Invariant Mass and the Center-of-Mass Frame

The invariant mass of a pair of HepLorentzVectors is given by:

$$w_1\mbox{.invariantMass2}(w_2) = \left(t_1+t_2\right)^2 - \left\vert \vec{v}_1 - \vec{v}_2 \right\vert ^2$$ (88)

$$w_1\mbox{.invariantMass}(w_2) = \left(t_1+t_2\right)^2 - \left\vert \vec{v}_1 - \vec{v}_2 \right\vert ^2 \times \mbox{sign}(t_1 + t_2)$$ (89)

The boost necessary top bring a pair of vectors into their Center-of-Mass frame is given by

$$w_1\mbox{.findBoostToCM}(w_2) = - \frac{\vec{v}_1 + \vec{v}_2}{t_1+t_2}$$ (90)

If the sum of the two 4-vectors is spacelike, this makes analytic sense but is physically meaningless; a ZMxpvTachyonic error will be ZMthrown. If the sum of the time components is zero, a ZMxpvInfiniteVector error will be ZMthrown.