NEW SOURCE FOR POWER-LAW TYPE DEVIATIONS FROM BJORKEN SCALING

  • We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall "energy" conservation yields the same new scaling variable xp,which reduces to the Weizmann variable,the Bloom-Gilman variable and the Bjorken variable at some approximations.The xp rescaling is expected to be a good scaling variable,and hence gives substantial power-law type corrections to the deviations from the Bjorken scaling.Understandings of the xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE are also given,indicating that it is likely a higher order effect in the coefficient functions; i.e,it does not belong to the higher twist effect.Therefore this xp rescaling is a new effect contributing to the power-law type corrections,and hence is of substantial importance to the extraction of a reliable value of the QCD scale Λ from the data.
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  • [1] R. P. Feynman, High Energy Collisions, Proc. Third Int. Conf. on High Energy Collision, Stony Brook, 1969, edited by C. N. Yang et al., (Gordon and Breach, New York,1969); Phys. Rev. Lett., 23(1969), 1415; Photon-Hadron Interactions, (Benjamin, New York, 1972).[2] J. D. Bjorken, Phys. Rev., 179(1969), 1547, J. D.Bjorken and E. A. Paschos, Phys. Rev., 185(1969),1975.[3] K. Wilson, Phys Rev., 179(1969), 1499; B. L. Ioffe, Phys. Lett., B30(1969), 123; R. A. Brandt and G.Preparata, Nucl.Phys., B27(1971), 541; Y. Frisliman, Ann. Phys., 66(1971), 373; N. Christ, B. Hasslacher and A. Mueller.Phys, Rev.;D6(1972), 3543.[4] E. Stueckelberg and G. Peterman, Helv. Phys. Acta, 5(1953), 499; M. Gell-Mann and F. Low, Phys. Rev 95(1954), 1300; C. G. Callan, Phys. Rev., D2(1970), 154; K. Symanzik, Comm. Mash. Phys., 18(1970),227; K. Wilson, Phys. Rev., D3(1971), 1818.[5] D.Gross and F. Wilczek, Phys. Rev. Lett., 30(1973), 1343; H. D. Politzer, ibid., 30(1973), 1346.[6] H.Georgi and H. D. Politzer, Phys. Rev., D9(1974), 416; D. Gross and F. Wilczek, ibid., D8(1973),3622; D9(1974), 980.[7] H. Georgi and H. D, Politzer, Phys. Rev. Lett., 36(1976), 1281; Erratum, ibid., 37(1976), 68 Phys,Rev., D14(1976), 1829.[8] R. M. Barnett, D. Schlatter and L.Trentadue, Phys. Rev. Lett,46(1981),1659; D. W. Duke and R. G. Roberts, Nucl.Phys., B165(1980), 243; F. Eisele, M. Gluck E. Hoffman and E. Reya, Phys.Rev., D26(1982), 41.[9] G. Altarelli and G. Parisi, Nucl. Phys., B126(1977), 298[10] See, for example, Appendix B of the first paper in Ref.17[11] E. D. Bloom and F.J. Gilman Phys. Rev.25(1970), 1140; Phys. Rev., D4(1971), 2901.[12] V. Rittenberg and H. R. Rubinstein, Phys. Lett., B35(1971), 50; F. W. Brasse et al., Nucl. Phys., B39(1972), 421[13] R .M.Barnett, Phys. Rev. Lett., 48(1982), 1657; Phys. Rev.,D27(1983), 41[14] S. J.Brodsky, TeV Physics and Beyond, Proc. Vlllth Summet School in Nuclear and Particle Physics,Launceston, Tasmania, 1987, edited by R. Delbourgo and J. R. Fox (World Scientific, Singapare, 1987), p.173, please see page 202[15] O. Nachtmann, Nucl Phys., B63(1973), 237.[16] B. Q. Ma, Phys. Lett,B176(1986), 179.[17] S. J. Brodsky, Lectures on Lepton Nucleon Scattering and Quantum Chromodynamics, edited by A. Jaffe and D. Ruelle (Birkhauser, Boston, 1982), p. 255; Quarks and Nuclear Forces, edited by D. C. Fries and B. Zeitnitz (Springer-Verlay, Berlin Heidelberg, 1982), p. 81 and references therein. See also S. J. Brodsky, T. Huang and G. P. Lepage, Praticles and Fields, edited by A. Z. Capri and A. N. Kamal (Plenum Publishing Corporation, 1983), p. 143[18] J. Ellis, Weak and Electromagnetic Interactions at High Energy, edited by R. Balian and C. H. Llewellyn Smith (North-Holland, 1977), p.1;see also, J. Ellis and R. L. Jaffe, U. C. Santa Cruz Summer School Lectures, SLAC-PUB-1253(1973).[19] E. Leader and E. Predazzi, An Introduction to Gaugo Theories and the "New Physics" (Cambridge University Press, Cambridge, 1982), ch. 14.[20] S. D. Drell, D. J. Levy and T.-M.Yan, Phys. Rev., 187(1969), 2159; Dl(1970), 1035;S. D.Drell and T. -M. Yan, Ann. Phys.,66(1971),578.[21] R. Barbieri, J. Ellis, M. K. Gaillard and G. G.Ross,Phys. Lett., B64(1976), 171[22] S. Weinberg, Phys. Rev., 150(1966), 1313.[23] P. A. M. Dirac, Rev. Mod. Phys., 21(1949), 392;see also, H. Leutwyler and J.Stern, Ann. Phys., 112 (1978), 94.[24] L. Susskind, Phys. Rev., 165(1968), 1535; K. Bardakci and M. B. Halpern, ibid., 176(1968), 1686,S.-J Chang and S. Ma,ibid., 180(1969), 1506; J. B.Kogut and D. Soper, ibid, DI(1970), 2901; J.D.Bjorken. J. B. Kogut and D. Sopcr, ibid.,D3(1971),1382.[25] 马伯强,北京大学技术物理系博士论文,1989.[26] F. J. Gilman, private commuflication (1986).[27] 龙鸣、黄涛,高能物理与核物理,10(1986),562;龙鸣,高能物理与核物理,10(1986),632.
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MA Bo-Qiang and SUN Ji. NEW SOURCE FOR POWER-LAW TYPE DEVIATIONS FROM BJORKEN SCALING[J]. Chinese Physics C, 1990, 14(5): 416-426.
MA Bo-Qiang and SUN Ji. NEW SOURCE FOR POWER-LAW TYPE DEVIATIONS FROM BJORKEN SCALING[J]. Chinese Physics C, 1990, 14(5): 416-426. shu
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NEW SOURCE FOR POWER-LAW TYPE DEVIATIONS FROM BJORKEN SCALING

    Corresponding author: MA Bo-Qiang,
  • Technical Physics Department,Peking University

Abstract: We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall "energy" conservation yields the same new scaling variable xp,which reduces to the Weizmann variable,the Bloom-Gilman variable and the Bjorken variable at some approximations.The xp rescaling is expected to be a good scaling variable,and hence gives substantial power-law type corrections to the deviations from the Bjorken scaling.Understandings of the xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE are also given,indicating that it is likely a higher order effect in the coefficient functions; i.e,it does not belong to the higher twist effect.Therefore this xp rescaling is a new effect contributing to the power-law type corrections,and hence is of substantial importance to the extraction of a reliable value of the QCD scale Λ from the data.

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