If one knows the resolution, then one can correct the signal (iteratively) via a technique used by NA44, which I describe here as well, in case you want to refresh your memory.

Our resolution comes from 3 sources:

- Energy loss in the target and trigger scintillator
- Multiple Coulomb Scattering in the target and trigger scintillator
- Hitfinding and tracking "intrinsic" resolution

With the help of Juan Romero and Gulshan, the first two of these were
implemented. Given a pion of a certain momentum, I start
it randomly in the target and propogate through the material-- energy loss
and MCS then give me the new momentum (of course it is a random process).

For cross-checking, Juan and I ran some identical sets of particles through
our independent codes. He posted both of our results on
this page.
(Note -- previously I had the wrong page listed here-- thanks Juan.)

For the "intrinsic" resolution of our detector (this means that after
the target and scintillator, the particle has some new momentum-- how well
do we measure this new momentum?), I had been using our canonical "dp/p=1%".
However, this seemed too good as compared to my old slow simulator simulations
(which were flawed for other reasons), and I wanted to get a resolution estimate
**from the data itself**.

It seems a good way to get an estimate of the intrinsic resolution by looking at weak decay peak widths. These secondary particles do NOT suffer MCS in target (which dominates scintillator anyway), so their resolution is mostly "intrinsic" only. Perfect "intrinsic" resolution (0%) should give a zero-width spike in the kaon invariant mass spectrum.

Dieter and Paul both have nice peaks, and their widths are pretty much consistent
with each other. I use Dieter's to estimate the intrinsic resolution. To do this,
I decay 10,000 lambdas and 10,000 kaons using a geant routine, boost the particles
to the system c.m. frame (i.e. y_{cm} of the Au+Au system), and then smear
the particles' momentum by:

p_{x} --> p_{x}*(1.0 + resolution*Gauss)

p_{y} --> p_{y}*(1.0 + resolution*Gauss)

p_{z} --> p_{z}*(1.0 + resolution*Gauss)

where Gauss is a random number from a gaussian distrib of unit sigma, and resolution would be 0.01 for 1% resolution.

Beam Energy |
L width (MeV/c) |
K0 width (MeV/c) |
dp/p (p) (%) |
dp/p (p) (%) |

2 |
1.17 |
4.6 |
1.5 |
2 |

4 |
3 |
6 |
3 |
3 |

6 |
3.5 |
8.7 |
3 |
4 |

8 |
4.4 |
7.9 |
3 |
4 |

Here are some plots of fits to the 3D signal in the Bertsch-Pratt decomposition (R

- 2 AGeV correlation function fits
- 4 AGeV correlation function fits
- 6 AGeV correlation function fits
- 8 AGeV correlation function fits

Note that we do __NOT__ expect the fits to converge as we increase our dp/p estimate. They
can/should change. The above plots are to show the sensitivity to our estimate.

Update - with the parameterized resolution, we our corrected fits fall somewhere in between the 1% and 3.5% estimates - see this discussion for details.