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Power counting for three-body decays of a near-threshold state · Around

2015

Power counting for three-body decays of a near-threshold state

Alhakami, Mohammad H., Birse, Michael C.

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We propose a new power counting for the effective field theory describing a near-threshold state with unstable constituents, such as the X(3872) meson.

In this counting, the momenta of the heavy particles, the pion mass and the excitation energy of the unstable constituent -- the D* in the case of the X -- are treated as small scales, of order Q.
The difference, delta, between the excitation energy of the D* and the pion mass is smaller than either by a factor ~20.
We therefore assign delta an order Q^2 in our counting.

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