How to correct the HBT signal for resolution effects:

In HBT, we extract the source geometry (or something related to it…) through the two-particle relative wavefunction, which dictates the probability of measuring a pair with momenta (**k _{1},k_{2}**), as compared to the probability of measuring such a pair if they did not know about each other (i.e. the particles did not interact through any effect like Coulomb, strong, or quantum statistics). This latter probability we get from event-mixing, so the correlation is

,

where R stands for "real" and B for "background".

Nature puts in this "extra weighting" based on (**k _{1},k_{2}**), and if we understand the relative wavefunction, we can get some idea of the source of the particles.

However, we do not measure (**k _{1},k_{2}**)—instead we measure (

We form a __correction function__

,

where here the unprimed momenta are the "true" ones, and the primed momenta are what we would measure in our detector. The rates (R and B) are obtained by

Note:

- We assume knowledge of the correlation function which we are trying to measure!!
**This implies an iterative approach**. - The "Filtered signal" R(k’
_{1},k’_{2}) is__binned__in the filtered (smeared) momenta, but__weighted__with the true momenta.**This is just as it would be in a real experiment—Nature does the weighting and we do the binning with momenta we measure.**

There is also an additional part of this correction to deal with the Coulomb correction, but I don’t list it here (out of laziness). It follows the same lines.