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Applicability of pQCD to Basic Hadronic Processes

This document discusses the applicability of perturbative Quantum Chromodynamics (pQCD) to fundamental hadronic processes. Key topics include the determination of hadron form factors, two-photon annihilation processes, hadron scatterings, and the decays of heavy hadrons. The presentation references crucial literature and outlines the methodology behind asymptotic distribution amplitudes and pion electromagnetic form factors. Although results show good agreement with experimental data, definitive statements regarding pQCD's applicability at accessible energies remain elusive.

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Applicability of pQCD to Basic Hadronic Processes

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  1. The applicability of pQCD to basic hadronic processes Goran Duplancic MPI für Physik, München goran@mppmu.mpg.de Ringberg workshop, 8-10 January 2007

  2. Exclusive processes: • The processes defining the hadron form factors • The two photon annihilation processes • The hadron scatterings • The decays of heavy hadrons

  3. G.P.Lepage and S.J.Brodsky, Phys. Lett. B 87, 359 (1979); Phys. Rev. Lett. 43, 545 (1979) [Erratum-ibid. 43, 1625 (1979)]; Phys. Rev. D 22, 2157 (1980) A.V.Efremov and A.V.Radyushkin, Theor. Math. Phys. 42, 97 (1980) [Teor. Mat. Fiz. 42, 147 (1980)]; Phys. Lett. B 94, 245 (1980) A.Duncan and A.H.Mueller, Phys. Lett. B 90, 159 (1980); Phys. Rev. D 21, 1636 (1980).

  4. Asymptotic (as) Chernyak-Zhitnitsky (CZ) Bakulev, Mikhailov, Stefanis (BMS) Distribution Amplitude (DA)

  5. Photon to pion transition form factor ( ) Kadantseva, Mikhailov, Radyushkin, Yad. Fiz. 44, 507 (1986); Aguila, Chase, Nucl. Phys.B 193, 517 (1981); Braaten, Phys. Rev. D 28, 524 (1983); Melic, Nizic, Passek, Phys. Rev. D 65, 053020 (2002)

  6. Pion electromagnetic form factor ( )

  7. Field, Gupta, Otto, Chang, Nucl. Phys. B 186, 429 (1981); Dittes, Radyushkin, Yad. Fiz. 34, 529 (1981); Sarmadi, Phys. Lett. B 143, 471 (1984); Khalmuradov, Radyushkin, Yad. Fiz. 42, 458 (1985); Braaten, Tse, Phys. Rev. D 35, 2255 (1987); Melic, Nizic, Passek, Phys. Rev. D 60, 074004 (1999)

  8. Pion pair production ( ) Brodsky and Lepage approximation (Phys. Rev. D 24, 1808 (1981):

  9. approx. Grzelak [DELPHI], Ascona 2001, 279; Heister et al. [ALEPH], Phys. Lett. B 569, 140 (2003); Nakazawa et al. [BELLE], Phys. Lett. B 615, 39 (2005)

  10. approx. (BELLE)

  11. approx.

  12. Pedlar et al. [CLEO Collaboration], Phys. Rev. Lett. 95, 261803 (2005)

  13. Distinct diagrams contributing to at NLO. The total number of diagrams is 422.

  14. G. D., Nizic, Phys. Rev. Lett. 97, 142003 (2006)

  15. approx.

  16. BLM scale setting procedure

  17. approx.

  18. approx. (BELLE)

  19. Brodsky and Lepage: NLO prediction: LO(BLM): BELLE data:

  20. Brodsky and Lepage: NLO prediction:

  21. approx.

  22. Final remarks for basic exclusive processes at large momentum transfer: + energy and angular dependence of NLO predictions are in very good agreement with the data normalization represents a problem the NLO corrections can be substantial,so a part of the normalization problem can be attributed to the size of uncalculated higher-order corrections However, assuming reasonable scale variation of the NLO prediction, or controlled perturbative series (LO > NLO > NNLO) it is not to be expected that inclusion of higher-order corrections would lead to a solution of the normalization problem. On the other hand, relative good agreement between theory and experiment for the ratios suggest that the specific form of the DA certainly plays a relevant role. - +- - +- Presented results are not conclusive enough to allow a definite statement regarding the applicability of the pQCD at the currently accessible energies, but it is hard to believe that momentum transfer smaller than 10 GeV would be enough.

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