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 f
or 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.
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 $(Gamma_rho/m_rh
o)^2$ 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.
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 $2 times 10^{-4}$.
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.
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 p
rogress 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 $D^0to P^+P^-$, $P=pi, K$, predicted to hold up to fourth order U-spin breaking terms of order $10^{-3}$. Here we study a similar relation for $D^0to V^+P^-, V =rho, K^*(892), P = pi, K$,
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 $D^0to K^{*+}pi^-$. We also comment briefly on U-spin breaking in $D^0to P^+V^-$.
A U-spin relation among four ratios of amplitudes for $D^0 to pi^+K^-$, $K^+pi^-$, $K^+K^-, pi^+pi^-$, including first, second and third order U-spin breaking, has been derived recently with a precision of $10^{-3}$. We study effects of new $|Delta C
|=1$ operators on this relation. We find that it is not affected by U-spin scalar operators, including QCD penguin and chromomagnetic dipole operators occurring in supersymmetric and extra-dimensional models. The relation is modified by new $U=1$ operators with a sensitivity of a few percent characteristic of second order U-spin breaking. Combining this relation with CP asymmetries in $D^0to K^+K^-, pi^+pi^-$ leads to a more solid constraint on $U=1$ operators than from asymmetries alone.
Complete error analysis for first high-precision flavor test in D decays
U-spin symmetry predicts equal CP rate asymmetries with opposite signs in pairs of $Delta S=0$ and $Delta S=1$ $B$ meson decays in which initial and final states are related by U-spin reflection. Of particular interest are six decay modes to final st
ates with pairs of charged pions or kaons, including $B_s to pi^+K^-$ and $B_sto K^+K^-$ 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 $B_s to pi^+K^-$ and $B^0to K^+pi^-$, 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 $B^pmto pi^pm({rm o
r} K^pm)pi^+pi^-$ and $B^pm to pi^pm K^+K^-$ for restricted regions in the Dalitz plots involving $pi^+pi^-$ and $K^+K^-$ with low invariant mass. U-spin is shown to predict corresponding $Delta S=0$ and $Delta S=1$ asymmetries with opposite signs and inversely proportional to their branching ratios, in analogy with a successful relation predicted thirteen years ago between asymmetries in $B_sto K^-pi^+$ and $B^0 to K^+ pi^-$. 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 $B^pm to pi^pm pi^+pi^-$. The closure of low-mass $pi^+pi^-$ and $K^+K^-$ channels involving only $pipi leftrightarrow Kbar K$ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in $B^pmto pi^pmpi^+pi^-$ and $B^pm to pi^pm K^+K^-$.
