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Register a new userAddendum to High order U-spin breaking: A precise amplitude relation in D0 decays
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Michael Gronau
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Complete error analysis for first high-precision flavor test in D decays
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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 states 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.
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.
Some years ago, a method was proposed for measuring the CP-violating phase gamma using pairs of two-body decays that are related by U-spin reflection (d <-> s). In this paper we adapt this method to charmless B -> PPP decays. Time-dependent Dalitz-plot analyses of these three-body decays are required for the measurement of the mixing-induced CP asymmetries. However, isobar analyses of the decay amplitudes are not necessary. A potential advantage of using three-body decays is that the effects of U-spin breaking may be reduced by averaging over the Dalitz plot. This can be tested independently using the measurements of direct CP asymmetries and branching ratios in three-body charged B decays.
Data on Ke4 decays allow one to extract experimental information on the elastic pi pi scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin breaking effects - generated by electromagnetic interactions and by the mass difference of the up and down quarks - are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin breaking effect in Ke4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on Ke4 decays and the prediction of pi pi scattering lengths disappears.
In this addendum to arXiv:1811.09603 we update our results including the recent measurement of ${cal R}(D)$ and ${cal R}(D^*)$ by the Belle collaboration: ${cal R}(D)_{rm Belle} = 0.307pm0.037pm0.016$ and ${cal R}(D^*)_{rm Belle}=0.283pm0.018pm0.014$, resulting in the new HFLAV fit result ${cal R}(D) = {0.340pm0.027 pm 0.013}$, ${cal R}(D^*) = {0.295pm0.011 pm 0.008 }$, exhibiting a $3.1,sigma$ tension with the Standard Model. We present the new fit results and update all figures, including the relevant new collider constraints. The updated prediction for ${cal R}(Lambda_c)$ from our sum rule reads ${cal R}(Lambda_c)= mathcal{R}_{rm SM}(Lambda_c) left( 1.15 pm 0.04 right) = 0.38 pm 0.01 pm 0.01$. We also comment on theoretical predictions for the fragmentation function $f_c$ of $bto B_c$ and their implication on the constraint from $B_{u/c}totau u$ data.
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