Masses of low-lying baryons in the ground states in a power-law potential model with pseudoscalar meson, one-gluon and centre-of-mass corrections
Abstract: The masses of low-lying baryons in the ground states are calculated in a relativistic potential model of independent quarks taking into account perturbatively the contribution of the quark-gluon coupling due to one-gluon exchange along with that of pseudoscalar meson exchange interaction and that of centre-of-mass motion. The effective potential representing phenomenologically the non-perturbative gluon interactions, including the gluon self-couplings, is chosen with equally mixed scalar and vector parts in a … Show more
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Cited by 13 publications
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The study of the purely leptonic decays of the ground charged vector mesons is very interesting and significant in determining the CKM matrix elements, obtaining the decay constant of vector mesons, examining the lepton flavor universality, and searching for new physics beyond the standard model. These purely leptonic decays of the ground charged vector mesons are induced by the weak interactions within the standard model, and usually have very small branching ratios, $$\mathcal{B}({\rho }^{-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( ρ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-13})$$ O ( 10 - 13 ) , $${{{\mathcal {B}}}}(K^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( K ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $${{{\mathcal {O}}}}(10^{-13})$$ O ( 10 - 13 ) , $$\mathcal{B}(D_{d}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( D d ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-10})$$ O ( 10 - 10 ) , $$\mathcal{B}(B_{u}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( B u ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-10})$$ O ( 10 - 10 ) , $$\mathcal{B}(D_{s}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( D s ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-6})$$ O ( 10 - 6 ) and $$\mathcal{B}(B_{c}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( B c ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-6})$$ O ( 10 - 6 ) . Inspired by the potential prospects of LHCb, Belle-II, STCF, CEPC and FCC-ee experiments, we discussed the probabilities of experimental investigation on these purely leptonic decays. It is found that the measurements of these decays might be possible and feasible with the improvement of data statistics, analytical technique, and measurement precision in the future. (1) With the hadron-hadron collisions, the purely leptonic decays of $${\rho }^{-}$$ ρ - , $$K^{{*}-}$$ K ∗ - , $$D_{d,s}^{{*}-}$$ D d , s ∗ - and $$B_{u,c}^{{*}-}$$ B u , c ∗ - mesons might be accessible at LHC experiments. (2) With the $$e^{+}e^{-}$$ e + e - collisions, the purely leptonic decays of $$D_{d,s}^{{*}-}$$ D d , s ∗ - and $$B_{u,c}^{{*}-}$$ B u , c ∗ - mesons might be measurable with over $$10^{12}$$ 10 12 $$Z^{0}$$ Z 0 bosons available at CEPC and FCC-ee experiments. In addition, the $$D_{d,s}^{{*}-}$$ D d , s ∗ - $${\rightarrow }$$ → $${\ell }^{-}{\nu }_{\ell }$$ ℓ - ν ℓ decays could also be studied at Belle-II and SCTF experiments.
The study of the purely leptonic decays of the ground charged vector mesons is very interesting and significant in determining the CKM matrix elements, obtaining the decay constant of vector mesons, examining the lepton flavor universality, and searching for new physics beyond the standard model. These purely leptonic decays of the ground charged vector mesons are induced by the weak interactions within the standard model, and usually have very small branching ratios, $$\mathcal{B}({\rho }^{-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( ρ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-13})$$ O ( 10 - 13 ) , $${{{\mathcal {B}}}}(K^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( K ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $${{{\mathcal {O}}}}(10^{-13})$$ O ( 10 - 13 ) , $$\mathcal{B}(D_{d}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( D d ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-10})$$ O ( 10 - 10 ) , $$\mathcal{B}(B_{u}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( B u ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-10})$$ O ( 10 - 10 ) , $$\mathcal{B}(D_{s}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( D s ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-6})$$ O ( 10 - 6 ) and $$\mathcal{B}(B_{c}^{{*}-}{\rightarrow }{\ell }^{-}{\nu }_{\ell })$$ B ( B c ∗ - → ℓ - ν ℓ ) $${\sim }$$ ∼ $$\mathcal{O}(10^{-6})$$ O ( 10 - 6 ) . Inspired by the potential prospects of LHCb, Belle-II, STCF, CEPC and FCC-ee experiments, we discussed the probabilities of experimental investigation on these purely leptonic decays. It is found that the measurements of these decays might be possible and feasible with the improvement of data statistics, analytical technique, and measurement precision in the future. (1) With the hadron-hadron collisions, the purely leptonic decays of $${\rho }^{-}$$ ρ - , $$K^{{*}-}$$ K ∗ - , $$D_{d,s}^{{*}-}$$ D d , s ∗ - and $$B_{u,c}^{{*}-}$$ B u , c ∗ - mesons might be accessible at LHC experiments. (2) With the $$e^{+}e^{-}$$ e + e - collisions, the purely leptonic decays of $$D_{d,s}^{{*}-}$$ D d , s ∗ - and $$B_{u,c}^{{*}-}$$ B u , c ∗ - mesons might be measurable with over $$10^{12}$$ 10 12 $$Z^{0}$$ Z 0 bosons available at CEPC and FCC-ee experiments. In addition, the $$D_{d,s}^{{*}-}$$ D d , s ∗ - $${\rightarrow }$$ → $${\ell }^{-}{\nu }_{\ell }$$ ℓ - ν ℓ decays could also be studied at Belle-II and SCTF experiments.
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schrödinger equation in a nonuniform and optimal spatial discretization offers accurate eigenvalues, densities and expectation values.The calculations are carried out for states with arbitrary n and ℓ quantum numbers. Comparisons are made with the available literature data and excellent agreement is observed. In all the cases, the present method yields considerably improved results over the other existing calculations. Some new states are reported. * Electronic address: akroy@unb.ca
In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The results are in very good agreement with exact numerical results. *
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