The Light-Cone Fock State Expansion and QCD Phenomenology

  • Stanley J. Brodsky
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 8)

Abstract

The concept of the “number of constituents” of a relativistic bound state, such as a hadron in quantum chromodynamics, is not only frame-dependent, but its value can fluctuate to an arbitrary number of quanta. Thus when a laser beam crosses a proton at fixed “light-cone” time τ = 3Dt + z/c = 3Dx 0 + x z , an interacting photon can encounter a state with any given number of quarks, anti-quarks, and gluons in flight (as long as n q - n = 3D3). The probability amplitude for each such n-particle state of on-mass shell quarks and gluons in a hadron is given by a light-cone Fock state wavefunction \({\Psi _{n/H}}({x_i}{\overrightarrow {,k} _{ \bot \iota }},\lambda )\) , where the constituents have longitudinal light-cone momentum fractions
$${x_i} = 3D\frac{{k_i^ + }}{{{p^ + }}} = 3D\frac{{{k^0} + k_i^x}}{{{p^0} + {p^z}}},\sum\limits_{i = 3D1}^n {{x_i} = 3D1} $$
(1)
relative transverse momentum
$${\overrightarrow k _{ \bot \iota }},\sum\limits_{i = 3D1}^n {{{\overrightarrow k }_{ \bot \iota }}} = 3D{\overrightarrow 0 _ \bot }$$
(2)
and helicities λ i . The ensemble {ψ n/H } of such hght-cone Fock wavefunctions is a key concept for hadronic physics, providing a conceptual basis for representing physical hadrons (and also nuclei) in terms of their fundamental quark and gluon degrees of freedom.[1]

Keywords

Coherence Verse 

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References

  1. [1]
    For a review and further references, see S. J. Brodsky and D.G. Robertson SLAC-PUB-95–7056, to be published in the proceedings of ELFE (European Laboratory for Electrons) Summer School on Confinement Physics, Cambridge, England. e-Print Archive: hep-ph/9511374Google Scholar
  2. [2]
    S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 28, 1983, 228.ADSCrossRefGoogle Scholar
  3. [3]
    H. J. Lu and S. J. Brodsky, Phys. Rev. D 48, 1993, 3310.ADSCrossRefGoogle Scholar
  4. [4]
    S. J. Brodsky, G. T. Gabadadze, A. L. Kataev and H. J. Lu, Phys. Lett. 372B, 1996, 133.Google Scholar
  5. [5]
    H. C. Pauli and S. J. Brodsky, Phys. Rev. D32, 1985, 2001.Google Scholar
  6. [6]
    S. J. Brodsky and H. C. Pauli, SLAC-PUB-5558, published in Schladming 1991, Proceedings.Google Scholar
  7. [7]
    S. J. Brodsky and S. D. Drell, Phys. Rev. D22 1980, 2236.Google Scholar
  8. [8]
    S. J. Brodsky and G.P. Lepage, in Perturbative Quantum Chromodynamics, A. H. Mueller, Ed. (World Scientific, 1989).Google Scholar
  9. [9]
    G. P. Lepage and S. J. Brodsky, Phys. Rev. D22,1980, 2157.Google Scholar
  10. [10]
    S. Dalley, and I. R. Klebanov, Phys. Rev D47, 1993, 2517.MathSciNetGoogle Scholar
  11. [11]
    F. Antonuccio and S. Dalley, Phys. Lett. B376, 1996, 154 e-Print Archive: hep-ph/9512106, and references therein.Google Scholar
  12. [12]
    F. Antonuccio, S.J. Brodsky, and S. Dalley SLAC-PUB-7472, e-Print Archive: hep-ph/9705413Google Scholar
  13. [13]
    A. H. Mueller, Nucl. Phys. B415, 1994, 373.ADSCrossRefGoogle Scholar
  14. [14]
    S. J. Brodsky, C.-R. Ji, A. Pang, and D. G. Robertson, SLAC-PUB-7473. e-Print Archive: hep-ph/9705221.Google Scholar
  15. [15]
    S. J. Brodsky, L. Frankfurt, J. F. Gunion, A. H. Mueller, and M. Strikman, Phys. Rev. D50, 1994, 3134. e-Print Archive: hep-ph/9402283ADSGoogle Scholar
  16. [16]
    S. J. Brodsky and A.H. Mueller, Phys. Lett. 206B, 1988, 685.Google Scholar
  17. [17]
    S. J. Brodsky, P. Hoyer, C. Peterson, and N. Sakai, Phys. Lett. 93B, 1980, 451.Google Scholar
  18. [18]
    B. W. Harris, J. Smith, and R. Vogt, Nucl. Phys. B461, 1996, 181. e-Print Archive: hep-ph/9508403ADSCrossRefGoogle Scholar
  19. [19]
    S. J. Brodsky and M. Karliner SLAC-PUB-7463, e-Print Archive: hep-ph/9704379Google Scholar
  20. [20]
    S. J. Brodsky and L A. Schmidt, Phys. Lett.B234, 1990, 144.Google Scholar
  21. [21]
    S. J. Brodsky and B-Q Ma, Phys. Lett. B381, 1996, 317. e-Print Archive: hep-ph/9604393Google Scholar
  22. [22]
    A. L Signal and A. W. Thomas, Phys. Lett. 191B, 1987, 205.Google Scholar
  23. [23]
    G. Bertsch, S.J. Brodsky, A.S. Goldhaber, and J.F. Gunion, Phys. Rev. Lett. 47, 1981, 297.ADSCrossRefGoogle Scholar
  24. [24]
    L. Frankfurt, G. A. Miller, and M. Strikman, Phys. Lett. B304, 1993, 1. e-Print Archive: hep-ph/9305228Google Scholar
  25. [25]
    Fermillab E791 Collaboration, in progress.Google Scholar
  26. [26]
    P. Kroll and M. Raulfs, Phys. Lett. B387, 1996, 848.Google Scholar
  27. [27]
    I. V. Musatov and A. V. Radyushkin, e-Print Archive: hep-ph/9702443Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Stanley J. Brodsky
    • 1
  1. 1.Stanford Linear Accelerator CenterStanford UniversityStanfordUSA

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