Study of Heavy Quarkonium with Energy Dependent Potential

Affiliation(s)

Nuclear and Particle Physics Group, Department of Physics, University of Allahabad, Allahabad, India.

Nuclear and Particle Physics Group, Department of Physics, University of Allahabad, Allahabad, India.

ABSTRACT

Heavy quark systems (c and b ) have been studied in the nonrelativistic framework using energy dependent interquark potential of the form harmonic oscillator with a small linear term as energy dependent as perturbation plus a inverse square potential. This potential admits exact analytical solution of the Schrodinger equation. Mass spectra, leptonic decay width, root mean square radii (), the expectation value of the radius (r) and <1/r> have been estimated for different quantum mechanical states for and systems. It is observed that energy dependent term in the potential leads to saturation of the mass spectra and degree of saturation is governed by the magnitude of perturbation. The calculated values of leptonic decay widths for 1s state are in very good agreement with the experimental data both for c and b systems.

Heavy quark systems (c and b ) have been studied in the nonrelativistic framework using energy dependent interquark potential of the form harmonic oscillator with a small linear term as energy dependent as perturbation plus a inverse square potential. This potential admits exact analytical solution of the Schrodinger equation. Mass spectra, leptonic decay width, root mean square radii (), the expectation value of the radius (r) and <1/r> have been estimated for different quantum mechanical states for and systems. It is observed that energy dependent term in the potential leads to saturation of the mass spectra and degree of saturation is governed by the magnitude of perturbation. The calculated values of leptonic decay widths for 1s state are in very good agreement with the experimental data both for c and b systems.

Cite this paper

P. Gupta and I. Mehrotra, "Study of Heavy Quarkonium with Energy Dependent Potential,"*Journal of Modern Physics*, Vol. 3 No. 10, 2012, pp. 1530-1536. doi: 10.4236/jmp.2012.310189.

P. Gupta and I. Mehrotra, "Study of Heavy Quarkonium with Energy Dependent Potential,"

References

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[4] S. N. Gupta and E. F. Radford, “Quarkonium spectra and Quantum Chromodynamics,” Physical Review D, Vol. 26, No. 11, 1982, pp. 3305-3308. doi:10.1103/PhysRevD.26.3305

[5] K. Igi and S. Ono, “Heavy-Quarkonium Systems and the QCD Scale Parameter,” Physical Review D, Vol. 33, No. 11, 1986, pp. 3349-3357. doi:10.1103/PhysRevD.33.3349

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[7] A. Martin, “A Simultaneous Fit of bb, cs, ss (bcs Pairs) and cs Spectra,” Physics Letter B, Vol. 100, 1981, p. 511.

[8] A. K. Rai, B. Patel and P. C. Vinodkumar, “Properties of qq Meson in Nonrelativistic QCD Formulism,” Physical Review C, Vol. 78, No. 5, 2008, Article ID: 055202. doi:10.1103/PhysRevC.78.055202

[9] Bhaghyesh, K. B. V. Kumar and A. P. Monteiro, “Heavy Quarkonium Spectra and Its Decays in a Nonrelativistic Model with Hulthen Potential,” Journal of Physics G: Nuclear and Particle Physics, Vol. 38, 2011, Article ID: 085001. doi:10.1088/0954-3899/38/8/085001

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[11] G. F. T. del Castillo and J. V. Castro, “Schrodinger-Pauli Equation for Spin-3/2 Particles,” Resista Mexicana de Fisica, Vol. 50, No. 3, 2004, pp. 306-310.

[12] R. J. Lombard, J. Mars and C. Volpe, “Wave Equations of Energy Dependent Potentials for Confined Systems,” Journal of Physics G: Nuclear and Particle Physics, Vol. 34, 2007, pp. 1879-1888.

[13] J. Formanck, R. J. Lombard and J. Mares, “An Extended Scenario for the Schrodinger Equation,” Czechoslovak Journal of Physics, Vol. 54, 2006, p. 289.

[14] G. C. Joshi and A. N. Mitra, “Centrifugal and Harmonic Oscillator Potential for Heavy Meson Spectroscopy,” Hadronic Journal, Vol. 1, 1978, p. 1591.

[15] V. P. Iyer and L. K. Sharma, “Heavy Meson Potentials,” Indian Journal of Pure and Applied Physics, Vol. 20, 1982, pp. 322-324.

[16] E. Cuervo-Reyes, et al., “Hadron Spectra with a Nonrelativistic Model with Confining Harmonic Potential,” Revista Brasilleria de Ensino de Fesica, Vol. 25, No. 1, 2003.

[17] K. J. Oyewumi and E. A. Bangudu, “Isotropic Harmonic Oscillator plus Inverse Quadratic Potential in N-Dimensional Space,” The Arabian Journal for Science and Engineering, Vol. 28, No. 2A, 2003, p. 173.

[18] C. Ansler, et al., “Particle Data Group,” Physics Letters B, Vol. 667, 2008, Article ID: 010001. http://pdg.lbl.gov.

[19] F. F. Schoberl and W. Lucha, “Solving the Schroedinger Equation for Bound States with Mathematica,” International Journal of Modern Physics C, Vol. 10, 1999, pp. 607-620.

[20] R. Van Royen and V. F. Weisskoph, “Vector Meson Leptonic Decay Width,” Il Nuovo Cimento A, Vol. 50, No. 3, 1967, pp. 617-645. doi:10.1007/BF02823542

[21] G. R. Boroum and H. Abdolmalki, “Variational and Exact Solutions of the Wavefunction at Origin (WFO) for Heavy Quarkonium by Using a Global Potential,” Physica Scripta, Vol. 80, 2009, Article ID: 065003.

[22] H. Chen, J. Zhang, Y.-B. Dong and P.-N. Shen, “Heavy Quarkonium Spectra in a Quark Potential Model,” Chinese Physics Letters, Vol. 18, No. 12, 2001, p. 1558. doi:10.1088/0256-307X/18/12/305

[1] E. Eichten, K. D. Lane, et al., “Spectrum of Charmed Quark Antiquark Bound States,” Physical Review Letters, Vol. 34, No. 6, 1975, pp. 369-372. doi:10.1103/PhysRevLett.34.369

[2] J. L. Richarson, “The Heavy Quark Potential J/ψ and Systems,” Physics Letters B, Vol. 82, 1979, p. 272.

[3] W. Buchmuller, “Quarkonia and Quantum Chromodynamics,” Physical Review Letters, Vol. 45, 1980, p. 403.

[4] S. N. Gupta and E. F. Radford, “Quarkonium spectra and Quantum Chromodynamics,” Physical Review D, Vol. 26, No. 11, 1982, pp. 3305-3308. doi:10.1103/PhysRevD.26.3305

[5] K. Igi and S. Ono, “Heavy-Quarkonium Systems and the QCD Scale Parameter,” Physical Review D, Vol. 33, No. 11, 1986, pp. 3349-3357. doi:10.1103/PhysRevD.33.3349

[6] C. Quigg and J. L. Rosner, “Realizing the Potential of Quarkonium,” Physics Report C, Vol. 56, 1979, p. 167.

[7] A. Martin, “A Simultaneous Fit of bb, cs, ss (bcs Pairs) and cs Spectra,” Physics Letter B, Vol. 100, 1981, p. 511.

[8] A. K. Rai, B. Patel and P. C. Vinodkumar, “Properties of qq Meson in Nonrelativistic QCD Formulism,” Physical Review C, Vol. 78, No. 5, 2008, Article ID: 055202. doi:10.1103/PhysRevC.78.055202

[9] Bhaghyesh, K. B. V. Kumar and A. P. Monteiro, “Heavy Quarkonium Spectra and Its Decays in a Nonrelativistic Model with Hulthen Potential,” Journal of Physics G: Nuclear and Particle Physics, Vol. 38, 2011, Article ID: 085001. doi:10.1088/0954-3899/38/8/085001

[10] D. B. Lichtenberg, “Energy Levels of Quarkonia in Potential Models,” International Journal of Modern Physics A, Vol. 2, 1987, p. 1669.

[11] G. F. T. del Castillo and J. V. Castro, “Schrodinger-Pauli Equation for Spin-3/2 Particles,” Resista Mexicana de Fisica, Vol. 50, No. 3, 2004, pp. 306-310.

[12] R. J. Lombard, J. Mars and C. Volpe, “Wave Equations of Energy Dependent Potentials for Confined Systems,” Journal of Physics G: Nuclear and Particle Physics, Vol. 34, 2007, pp. 1879-1888.

[13] J. Formanck, R. J. Lombard and J. Mares, “An Extended Scenario for the Schrodinger Equation,” Czechoslovak Journal of Physics, Vol. 54, 2006, p. 289.

[14] G. C. Joshi and A. N. Mitra, “Centrifugal and Harmonic Oscillator Potential for Heavy Meson Spectroscopy,” Hadronic Journal, Vol. 1, 1978, p. 1591.

[15] V. P. Iyer and L. K. Sharma, “Heavy Meson Potentials,” Indian Journal of Pure and Applied Physics, Vol. 20, 1982, pp. 322-324.

[16] E. Cuervo-Reyes, et al., “Hadron Spectra with a Nonrelativistic Model with Confining Harmonic Potential,” Revista Brasilleria de Ensino de Fesica, Vol. 25, No. 1, 2003.

[17] K. J. Oyewumi and E. A. Bangudu, “Isotropic Harmonic Oscillator plus Inverse Quadratic Potential in N-Dimensional Space,” The Arabian Journal for Science and Engineering, Vol. 28, No. 2A, 2003, p. 173.

[18] C. Ansler, et al., “Particle Data Group,” Physics Letters B, Vol. 667, 2008, Article ID: 010001. http://pdg.lbl.gov.

[19] F. F. Schoberl and W. Lucha, “Solving the Schroedinger Equation for Bound States with Mathematica,” International Journal of Modern Physics C, Vol. 10, 1999, pp. 607-620.

[20] R. Van Royen and V. F. Weisskoph, “Vector Meson Leptonic Decay Width,” Il Nuovo Cimento A, Vol. 50, No. 3, 1967, pp. 617-645. doi:10.1007/BF02823542

[21] G. R. Boroum and H. Abdolmalki, “Variational and Exact Solutions of the Wavefunction at Origin (WFO) for Heavy Quarkonium by Using a Global Potential,” Physica Scripta, Vol. 80, 2009, Article ID: 065003.

[22] H. Chen, J. Zhang, Y.-B. Dong and P.-N. Shen, “Heavy Quarkonium Spectra in a Quark Potential Model,” Chinese Physics Letters, Vol. 18, No. 12, 2001, p. 1558. doi:10.1088/0256-307X/18/12/305