sPHENIX HCal discussion

[John Lajoie <lajoie AT iastate.edu>]

Hi Stefan,

    Nice detective work, I'm really glad you are working through all the details!

    I think that what you suggest is very good.  We are still a little short without the full iHCAL, so I would still offer my suggestion in my previous email, but the situation doesn't look horrible.

Regards,
John

On 2/6/2018 10:49 AM, Stefan Bathe wrote:

Dear Edward and All,

First, thanks, Edward, for explaining how we can correct for shower leakage.  I appreciate it!  I’ll try to put a few words on this into the CDR.

Second, the inconsistency is resolved:  the measurements and parameterization I referenced earlier start from where the shower begins, not from the beginning of the calorimeter!  (I had missed that important point earlier, sorry about that.)  So one has to add one nuclear interaction length to those numbers (or 1.2 if one takes into account that the pion nuclear interaction length is 1.2 times the nuclear interaction length).  That’s the single nuclear interaction length I was missing.

Now, which value should we use for a realistic energy?  How about 20 GeV (for a ’typical’ 30 GeV jet where the leading particle carries 2/3 of the jet energy)?  Then I get from Table 4 in [AB81] (measurement of incident negative pions with 2.5 cm Fe sampling calorimeter): 

L(95%) =  5*12.5 cm Fe + 1.2 lambda = 62.6 cm Fe + 1.2 lambda = (3.7+1.2) lambda = 4.9 lambda (with lambda_Fe = 17 cm).

The calorimeter is (EMCal + iHCal + oHCal) = 

0.725 + 0.55 + 3.8 = 5.075 lambda if we build the full iHCal

0.725 + 0.25 + 3.8 = 4.775 lambda if we just build the Al frame 

So we are in fact very close to L(95%) in either case.  I would just suggest to change 5.5 lambda to 4.9 lambda for L(95%) in the CDR and quote the particle energy.

Regards,

Stefan 

-- 

--------------------------------------------------------------------------------- Stefan Bathe

Professor of Physics Baruch College, CUNY

Baruch:                                     BNL: 17 Lexington Ave                      Bldg. 510 office 940                                  office 2-229 phone 646-660-6272                phone 631-344-8490 ----------------------------------------------------------------------------------

On Feb 5, 2018, at 10:58 PM, Edward Kistenev <kistenev AT bnl.gov> wrote:

PS. Stephan, 

there is no literature which may answer the question about leakage to better then 10%. Reading through your references you will probably find that the coefficients in the formulas approximating averages are particle mass dependent and that the dependence is not just because the energy we measure  is kinetic, not the total. Showers have different spectra and particle composition at different depth, below 100GeV measured energy distribution for a constant momenta is absolutely nongaussian and response linearity is only in dreams.  What is interesting is that with all the problems we have with the shower fluctuations the amount of leakage is rather easy to compute even on the event-by-event basis (and correct). It has an rms equal to its value (almost poissonial), but the value itself has little dependence on particle mass and CG fluctuations (showers in the tails are all “equal”) are easy to control/compensate if calorimeter is longitudinally segmented. In essence this is how sPHENIX calorimeter was designed. It was supposed to consist of three longitudinal sections with HInner and HOuter (if creatively used) offering one extra section each (total 5). This is because the neighboring towers overlap. If you know the “line of flight” - energies in overlapping towers correspond to specific (changing event-by-event) shower localizations which are computable and usable for global CG computations. You may use tracking data to define the “line-of-flight” or use “in calorimeter tracking” iteratively. The non compensating nature of calorimeter can be handled in a similar way resulting in rather gaussian final energy distribution. All this is yet to be implemented but few words along these lines will not hurt the CDR. 

Edward

On Feb 5, 2018, at 10:19 PM, Edward Kistenev <kistenev AT bnl.gov> wrote:

Here is my beloved free pocket calculator addressing your problems down to better then 10%  (created at a time immemorial - BW). 

http://www.slac.stanford.edu/comp/physics/matprop.html

On Feb 5, 2018, at 9:37 PM, Stefan Bathe <bathe AT bnl.gov> wrote:

Dear Edward, John, and Jamie,

Which book is that, Edward?  It would be nice to be able to look up the references.

For 100 GeV (just to stay with my earlier example) I get 6.2 lambda from the first and 7.2 lambda from the second formula.  They are not within 10 % of each other nor within 10 % of the measurements for Fe I quoted earlier.

I agree we won’t see 100 GeV jets in AuAu.  I had to pick one energy to compare the numbers, and the kinematic limit seemed to me a convenient upper limit.  For 70 GeV all numbers will be about 0.2 lambda smaller.

Regards,

Stefan

-- 

--------------------------------------------------------------------------------- Stefan Bathe

Professor of Physics
Baruch College, CUNY

Baruch:                                     BNL:
17 Lexington Ave                      Bldg. 510
office 940                                  office 2-229 phone 646-660-6272                phone 631-344-8490
----------------------------------------------------------------------------------

On Feb 5, 2018, at 6:29 PM, Edouard Kistenev <kistenev AT bnl.gov> wrote:

10% approximation always looked fine to me

<PastedGraphic-1.tiff>

On Feb 5, 2018, at 3:23 PM, Stefan Bathe <bathe AT bnl.gov> wrote:

Dear All,

I find some inconsistencies with how many nuclear interaction lengths (lambda) are required to contain 95 % of the energy of a hadronic shower (L(95%)):

1) The CDR says 

L(95%) > 5.5 lambda 

in the introductory section of the HCal.  No energy is quoted.  So let’s assume 100 GeV pions as proxies for jets at kinematic limit for RHIC HI.

2) [WI00] (Fig 2.37, attached) gives 

L(95%) @ 100 GeV = 6.0 lambda

N.B.:  the reference is [AB81]!

3) [AB81] gives 

L(95%) @ 100 GeV: 87.5 cm Fe = 5.15 lambda (table 4)

contradicting Wigmans!

4) [HO78b] gives 

L(95%) @ 100 GeV: 82 cm Fe = 4.8 lambda (Fig. 10)

5) [KL91] gives

L(95%) @ 100 GeV: 82 cm Fe = 4.8 lambda (parameterization)

I’m inclined to dismiss Wigmans since the plot misrepresents the quoted reference.  Does anybody have better information?  Or maybe I’m misunderstanding something?

Regards,

Stefan

references:

—

[WI00] Wigmans, Calorimetry, Oxford, 2000” (p. 87, Fig. 2.37)

(see attachment)

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[HO78b] M.Holder et al., Nucl.Instr.Meth.,151,69 (1978),
Performance of a Magnetized Total Absorption Calorimeter Between 15-GeV and 140-GeV 5 cm Fe sampling L(95%) @ 100 GeV: 82 cm Fe = 4.8 lambda (from plot with data points and fit in paper; or parameterization in Kleinknecht textbook)

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwju8M2mxY_ZAhWHyoMKHTAyAgQQFgg_MAQ&url="http%3A%2F%2Fcds.cern.ch%2Frecord%2F879171%2Ffiles%2Fep113_001.pdf&usg=AOvVaw18tk97fLX9RJZVIoNU1SVM"

---

[AB81] Nucl.Instr.Meth.,180,429 (1981) 
The response and resolution of an iron-scintillator calorimeter for hadronic and electromagnetic showers between 10 GeV and 140 GeV 2 cm Fe sampling L(95%) @ 100 GeV: 87.5 cm Fe = 5.15 lambda (table) comments: - interaction required in first 37.5 cm of iron; possible bias
- referenced in Wigmans, but I cannot reproduce Wigmans plot from data in paper

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0ahUKEwjRoonEyI_ZAhVs4YMKHd-dCaUQFghTMAc&url="https%3A%2F%2Fcds.cern.ch%2Frecord%2F134124&usg=AOvVaw0ZxhJB8UKofvCs-ni1UPaX —

[KL92] "Kleinknecht, Detektoren fuer Teilchenstrahlung, Teubner, 1992”, I find the following parameterization:
L(95%) = [9.4 ln E(GeV) + 39] cm Fe.  With lambda = 17.1 cm (Fe)

also references [BL82] H. Bluemer, Diplomarbeit Dortmund, 1982

<Wigmans2.37.JPG>

--  --------------------------------------------------------------------------------- Stefan Bathe

Professor of Physics Baruch College, CUNY
Baruch:                                     BNL: 17 Lexington Ave                      Bldg. 510 office 940                                  office 2-229 phone 646-660-6272                phone 631-344-8490 ----------------------------------------------------------------------------------

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John Lajoie

Professor of Physics

Iowa State University

 

(515) 294-6952

lajoie AT iastate.edu

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