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Register a new userSU(3) flavor symmetry breaking and semileptonic decays of heavy mesons
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Assuming the ${bar D}^0, D^-, D^-_s$ and $B^+, B^0, B_s^0$ mesons belong to triplets of SU(3) flavor symmetry, we analyse the form factors in the semileptonic decays of these mesons. Both quark and meson mass differences are taken into account. We find a number of relations, in agreement with the present data as well as with previous analyses, and predict certain ratios of form factors, not yet measured, most notably the D meson decay constant $f_D = 209 pm 39$ MeV.
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In this paper, we calculate the decay rates of $D^+ to D^0 e^+ u$, $D^+_S to D^0 e^+ u$, $B^0_S to B^+ e^- bar{ u}$, $D^+_S to D^+ e^- e^+$ and $B^0_S to B^0 e^-e^+$ semileptonic decay processes, in which only the light quarks decay, while the heavy flavors remain unchanged. The branching ratios of these decay processes are calculated with the flavor SU(3) symmetry. The uncertainties are estimated by considering the SU(3) breaking effect. We find that the decay rates are very tiny in the framework of the Standard Model. We also estimate the sensitivities of the measurements of these rare decays at the future experiments, such as BES-III, super-$B$ and LHC-$b$.
We study the three-body anti-triplet ${bf B_c}to {bf B_n}MM$ decays with the $SU(3)$ flavor ($SU(3)_f$) symmetry, where ${bf B_c}$ denotes the charmed baryon anti-triplet of $(Xi_c^0,-Xi_c^+,Lambda_c^+)$, and ${bf B_n}$ and $M(M)$ represent baryon and meson octets, respectively. By considering only the S-wave $MM$-pair contributions without resonance effects, the decays of ${bf B_c}to {bf B_n}MM$ can be decomposed into irreducible forms with 11 parameters under $SU(3)_f$, which are fitted by the 14 existing data, resulting in a reasonable value of $chi^2/d.o.f=2.8$ for the fit. Consequently, we find that the triangle sum rule of ${cal A}(Lambda_c^+to nbar K^0 pi^+)-{cal A}(Lambda_c^+to pK^- pi^+)-sqrt 2 {cal A}(Lambda_c^+to pbar K^0 pi^0)=0$ given by the isospin symmetry holds under $SU(3)_f$, where ${cal A}$ stands for the decay amplitude. In addition, we predict that ${cal B}(Lambda_c^+to n pi^{+} bar{K}^{0})=(0.9pm 0.8)times 10^{-2}$, which is $3-4$ times smaller than the BESIII observation, indicating the existence of the resonant states. For the to-be-observed ${bf B_c}to {bf B_n}MM$ decays, we compute the branching fractions with the $SU(3)_f$ amplitudes to be compared to the BESIII and LHCb measurements in the future.
The semileptonic decays and two-body nonleptonic decays of light baryon octet ($T_8$) and decuplet ($T_{10}$) consisting of light $u,d,s$ quarks are studied with the SU(3) flavor symmetry in this work. We obtain the amplitude relations between different decay modes by the SU(3) irreducible representation approach, and then predict relevant branching ratios by present experimental data within $1 sigma$ error. We find that the predictions for all branching ratios except $mathcal{B}(Xirightarrow Lambda^0pi)$ and $mathcal{B}(Xi^*rightarrow Xipi)$ are in good agreement with present experimental data, that implies the neglected $C_+$ terms or SU(3) breaking effects might contribute at the order of a few percent in $Xirightarrow Lambda^0pi$ and $Xi^*rightarrow Xipi$ weak decays. We predict that $mathcal{B}(Xi^{-}rightarrow Sigma^0mu^-bar{ u}_mu)=(1.13pm0.08)times10^{-6}$, $mathcal{B}(Xi^{-}rightarrowLambda^0mu^-bar{ u}_mu)=(1.58pm0.04)times10^{-4}$, $mathcal{B}(Omega^-rightarrowXi^0mu^-bar{ u}_mu)=(3.7pm1.8)times10^{-3}$, $mathcal{B}(Sigma^-rightarrow Sigma^0e^-bar{ u}_e)=(1.35pm0.28)times10^{-10}$, $mathcal{B}(Xi^-rightarrow Xi^0e^-bar{ u}_e)=(4.2pm2.4)times10^{-10}$. We also study $T_{10}to T_8 P_8$ weak, electromagnetic or strong decays. Some of these decay modes could be observed by the BESIII, LHCb and other experiments in the near future. Due to the very small life times of $Sigma^0$, $Xi^{*0,-}$, $Sigma^{*0,-}$ and $Delta^{0,-}$, the branching ratios of these baryon weak decays are only at the order of $mathcal{O}(10^{-20}-10^{-13}$), which are too small to be reached by current experiments. Furthermore, the longitudinal branching ratios of $T_{8A} to T_{8B} ell^- bar{ u}_ell~(ell=mu,e)$ decays are also given.
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.
We present the first three-flavor lattice QCD calculations for $Dto pi l u$ and $Dto K l u$ semileptonic decays. Simulations are carried out using ensembles of unquenched gauge fields generated by the MILC collaboration. With an improved staggered action for light quarks, we are able to simulate at light quark masses down to 1/8 of the strange mass. Consequently, the systematic error from the chiral extrapolation is much smaller than in previous calculations with Wilson-type light quarks. Our results for the form factors at $q^2=0$ are $f_+^{Dtopi}(0)=0.64(3)(6)$ and $f_+^{Dto K}(0) = 0.73(3)(7)$, where the first error is statistical and the second is systematic, added in quadrature. Combining our results with experimental branching ratios, we obtain the CKM matrix elements $|V_{cd}|=0.239(10)(24)(20)$ and $|V_{cs}|=0.969(39)(94)(24)$, where the last errors are from experimental uncertainties.
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