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On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation

Year 2013, Volume: 3 Issue: 3, 134 - 142, 23.07.2016

L.k Sharma P.v.c Luhanga

Abstract

Motivated from a phenomenological viewpoint, three confining potentials have been studied in the Klein-Gordon equation framework. In particular we study the phenomena of quark leakage for these potentials. The transmission coefficient values have been obtained for all the potentials, using WKB [Wentzel, Kramers & Brillouin] method and compared with potentials already discussed by previous authors. We observe that one of the potentials considered by us strongly supports the existence of free quarks because of the comparatively large values of transmission coefficients, as predicted by our model

Keywords

Confining potentials tunnelling phenomenon quark leakage transmission coefficients

References

  • Gell-Mann, M. (1964), “A Schematic model of Baryons and Mesons”, Phys. Lett., 8, 214-215.
  • Zweig, G. (1964), “An SU3 Model for Strong Interaction Symmetry and its breaking”, CERN, Preprints 8182/TH. 401; “An SU(3) Model for Strong Interaction Symmetry and its Breaking II”, 8419/TH. 412.
  • La Rue, G.S., Fairbank, W.M. and Hebard, A.F. (1977), “Evidence For the Existence of Fractional Charge on Matter”, Phys. Rev. Lett., 38, 1011-1014.
  • Werle, J. (1993), Acta Physica Polonica B., “Quark confinement through hidden breaking of colour symmetry”. 24, 1115-1120.
  • Kang, J.S & Schnitzer, H.J. (1975); “Dynamics of light nad heavy bound quarks”, Phys Rev. D 12, 841-854.
  • Gunion, J.F. & Li, L.F. (1975); “Relativistic treatment of the quark-confinement model”, Phys. Rev. D 12, 3583-3588.
  • Sharma, L.K. & Luhanga, PVC. (2008). “Scalar potential in the Dirac equation and quark confinement”. Malaysian J. of Physics, 29(1&2), 1-8.
  • Sharma, L.K. & Sebitla, L.D. (2007). “Bound-state spectra of QQ system: Relativistic and NonRelativistic” Malaysian J. of Physics, 28(3&4), 63-70.
  • Sharma, L.K., Fiase, J.O., & Whende, W. (2004). “Heavy-meson spectroscopy for the superposition of general potential-cum-centrifugal potential” Chiang Mai J. of science, 31, 171- 180.
  • Sharma, L.K. &Fiase, J.O. (2003). “Meson Spectra: Power law potential model in the Dirac equation” Botswana J. of Tech. 12, 243-249.
  • Mundembe, V.R. &Sharma, L.K. (1998). “Toponium bound-state predictions of the modified Two-step potential model” Malaysian J. of Physics, 17, 113-121.
  • Sharma, P.C & Sharma, L.K. (1988). “Hadrons in a relativistic power law potential” Indian J. of pure and appl. Physics, 26, 347-352.
  • Sharma, L.K. & Sharma, G.S. (1984). “Quark potentials for mesons in the Klein-Gordon equation” Pramana, 22, 539-547.
  • Kajwadkar, A.P., & Sharma, L.K. (1983). “On scalar quark leakage in Klein-Gordon equation”. Indian J. of pure appl. Physics, 21, 195-196.
  • Sharma, L.K., Mehta, S., &Iyer, V.P. (1983). “Solution of the Dirac equation for the general evenpower potential with application to particle spectroscopy” J. of Mathematical Physics, 24, 2521- 2527.
  • Sharma, L.K. & Iyer, V.P. (1982). “High energy asymptotic expansion and Regge trajectories for the general even power potential in the K-G equation with applications”. J. of Mathematical Physics, 23, 1185-1189.
  • Sharma, L.K., Choubey, J. & Müller-Kirsten, H.J.W. (1980). “Large coupling expansions for energies and Regge trajectories of the general even power potential with applications”. J. of Mathematical Physics, 21, 1533-1538.
  • Sharma, L.K. Fiase, J.O. (2000). “Meson Spectra: Power law potential in the Dirac equation” Paper presented at the 7th conference on Intersections of particle & nuclear physics, May 22-28, Quebec City, Canada. Proceedings published by Americal Institute of Physics, CP 549-291.
  • Sharma, L.K., Jain, P.K. & Mundembe, V.R., (1999). “Modified two-step potential: Heavy Mesons”. J. of Appl. Science in Southern Africa (JASSA), 4, 70-79.
  • Abe, F. et al., (1995). “Observation of Top Quark Production in pp Collisions with the Collider Detector at Fermilab”, Phys. Rev. Lett. 74, 2626-2631.
  • Abachi, S. et al., (1995). “Observation of the Top Quark”, Phys. Rev. Lett. 74, 2632-2637.
  • Ram, B. & Halasa, R. (1979). “Meson spectra with harmonic-oscillator potential in the KleinGordon equation” Phys. Rev. D11, 3467-3469.
  • Ram, B. (1978). “On quark leakage through a confining potential”. Nuovo Cim. Lett. Al. 23, 321- 323.
  • Martin, A. (1980). “A FIT of Upsilon and Charmonium Spectra”, Phys. Lett., B93, 338-348.
  • Sharma, G.S., &Sharma, L.K. (1984). “Meson spectra with power-law potential in Dirac equation” Pramana, 22, 533-537.
  • Jena, S.N. (1983). “Fit of Charmonium And Upsilon Spectra by a Common Potential V(0) + A log (1+R)”, Phys. Lett., B123,445.
  • Merzbacher, E. (1970), Quantum Mechanics, 2nd edition (John-Wiley, NY).
  • Iyer, V.P. &Sharma, L.K. (1982). “Meson spectroscopy for a harmonic oscillator –cumcentrifugal potential in the Klein-Gordon equation”. Indian J. Pure & Appl. Physics, 20, 322-324.

Year 2013, Volume: 3 Issue: 3, 134 - 142, 23.07.2016

L.k Sharma P.v.c Luhanga

Abstract

References

  • Gell-Mann, M. (1964), “A Schematic model of Baryons and Mesons”, Phys. Lett., 8, 214-215.
  • Zweig, G. (1964), “An SU3 Model for Strong Interaction Symmetry and its breaking”, CERN, Preprints 8182/TH. 401; “An SU(3) Model for Strong Interaction Symmetry and its Breaking II”, 8419/TH. 412.
  • La Rue, G.S., Fairbank, W.M. and Hebard, A.F. (1977), “Evidence For the Existence of Fractional Charge on Matter”, Phys. Rev. Lett., 38, 1011-1014.
  • Werle, J. (1993), Acta Physica Polonica B., “Quark confinement through hidden breaking of colour symmetry”. 24, 1115-1120.
  • Kang, J.S & Schnitzer, H.J. (1975); “Dynamics of light nad heavy bound quarks”, Phys Rev. D 12, 841-854.
  • Gunion, J.F. & Li, L.F. (1975); “Relativistic treatment of the quark-confinement model”, Phys. Rev. D 12, 3583-3588.
  • Sharma, L.K. & Luhanga, PVC. (2008). “Scalar potential in the Dirac equation and quark confinement”. Malaysian J. of Physics, 29(1&2), 1-8.
  • Sharma, L.K. & Sebitla, L.D. (2007). “Bound-state spectra of QQ system: Relativistic and NonRelativistic” Malaysian J. of Physics, 28(3&4), 63-70.
  • Sharma, L.K., Fiase, J.O., & Whende, W. (2004). “Heavy-meson spectroscopy for the superposition of general potential-cum-centrifugal potential” Chiang Mai J. of science, 31, 171- 180.
  • Sharma, L.K. &Fiase, J.O. (2003). “Meson Spectra: Power law potential model in the Dirac equation” Botswana J. of Tech. 12, 243-249.
  • Mundembe, V.R. &Sharma, L.K. (1998). “Toponium bound-state predictions of the modified Two-step potential model” Malaysian J. of Physics, 17, 113-121.
  • Sharma, P.C & Sharma, L.K. (1988). “Hadrons in a relativistic power law potential” Indian J. of pure and appl. Physics, 26, 347-352.
  • Sharma, L.K. & Sharma, G.S. (1984). “Quark potentials for mesons in the Klein-Gordon equation” Pramana, 22, 539-547.
  • Kajwadkar, A.P., & Sharma, L.K. (1983). “On scalar quark leakage in Klein-Gordon equation”. Indian J. of pure appl. Physics, 21, 195-196.
  • Sharma, L.K., Mehta, S., &Iyer, V.P. (1983). “Solution of the Dirac equation for the general evenpower potential with application to particle spectroscopy” J. of Mathematical Physics, 24, 2521- 2527.
  • Sharma, L.K. & Iyer, V.P. (1982). “High energy asymptotic expansion and Regge trajectories for the general even power potential in the K-G equation with applications”. J. of Mathematical Physics, 23, 1185-1189.
  • Sharma, L.K., Choubey, J. & Müller-Kirsten, H.J.W. (1980). “Large coupling expansions for energies and Regge trajectories of the general even power potential with applications”. J. of Mathematical Physics, 21, 1533-1538.
  • Sharma, L.K. Fiase, J.O. (2000). “Meson Spectra: Power law potential in the Dirac equation” Paper presented at the 7th conference on Intersections of particle & nuclear physics, May 22-28, Quebec City, Canada. Proceedings published by Americal Institute of Physics, CP 549-291.
  • Sharma, L.K., Jain, P.K. & Mundembe, V.R., (1999). “Modified two-step potential: Heavy Mesons”. J. of Appl. Science in Southern Africa (JASSA), 4, 70-79.
  • Abe, F. et al., (1995). “Observation of Top Quark Production in pp Collisions with the Collider Detector at Fermilab”, Phys. Rev. Lett. 74, 2626-2631.
  • Abachi, S. et al., (1995). “Observation of the Top Quark”, Phys. Rev. Lett. 74, 2632-2637.
  • Ram, B. & Halasa, R. (1979). “Meson spectra with harmonic-oscillator potential in the KleinGordon equation” Phys. Rev. D11, 3467-3469.
  • Ram, B. (1978). “On quark leakage through a confining potential”. Nuovo Cim. Lett. Al. 23, 321- 323.
  • Martin, A. (1980). “A FIT of Upsilon and Charmonium Spectra”, Phys. Lett., B93, 338-348.
  • Sharma, G.S., &Sharma, L.K. (1984). “Meson spectra with power-law potential in Dirac equation” Pramana, 22, 533-537.
  • Jena, S.N. (1983). “Fit of Charmonium And Upsilon Spectra by a Common Potential V(0) + A log (1+R)”, Phys. Lett., B123,445.
  • Merzbacher, E. (1970), Quantum Mechanics, 2nd edition (John-Wiley, NY).
  • Iyer, V.P. &Sharma, L.K. (1982). “Meson spectroscopy for a harmonic oscillator –cumcentrifugal potential in the Klein-Gordon equation”. Indian J. Pure & Appl. Physics, 20, 322-324.
There are 28 citations in total.

Details

Other ID JA56KU69MM
Journal Section Articles
Authors

L.k Sharma This is me

P.v.c Luhanga This is me

Publication Date July 23, 2016
Published in Issue Year 2013 Volume: 3 Issue: 3

Cite

APA Sharma, L., & Luhanga, P. (2016). On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation. TOJSAT, 3(3), 134-142.
AMA Sharma L, Luhanga P. On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation. TOJSAT. July 2016;3(3):134-142.
Chicago Sharma, L.k, and P.v.c Luhanga. “On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation”. TOJSAT 3, no. 3 (July 2016): 134-42.
EndNote Sharma L, Luhanga P (July 1, 2016) On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation. TOJSAT 3 3 134–142.
IEEE L. Sharma and P. Luhanga, “On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation”, TOJSAT, vol. 3, no. 3, pp. 134–142, 2016.
ISNAD Sharma, L.k - Luhanga, P.v.c. “On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation”. TOJSAT 3/3 (July 2016), 134-142.
JAMA Sharma L, Luhanga P. On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation. TOJSAT. 2016;3:134–142.
MLA Sharma, L.k and P.v.c Luhanga. “On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation”. TOJSAT, vol. 3, no. 3, 2016, pp. 134-42.
Vancouver Sharma L, Luhanga P. On Scalar Quark Leakage through the Power-Law and Logarithmic Confining Potentials in the Klein-Gordon Equation. TOJSAT. 2016;3(3):134-42.