For the isolation cut, the most recent previous analysis (the W cross section PRD) used two criteria.  The first was designed primarily to make sure the e.m. shower (for the candidate lepton) was not one photon from pi^0 decay, in which case there would be another e.m. shower very close by.  The check was to compare the summed energy in the 2x2 tower cluster of the candidate (called E_T^e) to the sum in the 4x4 cluster centered on the 2x2 cluster.  The requirement was that E_T^e / (E_T in 4x4) > 0.95.  This ensured that the 12 towers surrounding the 2x2 cluster of interest had less than 5% of the transverse energy of the lepton candidate.

In the current analysis, nothing similar is done; that is, there is no purely e.m. isolation condition applied.

The second isolation cut is designed to discriminate against jet-like events, and is the more important test.  Since we seem to get hung up on notation, and ascii text is not so great for equations, I will define 4 quantities:

1 = energy of the candidate lepton from the BEMC
2 = momentum of the candidate lepton from the TPC
3 = all other e.m. energy in a cone of R=0.7 centered on candidate lepton
4 = all other charged particle momentum in the same cone

For 3 and 4, "all other" means excluding the energy or momentum of the candidate, respectively.

In the PRD, a cut is made on the quantity:  1 / (1+3+4)

In the current analysis, a cut is made on the quantity:  (1+2) / (1+2+3+4)