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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 19:24, 12 August 2011
, 19:24, 12 August 2011→Angular Distribution of Two-Body Decay
Let's begin with a general amplitude for the two-body decay of a state with angular momentum quantum numbers ''J'',''m''. Specifically, we want to know the amplitude of this state for having daughter 1 with momentum direction <math>\Omega=(\phi,\theta)</math> in the center of mass reference frame, and helicity <math>\lambda_1</math>, while daughter 2 has direction <math>-\Omega=(\phi+\pi,\pi-\theta)</math> and helicity <math>\lambda_2</math>.
Let's begin with a general amplitude for the two-body decay of a state with angular momentum quantum numbers ''J'',''m''. Specifically, we want to know the amplitude of this state for having daughter 1 with momentum direction <math>\Omega=(\phi,\theta)</math> in the center of mass reference frame, and helicity <math>\lambda_1</math>, while daughter 2 has direction <math>-\Omega=(\phi+\pi,\pi-\theta)</math> and helicity <math>\lambda_2</math>.
Let U be the decay operator from the initial state into the given 2-body final state. Insertion of the complete set of helicity basis vectors gives
<math>
\langle \Omega \lambda_1 \lambda_2 | U | J m \rangle
\langle \Omega \lambda_1 \lambda_2 | U | J m \rangle
=
=
| J m \lambda_1 \lambda_2 \rangle \langle J m \lambda_1 \lambda_2 |
| J m \lambda_1 \lambda_2 \rangle \langle J m \lambda_1 \lambda_2 |
U | J m \rangle
U | J m \rangle
</math></td>
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