The magnetic moment---a function of the electric charge form factor $F_{1}(q^{2})$ and the magnetic dipole form factor $F_{2}(q^{2})$ at zero four-momentum transfer $q^{2}$---of the ground-state $U$-spin =3/2 baryon decuplet $Δ^{-}$, $Ξ^{*\,-}$, $Σ^{*\,-}$ and $Ω^{-}$ and their ground-state spin 1/2 cousins $p$, $n$, $Λ$, $Σ^{+}$, $Σ^{0}$, $Σ^{-}$, $Ξ^{+}$, and $Ξ^{-}$ have been studied for many years with a modicum of success---only the magnetic moment of the $Ω^{-}$ has been accurately determined. In a recent study by us utilizing the infinite momentum frame, we calculated the magnetic moments of the \emph{physical} decuplet $U$-Spin =3/2 quartet members in terms of that of the $Ω^{-}$ without ascribing any specific form to their quark structure or intra-quark interactions. That study determined $F_{2}(q^{2})$ and was conducted nonperturbatively where the decuplet baryon momenta were all collinear. In this follow-up research---again utilizing the infinite momentum frame but now allowing for non-collinear momenta---we are able to determine $F_{1}(q^{2})$ where $q^{2}\leq 0$. We relate the electric charge form factor $F_{1}(q^{2})$ of the \emph{physical} decuplet $S\neq -3$, $U$-spin =3/2 quartet members to that of the $Ω^{-}$ ($S=-3$).
Axial-vector transitions of decuplet to octet baryons are parametrized at low energies guided by a complete and minimal chiral Lagrangian up to next-to-leading order. It is pointed out that beyond the well-known leading-order term, there is only one contribution at next-to-leading order. This contribution is flavor symmetric. Therefore the corresponding low-energy constant can be determined in any strangeness sector. As functions of this low-energy constant, we calculate the decay widths and Dalitz distributions for the decays of decuplet baryons to octet baryons, pions, and photons and for th…
The thermal properties of the light decuplet baryons are investigated in the framework of the thermal QCD sum rules. In particular, the behavior of the mass and residue of the $Δ$, $Σ^{*}$, $Ξ^{*}$ and $Ω$ baryons with respect to temperature are analyzed taking into account the additional operators coming up in the Wilson expansion at finite temperature. It is found that the mass and residue of these particles remain overall unaffected up to $T\simeq150~MeV$ but, beyond this point, they start to diminish, considerably.
Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking
We consider charmless weak decays of beauty-baryons into decuplet baryons and pseudoscalar mesons in a general framework based on $SU(3)$-flavor decomposition of the decay amplitudes. The dynamical assumption independent $SU(3)$ analysis accounts for the effects of an arbitrarily broken $SU(3)$ symmetry in these decays. An alternative approach in terms of quark diagrams is also provided and compared with the $SU(3)$ decomposition in the limit of exact $SU(3)$-flavor symmetry. Furthermore, the symmetries of the effective Hamiltonian is used to relate or neglect reduced $SU(3)$ amplitudes to der…
The ground and first excited states of the decuplet baryons are studied using the two-point QCD sum rule approach. The mass and residue of these states are computed and compared with the existing experimental data and other theoretical predictions. The results for the masses of the ground state particles as well as the excited $ Δ$ and $ Σ^{*} $ states are in good consistency with experimental data. Our results on the excited $ Ξ^{*} $ and $ Ω^{-} $ states reveal that the experimentally poorly known $ Ξ(1950) $ and $ Ω^{-}(2250) $ can be assigned as the first excited states in $ Ξ^{*} $ and $ …
In the present work, the masses of the decuplet baryons at finite temperature are investigated using thermal QCD sum rules. Making use of the quark propagator at finite temperature, we calculate the spectral functions to $T^{8}$ order, and find that there are no contributions to the spectral functions at $T^{8}$ order and the temperature corrections mainly come from that containing $T^4$ ones. The calculations show very little temperature dependence of the masses below $T=0.11{GeV}$. While above that value, the masses decrease with increasing temperature. The results indicate that the hadron-q…
Magnetic dipole moment form factor, $G_M^{(2)}(Q^2)$, describing the radial excitation of decuplet baryons to octet baryons electromagnetic transitions as well as the ratios, $R_{SM} = -\frac{1}{4 m_2^2} \sqrt{4 m_2^2 Q^2 + (m_2^2 - Q^2 -m_1^2)^2} \frac{G_C^{(2)}(Q^2)}{G_M^{(2)}(Q^2)}$ and $R_{EM} = -\frac{G_E^{(2)}(Q^2)}{G_M^{(2)}(Q^2)}$ are calculated in the framework of light-cone sum rules. We also estimate the degree of the violation of U-spin symmetry. The obtained results for the multipole form factors can be useful in searching the properties of radially excited baryon states.
Effective quark model with chiral U(3)XU(3) symmetry for baryon octet and decuplet
我们提出了一个有效的夸克模型，它适用于由QCD激发的具有线性上升禁闭势的低位重子八重态和十重态，并结合了手征U（3）XU（3）对称性线性实现的扩展Nambu-Jona-Lasinio（ENJL）模型。重子被认为是外部重态，通过ENJL-模型中定义的夸克-介子相互作用与具有固定旋量结构的局部三夸克流耦合并与低位介子耦合。在组分夸克圈表象中，我们计算了（pi NN），（pi N Delta）和（gamma N Delta）相互作用的耦合常数以及（sigma_{πN}）项。所得结果与实验数据和其它有效场论方法相符合。
The magnetic moments of $J^P=\frac{3}{2}^+$ decuplet baryons have been calculated in the chiral constituent quark model ($χ$CQM) with explicit results for the contribution coming from the valence quark polarizations, sea quark polarizations, and their orbital angular momentum. Since the $J^P=\frac{3}{2}^+$ decuplet baryons have short lifetimes, the experimental information about them is limited. The $χ$CQM has important implications for chiral symmetry breaking as well as SU(3) symmetry breaking since it works in the region between the QCD confinement scale and the chiral symmetry breaking sca…
A complete and minimal relativistic Lagrangian is constructed at next-to-leading order for SU(3) chiral perturbation theory in the presence of baryon octet and baryon decuplet states. The Lagrangian has 13 terms for the pure decuplet sector, 6 terms for the transition sector from baryon octet to decuplet and (as already known from the literature) 16 terms for the pure octet sector. The minimal field content of 25 of these terms is meson-baryon four-point interactions. 3 terms give rise to the mass splitting for baryon octet and decuplet states, respectively. 2 terms give rise to overall mass s…
