Bound states of heavy <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>Q¯ <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>2</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span> systems

L. Heller; J. A. Tjon

doi:10.1103/PhysRevD.32.755

Access by Xinjiang University

Bound states of heavy $Q^{2}$ Q¯ ${}^{2}$ systems

L. Heller

J. A. Tjon

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

PDF

Phys. Rev. D 32, 755 – Published 1 August, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.755

Abstract

The Born-Oppenheimer approximation for heavy quarks in the MIT bag is extended to the $Q^{2}$ Q $¯^{2}$ system, where the glue plus volume energy becomes an operator in color space. Taking its lowest eigenvalue as the approximate potential energy, the four-body Schrödinger equation is solved variationally for the ground-state energy. With this approximation, it is found that heavy-quark systems such as $c^{2}$ c $¯^{2}$ are stable against breakup into two ψ (cc¯) mesons. It is necessary to solve the coupled-channel (in color space) problem to confirm this result.

References (20)

S. W. Otto and J. D. Stack, Phys. Rev. Lett. 52, 2328 (1984).
P. Hasenfratz, J. Kuti, and A. S. Szalay, in Charm, Color and the J/ psi, proceedings of the X Rencontre de Moriond, Méribel-les-Allues, France, 1975, edited by J. Tran Thanh Van (CNRS, Paris, 1975).
W. C. Haxton and L. Heller, Phys. Rev. D 22, 1198 (1980).
A. T. Aerts and L. Heller, Phys. Rev. D 25, 1365 (1982).
L. Heller, in Quarks and Nuclear Forces, Vol. 100 of Springer Tracts in Modern Physics, edited by D. C. Fries and B. Zeitnitz (Springer, Berlin, 1982), p. 145.
A. T. Aerts and L. Heller, Phys. Rev. D 23, 185 (1981).
P. J. Steinhardt, Phys. Rev. D 21, 2390 (1980), solved the two-dimensional bag, but only for the Abelian case of two positive and two negative charges, and in a special geometry.
In the present paper, we do not make use of the upper eigenvalue nor the mixing angle theta. We expect that a proper treatment of deformed bags will show that $V_{18}$ (and theta) vanish sufficiently rapidly that there is no van der Waals force.
T. De Grand, R. L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12, 2060 (1975).
In Refs. 3 and 4, a phenomenological zero-point energy was also included, and the coupling constant appearing in the potential was itself taken to be a function of the coordinates. Consequently, the parameters in the present work are different from the ones appearing there.
K. Schmidt (private communication).
P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York, 1964).
P. J. Mulders, G. Bhamathi, L. Heller, A. T. Aerts and A. K. Kerman, Phys. Rev. D 27, 2708 (1983).
C. Rebbi, Phys. Rev. D 12, 2407 (1975); ibid. 14, 2362 (1976); T. DeGrand and C. Rebbi, ibid. 17, 2358 (1978).
P. Hasenfratz, R. R. Horgan, J. Kuti and J. M. Richard, Phys. Lett. 94 B, 401 (1980); ibid. 95 B, 299 (1980).
For the special case of light quarks that all occupy the same mode in a spherical bag, the two procedures give the same energy.
J.-P. Ader, J.-M. Richard and P. Taxil, Phys. Rev. D 25, 2370 (1982).
For any geometry in which the Coulomb and confining terms in Eq. (14) commute, the procedure in Ref. 17 gives the same eigenvectors and eigenvalues as in the present paper.
For $Q^{2 \bar{Q}}$ ${}^{2}$ see H. J. Lipkin, Phys. Lett. 45 B, 267 (1973); J. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982); Phys. Rev. D 27, 588 (1983) J. L. Ballot and J. M. Richard, Phys. Lett. 123 B, 449 (1983).
K. Yazaki, in Few Body Problems in Physics, proceedings of the Tenth International IUPAP Conference, Karlsruhe, 1983, edited by B. Zeitnitz [Nucl. Phys. A 416, 87c (1984)].

[c1] S. W. Otto and J. D. Stack, Phys. Rev. Lett. 52, 2328 (1984).

[c2] P. Hasenfratz, J. Kuti, and A. S. Szalay, in Charm, Color and the J/ psi, proceedings of the X Rencontre de Moriond, Méribel-les-Allues, France, 1975, edited by J. Tran Thanh Van (CNRS, Paris, 1975).

[c3] W. C. Haxton and L. Heller, Phys. Rev. D 22, 1198 (1980).

[c4] A. T. Aerts and L. Heller, Phys. Rev. D 25, 1365 (1982).

[c5] L. Heller, in Quarks and Nuclear Forces, Vol. 100 of Springer Tracts in Modern Physics, edited by D. C. Fries and B. Zeitnitz (Springer, Berlin, 1982), p. 145.

[c6] A. T. Aerts and L. Heller, Phys. Rev. D 23, 185 (1981).

[c7] P. J. Steinhardt, Phys. Rev. D 21, 2390 (1980), solved the two-dimensional bag, but only for the Abelian case of two positive and two negative charges, and in a special geometry.

[c8] In the present paper, we do not make use of the upper eigenvalue nor the mixing angle theta. We expect that a proper treatment of deformed bags will show that $V_{18}$ (and theta) vanish sufficiently rapidly that there is no van der Waals force.

[c9] T. De Grand, R. L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12, 2060 (1975).

[c10] In Refs. 3 and 4, a phenomenological zero-point energy was also included, and the coupling constant appearing in the potential was itself taken to be a function of the coordinates. Consequently, the parameters in the present work are different from the ones appearing there.

[c11] K. Schmidt (private communication).

[c12] P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York, 1964).

[c13] P. J. Mulders, G. Bhamathi, L. Heller, A. T. Aerts and A. K. Kerman, Phys. Rev. D 27, 2708 (1983).

[c14] C. Rebbi, Phys. Rev. D 12, 2407 (1975); ibid. 14, 2362 (1976); T. DeGrand and C. Rebbi, ibid. 17, 2358 (1978).

[c15] P. Hasenfratz, R. R. Horgan, J. Kuti and J. M. Richard, Phys. Lett. 94 B, 401 (1980); ibid. 95 B, 299 (1980).

[c16] For the special case of light quarks that all occupy the same mode in a spherical bag, the two procedures give the same energy.

[c17] J.-P. Ader, J.-M. Richard and P. Taxil, Phys. Rev. D 25, 2370 (1982).

[c18] For any geometry in which the Coulomb and confining terms in Eq. (14) commute, the procedure in Ref. 17 gives the same eigenvectors and eigenvalues as in the present paper.

[c19] For $Q^{2 \bar{Q}}$ ${}^{2}$ see H. J. Lipkin, Phys. Lett. 45 B, 267 (1973); J. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982); Phys. Rev. D 27, 588 (1983) J. L. Ballot and J. M. Richard, Phys. Lett. 123 B, 449 (1983).

[c20] K. Yazaki, in Few Body Problems in Physics, proceedings of the Tenth International IUPAP Conference, Karlsruhe, 1983, edited by B. Zeitnitz [Nucl. Phys. A 416, 87c (1984)].

Physical Review D

Export citation

Export citation

Bound states of heavy $Q^{2}$ Q¯ ${}^{2}$ systems

Abstract

References (20)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Bound states of heavy Q2Q¯ 2 systems

Abstract

References (20)

Bound states of heavy $Q^{2}$ Q¯ ${}^{2}$ systems