sPHENIX is a new detector at RHIC.

[Gabor David <david AT bnl.gov>]

        Dear Kurt and Ron,

        looking at your slide 4 presented today (spatial distribution)
of hadrons I mentioned that we did things like that in the past and
even promised slides.  Unfortunately, the work was done in Debrecen,
Hungary 2004 with students... so no slides any more; but luckily I
found my notes made at the end of the course.

        Here's what we did.  We worked with pions, kaons
and protons, varying their impact momentum, impinging upon the
PHENIX EMCal orthogonally. For each momentum we simulated a
few thousand particles, and let GEANT tell us the response
in the towers of the cluster.  We looked both at the event
average (as you do on your top right plots) and individual
events, to get a "feeling" what's going on.  Again, it was
only an EMCal, leaking energy, but this is the trickiest
detector in your work, too.

        We quickly found out that we need some mixture of a
narrow Gaussian (A1, sigma1, corresponding to the e.m. part
of the shower) and a wider one (A2, sigma2, the hadron part),
and that you have to randomize the ratio A1/A2, and A1, A2,
sigma1, sigma2 are weakly dependent on pT.  (For the hadron
part of course you can try other distributions that spread out,
but we didn't find anything that would have worked better
than a wider Gaussian.)

        The overall description of the average shower spread
was quite reasonable, but at closer look in the the GEANT showers
the ratio of the energy in the central tower to the total deposited
energy was always slightly less than in the parametrization - which
in turn described the bulk and the tails very well.  That's
when we realized that we have to add a 3rd component, the
minimum ionization energy deposited BEFORE the shower starts,
and of course the depth where the showers starts should be
randomized.  This depth then gives you both the minion deposit
and the amount of energy leakage at the end on the detector.

        So our best model had three components: a MIP (effecting
only one tower), an e.m. and a hadronic Gaussian.  Remember, we are 
talking about an EMCal which usually leaks hadron energy,
the question is how much.  Therefore, the parameters to play with
(and ultimately randomize event-by-event) were
        1/ the depth where the hadron shower starts -> this
dtermines the minion deposit and the fraction of the total
hadron energy you have to still assign to the e.m. and hadron
part of the shower
        2/ the widths of the e.m. and hadron Gaussian
        3/ the ratio of the electromagnetic deposit to the
hadronic one (and again, the sum of these two is still
usually much smaller than the initial particle energy).

        All this may sound complicated, but in fact isn't
(several students got quite impressive results in a week);
but one certainly has to play a bit until the right ranges
of the parameters above (the ranges where to randomize them).

        If something is unclear, please stop by in my office.

        Gabor



--
Gabor David  (david AT bnl.gov)
Brookhaven National Laboratory
Physics Department, Bldg 510/c
UPTON NY 11973
Tel: (631)344-3016
FAX: (631)344-3253