Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

Eric Braaten; Kingman Cheung; Sean Fleming; Tzu Chiang Yuan

doi:10.1103/PhysRevD.51.4819

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Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

Eric Braaten

Kingman Cheung and Sean Fleming

Tzu Chiang Yuan

Theory Group, Fermilab, Batavia, Illinois 60510

Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208

Davis Institute for High Energy Physics, Department of Physics, University of California, Davis, California 95616

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Phys. Rev. D 51, 4819 – Published 1 May, 1995

DOI: https://doi.org/10.1103/PhysRevD.51.4819

Abstract

The perturbative QCD fragmentation functions for a heavy quark to fragment into heavy-light mesons are studied in the heavy-quark limit. The fragmentation functions for S-wave pseudoscalar and vector mesons are calculated to next-to-leading order in the heavy-quark mass expansion using the methods of heavy-quark effective theory. The results agree with the $m_{b}$ →∞ limit of the perturbative QCD fragmentation functions for b¯ into $B_{c}$ and $B_{c}^{*}$ . We discuss the application of the perturbative QCD fragmentation functions as a model for the fragmentation of heavy quarks into heavy-light mesons. Using this model we predict the fraction $P_{V}$ of heavy-light mesons that are produced in the vector meson state as functions of the longitudinal momentum fraction z and the transverse momentum relative to the jet axis. The fraction $P_{V}$ is predicted to vary from about 1/2 at small z to almost 3/4 near z=1.

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[c1] See, for example, B. Grinstein, Annu. Rev. Nucl. Part. Sci. 42, 101 (1992); M. Neubert, Phys. Rep. 245, 259 (1994).

[c2] R. Jaffe and L. Randall, Nucl. Phys. B412, 79 (1994).

[c3] E. Braaten and T. C. Yuan, Phys. Rev. Lett. 71, 1673 (1993).

[c4] C. H. Chang and Y. Q. Chen, Phys. Lett. B 284, 127 (1992); Phys. Rev. D 46, 3845 (1992).

[c5] E. Braaten, K. Cheung and T. C. Yuan, Phys. Rev. D 48, 4230 (1993).

[c6] E. Braaten, K. Cheung and T. C. Yuan, Phys. Rev. D 48, R5049 (1993).

[c7] K. Cheung, Phys. Rev. Lett. 71, 3413 (1993).

[c8] K. Cheung and T. C. Yuan, Phys. Lett. B 325, 481 (1994).

[c9] E. Braaten, M. A. Doncheski, S. Fleming and M. L. Mangano, Phys. Lett. B 333, 548 (1994).

[c10] C. Peterson, D. Schlatter, I. Schmidt and P. Zerwas, Phys. Rev. D 27, 105 (1983).

[c11] M. Suzuki, Phys. Rev. D 33, 676 (1986).

[c12] G. Curci, W. Furmanski and R. Petronzio, Nucl. Phys. B175, 27 (1980); J. C. Collins and D. E. Soper, ibid. B194, 445 (1982); ibid. B193, 381 (1981).

[c13] J. P. Ma, Phys. Lett. B 332, 398 (1994).

[c14] P. D. B. Collins and T. P. Spiller, J. Phys. G 11, 1289 (1985).

[c15] F. Ezawa, Nuovo Cimento 23A, 271 (1974); G. R. Farrar and J. D. Jackson, Phys. Rev. Lett. 35, 1416 (1975); G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).

[c16] D. Bortoletto et al., Phys. Rev. D 37, 1719 (1988).

[c17] B. Andersson et al., Phys. Rep. 97, 33 (1983); M. G. Bowler, Z. Phys. C 11, 169 (1981); ibid. 22, 155 (1984).

[c18] G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51, 1125 (1995).

[c19] Y. Q. Chen, Phys. Rev. D 48, 5158 (1993); T. C. Yuan, ibid. 50, 5664 (1994).

[c20] A. F. Falk and M. E. Peskin, Phys. Rev. D 49, 3320 (1994).

[c21] K. Cheung and T. C. Yuan, Phys. Rev. D 50, 3181 (1994).

[c22] K. Cheung and R. J. Oakes, Phys. Lett. B 333, 181 (1994).

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Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

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