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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 00:19, 20 August 2011
, 00:19, 20 August 2011→Assembly of the full amplitude
Identification of <math>\epsilon_i</math> with <math>\epsilon_i'</math> and <math>\epsilon_f</math> with <math>\epsilon_f'</math> implies that only terms with <math>\epsilon_R=\epsilon_R'</math> survive in the sum over exchange quantum numbers. The quadratic sum expression above for the differential cross section invokes a double-sum over all of the internal quantum numbers that have been introduced, plus the spins of the initial and final nucleons. This sum is of the generic form
Identification of <math>\epsilon_i</math> with <math>\epsilon_i'</math> and <math>\epsilon_f</math> with <math>\epsilon_f'</math> implies that only terms with <math>\epsilon_R=\epsilon_R'</math> survive in the sum over exchange quantum numbers. The quadratic sum expression above for the differential cross section invokes a double-sum over all of the internal quantum numbers that have been introduced, plus the spins of the initial and final nucleons. This sum is of the generic form
:<math>
:<math>
\sum_{X,M_X,\cdots} \cdots \sum_{\epsilon_R\epsilon_i\epsilon_f}
\sum_{X,M_X,\cdots} \cdots \sum_{\epsilon_i\epsilon_f}
|w_{\lambda_R \epsilon_R; \epsilon_i \epsilon_f}|^2
</math>
Note that the measured cross section only depends on the summed
modulus squared of the ''w'' coefficients, and not on their
individual values or phases. Because of this, the sum over nucleon
helicities can be dropped, and the ''w'' factors absorbed into
the ''v'' coefficients by multiplying the ''v'' defined above with
the square root of the above sum.
=== Mass dependence ===
=== Mass dependence ===