Final (main) Block G, describing $X + s_{12} (\to p_1 p_2) + s_{34} (\to p_3 p_4)$.

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

In practice, this block allows to trade the energies of the four inputs $p_{1 \dots 4}$ for the two propagator invariants $s_{12}$ and $s_{34}$. The angles of the input particles are not affected.

Warning: this change of variable is only valid if the four inputs $p_{1 \dots 4}$ are massless!

The change of variable is done by solving the following system:

• $s_{12} = (p_1 + p_2)^2$
• $s_{34} = (p_3 + p_4)^2$
• Conservation of momentum (with $\vec{p}_T^{b}$ the total transverse momentum of possible other particles in the event):
  • $p_{1x} + p_{2x} + p_{3x} + p_{4x} = - p_{Tx}^{b}$
  • $p_{1y} + p_{2y} + p_{3y} + p_{4y} = - p_{Ty}^{b}$

Up to four solutions are possible for $(p_1, p_2, p_3, p_4)$.

Integration dimension

This module requires 0 phase-space point.

Global parameters

Inputs

Outputs

Note

This block has been validated and is safe to use.

See also

Looper module to loop over the solutions of this Block

Definition at line 79 of file BlockG.cc.