| 29 | | == Model Description == |
| | 29 | == Model Description -- helicity polarization as a Feynman rule == |
| | 30 | |
| | 31 | The broad idea of the ''helicity polarization as a Feynman rule'' is to treat the helicity-truncated propagator (see [ [#BuarqueFranzosi 2] ] for details) as the Feynman rule for a particle that sits in a definite helicity polarization. |
| | 32 | The helicity-truncated propagator is given by |
| | 33 | {{{ |
| | 34 | #!latex |
| | 35 | \begin{align} |
| | 36 | \Pi_{\mu\nu}^{V\lambda}(q) = \frac{-i\varepsilon_\mu(q,\lambda)\ \varepsilon^*_\nu(q,\lambda)}{q^2-M_V^2 +iM_V\Gamma_V} |
| | 37 | \end{align} |
| | 38 | |
| | 39 | and is related to the full propagator by |
| | 40 | |
| | 41 | \begin{align} |
| | 42 | &\Pi_{\mu\nu}^V (q) = |
| | 43 | \frac{-i\left(g_{\mu\nu} - q_\mu q_\nu / M_V^2\right)}{q^2-M_V^2 +iM_V\Gamma_V}\ |
| | 44 | \\ |
| | 45 | &=\sum_{\lambda\in\{0,\pm1,A\}} |
| | 46 | \eta_\lambda\ \left( |
| | 47 | \frac{-i\varepsilon_\mu(q,\lambda)\ \varepsilon^*_\nu(q,\lambda)}{q^2-M_V^2 +iM_V\Gamma_V} \right)\ . |
| | 48 | \end{align} |
| | 49 | }}} |
| | 50 | |
| | 51 | Here, {{{$\eta_\lambda=+1$}}}, unless {{{$\lambda=0$}}} and {{{$V_{\lambda}$}}} is in the t-channel; in that case {{{$\eta_\lambda=-1$}}}. |
