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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 01:41, 16 August 2011
, 01:41, 16 August 2011→Assembly of the full amplitude
The di-pion system in the decay of the <math>\omega</math> is non-resonant, so its width is entered as infinity. The mass-dependent terms in the expressions above are given by the explicitly unitary Breit-Wigner form:
The di-pion system in the decay of the <math>\omega</math> is non-resonant, so its width is entered as infinity. The mass-dependent terms in the expressions above are given by the explicitly unitary Breit-Wigner form:
:<math>
:<math>
BW_L(m,\Gamma^0)=\frac{m_0 \Gamma_L(m)}{m_0^2-m^2-im_0\Gamma_L(m)}
BW_L(m; m_0,\Gamma_0)=\frac{m_0 \Gamma_L(m)}{m_0^2-m^2-im_0\Gamma_L(m)}
</math>
</math>
where,
where,
:<math>
:<math>
\Gamma_L(m)=\Gamma^0 \frac{m_0}{m} \frac{q}{q_0} \frac{F^2_L(q)}{F^2_L(q_0)}
\Gamma_L(m;m_0,\Gamma_0)=\Gamma_0 \frac{m_0}{m} \frac{q}{q_0} \frac{F^2_L(q)}{F^2_L(q_0)}
</math>
</math>
where ''q'' is the breakup momentum of the daughter particles and ''q<sub>0</sub>'' is the same, evaluated at ''m<sub>0</sub>''.
where ''q'' is the breakup momentum of the daughter particles and ''q<sub>0</sub>'' is the same, evaluated at ''m<sub>0</sub>''.