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Register a new userSU(3) flavor symmetry considerations for the $bar{K}N$ coupled channels system
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We study the impact of SU(3) flavor symmetry breaking on the properties of dynamically generated $Lambda^*$ states within an effective separable potential model describing the coupled channels $bar{K}N$ system. The model is based on the chiral meson-baryon Lagrangian at next-to-leading order, and constitutes an improvement over a previous model developed by our group, with its applicability being extended to higher energies covering the $Lambda(1670)$ resonance region. It is demonstrated that the ratios of channel couplings to the resonant states can vary dramatically when the flavor breaking is gradually switched off, tracing a path to the restored SU(3) symmetry. We conclude that the couplings determined from physical observables cannot be used to reliably relate a given resonance to a specific flavor multiplet.
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We investigate the $bar KN$ and coupled channels system in a finite volume and study the properties of the $Lambda(1405)$ resonance. We calculate the energy levels in a finite volume and solve the inverse problem of determining the resonance position in the infinite volume. We devise the best strategy of analysis to obtain the two poles of the $Lambda(1405)$ in the infinite volume case, with sufficient precision to distinguish them.
Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interactions
The weak and electromagnetic radiative baryon decays of octet $T_{8}$, decuplet $T_{10}$, single charmed anti-triplet $T_{c3}$ and sextet $T_{c6}$, single heavy bottomed anti-triplet $T_{b3}$ and sextet $T_{b6}$ are investigated by using SU(3) flavor symmetry irreducible representation approach. We analyze the contributions from a single quark transition $q_1to q_2gamma$ and $W$ exchange transitions, and find that the amplitudes could be easily related by SU(3) flavor symmetry in the $T_{b3,b6}$ weak radiative decays, $T_{c3,c6}$ weak radiative decays, $T_{10}to T_{8}gamma $ weak decays, $T_{10}to T_{10}gamma $ weak decays and $T_{10}to T_{8}gamma $ electromagnetic decays. Nevertheless, the amplitude relations are a little complex in the $T_{8}to T_{8}gamma$ and $T_{8}to T_{10}gamma$ weak decays due to quark antisymmetry in $T_{8}$ and $W$ exchange contributions. Predictions for branching ratios of $Lambda^{0}_bto ngamma$, $Xi^{-}_bto Xi^-gamma$, $Xi^{-}_bto Sigma^-gamma$, $Xi^{0}_bto Sigma^0gamma$, $Xi^{0}_bto Lambda^0gamma$, $Xi^{0}_bto Xi^0gamma$, $Xi^{*}to Xigamma$, $Sigma^{*0}to Sigma^{0}gamma$, $Delta^0to ngamma$ and $Delta^+to pgamma$ are given. The results in this work can be used to test SU(3) flavor symmetry approach in the radiative baryon decays by the future experiments at BESIII, LHCb and Belle-II.
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.
In this work, an Effective Field Theory (EFT) incorporating light SU(3)-flavour and heavy quark spin symmetry is used to describe charmed meson-antimeson bound states. At Lowest Order (LO), this means that only contact range interactions among the heavy meson and antimeson fields are involved. Besides, the isospin violating decays of the X(3872) will be used to constrain the interaction between the $D$ and a $bar{D}^*$ mesons in the isovector channel. Finally, assuming that the X(3915) and Y(4140) resonances are $D^*bar{D}^*$ and $D_s^*bar{D}_s^*$ molecular states, we can determine the four Low Energy Constants (LECs) of the EFT that appear at LO and, therefore, the full spectrum of molecular states with isospin I=0, 1/2 and 1.
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