Charge Selection

Paolo Zuccon

Perugia 17/09/2005

Outline

• Preselection of clean samples• Gain and eta corrections• Likelihood functions definition• Charge selection

Clean Samples

• Seed Threshold S/N>3

• Choose only the highest cluster on each ladder/side

• Low Charges == Require no cluster with signal >1000

• Raw alignment between the clusters separately on S and on K sides

• Fit with a good chi-square probabilty

• Request that the signal on the S side 6th ladder is within the peak of the desired charge (p, He, Li).

Signal Characterization

• The response of the silicon detector to the different charges has been studied using the clean samples of p, He and Li

• The signal has been fitted with a Gaussian Landau + exp tail.

• For each ladder 4 fits have been made considering separately for the two sides:

two ranges:Up ( < 0,2 > 0.8) Low (0,4 < < 0,6).

• For each type of incident particle we have 4 kind of signal:

S-up S-low K-up K-low

We studied the relative gain in each sample and the amplitude of the correction for the different ions.

Gain Spread – S SideR

elat

ive

Gai

n

Ladder

Gain Spread – K SideR

elat

ive

Gai

n

Ladder

Eta Correction – S Side

Eta Correction – K Side

Side S / Side K Low

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1 2 3 4 5 6

Ladder

Ra

tio

Proton S/K_Low

Helium S/K_Low

Lithium S/K_Low

Side S / Side K

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1 2 3 4 5 6

Ladder

Ra

tio

Proton S/K_Up

Helium S/K_Up

Lithium S/K_Up

Probability density functions Find the typical signal of an AMS-02 ladder corresponding to the

various ions ( p, He ,Li) Use the normalized signal as probability density function (pdf) for

a given ion.

Our Choice: Consider as reference the signals S-up and K-up of Ladder 1 Apply the gain corrections and the corrections (typical of a

given ion hypothesis) to report all the ladders signal to the one of ladder 1

Calculate the probabilty for the energy loss X_{i} to come from a given ion

Likelihood functions• Use the combined probability from 5 ladders to build a likelihood function

• Pass to Log Likelihood with a check for underflows: If pdf(x) < 10-50 pdf(x) = 10-50

• Normalize and trasform: L = 1 – L / (n log(10-50))

• Calculated Likelihoods: – LikeSp LikeKp – LikeSHe LikeKHe – LikeSLi LikeKLi

Protons

HeliumBeryllium Lithium

Protons

Helium

Beryllium

Lithium

Selected samples

To understand the real likelihood values taken by the different species we need (almost) pure samples.

What we have is:• A/Z = 1 Protons Pure• A/Z = 2 Mostly He but large contribution of p and Li• A/Z=2.25 almost equal amount of p He and Li

Selecting only the desired peak on the 6th

ladder we obtain an almost pure sample but at which level ?

We use the knowledge of the shape of the signal to evaluate it !

p = 0,02 %

He = 99.98 %

Li = 1.7 10-9%

A/Z=2

p = 0,01 %

He = 1,78 %

Li = 98,21%

A/Z =2,25

P selection = 99,91% He selection = 98%

Likelihood Ratio Lp/LHe

Likelihood Ratio Lp/LHe

He Eff = 99,7% misidentified as Li = 0,003 % Li Eff = 99,5% misidentified as He= 0,23%

Likelihood Ratio LHe/LLi

Conclusions

• The likelihood method provides an efficient way to select clean samples of the different charges

• Need to repeat the exercise for the higher charges