$\require{cancel}$ Final (main) Block C, describing $s_{123} (\to p_3 + s_{12} (\to \cancel{p_1} p_2))$

This Block addresses the change of variables needed to pass from the standard phase-space parametrisation for $p_{1 \dots 3} \times \delta^4$ to a parametrisation in terms of the two (squared) masses of the intermediate propagators and the angular variables of $p3$.

The integration is performed over $s_{12}, s_{123}\, \theta_3, \phi_3$ with $p_{1 \dots 3}$ as input. Per integration point, the LorentzVector of the invisible particle, $p_1$, is computed as well as the energy of the (necessarily massless) particle $p_3$, based on the following set of equations:

• $s_{12} = (p_1 + p_2)^2$
• $s_{123} = (p_1 + p_2 + p_3)^2$
• Conservation of momentum (with $\vec{p}_T^{branches}$ the total transverse momentum of all branches represented):
  • $p_{1x} + E_3 \sin\theta_3\cos\phi_3 = - p_{Tx}^{branches}$
  • $p_{1y} + E_3 \sin\theta_3\cos\phi_3 = - p_{Ty}^{branches}$

Up to four solutions are possible for $(E1, \alpha)$, where $\alpha = 2 p_1 \dot p_2$.

Integration dimension

This module requires 0 phase-space point.

Global parameters

Parameters

Inputs

Outputs

Note

This block has been partially validated and is probably safe to use.

See also

Looper module to loop over the solutions of this Block

Definition at line 81 of file BlockC.cc.