$\require{cancel}$ Final (main) Block F, describing $q_1 q_2 \to X + s_{13} (\to \cancel{p_1} p_3) + s_{24} (\to \cancel{p_2} p_4)$

Final (main) Block F on $q_1 q_2 \to X + s_{13} + s_{24} \to X + p_1 p_2 p_3 p_4$, where $q_1$ and $q_2$ are Bjorken fractions, $s_{13}$ and $s_{24}$ are particles decaying respectively into $p_1$ (invisible particle) and $p_3$ (visible particle), and $p_2$ (invisible particle) and $p_4$ (visible particle).

This Block addresses the change of variables needed to pass from the standard phase-space parametrization to the $\frac{1}{16\pi^2 E_1 E_2} dq_{1} dq_{2} ds_{13} d_s{24} \times J$ parametrization.

The integration is performed over $q_{1}$, $q_{2}$, $s_{13}$ and $s_{24}$ with $p_3$ and $p_4$ as inputs. Per integration point, the LorentzVectors of the invisible particle, $p_1$ and $p_2$, are computed based on this set of equations:

• $s_{13} = (p_1 + p_3)^2$
• $s_{24} = (p_2 + p_4)^2$
• Conservation of momentum (with $p^{vis}$ the total momentum of visible particles):
  • $p_{1x} + p_{2x} = - p_{x}^{vis}$
  • $p_{1y} + p_{2y} = - p_{y}^{vis}$
• $p_{1z} + p_{2z} = s^{1/2} (q_1 - q_2)/2 - p_z^{vis}$
• $E_{1} + E_{2} = s^{1/2} (q_1 + q_2)/2 - E^{vis}$
• $p_1^2 = m_1^2$
• $p_2^2 = m_2^2$

The observed MET is not used in this block since to reconstruct the neutrinos the system requires as input the total 4-momentum of the visible objects (energy and longitudinal momentum included).

Up to 2 ( $p_1$, $p_2$) solutions are possible.

Integration dimension

This module requires 2 phase-space points.

Global parameters

Parameters

| Name | Type | Description | | m1
m2 | double, default 0 | Masses of the invisible particles $p_1$ and $p_2$ |

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 95 of file BlockF.cc.