Radiative meson transitions in the quark model

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

• Impulse approximation

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Typically used approximations

• Impulse approximation

quark
quark

antiquark
antiquark
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Typically used approximations

• Impulse approximation
• Using SHO meson wave functions

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Typically used approximations

• Impulse approximation
• Using SHO meson wave functions

Gaussian
r
r
Coulomblinear
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Typically used approximations

• Impulse approximation
• Using SHO meson wave functions
• Dipole (long wave-length) approximation

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Typically used approximations

• Impulse approximation
• Using SHO meson wave functions
• Dipole (long wave-length) approximation
• The momentum of the photon
• (no recoil)
• In reality

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Typically used approximations

• Impulse approximation
• Using SHO meson wave functions
• Dipole (long wave-length) approximation
• Non-relativistic approximation

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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)

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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

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Motivation

• Perform the detailed study of meson radiative
  transitions

• Use realistic wave functions
• Relativistic corrections / effects
• Higher order diagrams (beyond the impulse
  approximation)
• Bound state formalism

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Our method

• Hamiltonian
• Electromagnetic interaction

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Non-relativistic approximation

• Hamiltonian
• Electromagnetic interaction

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Results for cc mesons
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Results for light mesons
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Higher order diagrams
Nonrelativistic approximation of Hamiltonian
other terms
model
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Higher order diagrams
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VMD model diagram
We have to sum over the intermediate states
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Second order diagram
This diagram does not contribute if we dont sum
over the intermediate states
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Second order diagram

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These diagrams cancel for cc mesons
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Second order diagram
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Effects of higher order diagrams (GeV-1/2)
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Cornell model

- order
neglected
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END
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Potential energy of quark interaction in a meson
V(r)
Linear dependence
Coulomb dependence
r
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where
Decay rate
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• Vector meson dominance model
• Quark model

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