1. Radiative meson transitions in the quark model Olga Lakhina University of Pittsburgh Research Advisor Eric Swanson

2. Typically used approximations  Impulse approximation

3. quark antiquark + quark antiquark Typically used approximations  Impulse approximation

4. Typically used approximations  Impulse approximation  Using SHO meson wave functions

5. Typically used approximations  Impulse approximation  Using SHO meson wave functions Gaussian Coulomb+linear rr

6. Typically used approximations  Impulse approximation  Using SHO meson wave functions  Dipole (long wave-length) approximation

7. Typically used approximations  Impulse approximation  Using SHO meson wave functions  Dipole (long wave-length) approximation The momentum of the photon: (no recoil) In reality

8. Typically used approximations  Impulse approximation  Using SHO meson wave functions  Dipole (long wave-length) approximation  Non-relativistic approximation

9. Typically used approximations  Impulse approximation  Using SHO meson wave functions  Dipole (long wave-length) approximation  Non-relativistic approximation Not true (especially for the light quarks)

10. Typically used approximations  Impulse approximation  Using SHO meson wave functions  Dipole (long wave-length) approximation  Non-relativistic approximation  Applied to only light or heavy quark sector

11. Perform the detailed study of meson radiative transitions Motivation Use realistic wave functions Relativistic corrections / effects Higher order diagrams (beyond the impulse approximation) Bound state formalism

12. Our method Hamiltonian : Electromagnetic interaction:

13. Non-relativistic approximation Hamiltonian: Electromagnetic interaction:

14. Results for cc mesons

15. Results for light mesons

16. Higher order diagrams Nonrelativistic approximation of Hamiltonian: model: + other terms

17. Higher order diagrams

18. VMD model diagram We have to sum over the intermediate states

19. This diagram does not contribute if we don’t sum over the intermediate states Second order diagram

20. + = 0 These diagrams cancel for cc mesons

21. Second order diagram

22. Effects of higher order diagrams (GeV -1/2 )

23. Cornell model + neglected - order

24. END

25. r V(r) Potential energy of quark interaction in a meson Coulomb dependence Linear dependence

26. where Decay rate:

27. Vector meson dominance model Quark model