Relativistic form factors for clusters with nonrelativistic wave functions

A. N. Mitra; Indra Kumari

doi:10.1103/PhysRevD.15.261

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Relativistic form factors for clusters with nonrelativistic wave functions

A. N. Mitra^*

Indra Kumari

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

Department of Physics, University of Delhi, Delhi-7, India

^*University Grants Commission (India) National Fellow. Permanent address: Department of Physics, University of Delhi, Delhi-7, India.

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Phys. Rev. D 15, 261 – Published 1 January, 1977

DOI: https://doi.org/10.1103/PhysRevD.15.261

Abstract

Using a simple variant of an argument employed by Licht and Pagnamenta (LP) on the effect of Lorentz contraction on the elastic form factors of clusters with nonrelativistic wave functions, it is shown how their result can be generalized to inelastic form factors so as to produce (i) a symmetrical appearance of Lorentz contraction effects in the initial and final states, and (ii) asymptotic behavior in accord with dimensional scaling theories. A comparison of this result with a closely analogous parametric form obtained by Brodsky and Chertok from a propagator chain model leads, with plausible arguments, to the conclusion of an effective mass $M$ for the cluster, with $M^{2}$ varying as the number $n$ of the quark constituents, instead of as $n^{2}$ . A further generalization of the LP formula is obtained for an arbitrary duality-diagram vertex, again with asymptotic behavior in conformity with dimensina scaling. The practical usefulness of this approach is emphasized as a complementary tool to those of high-energy physics for phenomenological fits to data up to moderate values of $q^{2}$ .

References (18)

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R. Blankenbecler et al., Nucl. Phys. 12, 629 (1969) M. Gourdin et al., Nuovo Cimento 37, 524 (1965)
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S. Brodsky and B. Chertok, Phys. Rev. D 14, 3003 (1976)
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K. Fujimura et al., Prog. Theor. Phys. 44, 193 (1970)
A. Licht and A. Pagnamenta, Phys. Rev. D 2, 1150 (1970)
H. Harari, Phys. Rev. Lett. 29, 562 (1969) J. Rosner, ibid.29, 689 (1969)
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A. N. Mitra, Phys. Rev. D 14, 855 (1976)
Y. S. Kim and M. Noz, Phys. Rev. D 12, 129 (1975)
Indra Kumari and A. N. Mitra (unpublished)
H. A. Bethe, Phys. Rev. 103, 1353 (1956)
R. P. Feynman et al., Phys. Rev. D 3, 2706 (1971)
G. Farrar and D. Jackson, Phys. Rev. Lett. 35, 1416 (1975)
B. F. Bayman and A. N. Mitra, unpublished work

[c1] A. Jaffe, Phys. Rev. Lett. 17, 661 (1966) J. Harte, Phys. Rev. 165, 1557 (1968) J. Ball and F. Zachariasen, ibid. 170, 1541 (1968)

[c2] R. Blankenbecler et al., Nucl. Phys. 12, 629 (1969) M. Gourdin et al., Nuovo Cimento 37, 524 (1965)

[c3] S. Brodsky and G. Farrar, Phys. Rev. Lett. 31, 1153 (1973) Phys. Rev. D 11, 1309 (1975) V. Matveev et al., Lett. Nuovo Cimento 7, 719 (1973)

[c4] R. Arnold et al., Phys. Rev. Lett. 35, 776 (1975)

[c5] S. Brodsky and B. Chertok, Phys. Rev. D 14, 3003 (1976)

[c6] J. Gunion, Phys. Rev. D 4, 718 (1971) F. Gross, ibid. 10, 223 (1974) R. Arnold, private communication

[c7] R. Woloshyn, Phys. Rev. Lett. 36, 220 (1976)

[c8] K. Fujimura et al., Prog. Theor. Phys. 44, 193 (1970)

[c9] A. Licht and A. Pagnamenta, Phys. Rev. D 2, 1150 (1970)

[c10] H. Harari, Phys. Rev. Lett. 29, 562 (1969) J. Rosner, ibid.29, 689 (1969)

[c11] A. Le Yaouanc et al., Phys. Rev. D 8, 2223 (1973)

[c12] A. N. Mitra, Phys. Rev. D 14, 855 (1976)

[c13] Y. S. Kim and M. Noz, Phys. Rev. D 12, 129 (1975)

[c14] Indra Kumari and A. N. Mitra (unpublished)

[c15] H. A. Bethe, Phys. Rev. 103, 1353 (1956)

[c16] R. P. Feynman et al., Phys. Rev. D 3, 2706 (1971)

[c17] G. Farrar and D. Jackson, Phys. Rev. Lett. 35, 1416 (1975)

[c18] B. F. Bayman and A. N. Mitra, unpublished work

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Relativistic form factors for clusters with nonrelativistic wave functions

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References (18)

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