# Presentation: 013098

## Silicon dE/dx and Particle ID

- Ingyin Zaw, Andy Foland, Josh Rosaler
- Harvard University
- B Physics Analysis Kernel Meeting
- Aug. 20, 2004

## Silicon dE/dx (Reminder)

- Silicon is a solid
- Pro: Landau widths of individual hits reduced; little environmental interference
- Con: Density effect kicks in immediately
- Fermi plateau 6% above minI
- No crossover region
- There are only 8 possible layers
- L00 is too scary to reasonably contemplate -> only 7 layers
- Central ISL -> only 6 layers
- Scarcity of hits limits resolution
- Experimentally, need to:
- Calibrate charge deposition
- Find optimal estimator given charge deposited in each layer
- Demonstrate Universal Curve

## Slide 3

## Chip by Chip Calibration

- SVX

- ISL

- Line up most probable values (MPV) for each chip.

## A Tale of Two Versions

- We did the calibration in 4.11.2 and 5.3.1
- In 4.11.2:
- ISL was only calibrated by bulkhead, layer, and side
- In 5.3.1:
- Twice as much data
- Calibrated ISL chip-by-chip
- Compared SVX chip scales in the two versions
- They are the same up to fitting errors.

- mean = 0.997
-  = 0.029

## Per-track dE/dx

- Simplest approach
- Average the  and z sides on a layer (since they see intrinsically the same deposition)
- Form the average of all clusters on the track
- Hopefully mean is then proportional to track MPV
- Two problems
- Landau distribution formally has no mean
- This estimator has large high-side tails
- Poor resolution even in the core

## “Slowing Power”

- Instead of averaging the charge depositions for each hit, average the recipricals
- Slowing power = 1/<1/xi>
- Where xi = the charge deposition for each layer
- Take whichever side is present or the average of the two sides when both are present
- The resolution and tails are much better than mean track deposition

## Strips and Depositions

- We can use this spatial information to improve resolution.

- 1

- 2

- 3

- 4

- 5

- MP ≈ 24.0
- eff ≈ 5.5

- MP ≈ 29.3
- eff ≈ 5.7

- MP ≈ 37.3
- eff ≈ 8.2

- MP ≈ 52.7
- eff ≈ 19.5

- MP ≈ 81.7
- eff ≈ 36.4

## Truncated Mean Using Spatial Information

- Strip number plots suggest we can be smarter in two ways
- Eliminate 4 and 5 strip clusters which contain very little info about the MPV
- Re-center 1,2,3 to line up to minimize within-track scatter
- Better mean measurement
- Calculate the mean of the remaining hits

## Slowing Power with Spatial Information

- We can use the strip number spatial information
- Eliminate clusters with 4 or more strips
- Calculate the slowing power with the rest of the clusters
- Resolution is worse than truncated mean using spatial information but tails are better

## Apply to Other Particles

******

- (*p*, not *p**T*!)

**Mean**
**ADC**
**Counts**
- (corrected)

- Green = electrons ( -> e+ e-), Blue = pions (Ks -> + -),
- Red = protons ( -> p± ±)

## Universal Curve with Truncated Mean

**Mean**
**ADC**
**Counts**
- (corrected)

******

- Green = electrons ( -> e+ e-), Blue = pions (Ks -> + -),
- Red = protons ( -> p± ±)

## Universal Curve with Slowing Power

**Mean**
**ADC**
**Counts**
- (corrected)

******

##  The Bifurcated GaussianAll tails are not created equal

-  The Bifurcated GaussianAll tails are not created equal

- Slowing power per-track dE/dx looks fairly Gaussian but the high side tail is longer
- Fit a Gaussian with 2 different widths, 1 and 2 for the low and high sides
- Will give a more accurate measure of separations

- MP = 31.91
- 1 = 4.38
- 2 = 7.20

## Disclaimer: Parameterization of the universal curve will change
Fit bifurcated Gaussians in each momentum bin and calculate separations 
p- separation at 1 up to p = 1.45 GeV
K- separation at 1 up to p = 0.75 GeV 

- Disclaimer: Parameterization of the universal curve will change
- Fit bifurcated Gaussians in each momentum bin and calculate separations
- p-** separation at 1 up to p = 1.45 GeV
- K-** separation at 1 up to p = 0.75 GeV

## Coming Soon:dE/dx with Maximum Likelihood

- Coming Soon:dE/dx with Maximum Likelihood

- Get probability distribution functions from data
- Use hit charge deposition distributions based on the side and number of strips
- Characterize each as a bifurcated Gaussian with an additional exponential tail
- Characterized by 4 parameters, each varying linearly with MPV
- Define likelihood : L(u) = ********* ***pu(xi)
- Minimize ln(L) to find the mean ionization for a track given the deposition of the hits

## Likelihood in Toy MC

- Simulate tracks with a random number generator
- Use likelihood method to get the deposition for the track
- Get significantly better resolution than other methods
- Expect ~12% resolution for energy deposition (compared to 11% in COT)

- 1 = 3.3
- 2 = 5.8

## Plans

- Put chip scales in the calibration database
- Maximum Likelihood :
- Apply likelihood method to data
- Redo universal curve fit and recalculate separations
- Add function to Si dE/dx class which returns a devaiation from the MPV assuming that the particle is x (x = e, , , K, p) based on its momentum and energy deposition
- Mechanize calibration so that it can be updated periodically (~ every 6 months or when events warrant)  because radiation damage will degrade the peak

## Conclusions

- Calibrated both SVX and ISL chip by chip
- Demonstrated universal curve with electrons, protons, and pions
- Separations at 1 up to
- 1.45 GeV for p-
- 0.75 GeV for K-
- Developed a log likelihood method using side and spatial information
- Hope to improve separations