Evolution Equations for Nonlocal Hadron Operators

  • Su-Long Nyeo

Abstract

The study of high-energy scattering processes of hadrons involving transfer of large momenta can be carried out with the help of the operator-product expansion (OPE) (Wilson, 1969) for products of local operators. Such an expansion has often been given in terms of local operators of different twists at short or light-like distances. However, as indicated by several calculations (Geyer, 1982; Balitsky, 1983; Braunschweig et al., 1984; Geyer et al., 1985), it is more effective to use a nonlocal light-cone expansion (LCE) called the string operator expansion (SOE), which is given in terms of gauge-invariant nonlocal operators. This expansion enjoys the fact that it is a true identity in the Fock space (Anikin and Zavialov, 1978), whereas a local LCE is valid only on a dense subset of the Fock space (Bordag and Robaschik, 1980). Moreover, the use of the SOE is physically very appealing, since hadrons, whose dynamics can be very well described by quantum chromodynamics (QCD), are extended objects and should be more naturally described by appropriate gauge-invariant nonlocal operators (Graigie and Dorn, 1981). Thus, nonlocal operators can play an important role both in our understanding of QCD and in practical computations. Therefore, it is hoped that the SOE can provide a more effective and systematic approach to the understanding of nonleading twist effects in QCD.

Keywords

Anomalous Dimension Light Cone Quantum Chromo Dynamic Nonlocal Operator Weyl Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anikin, S.A., and O.I. Zavialov, 1978, Short-distance and light-cone expansions for products of currents, Ann. Phys. ( NY ) 116: 135.MathSciNetADSCrossRefGoogle Scholar
  2. Balitsky, I.I., 1983, String operator expansion of the T product of two currents near the light cone, Phys. Lett. 124B: 230.Google Scholar
  3. Balitsky, I.I., and Braun, V.M., 1988/89, Evolution equations for QCD string operators, Nucl. Phys. B311: 541.Google Scholar
  4. Balitsky, I.I, Braun V.M., and Kolesnichenko, A.V., 1989, Radiative decay E+ Py in quantum chromodynamics, Nucl. Phys. B312: 509.ADSCrossRefGoogle Scholar
  5. Bordag, M., and Robaschik, D., 1980, Light-cone expansion in renormalized perturbation theory, Nucl. Phys. B169: 445.Google Scholar
  6. Braun, V.M., and Filyanov, I.B., 1990, Conformal invariance and pion wave functions of nonleading twist, Z. Phys. C48: 239.Google Scholar
  7. Braunschweig, Th., Geyer, B., Hoiejsí, J., and Robaschik, D., 1987, Hadron operators on the light cone, Z. Phys. C33: 275.Google Scholar
  8. Braunschweig, Th., Geyer, B., and Robaschik, D., 1987, Anomalous dimensions of flavour singlet light-cone operators, Ann. Phys. ( Leipzig ) 44: 403.Google Scholar
  9. Braunschweig, Th., Hoiejsí, J., and Robaschik, D., 1984, Nonlocal light-cone expansion and its applications to deep inelastic scattering processes, Z. Phys. C23: 19.Google Scholar
  10. Brodsky, S.J., and Lepage, G.P., 1980, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D22: 2157.Google Scholar
  11. Geyer, B., 1982, Anomalous dimensions in local and non-local light cone expansion, Czech. J. Phys. B32: 645.Google Scholar
  12. Geyer, B., Robaschik, D., Bordag, M., and Hoiejsí, J., 1985, Nonlocal light-cone expansions and evolution equations, Z. Phys. C26: 591.MathSciNetGoogle Scholar
  13. Graigie, N.S., and Dorn, H., 1981, On the renormalization and short-distance properties of hadronic operators in QCD, Nucl. Phys. B185: 204.ADSGoogle Scholar
  14. Kremer, M., 1980, Anomalous dimensions of gauge-invariant three-fermion local operators of twist three, Nucl. Phys. B 168: 272.Google Scholar
  15. Novikov, V.A., Shifman, M.A., Vainshtein, A.I., and Zakharov, V.I., 1984, Calculations in external fields in quantum chromodynamics. technical review., Fortschr. Phys. 32: 585.CrossRefGoogle Scholar
  16. Nyeo, S.-L., 1992, Anomalous dimensions of nonlocal baryon operators, Z. Phys. C54: 615.Google Scholar
  17. Ohrndorf, Th., 1982, Constraints from conformal covariance on the mixing of operators of lowest twist, Nucl. Phys. B198: 26.Google Scholar
  18. Okawa, M., 1980, Higher twist effects in asymptotically free gauge theories: the anomalous dimensions of four-quark operators, Nucl. Phys. B172: 481.Google Scholar
  19. Peskin, M.E., 1979, Anomalous dimensions of three-quark operators, Phys. Lett. 88B: 128.Google Scholar
  20. Shuryak, E.V., and Vainshtein, A.I., 1982, Theory of power corrections to deep inelastic scattering in quantum chromodynamics (I). Q-2 effects, Nucl. Phys. B 199: 451.CrossRefGoogle Scholar
  21. Tesima, K., 1982, The operator product expansion of the product of three local fields, Nucl. Phys. B202: 523.Google Scholar
  22. Wilson, K., 1969, Non-lagrangian models of current algebra, Phys. Rev. 179: 1499.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Su-Long Nyeo
    • 1
  1. 1.Department of PhysicsNational Cheng Kung UniversityTainan, Taiwan 701Republic of China

Personalised recommendations