Addendum to Overview of $Lambda_c$ decays

An earlier analysis of observed and anticipated $Lambda_c$ 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.

An overview of $Lambda_c$ decays

The decays of the ground-state charmed baryon $Lambda_c$ 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 $Lambda_c to Lambda^* ell^+ u_ell$, where $Lambda^*$ is an excited resonance. The discussion is in part a counterpart to a previous analysis of inclusive $D_s$ decays.

Reexamining the photon polarization in $Bto Kpipigamma$

We reexamine, update and extend a suggestion we made fifteen years ago for measuring the photon polarization in $b to sgamma$ by observing in $B to Kpipigamma$ an asymmetry of the photon with respect to the $Kpipi$ 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 $pi^0$ an asymmetry around $+30%$ is calculated, dominated by interference of two intermediate $K^*pi$ states, while an asymmetry around $+10%$ in decays including final $pi^+pi^-$ is dominated by interference of $S$ and $D$ wave $K^*pi$ amplitudes. In decays via $K_1(1270)$ to final states including a $pi^0$ a negative asymmetry is favored up to $-10%$ if one assumes $S$ wave dominance in decays to $K^*pi$ and $Krho$, while in decays involving $pi^+pi^-$ 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 $K_1 to K^*pi, Krho$ by performing dedicated amplitude analyses of $Bto J/psi(psi) Kpipi$. In order to increase statistics in studies of $Bto Kpipigamma$ we suggest using isospin symmetry to combine in the same analysis samples of charged and neutral $B$ decays.

Controlling $rho$ width effects for a precise value of $alpha$ in $B to rho rho$

It has been pointed out that the currently most precise determination of the weak phase $phi_2 = alpha$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix achieved in $B to rhorho$ decays is susceptible to a small correction at a level of $(Gamma_rho/m_rho)^2$ due to an $I=1$ amplitude caused by the $rho$ width. Using Breit-Wigner distributions for the two pairs of pions forming $rho$ mesons, we study the $I=1$ contribution to $Bto rhorho$ decay rates as function of the width and location of the $rho$ band. We find that in the absence of a particular enhancement of the $I=1$ amplitude reducing a single band to a width $Gamma_rho$ at SuperKEKB leads to results which are completely insensitive to the $rho$ 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 $rho$ bands of width $Gamma_rho$. 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.

Improving the measurement of the CKM phase $phi_2 = alpha$ in $B to pi pi$ and $B to rho rho$ decays

CP-violating asymmetries in $B to pi pi$ and $B to rho rho$ decays can help specify the weak phase $phi_2 = alpha$ 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 $B^0 to pi^0 pi^0$ and $B^0 to rho^0 rho^0$. Reducing the errors on $B to rho rho$ measurements by a factor of two can potentially lead to an error in $phi_2 = alpha$ just above $2^circ$, at which level isospin-breaking corrections must be considered.

From $Xi_b to Lambda_b pi$ to $Xi_c to Lambda_c pi$

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 $Xi^-_b to Lambda_b pi^-$ in agreement with a LHCb measurement. The same quark process contributes to $Xi^0_c to Lambda_c pi^-$, 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 ${cal B}(Xi_c^0 to Lambda_c pi^-) = (1.94 pm 0.70)times 10^{-3}$ and ${cal B}(Xi_c^+ to Lambda_c pi^0) = (3.86 pm 1.35)times 10^{-3}$. For destructive interference, the respective branching fractions are expected to be less than about $10^{-4}$ and $2 times 10^{-4}$.

S-wave nonleptonic hyperon decays and $Xi^-_b to pi^- Lambda_b$

The decay $Xi^-_b to pi^- Lambda_b$ 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 $Xi_b$, 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 $Lambda$, $Sigma$, and $Xi$ in a picture inspired by duality. The calculated branching fraction ${cal B}(Xi^-_b to pi^- Lambda_b) = (6.3 pm 4.2) times 10^{-3}$ 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 $2.0 times 10^{-3}$.

Comment on A possible explanation of the D0 like-sign dimuon charge aymmetry

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 $b to c ell u$, vanishes.

Test for exotic isoscalar resonance dominating $D^0 to pi^+ pi^- pi^0$ decays

The decay $D^0 to pi^+ pi^- pi^0$ appears to be dominated by $rho pi$ 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.

Triple product asymmmetries in $Lambda_b$ and $Xi_b$ decays

The LHCb experiment is capable of studying four-body decays of the $b$-flavored baryons $Lambda_b$ and $Xi_b^0$ 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.