# Presentation: 500767

## Dan is interested in the calibration of the HCAL for jets.

**He defines “R” as the measured energy of a pion, probably in ADC counts**
**R = e Ee + h Eh**
**Ee is the fraction of the pion energy in the form of photons**
**Eh is the hadronic fraction**
**In most models, the fraction of the true energy in photons is**
**F0=Ee/E ~ 0.11[ln(E)]**
**(1-F0)=Eh/E**
**E= (eF0 + h(1-F0))/R**
**Dan’s goal is to estimate the constant h (or, equivalently, e/h) from test beam data, and then to identify individual pions in jets, use the distribution of the energy for each pion in the ECAL and HCAL to estimate its F0 and use this to get a better resolution on its energy.  **

## We want to related e and h to the constant that is commonly calcualted

**E=R/e/(e/********) where**
**E is the true energy of the pion**
**e is a calibration constant tuned for electrons (ADC counts to energy)**
**e/******** is another constant, which moves R/e to the correct true mean**

## If you do the algebra, you can get relations between e/ and h

**e/******** = e/h  (1/(1+(e/h-1)F0)**
**e/h = e/******** (1-F0)/(1-F0*e/********)**
**Dan also points out that we have two different calorimeters**
**E=EE+EH**
**EE is the part of the energy deposited in the ECAL**
**EH is the part of the erngy deposited in the HCAL**
**And that you thus need two e/********’s, one for ECAL and one for HCAL**
**For some strange reason, the HCAL NIM paper quotes e/h, instead of what they directly measure (e/********) (maybe to make it easy to compare to shower models.  They quote e/h=1.39**

## ECAL+HCAL

**Dan’s version of my first two slides**

## e Beam Data - 100 GeV

**e****E****=0.94 using only ECAL. For HCAL, norm is = 1 at 300 GeV --> with e/h = 1.39 that e/pi should be 1.12. Thus e****H**** = 1.12. This fixes the 2 calibration constants.**

**I have no idea why he puts this plot here.  However, the algebra converts e/h=1.39 to e/pi for a 300 GeV particle.**

## Measure e/h of HCAL

**Measure e/h of HCAL**

**I have no idea what he wants us to see from this plot**

## HCAL - e/h

**Use test beam data - ECAL linear and calibrated. HCAL for mip in ECAL yields e/h for HCAL of 1.39 (NIM paper) with Wigmans Fo of 0.11 ln(E).**

**I think this shows how the NIM takes the measued 1/(e/********) and turns it into e/h.  Note that at 300, ********/e is around 0.875.  1/0.875 is 1.14, in reasonable agreement with his calculation 2 slides back.  This is what we’ll need to do for the ECAL as well**

## Measure e/h of ECAL?

**To find e/h for ECAL, measure e/pi at different energies for showers where there is a substantial energy (> 30% of the beam energy) in ECAL. For the set of e/pi find e/h for ECAL. Assign e/h = 1.60 to ECAL.**

## e/h for ECAL and HCAL

**Use e/h = 1.6 for ECAL, = 1.39 for HCAL and Wigmans for Fo. Use energy seen in ECAL and HCAL to estimate Fo and e/pi event by event.**

**Not at all clear why he assumes e/h=1.6.**
**Somehow in jets, identify individual pions, and for them, use the fraction of the pion energy in ECAL to estimate f0**

## e/h for ECAL and HCAL

**Raw resolutions, with out this new technique, for several pion energies?**

## E/h for ECAL and HCAL

**Shows how the energy is distributed between ECAL and HCAL. But, why is Ee negative?**

## Gaussian Fits

**Gaussain fits give the same results as the sample mean and sample r.m.s. Chisq/DOF is ~ 1. Examples for 300 GeV and 20 GeV are shown.**

**I have no idea what this shows**

## Linearity and Resolution

**Linearity is restored to a few %. The resolution is Gaussian to a high level of accuracy with ~ NO constant term and a 110% stochastic coefficient**