Clustering Algebra
Go to plane of decay products, then boost to Pz = 0
Start
DOF counting:
- \(P_1^\mu\) - 3 DoF : \(P_x\), \(P_z\) and m
- \(P_2^\mu\) - 3 DoF : \(P_x\), \(P_z\) and m
- 1 constraint \(P_z^1 + P_z^2 = 0\)
End
One combined vector
DOF counting:
- \(P_T\), \(\theta\) , z, \(m_1\), \(m_2\)
Clustering
\[ P_{comb}^\mu = P_1^\mu + P_2^\mu = \begin{pmatrix} E_1 + E_2 \\ P_T^1 + P_T^2 \\ 0 \\ 0 \end{pmatrix} \]