Scaled Invariant Mass Squared Algorithms

There are two algorithms available, each with the same 3 variants ( or schemes ). The first algorithm is known as the JADE algorithm, which defines the invariant mass as:

M² = 2E₁E₂(1 - cos$\theta_{12}^{}$).

The second is known as the DURHAM algorithm and uses a proposal by Dokshitzer for invariant mass, which is less sensitive to soft gluons:

M² = 2(MIN(E₁, E₂))²(1 - cos$\theta_{12}^{}$).

Both algorithms combine particles into jets using one of the following combination schemes:

E scheme

P_ij = P_i + P_j
E_ij = E_i + E_j

P scheme

P_ij = P_i + P_j
E_ij = | P_ij|

E₀ scheme

E_ij = E_i + E_j
P_ij = E_ij(P_i + P_j)/| P_i + P_j|

For more details, please read the internal reports ALEPH 90-149 (SOFTWR 90-015) and ALEPH 91-151 ( SOFTWR 91-006 ).