Conformal constraints and the evolution of the nonsinglet meson distribution amplitude

D. Müller

doi:10.1103/PhysRevD.49.2525

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Conformal constraints and the evolution of the nonsinglet meson distribution amplitude

D. Müller

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309

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Phys. Rev. D 49, 2525 – Published 1 March, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.2525

Abstract

Using conformal Ward identities, the influence of conformal symmetry breaking on the evolution of the flavor-nonsinglet quark-antiquark distribution amplitude is investigated in dimensional regularization and a minimal subtracted scheme. It is found that a conformal consistency relation provides some simplification for construction of the distribution amplitude. Both the evolution in the next-to-leading approximation and a closed expression for the $O (α_{s})$ correction to the eigenfunctions of the evolution kernel in the $β = 0$ case can thus be determined analytically.

References (28)

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A. V. Efremov and A. V. Radyushkin, Phys. Lett. 94B, 245 (1980)
M. K. Chase, Nucl. Phys. B167, 125 (1980)
H.-N. Li and G. Sterman, Nucl. Phys. B381, 129 (1992)
F. Del Aguila and M. K. Chase, Nucl. Phys. B193, 517 (1981) F.-M. Dittes and A. V. Radyushkin, Yad. Fiz. 34, 529 (1981) [Sov. J. Nucl. Phys. 34, 293 (1981)] R. D. Field, R. Gupta, S. Otto, and L. Chang, Nucl. Phys. B186, 429 (1981)
E. P. Kadantseva, S. V. Mikhailov, and A. V. Radyushkin, Yad. Fiz. 44, 507 (1986) [Sov. J. Nucl. Phys. 44, 326 (1986)]
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F.-M. Dittes and A. V. Radyushkin, Phys. Lett. 134B, 359 (1984) M. H. Sarmadi, ibid. 143B, 471 (1984)
G. R. Katz, Phys. Rev. D 31, 652 (1985) S. V. Mikhailov and A. V. Radyushkin, Nucl. Phys. B254, 89 (1985)
S. J. Brodsky, P. Damgaard, Y. Frishman, and G. P. Lepage, Phys. Rev. D 33, 1881 (1986)
S. J. Brodsky, Y. Frishman, G. P. Lepage, and C. Sachradja, Phys. Lett. 91B, 239 (1980)
V. K. Dobrev, V. B. Petkova, S. G. Petrova, and I. T. Todorov, Phys. Rev. D 13, 887 (1976)
Yu. M. Makeenko, Yad. Fiz. 33, 842 (1981) [Sov. J. Nucl. Phys. 33, 440 (1981)] Th. Ohrndorf, Nucl. Phys. B198, 26 (1982) N. S. Craigie, V. K. Dobrev, and I. T. Todorov, Ann. Phys. (N.Y.) 159, 411 (1985)
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D. Müller, Z. Phys. C 49, 293 (1991)
G. Mack and A. Salam, Ann. Phys. (N.Y.) 53, 174 (1969)
G. 't Hooft, Nucl. Phys. B61, 455 (1973)
J. C. Collins, Nucl. Phys. B80, 341 (1974)
S. Sarkar, Nucl. Phys. B83, 108 (1974)
N. K. Nielsen, Nucl. Phys. B65, 413 (1973) R. P. Zaikov, Mod. Phys. Lett. A 3, 703 (1988)
D. Müller, Dr. thesis, University Leipzig, 1992
E. G. Floratos, D. A. Ross, and C. T. Sachrajda, Nucl. Phys. B129, 66 (1977) ibid.B139, 545(E) (1978) A. González-Arroyo, C. López, and F. J. Ynduráin, B153, 161 (1979)
S. V. Mikhailov and A. V. Radyushkin, Nucl. Phys. B273, 297 (1986)
F.-M. Dittes, D. Müller, D. Robaschik, B. Geyer, and J. Hořejši, Phys. Lett. B 209, 325 (1988)

[c1] S. J. Brodsky and G. P. Lepage, Phys. Lett. 87B, 359 (1979) Phys. Rev. Lett. 43, 545 (1979) ibid.43, 1625(E) (1979)

[c2] A. V. Efremov and A. V. Radyushkin, Phys. Lett. 94B, 245 (1980)

[c3] M. K. Chase, Nucl. Phys. B167, 125 (1980)

[c4] H.-N. Li and G. Sterman, Nucl. Phys. B381, 129 (1992)

[c5] F. Del Aguila and M. K. Chase, Nucl. Phys. B193, 517 (1981) F.-M. Dittes and A. V. Radyushkin, Yad. Fiz. 34, 529 (1981) [Sov. J. Nucl. Phys. 34, 293 (1981)] R. D. Field, R. Gupta, S. Otto, and L. Chang, Nucl. Phys. B186, 429 (1981)

[c6] E. P. Kadantseva, S. V. Mikhailov, and A. V. Radyushkin, Yad. Fiz. 44, 507 (1986) [Sov. J. Nucl. Phys. 44, 326 (1986)]

[c7] S. J. Brodsky and G. P. Lepage, in Quantum Chromodynamics (La Jolla Institute, 1978), Proceedings of the Summer Workshop, edited by W. Frazer and F. Henyey, AIP Conf. Proc. No. 55 (AIP, New York, 1979)

[c8] F.-M. Dittes and A. V. Radyushkin, Phys. Lett. 134B, 359 (1984) M. H. Sarmadi, ibid. 143B, 471 (1984)

[c9] G. R. Katz, Phys. Rev. D 31, 652 (1985) S. V. Mikhailov and A. V. Radyushkin, Nucl. Phys. B254, 89 (1985)

[c10] S. J. Brodsky, P. Damgaard, Y. Frishman, and G. P. Lepage, Phys. Rev. D 33, 1881 (1986)

[c11] S. J. Brodsky, Y. Frishman, G. P. Lepage, and C. Sachradja, Phys. Lett. 91B, 239 (1980)

[c12] V. K. Dobrev, V. B. Petkova, S. G. Petrova, and I. T. Todorov, Phys. Rev. D 13, 887 (1976)

[c13] Yu. M. Makeenko, Yad. Fiz. 33, 842 (1981) [Sov. J. Nucl. Phys. 33, 440 (1981)] Th. Ohrndorf, Nucl. Phys. B198, 26 (1982) N. S. Craigie, V. K. Dobrev, and I. T. Todorov, Ann. Phys. (N.Y.) 159, 411 (1985)

[c14] Higher Transcendental Functions (Bateman Manuscript Project), edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. II

[c15] M. Bordag, B. Geyer, J. Hořejši, and D. Robaschik, Z. Phys. C 26, 591 (1985)

[c16] V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112, 173 (1984) V. M. Braun and I. E. Filyanov, Z. Phys. C 44, 157 (1989) S. V. Mikhailov and A. Radyushkin, Yad. Fiz. 49, 794 (1989) [Sov. J. Nucl. Phys. 49, 494 (1989)] I. Halperin, Z. Phys. C 56, 615 (1992)

[c17] S. V. Esaibegyan and S. N. Tamaryan, Yad. Fiz. 51, 485 (1990) [Sov. J. Nucl. Phys. 51, 310 (1990)]

[c18] D. Daniel, R. Gupta, and D. G. Richards, Phys. Rev. D 43, 3715 (1991)

[c19] D. Müller, Z. Phys. C 49, 293 (1991)

[c20] G. Mack and A. Salam, Ann. Phys. (N.Y.) 53, 174 (1969)

[c21] G. 't Hooft, Nucl. Phys. B61, 455 (1973)

[c22] J. C. Collins, Nucl. Phys. B80, 341 (1974)

[c23] S. Sarkar, Nucl. Phys. B83, 108 (1974)

[c24] N. K. Nielsen, Nucl. Phys. B65, 413 (1973) R. P. Zaikov, Mod. Phys. Lett. A 3, 703 (1988)

[c25] D. Müller, Dr. thesis, University Leipzig, 1992

[c26] E. G. Floratos, D. A. Ross, and C. T. Sachrajda, Nucl. Phys. B129, 66 (1977) ibid.B139, 545(E) (1978) A. González-Arroyo, C. López, and F. J. Ynduráin, B153, 161 (1979)

[c27] S. V. Mikhailov and A. V. Radyushkin, Nucl. Phys. B273, 297 (1986)

[c28] F.-M. Dittes, D. Müller, D. Robaschik, B. Geyer, and J. Hořejši, Phys. Lett. B 209, 325 (1988)

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Conformal constraints and the evolution of the nonsinglet meson distribution amplitude

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