Hitfinding/tracking resolution effects on HBT

At the Stony Brook meeting in August98, I described the resolution correction I am doing for the HBT signal.
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:

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. ycm of the Au+Au system), and then smear the particles' momentum by:

px --> px*(1.0 + resolution*Gauss)
py --> py*(1.0 + resolution*Gauss)
pz --> pz*(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.

Results

The results from such a study were that I could reproduce Dieter's widths with the following "intrinsic" resolutions:

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


So What?

OK, so it looks like the intrinsic pion resolution is better described by something on the order of 3.5% instead of 1%, at least for the higher energies. What is the effect on the HBT?
Here are some plots of fits to the 3D signal in the Bertsch-Pratt decomposition (Rout,Rside,Rlong) with NO correction at all, with 1% intrinsic resolution assumed, and with 3.5% intrinsic resolution assumed. (Sorry for the red background.) As you can see, it is a significant effect that our intrinsic resolution is 3.5%.

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.