[PPT] - FAST SIMULATION of HADRONIC SHOWERS for ATLAS HCAL Stanislav Tokr PowerPoint Presentation

SLIDE 1

4/25/2005

S. Tokar

1

FAST SIMULATION of HADRONIC SHOWERS for ATLAS HCAL

Stanislav Tokár Comenius University, Bratislava People involved:

Yu. Kuľchitsky1, J. Šutiak2, T. Ženiš2

1 JINR Dubna, 2 Comenius Univ. Bratislava

SLIDE 2

4/25/2005

S. Tokar

2

Motivation

Challenge in present high energy physics:

Insufficient to know a particle process on theory level (X-sections)
It should be known also on experimental level:

Detectors resolutions and reconstruction efficiencies Capability of experiment to distinguish signal process from bkgd one

Two approaches:

Full simulation of the wanted processes

All available physics taken into account Powerful computing system + team of people + time consuming Due to shower simulations

Fast simulation

Full simulation of showers in calorimeter replaced by fast parametrisation tuned by experiment Reliable results obtained much faster (> 1000× Full simulation)

SLIDE 3

4/25/2005

S. Tokar

3

Principles of Fast MC

Goal: find spatial energy deposition in calorimeter without full simulation - using 3D parametrisation of hadronic shower ( for ATLAS Had-Calorimeter) Main principles of our approach: Incident energy is devided into a certain # energy spots The spots are distribured according to known shower topology Electromagnetic and hadronic components are treated separately Realistic fluctuations of shower profile: individual shower profile constructed for each incident particle

Part.Nucl.Lett 2[117](2003)52

SLIDE 4

4/25/2005

S. Tokar

4

Simulation algorithm

For each incident particle: Position of the 1st interaction (shower origin) is found Shower profile is constructed from a few sub-shower profiles Incident energy is divided into EM and HD components Proper number of energy spots and their size is found The spots are distributed and energy of spots absorbed in active medium is accumulated

electromagnetic hadronic Depends on Cal. energy resolution and sampling fraction

SLIDE 5

4/25/2005

S. Tokar

5

Resolution vs # of energy spots

Calorimeter energy resolution: If N spots is distributed in calorimeter ⇒ NA = sfN spots is absorbed in active medium NA is a random variable obeying Poisson law: st.dev.=

E

a b E E σ ε = = ⊕

sampling term constant term Sampling fraction

A

N

A A

E N N

2 f

E N a s =

A E

N 1 σ = = Energy resolution: ⇒ Spot energy: qeff = a2sf

# of spots

SLIDE 6

4/25/2005

S. Tokar

6

Shower Profiles

3-dimensional parametrisation of hadronic shower profile from the 1st interaction point:

( ) ( ) ( ) ( )

, , ,

e h

x r w x r 1 w x r Ψ Ψ = ⋅ + − ⋅ Ψ

Electromagnetic component Hadronic component w ≡share of electromag. energy in shower – big fluctuations !

( ) ( ) ( )

1

e ,h

e ,h e ,h e ,h

dE x,r x x,r E dx φ = ⋅ ⋅ Ψ

dE/dx ≡ longitudinal profile, φ ≡ radial profile

SLIDE 7

4/25/2005

S. Tokar

7

Fraction of el-mag energy

( )

1 1 e h f w e h f

π π

⋅ = − ⋅ +

Mean EM fraction <w> depends on energy of π0 produced ( ):

f

π

0 11 f . ln E

π

= ⋅

Fluctuation of EM fraction:

( ) ( )

1

w w w

( w w ) w w

w w e p( w ) ( )

α β α

β Γ α

− − −

− ⋅ =

w w

w w α β = +

Fluctuation of EM fraction w: pions 100 GeV αw, βw ≡parameters

SLIDE 8

4/25/2005

S. Tokar

8

Longitudinal profile of HD component

h

x / h

e

β

−

Position of the shower beginning is sampled from Average profile of hadronic shower:

1

h

x / h h

dE x e ( x ) dx ( )

β α α

β Γ α

− −

= [x] ≡λI (interaction length) Longitudinal profile of H-component Can be found by GEANT dots: Geant simulation full line: fit by the function

SLIDE 9

4/25/2005

S. Tokar

9

Individual longit. shower profile

From the origin a few “principal” particles emerge
Each of them starts sub-shower at its interaction place
Individual HD-shower is a sum of the sub-showers:

( ) ( , , )

h i i h h i

dE x f G x x 1 dx α β = ⋅ − −

∑

Origin of ith sub-shower Energy fraction carried by ith particle An example of individual hadronic shower: sub-showers full shower

SLIDE 10

4/25/2005

S. Tokar

10

Longitudinal profile of EM component

produced π0 vs depth: ( , , ) ( ) ( , , )

x 1 t e 1 e e e e

dE E G x e G x t dt dx f 1 f

λ π

α β α β

−

⋅ − ⋅   = + ⋅ −    

∫

EM longitudinal shower profile

( ) ( )

/

, ,

1 x

x e G x

α β α

α β β Γ α

− −

⋅ = ⋅

( ) ( ) exp

2 1 f 1 1 2 f 1

f p f N µ σ   − = −      

f1 fluctuations Averaged EM profile

SLIDE 11

4/25/2005

S. Tokar

11

Individual EM profile

An example of individual EM shower profile: EM sub-showers Full EM shower

( )

( , , ) ( , , )

e 1 e e 2 i e e i 2

dE x 1 f G x E dx f G x x

π

α β α β

≥

= ⋅ + ⋅ −

∑

Individual longitudinal shower profile incident energy: 100 GeV

G(x,α,β) ≡ gamma distribution

SLIDE 12

4/25/2005

S. Tokar

12

Radial shower profiles

Parametrization of radial profile:

1

r r

( x ) r / ( x ) r

E ( x,r ) c r e r x

α β

∆ ∆ ∆

− −

= ⋅ 2

r

E ( x,r ) ( x,r ) dE( x ) r x r dx ∆ φ π ∆ ∆ = ⋅ ⋅

Related to the profile function as: No fluctuations of radial profile included ! 100 GeV EM shower EM radial profile 100 GeV HD shower HD radial profile

SLIDE 13

4/25/2005

S. Tokar

13

Parameters of the method

For shower profile and its fluctuations - 25 parameters:

Fluctuation of π0 energy fraction ( 2 ) Longitudinal profile of EM component ( 3 )

and its fluctuations ( 4 )

Longitudinal profile of H component ( 2 )

and its fluctuations ( 2 )

Radial EM component ( 6 ) Radial HD component ( 6 )

At given energy

Dependence of parameters on energy: Pi(E) = pi+qi ln E or Pi(E) = pi+qiE or Pi(E) =const

SLIDE 14

4/25/2005

S. Tokar

14

Parameters values

Shower parameters values + energy dependence

Radial parameters Longitudinal parameters

SLIDE 15

4/25/2005

S. Tokar

15

Fast MC vs Testbeam data

The fast MC is compared with the test beam data of 5 1m-modules for different incident pion energies (20 – 300) GeV and different input conditions – varied: Tilt angle Beam position Test beam setup:

5 modules
Each didided into

20 cells (4 samplings, 5 towers)

Cell read by 2 PMT

SLIDE 16

4/25/2005

S. Tokar

16

Calorimeter structure

Incident beam

SLIDE 17

4/25/2005

S. Tokar

17

Fast MC vs Data – full responses

Full responses: Fast MC vs Test beam data for incident pion energies: 50, 100, 200 and 300 GeV, tilt angle: 10°

TB data Fast MC 100 GeV 300 GeV 50 GeV 200 GeV

SLIDE 18

4/25/2005

S. Tokar

18

Fast MC vs TB data - samplings

Sampling responses: Fast MC vs Test beam data

Incident energy: 100 GeV Particle type: π− Position of beam: M3 center Incident angle: 10° Shower depth dependence

TB data Fast MC

SLIDE 19

4/25/2005

S. Tokar

19

Fast MC vs TB data - modules

Incident energy: 100 GeV Particle type: π− Position of beam: M3 center Incident angle: 10° Shower transversal dependence

TB data Fast MC

Module responses: Fast MC vs Test beam data

SLIDE 20

4/25/2005

S. Tokar

20

Fast MC vs TB data - towers

Tower responses: Fast MC vs Test beam data

3 Incident energy: 100 GeV Particle type: π− Position of beam: M3 center Incident angle: 10° Shower transversal dependence

TB data Fast MC

SLIDE 21

4/25/2005

S. Tokar

21

Conclusions and perspectives

Fast MC method for sampling calorimeter based on idea

f building shower from sub-showers was created

Good description of energy response at least in the interval 50-300 GeV Good description of fluctuation on calorimeter cell level Method is easy adaptable for jets To be done: Test method for low energies (1-20) GeV

For application in ATLAS to include Elektromag. Cal.

SLIDE 22

4/25/2005

S. Tokar

22

Thank you very much! Boľšoje spasibo !!!

SLIDE 23

4/25/2005

S. Tokar

23

KALORIMETRIA

Meranie energie častíc
Fyzika hadrónovej spŕšky
Modelovanie spŕšky - programový balík GEANT

SLIDE 24

4/25/2005

S. Tokar

24

D) Radiálny profil

parametrizácia pre EM aj hadrónovú zložku:
závislosť αr od x pre EM zložku:
závislosť αr od x pre hadrónovú zložku:

( )

( ) ( ) ( ) ( )

1 / 1 /

,

r r r r

x r x x r x

cr e r r E x r x r r cr e r r

α β α β − − − −

 > ∆  =  ∆ ∆ ⋅ <  

( )

1

/ 0 1 2

e

x re e

x e

α

α α

−

= −

( ) ( ) ( )

1 2 3 4

0,30 30,180

e e re e e

x x x x x β β β β β + ∈   =  + ∈  

( ) ( )

0 ln rh h h

x x α α α = +

( ) ( ) ( )

1 2 3 4

0,30 30,180

h h rh h h

x x x x x β β β β β + ∈   =  + ∈  

SLIDE 25

4/25/2005

S. Tokar

25

POROVNANIE S EXPERIMENTÁLNYMI DÁTAMI 100 Gev

Energia uložená v moduloch, plná čiara – experimentálne dáta, body – rýchle simulácie Energia uložená v toweroch, plná čiara – experimentálne dáta, body – rýchle simulácie

SLIDE 26

4/25/2005

S. Tokar

26

POROVNANIE S EXPERIMENTÁLNYMI DÁTAMI 200 Gev

Celková uložená energia, plná čiara – experimentálne dáta, body – rýchle simulácie Energia uložená v samplingoch, plná čiara – experimentálne dáta, body – rýchle simulácie

SLIDE 27

4/25/2005

S. Tokar

27

POROVNANIE S EXPERIMENTÁLNYMI DÁTAMI 200 Gev

Energia uložená v moduloch, plná čiara – experimentálne dáta, body – rýchle simulácie Energia uložená v toweroch, plná čiara – experimentálne dáta, body – rýchle simulácie

SLIDE 28

4/25/2005

S. Tokar

28

POROVNANIE S EXPERIMENTÁLNYMI DÁTAMI 50 Gev

Celková uložená energia, plná čiara – experimentálne dáta, body – rýchle simulácie Energia uložená v samplingoch, plná čiara – experimentálne dáta, body – rýchle simulácie

SLIDE 29

4/25/2005

S. Tokar

29

POROVNANIE S EXPERIMENTÁLNYMI DÁTAMI 50 Gev

Energia uložená v moduloch, plná čiara – experimentálne dáta, body – rýchle simulácie Energia uložená v toweroch, plná čiara – experimentálne dáta, body – rýchle simulácie

SLIDE 30

4/25/2005

S. Tokar

30

ZÁVER

pomocou Monte Carlo simulácii (program GEANT) sme skúmali

topológiu hadrónových spŕšok v kalorimetri s cieľom nájsť základné tendencie

našli sme parametrizáciu profilu spŕšky a spôsob zahrnutia jeho

fluktuácii

na základe týchto znalostí bol vytvorený program pre rýchle

simulácie

dosiahli sme výbornú zhodu s reálnymi experimentál-nymi

dátami

( )

( ) ( ) exp ( )

1 1

E f x dE x x dx E 1 f

π π π π π

δ λ λ    = −  −   