A calculation of SU(4) Clebsch–Gordan coefficients

Haacke, E. Mark; Moffat, J. W.; Savaria, P.

doi:10.1063/1.522843

Cited by 30 publications

(11 citation statements)

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“…Let us consider first the coupling of the baryon current to the pseudoscalar mesons. The relations between all the relevant BBP coupling constants can be easily obtained by using SU(4) Clebsch-Gordan cofficients [46] and the above relations. They read…”

Section: The Ycn Interactionmentioning

confidence: 99%

Charmed nuclei within a microscopic many-body approach

2019

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Single-particle energies of the Λc chamed baryon are obtained in several nuclei from the relevant self-energy constructed within the framework of a perturbative many-body approach. Results are presented for a charmed baryon-nucleon (YcN ) potential based on a SU(4) extension of the mesonexchange hyperon-nucleon potentialÃ of the Jülich group. Three different models (A, B and C) of this interaction, that differ only on the values of the couplings of the scalar σ meson with the charmed baryons, are considered. Phase shifts, scattering lengths and effective ranges are computed for the three models and compared with those predicted by the YcN interaction derived in Eur. Phys. A 54, 199 (2018) from the extrapolation to the physical pion mass of recent results of the HAL QCD Collaboration. Qualitative agreement is found for two of the models (B and C) considered. Our results for Λc-nuclei are compatible with those obtained by other authors based on different models and methods. We find a small spin-orbit splitting of the p−, d− and f −wave states as in the case of single Λ-hypernuclei. The level spacing of Λc single-particle energies is found to be smaller than that of the corresponding one for hypernuclei. The role of the Coulomb potential and the effect of the coupling of the ΛcN and ΣcN channels on the single-particle properties of Λc−nuclei are also analyzed. Our results show that, despite the Coulomb repulsion between the Λc and the protons, even the less attractive one of our YcN models (model C) is able to bind the Λc in all the nuclei considered. The effect of the ΛcN − ΣcN coupling is found to be almost negligible due to the large mass difference of the Λc and Σc baryons.

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Section: The Ycn Interactionmentioning

confidence: 99%

Charmed nuclei within a microscopic many-body approach

2019

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“…where q 1 and q 2 are the four-momentum of the initial and final pseudoscalar mesons respectively, and C 15 F (15 ⊗ 15) is the SU(4) Clebsch Gordan Coefficient that we take from [28] and g 15 F is the reduced matrix element that by comparison with the result of the Lagrangian is given by…”

Section: A Lagrangian and Feynman Diagramsmentioning

confidence: 99%

Dynamically generatedNandΛresonances in the hidden charm sector around 4.3 GeV

et al. 2011

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The interactions ofDΣ c -DΛ c ,D * Σ c -D * Λ c , and related strangeness channels, are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. A series of meson-baryon dynamically generated relatively narrow N * and Λ * resonances are predicted around 4.3 GeV in the hidden charm sector. We make estimates of production cross sections of these predicted resonances inpp collisions for PANDA at the forthcoming FAIR facility. π 0 √ 2 + η 8

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“…The C ab coefficients can be obtained by the SU(4) Clebsch Gordan Coefficients which we take from Ref. [14]. We list the values of the C ab coefficients for P B → P B with isospin and strangeness (I, S) = (1/2, 0) and (0, -1) explicitly in Table I and Table II, respectively. With the transition potential, the coupled-channel scattering matrix can be obtained by solving the coupledchannel Bethe-Salpeter equation in the on-shell factorization approach of Refs.…”

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Prediction of NarrowNandΛResonances with Hidden Charm above 4 GeV

et al. 2010

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The interaction between various charmed mesons and charmed baryons are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. Several meson-baryon dynamically generated narrow N * and Λ * resonances with hidden charm are predicted with mass above 4 GeV and width smaller than 100 MeV. The predicted new resonances definitely cannot be accommodated by quark models with three constituent quarks and can be looked for at the forthcoming PANDA/FAIR experiments.PACS numbers: 14.20. Gk, 13.30.Eg, 13.75.Jz Up to now, all established baryons can be ascribed into 3-quark (qqq) configurations [1], although some of them were suggested to be meson-baryon dynamically generated states [2][3][4][5][6][7][8] or states with large (qqqqq) components [9][10][11]. A difficulty to pin down the nature of these baryon resonances is that the predicted states from various models are around the same energy region and there are always some adjustable ingredients in each model to fit the experimental data. In this letter, we report a study of the interactions between various charmed mesons and charmed baryons within the framework of the coupled channel unitary approach with the local hidden gauge formalism. Several meson-baryon dynamically generated narrow N * and Λ * resonances with hidden charm are predicted with mass above 4 GeV and width smaller than 100 MeV. The predicted new resonances can be looked for at the forthcoming PANDA/FAIR experiments [13]. If confirmed, they definitely cannot be accommodated by quark models with three constituent quarks.We follow the recent approach of Ref.[12] and extend it from three flavors to four. We consider the P B → P B and V B → V B interaction by exchanging a vector meson, as shown by the Feynman diagrams in Fig. 1.The effective Lagrangians for the interactions involved are [12]:where P and V stand for pseudoscalar and vector mesons of the 16-plet of SU(4), respectively. Under the low energy approximation, the three momentum versus the mass of the meson can be neglected. We can just take the γ 0 component of Eq. (1). The threemomentum and energy of the exchanged vector are both much smaller than its mass, so its propagator is approximately g µν /M 2 V . Then with g = M V /2f the transition potential corresponding to the diagrams of Fig. 1 are given bywhere the a, b stand for different channels of P 1 (V 1 )B 1 and P 2 (V 2 )B 2 , respectively. The E is the energy of corresponding particle. The ǫ is the polarization vector of the initial or final vector. And the ǫ 0 1,2 component is neglected consistently with taking p/M V ∼ 0, with p the momentum of the vector meson. The C ab coefficients can be obtained by the SU(4) Clebsch Gordan Coefficients which we take from Ref. [14]. We list the values of the C ab coefficients for P B → P B with isospin and strangeness (I, S) = (1/2, 0) and (0, -1) explicitly in Table I and Table II, respectively. With the transition potential, the coupled-channel scattering matrix can be obtained by solving the coupledc...

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A calculation of SU(4) Clebsch–Gordan coefficients

Abstract: All the Clebsch–Gordan coefficients for SU(4) that would be required for particle physics, including those decomposed with respect to SU(3), are obtained by using the general formalism of Baird and Biedenharn.

Cited by 30 publications

References 11 publications

Charmed nuclei within a microscopic many-body approach

Charmed nuclei within a microscopic many-body approach

Dynamically generatedNandΛresonances in the hidden charm sector around 4.3 GeV

Prediction of NarrowNandΛResonances with Hidden Charm above 4 GeV

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A calculation of SU(4) Clebsch–Gordan coefficients

Abstract: All the Clebsch–Gordan coefficients for SU(4) that would be required for particle physics, including those decomposed with respect to SU(3), are obtained by using the general formalism of Baird and Biedenharn.

Cited by 30 publications

References 11 publications

Charmed nuclei within a microscopic many-body approach

Charmed nuclei within a microscopic many-body approach

Dynamically generatedN*andΛ*resonances in the hidden charm sector around 4.3 GeV

Prediction of NarrowN*andΛ*Resonances with Hidden Charm above 4 GeV

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Dynamically generatedNandΛresonances in the hidden charm sector around 4.3 GeV

Prediction of NarrowNandΛResonances with Hidden Charm above 4 GeV