10^{-4}$ and $2 \times 10^{-4}$.
The decay $Ξ^-_b \to π^- Λ_b$ has recently been observed by the LHCb Collaboration at CERN. In contrast to most weak decays of $b$-flavored baryons, this process involves the decay of the strange quark in $Ξ_b$, and thus has features in common with nonleptonic weak decays of hyperons. Thanks to the expected pure S-wave nature of the decay in question in the heavy $b$ quark limit, we find that its amplitude may be related to those for S-wave nonleptonic decays of $Λ$, $Σ$, and $Ξ$ in a picture inspired by duality. The calculated branching fraction ${\cal B}(Ξ^-_b \to π^- Λ_b) = (6.3 \pm 4.2) \times 10^{-3}$ is consistent with the range allowed in the LHCb analysis. The error is dominated by an assumed 30\% uncertainty in the amplitude due to possible U(3) violation. A more optimistic view based on sum rules involving nonleptonic hyperon decay S-wave amplitudes reduces the error on the branching fraction to $2.0 \times 10^{-3}$.
The decay $D^0 \to π^+ π^- π^0$ appears to be dominated by $ρπ$ states in a configuration of zero total isotopic spin. The spin $J$, parity $P$, and charge-conjugation eigenvalue $C$ of this final state are therefore $J^{PC} = 0^{--}$, which cannot be formed of a quark $q$ and antiquark $\bar q$. If a resonance near $M(D^0)$ dominates the final state, it must be a {\it hybrid} composed of a quark-antiquark pair and a constituent gluon, or a {\it tetraquark} $q q \bar q \bar q$. A test for this resonance in electroproduction is proposed.
We show that a contribution due to a second order amplitude with intermediate $\bar u d$ in a loop, which was claimed by Descotes-Genon and Kamenik to dominate the CP asymmetry in $b \to c \ell ν$, vanishes.
The LHCb experiment is capable of studying four-body decays of the $b$-flavored baryons $Λ_b$ and $Ξ_b^0$ to charmless final states consisting of charged pions, kaons, and baryons. We remark on the search in such modes for CP-violating triple product asymmetries and for CP rate asymmetries relative to decays involving charmed baryons.
Flavor SU(3) symmetry, including $30\%$ first order SU(3) breaking, has been shown to describe adequately a vast amount of data for charmed meson decays to two pseudoscalar mesons and to a vector and a pseudoscalar meson. We review a recent dramatic progress achieved by applying a high order perturbation expansion in flavor SU(3) breaking and treating carefully isospin breaking. We identify a class of U-spin related $D^0$ decays to pairs involving charged pseudoscalar or vector mesons, for which high-precision nonlinear amplitude relations are predicted. Symmetry breaking terms affecting these relations are fourth order U-spin breaking, and terms which are first order in isospin breaking and second order in U-spin breaking. The predicted relations are shown to hold experimentally at a precision varying between $10^{-3}$ and $10^{-4}$, in agreement with estimates of high order terms. We also discuss amplitude relations for $D^0$ decays to pairs of neutral pseudoscalar mesons, and relations for rate asymmetries between decays involving $K^0_S$ and $K^0_L$ which hold up to second order U-spin breaking.
Recently we derived a nonlinear U-spin amplitude relation for $D^0\to P^+P^-$, $P=π, K$, predicted to hold up to fourth order U-spin breaking terms of order $10^{-3}$. Here we study a similar relation for $D^0\to V^+P^-, V =ρ, K^*(892), P = π, K$, expected to hold at an even higher accuracy of order $10^{-4}$. We confirm this prediction in spite of a large experimental error of about 20% in the amplitude of $D^0\to K^{*+}π^-$. We also comment briefly on U-spin breaking in $D^0\to P^+V^-$.
Complete error analysis for first high-precision flavor test in D decays
In charmless B -> PPP decays, where P is a pseudoscalar meson, there are six possibilities for the symmetry of the final state. In this paper, for P=pi,K, we examine the properties of the fully-symmetric final state. We present expressions for all 32 B -> PPP decay amplitudes as a function of both SU(3) reduced matrix elements and diagrams, demonstrating the equivalence of diagrams and SU(3). We also give 25 relations among the amplitudes in the SU(3) limit, as well as those that appear when the diagrams E/A/PA are neglected. In the SU(3) limit, one has the equalities \sqrt{2} A(B+ -> K+ pi+ pi-)_{FS} = A(B+ -> K+ K+ K-)_{FS} and \sqrt{2} A(B+ -> pi+ K+ K-)_{FS} = A(B+ -> pi+ pi+ pi-)_{FS}, where FS denotes the fully-symmetric final state. These provide good tests of the standard model that can be carried out now by the LHCb Collaboration.
Some flavor SU(3) results are presented for decays of the $Λ_b$ baryon into non-charmed final states $PB$, where $P$ is a pseudoscalar mesons and $B$ is a spin-1/2 baryon. Although these relations are among amplitudes and hence not yet subject to direct experimental test, they can form the basis for triangle inequalities among decay rates.
U-spin symmetry predicts equal CP rate asymmetries with opposite signs in pairs of $ΔS=0$ and $ΔS=1$ $B$ meson decays in which initial and final states are related by U-spin reflection. Of particular interest are six decay modes to final states with pairs of charged pions or kaons, including $B_s \to π^+K^-$ and $B_s\to K^+K^-$ for which asymmetries have been reported recently by the LHCb collaboration. After reviewing the current status of these predictions, highlighted by the precision of a relation between asymmetries in $B_s \to π^+K^-$ and $B^0\to K^+π^-$, we perform a perturbative study of U-spin breaking corrections, searching for relations for combined asymmetries which hold to first order. No such relation is found in these six decays, in two-body decays involving a neutral kaon, and in three-body $B^+$ decays to charged pions and kaons.
CP asymmetries have been measured recently by the LHCb collaboration in three-body $B^+$ decays to final states involving charged pions and kaons. Large asymmetries with opposite signs at a level of about 60% have been observed in $B^\pm\to π^\pm({\rm or} K^\pm)π^+π^-$ and $B^\pm \to π^\pm K^+K^-$ for restricted regions in the Dalitz plots involving $π^+π^-$ and $K^+K^-$ with low invariant mass. U-spin is shown to predict corresponding $ΔS=0$ and $ΔS=1$ asymmetries with opposite signs and inversely proportional to their branching ratios, in analogy with a successful relation predicted thirteen years ago between asymmetries in $B_s\to K^-π^+$ and $B^0 \to K^+ π^-$. We compare these predictions with the measured integrated asymmetries. Effects of specific resonant or non-resonant partial waves on enhanced asymmetries for low-pair-mass regions of the Dalitz plot are studied in $B^\pm \to π^\pm π^+π^-$. The closure of low-mass $π^+π^-$ and $K^+K^-$ channels involving only $ππ\leftrightarrow K\bar K$ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in $B^\pm\to π^\pmπ^+π^-$ and $B^\pm \to π^\pm K^+K^-$.
A difference of several tenths of a percent has been observed between the direct CP asymmetries of $D^0\to K^+K^-$ and $D^0\to π^+π^-$. It has been noted recently that CP asymmetries in such singly-Cabibbo-suppressed (SCS) decays can affect the determination of the weak phase $γ$ using the Gronau-London-Wyler method of comparing rates for $B^+ \to D K^+$ and $B^- \to D K^-$, where $D$ is a superposition of $D^0$ and $\od$ decaying to a CP eigenstate. Using an analysis of the CP asymmetries in SCS decays based on a $c \to u$ penguin amplitude with standard model weak phase but enhanced by CP-conserving strong interactions, we estimate typical shifts in $γ$ of several degrees and pinpoint measurements which would reduce uncertainties to an acceptable level.