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Register a new userSU(3) in D decays: From $30%$ symmetry breaking to $10^{-4}$ precision
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Michael Gronau
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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.
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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.
The validity of SU(4)-flavor symmetry relations of couplings of charmed $D$ mesons to light mesons and baryons is examined with the use of $^3{rm P}_0$ quark-pair creation model and nonrelativistic quark model wave functions. We focus on the three-meson couplings $pipirho$, $KKrho$ and $DDrho$ and baryon-baryon-meson couplings $NNpi$, $NLambda K$ and $NLambda_c D$. It is found that SU(4)-flavor symmetry is broken at the level of 30% in the $DDrho$ tree-meson couplings and 20% in the baryon-baryon-meson couplings. Consequences of these findings for DN cross sections and existence of bound states D-mesons in nuclei are discussed.
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.
By extending the SU(3) flavour symmetry breaking expansion from up, down and strange sea quark masses to partially quenched valence quark masses we propose a method to determine charmed quark hadron masses including possible QCD isospin breaking effects. Initial results for some open charmed pseudoscalar meson states and singly and doubly charmed baryon states are encouraging and demonstrate the potential of the procedure. Essential for the method is the determination of the scale using singlet quantities, and to this end we also give here a preliminary estimation of the recently introduced Wilson flow scales.
We find expressions for the weak decay amplitudes of baryons containing two b quarks (or one b and one c quark -- many relationship are the same) in terms of unknown reduced matrix elements. This project was originally motivated by the request of the FNAL Run II b Physics Workshop organizers for a guide to experimentalists in their search for as yet unobserved hadrons. We include an analysis of linear SU(3) breaking terms in addition to relationships generated by unbroken SU(3) symmetry, and relate these to expressions in terms of the complete set of possible reduced matrix elements.
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