Asymptotic mass spectrum and thermodynamics of the Abelian bag model

J. I. Kapusta

doi:10.1103/PhysRevD.23.2444

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Asymptotic mass spectrum and thermodynamics of the Abelian bag model

J. I. Kapusta

Theoretical Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545

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Phys. Rev. D 23, 2444 – Published 15 May, 1981

DOI: https://doi.org/10.1103/PhysRevD.23.2444

Abstract

A statistical evaluation of the mass spectrum in the bag model is made using the microcanonical ensemble. The mass spectrum behaves asymptotically as $ρ (m) \sim c m^{- 3} \exp (\frac{m}{T_{0}})$ , where $c$ and $T_{0}$ depend on the bag constant, on the number of degrees of freedom of massless elementary fields in the bag, and on whether those fields obey Bose-Einstein, Fermi-Dirac, or Maxwell-Boltzmann statistics. Hence this model satisfies the strong bootstrap condition. The case of eight elementary Abelian vector fields is focused on. The thermodynamics of a system of such composite hadrons naively exhibits a maximum temperature $T_{0}$ . However, due to the finite size of hadrons, many-body effects cause the mass spectrum to have a density-dependent cutoff. A first-order phase transition to a gas of free elementary fields is found at a temperature $T_{c} = 1.05 T_{0}$ .

References (37)

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[c1] Proceedings of the International Symposium on the Statistical Mechanics of Quarks and Hadrons, Bielefeld, Germany, 1980, edited by H. Satz (North-Holland, Amsterdam, to be published)

[c2] J. D. Walecka, Phys. Lett. 59B, 109 (1975)

[c3] R. A. Freedman, Phys. Lett. 71B, 369 (1977)

[c4] R. Hagedorn, Nuovo Cimento Suppl. 3, 147 (1965)

[c5] C. J. Hamer and S. C. Frautschi, Phys. Rev. D 4, 2125 (1971)

[c6] W. Nahm, Nucl. Phys. B45, 525 (1972)

[c7] R. Hagedorn, in Cargèse Lectures in Physics, edited by E. Schatzmann (Gordon and Breach, New York, 1973), Vol. 6

[c8] B. A. Freedman and L. D. McLerran, Phys. Rev. D 16, 1130 (1977) ibid.16, 1147 (1977) ibid.16, 1169 (1977)

[c9] J. I. Kapusta, Nucl. Phys. B148, 461 (1979)

[c10] N. Cabibbo and G. Parisi, Phys. Lett. 59B, 67 (1975)

[c11] A. Chodos, R. L. Jaffe, K. Johnson, and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974)

[c12] G. Chapline and M. Nauenberg, Phys. Rev. D 16, 450 (1977)

[c13] B. Freedman and L. McLerran, Phys. Rev. D 17, 1109 (1978)

[c14] T. DeGrand, R. L. Jaffe, K. Johnson, and J. Kiskis, Phys. Rev. D 12, 2060 (1975)

[c15] R. L. Jaffe and K. Johnson, Phys. Lett. 60B, 201 (1976)

[c16] J. F. Donoghue, in High Energy Physics—1980, proceedings of the XXth International Conference, Madison, Wisconsin, edited by L. Durand and L. G. Pondrom (AIP, New York, 1981)

[c17] K. A. Milton, Phys. Rev. D 22, 1441 (1980)

[c18] J. F. Donoghue and K. Johnson, Phys. Rev. D 21, 1975 (1980)

[c19] R. Giles (unpublished), quoted in [16]

[c20] K. Huang and S. Weinberg, Phys. Rev. Lett. 25, 895 (1970)

[c21] S. Frautschi, Phys. Rev. D 3, 2821 (1971)

[c22] J. V. Lepore and R. N. Stuart, Phys. Rev. 94, 1724 (1954)

[c23] R. H. Milburn, Rev. Mod. Phys. 27, 1 (1955)

[c24] J. Baacke, Acta Phys. Pol. B8, 625 (1977)

[c25] V. B. Magalinskii and Ia. P. Terletskii, Zh. Eksp. Teor. Fiz. 32, 584 (1957) [Sov. Phys.-JETP 5, 483 (1957)]

[c26] G. H. Hardy and S. Ramanujan, Proc. London Math. Soc. 17, 75 (1918)

[c27] R. Dashen, S. Ma, and H. J. Bernstein, Phys. Rev. 187, 345 (1969)

[c28] K. F. Herzfeld, Ann. Phys. (Paris) 51, 261 (1916)

[c29] E. Fermi, Z. Phys. 26, 54 (1924)

[c30] G. Baym, Physica 96A, 131 (1979)

[c31] R. F. Sawyer, Astrophys. J. 176, 205 (1972)

[c32] G. Baym, H. A. Bethe, and C. J. Pethick, Nucl. Phys. A175, 225 (1971)

[c33] F. Karsch and H. Satz, Phys. Rev. D 22, 480 (1980)

[c34] R. D. Carlitz, Phys. Rev. D 5, 3231 (1972)

[c35] J. I. Kapusta, Nucl. Phys. B (to be published) and Ref. 1

[c36] B. Müller and J. Rafelski, Phys. Lett. B (to be published)

[c37] R. Hagedorn and J. Rafelski, Phys. Lett. 97B, 136 (1980) [1]

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Asymptotic mass spectrum and thermodynamics of the Abelian bag model

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