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

Typically used approximations  Impulse approximation

quark antiquark + quark antiquark Typically used approximations  Impulse approximation

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

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

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

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

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

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)

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

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

Our method Hamiltonian : Electromagnetic interaction:

Non-relativistic approximation Hamiltonian: Electromagnetic interaction:

Results for cc mesons

Results for light mesons

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

Higher order diagrams

VMD model diagram We have to sum over the intermediate states

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

+ = 0 These diagrams cancel for cc mesons

Second order diagram

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

Cornell model + neglected - order

END

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

where Decay rate:

Vector meson dominance model Quark model