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photon spectrum in the soft-energy region

This talk discusses the calculation of the orthopositronium (o-Ps) decay spectrum in the soft-energy region using the NRQED approach and the threshold expansion of 1-loop diagrams. The results have relevance for heavy quarkonium and Upsilon decays.

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photon spectrum in the soft-energy region

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  1. photon spectrum in the soft-energy region Pedro Ruiz-Femenía RWTH Aachen University arXiv:0705.1330 Nucl.Phys.B 788 (2008) Talk at EFT09: International Workshop on Effective Field Theories 2-6 February 2009, Valencia

  2. Outline • Motivation • The oPs decay spectrum for • The soft-radiation loop momentum region • spectrum for • Summary • NRQED calculation • QED spectrum in the soft-energy region ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  3. Motivation • orthopositronium (o-Ps) decay spectrum for • NRQED, includes binding effects • satisfies Low´s theorem for [ Manohar, RF ’03 ] • valid for the whole region ? new non-relativistic mode? does NRQED provide the right expansion for ? ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  4. NRQED computation of the oPs spectrum • there is a long-distance part in the decay when one of the photons in the final state is not hard short-distance part hard photons long-distance part Coulomb Hamiltonian ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  5. Dipole approximation dipole approx. Atomic transitions in Ps Multipole expansion valid for o-Ps  3 decay with one small-energy photon [ Voloshin ’04 ] ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  6. oPs calculation without multipole expanding the e.m. field [RF ’07 ] dipole approx. ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  7. EFT oPs spectrum: results ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  8. from the NRQED computation in the region QED computation • exact phase-space distribution at one-loop is known [ Adkins ’05 ] ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  9. Threshold expansion of QED 1-loop diagrams Beneke, Smirnov ‘98 • asymptotic expansion of loop integrals involving heavy massive particles close to threshold • separation of regions achieved by expanding loop momenta according to the v-scaling above (each region contributes to a single power of v) ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  10. Ladder graph ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  11. 1-loop QED result for • agrees with NLO term of NRQED calculation ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  12. Relevance for Heavy Quarkonium • photon spectrum can be written as a sum of a direct contrib. and a fragmentation contrib. ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  13. 1-loop QCD correction for ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  14. Results for the direct Upsilon decay spectrum Krämer ‘99 Catani, Hautmann ’95 Maltoni, Petrelli ‘99 ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  15. Results for the direct Upsilon decay spectrum ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  16. Summary • NRQED calculation of the photon spectrum valid for all • Threshold expansion of 1-loop diagrams • Application to the soft-energy direct photon spectrum in Upsilon decays is straightforward ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

  17. EFT oPs spectrum: ________________________________________________________ EFT09: International Workshop on Effective Field Theories, Valencia, Feb 2nd

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