Side Channel Analysis (CorrPA), comparison between HW-results and measured power traces I think I have missed something very fundamental.

I am trying to understand the step in DPA where you compare your hypothetical power consumptions with your measured ones.
The Matrix H with Matrix T.

Matrix T is of size D x T, where D is the number of data blocks and T is the number of measured points in one power trace. This implies that an element value in this matrix T can be of 0.58W (just an example).

If I use Hamming Weight, as power model, I will end up with a real number.
E.g., 0110 0111 = 5 (dimensionless). How can this number correlate with the power traces that are in Watts? (e.g., If I use Pearsons).
You should use the value you found (in watt). Try to have a look at this  file, it's really well explained in my opinion. If you look for page 21 for instance, you'll see that the plaintext produces a certain waveform; then, after the hypotesis and the S-Box output, the correlation is clearly done with the power model obtained and the value of the traces (page 23)