Baryon Pole Research Articles

Magnetic moments of the spin−1/2 singly charmed baryons in covariant baryon chiral perturbation theory

Recent experimental advances have reignited theoretical interests in heavy-flavor hadrons. In this work, we study the magnetic moments of the spin-1/2 singly charmed baryons up to the next-to-leading order in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme. The pertinent low energy constants $g_{1-4}$ are fixed with the help of the quark model and the heavy quark spin flavor symmetry, while the remaining $d_2$, $d_3$, $d_5$ and $d_6$ are determined by fitting to the lattice QCD pion-mass dependent data. We study the magnetic moments as a function of $m_\pi^2$ and compare our results with those obtained in the heavy baryon chiral perturbation theory. We find that the loop corrections induced by the anti-triplet states are dominated by the baryon pole diagram. In addition, we predict the magnetic moments of the spin-1/2 singly charmed baryons and compare them with those of other approaches.

Role of bare propagator poles in phenomenological Dyson–Schwinger type models

The generation of dressed meson-nucleon scat- tering-matrix poles is presented. A possible scenario for the interrelation of bare and dressed baryon poles is shown by using a particular version of coupled-channel Dyson- Schwinger type model. These findings are then applied to the Roper resonance, and the conclusion is drawn that it is dynamic in nature. A possible correlation between bare and dressed propagator poles on one side and the quantities of constituent quark-model calculations on the other side are discussed.

Radiative Decays of the K-p System in the Baryon Pole Model

The radiative widths of K−p→ Λγ and K−p→ Σγ decays are estimated within the baryon pole model and are compared with recent experimental rates. In the present calculation the role of the vector meson K1(1270) is shown to be important for the consistent agreement with the experimental data, subsidiary to the significance of Λ(1405) exchange from the parity conservation. Our results are presented for both of pseudoscalar and pseudovector couplings and are compared with those of other model calculations. Based on these results, discussions are given for estimates of the radiative widths ΓΛ1405→Λγ and ΓΛ1405→Σ0γ .

Penguin-induced radiative baryonic B decays revisited

Weak radiative baryonic B decays B¯→B1B¯2γ mediated by the electromagnetic penguin process b→sγ are re-examined within the framework of the pole model. The meson pole contribution that has been neglected before is taken into account in this work. It is found that the intermediate K∗ contribution dominates in the Σp¯γ mode and is comparable to the baryon pole effect in Λp¯γ and ΞΛ¯γ modes. The branching ratios for B−→Λp¯γ and B−→Ξ0Σ¯−γ are of order 2.6×10−6 and 6×10−7, respectively. The threshold enhancement effect in the dibaryon mass spectrum is responsible by the meson pole diagram. We also study the angular distribution of the baryon in the dibaryon rest frame. The baryon pole diagrams imply that the antibaryon tends to emerge in the direction of the photon in the baryon-pair rest frame. The predicted angular asymmetry agrees with experiment for B−→Λp¯γ. Measurements of the correlation of the photon with the baryon allow us to discriminate between different models for describing the radiative baryonic B decays. For decays B→ΞΣ¯γ, a large correlation of the photon to the Σ¯ and a broad bump in the dibaryon mass spectrum are predicted.

Meson-baryon form factors in the chiral color dielectric model

The renormalized form factors for pseudoscalar meson-baryon coupling are computed in the chiral color dielectric model. This has been done by rearranging the Lippmann-Schwinger series for the meson-baryon scattering matrix so that it can be expressed as a baryon pole term with renormalized form factors and baryon masses and the rest of the terms which arise from the crossed diagrams. Thus we are able to obtain an integral equation for the renormalized meson-baryon form factors in terms of the bare form factors as well as an expression for the meson self-energy. This integral equation is solved, and renormalized meson baryon form factors and renormalized baryon masses are computed. The parameters of the model are adjusted to obtain a best fit to the physical baryon masses. The calculations show that the renormalized form factors are energy dependent and differ from the bare form factors primarily at momentum transfers smaller than 1 GeV. At nucleon mass, the change in the form factors is about 10% at zero momentum transfer. The computed form factors are soft with the equivalent monopole cutoff mass of about 500 MeV. The renormalized coupling constants are obtained by comparing the chiral color dielectric model interaction Hamiltonian with the standard form of the meson-nucleon interaction Hamiltonian. The ratio of $\ensuremath{\Delta}N\ensuremath{\pi}$ and $\mathrm{NN}\ensuremath{\pi}$ coupling constants is found to be about 2.15. This value is very close to the experimental value.

Pole model of B-meson decays into baryon-antibaryon pairs.

We reconsider in detail the pole model for baryonic B decays, first crudely estimated by Deshpande et al. We make a complete calculation on the basis of the quark model by an extensive evaluation of strong- and weak-interaction vertices. We also consider charmed decays, and the previously lacking ${\mathit{J}}^{\mathit{P}}$=1/${2}^{\mathrm{\ensuremath{-}}}$ baryon poles that lead to large parity-violating amplitudes. The strong couplings are calculated in absolute magnitude by our quark-pair-creation model in a crossed channel. The effects of unequal quark masses are fully taken into account, correcting previous published results, and introducing a large set of new calculations for baryon couplings. We emphasize the selection rules and algebraic ratios of rates that follow from either color antisymmetry of the baryon wave functions or from the pole model. We pay particular attention to the ratio of parity-conserving to parity-violating rates, as it enters in tests of CP violation involving modes such as pp\ifmmode\bar\else\textasciimacron\fi{}. At the same time, we make a detailed discussion of the very principles of the pole model, which exhibits a series of yet overlooked problems: ambiguity in the choice of relativistic couplings, extrapolation of strong couplings to complex momentum transfer, and of weak baryon-baryon matrix elements to nonzero and large transfers. For both theoretical and experimental reasons, it is suggested that decays with a \ensuremath{\Delta} are largely overestimated because of a basic weakness of the pole model for high spin. On the other hand, results with 1/${2}^{+}$ baryons in the final state share several features of the QCD-sum-rule calculation by Chernyak and Zhitnisky, while differing in detailed predictions that must await experimental test.

Factorizable and meson-pole contributions to hyperon nonleptonic decays

All vacuum-insertion contributions to hyperon nonleptonic decays can be identified within the framework of current algebra. The contribution to the s-wave amplitude has been identified by Donoghue, Golowich, Holstein, and Ponce. His pointed out that the p-wave factorizable term for the penguin operator which is not normal-ordered emerges from the disconnected contributions to the baryon poles. This separable amplitude is shown to be equivalent to the K-meson pole in the normal-ordering representation. The inclusion of a kaon pole is thus mandatory in the normal ordering scheme, but is negligible if the weak hamiltonian is not normal-ordered.

Nonleptonic hyperon decays-wave amplitudes and negative-parity excited baryons

The contribution of negative-parity excited baryons is calculated and found to be small relative to other contributions (i.e. the equal-time commutator and the vector-meson pole) which have been successfully employed in the recent past. While positive-parity excited baryons help to explainp-wave (B) amplitudes, 1/2− baryon poles do not spoil the existing description ofs-wave (A) amplitudes.

Implications of quantum chromodynamic sum rules for sizes of nucleon andΔbaryon

The residues of the nucleon and $\ensuremath{\Delta}$ baryon poles in the baryonic current propagator are evaluated for the MIT and chiral bag models. It is found that the values obtained with a bag radius of 0.8 to 1 fm match those predicted by the quantum chromodynamic sum rules which take into account the chiral structure of the physical vacuum state. Smaller bag radii give increasingly poorer agreement.

Formula omitted] hyperon decays: A parallel treatment of S- and P-wave amplitudes

The usual description of the S- and P-waves of the non-leptonic hyperon decays (i.e. softpion terms and contribution of the meson topology) is enlarged by including in a parallel way for both waves the baryon pole terms due to the next lowest level of the baryon spectrum: 1 2 − poles of the ( 70 , 1 −) multiplet for the S-waves and 1 2 + poles of the first radially excited ( 56 , 0 +) multiplet for the P-waves. These poles are numerically important, crucial in understanding the relative magnitude of the S- and P-waves, and necessary to reproduce every amplitude to about 10% with only one fitting parameter. Further, a model-independent determination of the meson topology, which avoids the assumption of factorization with vacuum insertion, shows that the effective ( V − A)( V + A) interaction (penguin type) dominates the effective ( V − A)( V − A) interaction in this topology.

Baryon poles in proton decay amplitudes

The decay rate of the p→ π 0e + mode is calculated in SU(5) grand unified theory using a pole model with proton and 1 2 − baryon poles. Baryon-to-vacuum amplitudes are calculated in the framework of the MIT bag model. It is found that the partial decay rate [∼(5×10 31 yr) −)] is close to the partial decay rates calculated by different methods.

Weak radiative decays of Σ and Λ hyperons

Unitarity and dispersion theory are used to calculate the contribution of the πN intermediate state to the weak radiative decays of Σ and Λ hyperons. The contribution from the octet baryon poles is also calculated. The current × current form is assumed for the weak Hamiltonian so that the weak parity-violating two-body vertex vanishes in the limit of SU (3) symmetry and the parity-violating octet baryon pole terms are zero. Consequently the parity-violating weak radiative decay amplitude comes entirely from the πN intermediate state. Our main results are: (i) the contribution of the πN intermediate state is comparable to the contribution of the octet baryon pole terms and (ii) the correct sign and order of magnitude for the asymmetry parameter α and a branching ratio in moderate agreement with the recent experiment of Gershwin et al. are obtained for the decay Σ + → P γ.

Nonleptonic Decays of Hyperons and Current Algebra,

Nonleptonic decays of baryons are studied within the framework of current algebra, current-current interaction, and hard pions. A formalism which avoids the usual ambiguity of off-mass-shell extrapolation for the $P$-wave decays is developed, from which formulas for the decay amplitudes can be derived. Two models are discussed. The first model contains the equal-time commutator and the baryon pole terms, but allows for the $\mathrm{SU}(3)$ symmetry breaking through the presence of the parity-violating spurion matrix elements between baryons. The second model adds the $\frac{3}{2}+$ decuplet and ${{Y}_{0}}^{*}(1405)$ contributions to the first model, but the $\mathrm{SU}(3)$ symmetry-breaking matrix elements are not considered. Reasonable agreement with experiment is obtained in both models.

Backward-Scattering Extrapolations and Baryon Couplings

Extrapolation of an asymptotic cross section to a baryon pole cannot uniquely determine the coupling constant. The only asymptotic quantities capable of doing this are the $R$ and $A$ parameters. The notorious discrepancy between extrapolation of $\frac{d\ensuremath{\sigma}({\ensuremath{\pi}}^{\ensuremath{-}}p)}{\mathrm{du}}$ and the known $\ensuremath{\Delta}$ width is shown to be purely illusory.

Estimation of the Asymptotic Pseudoscalar-Meson-Baryon Total Cross Section from the Amati-Bertocchi-Fubini-Stanghellini-Tonin Multiperipheral Model

The high-energy forward scattering of a pseudoscalar meson ($\ensuremath{\mu}$) and a baryon ($B$) is discussed on the basis of the Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model. Assuming that the low-energy $\ensuremath{\mu}B$ amplitude is dominated by the baryon pole plus the first elastic resonance, and using the approximate solution to the $\ensuremath{\mu}\ensuremath{\mu}$ integral equation proposed by Abarbanel, Chew, Goldberger, and Saunders, we derive an expression for the high-energy limit of ${\ensuremath{\sigma}}_{\ensuremath{\mu}B}^{\mathrm{tot}}$. A numerical estimate based on SU(3) symmetry is given.

On ΔS=2 Transitions in Nonleptonic Hyperon Decays

In order to explain the phenomena of CP violation using the current-current interaction, several authors, including one of the present authors (M. K.), have introduced a neutral current in the form of the universal V-A current-current interaction. Then there appears a part in the Hamiltonian to produce the ΔS=2 transition in first order. In this article, we treat the nonleptonic hyperon decays with ΔS=2, Ξ→Nπ, and obtain decay rates and asymmetry parameters using both the above interaction and the second order effect of the usual current-current interaction. In the latter case use is made of the baryon pole model. Comparison between the two calculations shows that there is a possibility of a considerable change in the asymmetry parameters of the decays Ξ→Nπ in the presence of the above-mentioned neutral current.

Contributions of Spin-J Baryon Poles to πN → πN and πN → γN Amplitudes

Contributions of baryon poles of spin J to the πN → πN and πN → γN amplitudes have been calculated using the Wigner-Bargmann formalism. An ambiguity arising from off-the-mass-shell continuation of the propagator has been discussed and a continuation which gives pure spin-J behavior of the propagator for timelike propagator momentum has been given. Moreover, it has been shown that the parts of the amplitudes (with timelike propagator momentum) containing the highest power of the cosine of the scattering angle are free of this ambiguity.

TheK¯KΠN¯N-amplitude in a Veneziano type model with spin

The generalized Veneziano Model has been applied by Chanet al. to the processes (K¯KΠN¯N) with very impressive results, but in this treatment baryon spin was neglected. In this work we give a covariant spin and isospin decomposition of the above class of processes. Postulating factorization at the lowest meson and baryon poles and using the very stringent duality diagram prescription we are led to a Veneziano type ansatz for the various invariant amplitudes.

Baryon Pole Model forS-Wave Hyperon Decay

The role of the decuplet particle poles in a baryon pole model for the parity-violating amplitude is investigated from the algebraic point of view. The conditions under which the baryon pole model, with decuplet poles, reproduces the results of the ${K}^{*}$ pole model and of current algebra are analyzed.

Formula omitted] baryon resonances and nonleptonic hyperon decays

The relative importance of J P = 1 2 ± baryon resonances in nonleptonic hyperon decays is investigated within a dispersion relation formulation of the current algebra-PCAC method with a view to establishing which resonances can be neglected. The dispersion relation formulation is reviewed, equal-time commutator and octet baryon pole terms are calculated, and then pion-octet baryon intermediate states are included in the calculation of the imaginary parts of the amplitudes for the dispersion relations. The imaginary parts of the amplitudes then involve pion-octet baryon scattering amplitudes for which a resonance approximation is used and weak nonleptonic amplitudes which are approximated by the equal-time commutator and octet baryon pole terms. An evaluation of the resulting dispersion integrals shows that it is safe to neglect resonances with J P = 1 2 + (J P = 1 2 − ) in S-wave ( P-wave) decays and, also, that the P-wave amplitude of Σ + → n + π + may be substantially enhanced by the resonance N′(1470).