MomentumScale

This package is able to decompose the momentum scale biases in a global scale $\varepsilon_{s}$ and a residual Z $\varepsilon_{dz}$ (or alternatively radial) scale based on the following equations:

$${m'}_{\mu\mu}^2/m_{\mu\mu}^2 - 1\approx + 2 A^{+}_s \varepsilon_{s}(\eta^+,\phi^+) + 2 A^{-}_s \varepsilon_{s}(\eta^-,\phi^-) + 2 A^{+}_z \varepsilon_{dz}(\eta^+,\phi^+) + 2 A^{-}_z \varepsilon_{dz}(\eta^-,\phi^-) \\$$

where $A^{\pm}_s = E^{\pm}E^{\mp}\left( \pmb{\beta}^{\pm} - \pmb{\beta}^{\mp} \right )^2 /m_{\mu\mu}^2 $ and $A^{\pm}_z = E^{\pm}E^{\mp}\left[ \left(\beta_{\mathrm{z}}^{\pm} \right)^2 - \pmb{\beta}_{\mathrm{z}}^{\mp} \cdot \pmb{\beta}_{\mathrm{z}}^{\pm}\right] /m_{\mu\mu}^2 $.

The parameters are equivelent to: $E^+E^-\left( \pmb{\beta}^+ - \pmb{\beta}^- \right)^2 = m^2_{\mu\mu} - m^2_\mu \left(E^+ + E^- \right)^2/E^+E^- $
and that $E^+E^-\left( \left( \beta^+\right)^2 - \pmb{\beta}^+ \cdot \pmb{\beta}^- \right) = m^2_{\mu\mu}/2 - m_{\mu}^2 (1+E^{-}/E^{+}) $

The python file MC_Mass.py fills the histograms which are then fitted using TestFit.C some manual intervention is needed at the moment to ensure the binning assumed in both is the same