[PPT] - Luminosity Spectrum Reconstruction - Impact of Detector Resolution PowerPoint Presentation

SLIDE 1

Luminosity Spectrum Reconstruction - Impact of Detector Resolution Mismodelling

Philipp Zehetner

CERN Summer Student Supervised by Esteban Fullana and Andr´ e Sailer

August 31, 2018

SLIDE 2

Preview

1. Short Introduction to Luminosity Spectra
2. Simulating the Luminosity Spectrum
3. Motivation for my Project
4. Analysis and Results
5. Outlook

SLIDE 3

What is the Luminosity Spectrum?

E [GeV] 500 1000 1500 dN/dE

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10

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10

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4

10

3

10

2

10 Figure: Simulated CLIC luminosity spectrum for 3 TeV

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Why is it not a delta-distribution?

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Why is it not a delta-distribution?

◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the

bunch. This is a property of the accelerator.

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Why is it not a delta-distribution?

◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the

bunch. This is a property of the accelerator.

◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center.

SLIDE 7

Why is it not a delta-distribution?

◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the

bunch. This is a property of the accelerator.

◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center. ◮ Beamstrahlung Deflected particles radiate photons and thus reduce the particle’s energy.

SLIDE 8

Why is it not a delta-distribution?

◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the

bunch. This is a property of the accelerator.

◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center. ◮ Beamstrahlung Deflected particles radiate photons and thus reduce the particle’s energy. ◮ Correlation between energies If a particle collides with a particle at the front it is less likeley to have radiated beamstrahlung as it travelled less in the other particles’ field.

SLIDE 9

Beam-Energy-Spread

m] µ Z [

150 -100
50

50 100 150

Beam

E/E ∆

0.01

0.01

(a) Energy dependece on longitudinal position

Beam

E/E ∆ x=

0.004-0.002

0.002 0.004 dN/dx 100 200 300 400 Energy spread

(b) Beam-energy-spread as simulated by GuineaPig

SLIDE 10

Energy Correlation

1

10 1 10

2

10

3

10

Beam

/E

1

E 0.5 1

Beam

/E

2

E 0.5 1

Energy spectrum simulated with GuineaPig for 3 TeV

SLIDE 11

Why do we care?

SLIDE 12

Why do we care?

◮ Cross-sections depend on the centre-of-mass energy Assuming that all particles have the nominal energy is just wrong and would yield large errors on the cross-sections which propagate in many other measurements

SLIDE 13

Why do we care?

◮ Cross-sections depend on the centre-of-mass energy Assuming that all particles have the nominal energy is just wrong and would yield large errors on the cross-sections which propagate in many other measurements ◮ Lorentz boost depends on energy difference and observables measured in the lab-frame depend on the Lorentz

boost. If one particle has lost energy, lab frame and centre-of-mass

frame are not identical anymore

SLIDE 14

How can we ’calculate’ it?

SLIDE 15

How can we ’calculate’ it?

◮ We can’t (at least not directly) The pinch effect and thus the Beamstrahlung highly depend on the exact geometry of the bunch which can’t be measured

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How can we ’calculate’ it?

◮ We can’t (at least not directly) The pinch effect and thus the Beamstrahlung highly depend on the exact geometry of the bunch which can’t be measured ◮ It can be measured indirectly using Bhabha scattering E.g. as described in Luminosity Spectrum Reconstruction at Linear Colliders by St´ ephane Poss and Andr´ e Sailer.

SLIDE 17

The Model

The model consists of four different parts: ◮ Peak: No particle radiated beamstrahlung ◮ Body: Both particles radiated beamstrahlung ◮ Arm1: Particle 2 radiated beamstrahlung ◮ Arm2: Particle 1 radiated beamstrahlung

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3

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1

x 0.97 0.98 0.99 1 1.01

2

x 0.97 0.98 0.99 1 1.01 Peak Peak

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3

10

1

x 0.97 0.98 0.99 1 1.01

2

x 0.97 0.98 0.99 1 1.01 Arm1 Arm1

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3

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1

x 0.97 0.98 0.99 1 1.01

2

x 0.97 0.98 0.99 1 1.01 Arm2 Arm2

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1

x 0.97 0.98 0.99 1 1.01

2

x 0.97 0.98 0.99 1 1.01 Body Body

SLIDE 18

Mathematical Model

L (x1, x2) = pPeakδ (1 − x1) ⊗ BES

x1; [p]1

Peak

δ (1 − x2) ⊗ BES
x2; [p]2

Peak

+pArm1δ (1 − x1) ⊗ BES
x1; [p]1

Arm1

BB
x2; [p]2

Arm1, βArm Limit

+pArm2BB
x1; [p]1

Arm2, βArm Limit

δ (1 − x2) ⊗ BES
x2; [p]2

Arm2

+pBodyBG
x1; [p]1

Body, βBody Limit

BG
x2; [p]2

Body, βBody Limit

(1)

◮ 19 free parameters

SLIDE 19

Extracting the Luminosity Spectrum

MC events generated according to the model Events simulated with GuineaPig later: Data

SLIDE 20

Extracting the Luminosity Spectrum

MC events generated according to the model Events simulated with GuineaPig later: Data after Bhabha scattering after Bhabha scattering

BHWIDE BHWIDE

SLIDE 21

Extracting the Luminosity Spectrum

MC events generated according to the model Events simulated with GuineaPig later: Data after Bhabha scattering after Bhabha scattering

BHWIDE BHWIDE

Detector Level Detector Level

Gaussian

Smearing

Gaussian

Smearing

SLIDE 22

Extracting the Luminosity Spectrum

MC events generated according to the model Events simulated with GuineaPig later: Data after Bhabha scattering after Bhabha scattering

BHWIDE BHWIDE

Detector Level Detector Level

Gaussian

Smearing

Gaussian

Smearing Fitted model as good approximation for the luminosity spectrum

SLIDE 23

Error Propagation

◮ Create 38 new luminosity spectra by shifting each parameter by ±σ ◮ The error on the top mass for each parameter is the difference between the nominal value and the one obtained by the shifted luminosity spectrum ◮ The total error is the square sum of the errors taking in account the covariance matrix

SLIDE 24

Reference

◮ All plots shown so far were taken from Luminosity Spectrum Reconstruction at Linear Colliders written by St´ ephane Poss and Andr´ e Sailer ◮ They were assuming the final energy stage of 3 TeV

E u r . P h y s . J . C m a n u s c r i p t N

.

( w i l l b e i n s e r t e d b y t h e e d i t

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Luminosity Spectrum Reconstruction at Linear Colliders

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a s s e n e r g y [ 1 , 2 , 3 , 4 ] . T h e r e s u l t i n g

ae-mail: stephane.poss@cern.ch be-mail: andre.sailer@cern.ch

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l y b e a c h i e v e d w i t h a m e a s u r e m e n t

f

t h e a n g l e s

f

t h e

u

t g

i

n g e l e c t r

n

s f r

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B h a b h a s c a t t e r i n g . T h e a n g l e s

f

t h e t w

p

a r t i c l e s a r e t h e m

s

t p r e c i s e l y m e a s u r a b l e

b

s e r v a b l e [ 5 ] . T h e a n g l e s

1The luminosity spectrum is a dimensionless probability density func- tion that is mathematically equivalent to the use of electron structure functions and parton density functions. 2Unless explicitly stated, electron always refers to both electrons and positrons.

a r X i v : 1 3 9 . 3 7 2 v 3 [ p h y s i c s . i n s

d

e t ] 1 1 A p r 2 1 4

Luminosity Spectrum Reconstruction at Linear Colliders

SLIDE 25

My Project

Project proposal: [...] The proposal aims to study the sensitivity of the luminosity determination due to miss-modelling of the detector by the simulation. The supervisors will propose the student to look for papers for a reasonable approach of disagreement based on current (LHC) or past (LEP) experiments and implement them in the code for the luminosity

determination. This includes resolution miss-miss-modeling but also

energy scale shift or detector inefficiencies.

SLIDE 26

Motivation

Properties of the detector such as its resolution are important input parameters for reconstucting the luminosity spectrum. They need to be estimated or measured and thus will have uncertainties. These uncertainties propagate to the luminosity spectrum and thus to all subsequent measurements We want to know how this impacts errors on actual physics analysis.

SLIDE 27

Analysis Steps

What if we don’t know the exact resolution of our detector?

SLIDE 28

Analysis Steps

What if we don’t know the exact resolution of our detector? Monte Carlo generator: 10M e+e− pairs

SLIDE 29

Analysis Steps

What if we don’t know the exact resolution of our detector? Monte Carlo generator: 10M e+e− pairs 10M e+e− pairs after Bhabha scattering

BHWIDE

SLIDE 30

Analysis Steps

What if we don’t know the exact resolution of our detector? Monte Carlo generator: 10M e+e− pairs 10M e+e− pairs after Bhabha scattering

BHWIDE

Detector Level Detector Level

Gaussian Smearing σi Gaussian Smearing σj

SLIDE 31

Analysis Steps

What if we don’t know the exact resolution of our detector? Monte Carlo generator: 10M e+e− pairs 10M e+e− pairs after Bhabha scattering

BHWIDE

Detector Level Detector Level

Gaussian Smearing σi Gaussian Smearing σj

Value/error of 19 free parameters χ2

Reweighting fit input as Data input as MC

SLIDE 32

Plot Structure

MC input as Data: σ

Resolution scan in (E or Θ )

MC input as MC: σ

Resolution scan in (E or Θ )

SLIDE 33

Plot Structure

MC input as Data: σ

Resolution scan in (E or Θ )

MC input as MC: σ

Resolution scan in (E or Θ ) good guess

g

d

resolution

b a d

resolution

SLIDE 34

Plot Structure

MC input as Data: σ

Resolution scan in (E or Θ )

MC input as MC: σ

Resolution scan in (E or Θ ) good guess

g

d

resolution

b a d

resolution

resolution better than simulated resolution worse than simulated

SLIDE 35

χ2 results for Θ and Energy resolution scan

Θ

0.97 0.98 0.99 1 1.01 1.02 1.03

Chi^2/ndf of fit

MC input as Data: Smearing on Theta * 10^-7 50 55 60 65 70 75 80 MC input as MC: Smearing on Theta * 10^-7 50 55 60 65 70 75 80

Chi^2/ndf of fit

31 × 31 = 961 data points Energy

1 1.1 1.2 1.3 1.4 1.5

Chi^2/ndf of Fit

MC input as Data: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280

Chi^2/ndf of Fit

41 × 41 = 1681 data points σE =

a √ E ⊕ b

SLIDE 36

Impacts on top mass measurements: Theta

0.97 0.98 0.99 1 1.01 1.02 1.03

Chi^2/ndf of fit

MC input as Data: Smearing on Theta * 10^-7 50 55 60 65 70 75 80 MC input as MC: Smearing on Theta * 10^-7 50 55 60 65 70 75 80

Chi^2/ndf of fit

x x x x x

SLIDE 37

Impacts on top mass measurements: Theta

0.97 0.98 0.99 1 1.01 1.02 1.03

Chi^2/ndf of fit

MC input as Data: Smearing on Theta * 10^-7 50 55 60 65 70 75 80 MC input as MC: Smearing on Theta * 10^-7 50 55 60 65 70 75 80

Chi^2/ndf of fit

x x x x x 10.2 MeV 9.9 MeV 10.1 MeV 9.9 MeV 10.0 MeV

SLIDE 38

Luminosity Spectrum for mismodelling Θ

0.95 0.96 0.97 0.98 0.99 1 1.01

4

10

5

10

Lumi

Model input 50vs80: Luminosity Spectrum 64vs65: Luminosity Spectrum

Lumi

SLIDE 39

Problematic Missmodelling: Energy resolution

Relative deviation of parameter 0: weight_peak MC input as Data: Energy smearing parameter a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Energy smearing parameter a * 10^-3 200 210 220 230 240 250 260 270 280 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 Relative deviation of parameter 0: weight_peak

Relative error of parameter 0: weight_peak

MC input as Data: Energy smearing parameter a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Energy smearing parameter a * 10^-3 200 210 220 230 240 250 260 270 280 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Relative error of parameter 0: weight_peak

1. ’Stable zone’ around diagonal: small error and little deviation
2. off-diagonal corners: large deviation, errors drop to zero

SLIDE 40

Impacts on top mass measurements: Energy

1 1.1 1.2 1.3 1.4 1.5

Chi^2/ndf of Fit

MC input as Data: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280

Chi^2/ndf of Fit

x x x x x x x x x

SLIDE 41

Impacts on top mass measurements: Energy

1 1.1 1.2 1.3 1.4 1.5

Chi^2/ndf of Fit

MC input as Data: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280

Chi^2/ndf of Fit

x x x x x x x x x 16 MeV 11 MeV 10 MeV 10 MeV 10 MeV 10 MeV 12 MeV

SLIDE 42

Impacts on top mass measurements: Energy

1 1.1 1.2 1.3 1.4 1.5

Chi^2/ndf of Fit

MC input as Data: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280

Chi^2/ndf of Fit

x x x x x x x x x 16 MeV 11 MeV 10 MeV 10 MeV 10 MeV 10 MeV 12 MeV 164 MeV

SLIDE 43

Impacts on top mass measurements: Energy

1 1.1 1.2 1.3 1.4 1.5

Chi^2/ndf of Fit

MC input as Data: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280 MC input as MC: Smearing on Energy a * 10^-3 200 210 220 230 240 250 260 270 280

Chi^2/ndf of Fit

x x x x x x x x x 16 MeV 11 MeV 10 MeV 10 MeV 10 MeV 10 MeV 12 MeV 164 MeV 8 MeV

SLIDE 44

How reliable are the 8 MeV?

◮ The good resoultion guess does converge very well to the input model ◮ The bad resolution guess does not converge to our input model and the peak loses its second maximum.

0.95 0.96 0.97 0.98 0.99 1 1.01

4

10

5

10

Lumi

Model input 280vs200: Luminosity Spectrum 240vs242: Luminosity Spectrum

Lumi

SLIDE 45

Conclusions

1. Errors from mismodelling Θ resolution were smaller than our

statistical error.

SLIDE 46

Conclusions

1. Errors from mismodelling Θ resolution were smaller than our

statistical error.

2. Errors from mismodelling energy resolution stay relatively small,

when mismodelling the resolution by not more than ±15%

SLIDE 47

Conclusions

1. Errors from mismodelling Θ resolution were smaller than our

statistical error.

2. Errors from mismodelling energy resolution stay relatively small,

when mismodelling the resolution by not more than ±15%

3. Larger deviations either drastically increase the error, or yield

unreliable results on error propagation

SLIDE 48

Outlook - Future Work

◮ Confirming 10 MeV as an statistical error This can be done either using a smaller or larger set of e+e− pairs, but using a significantly larger set might yield more interesting results e.g. better estimates on the error from mismodelling the angular resolution ◮ Simulating an energy shift as also described in the project

proposal. Repeating the last steps of the analysis but shifting the

energy scale instead of changing the resolution. ◮ Simulating the full detector Applying a Gaussian smearing to observables is only a very basic detector simulation which could be refined. ◮ Repeating the analysis for different energies At 1.5 TeV and 3 TeV detectors will have a different resolution so we can expect the impact of missmodelling to be different as well.

SLIDE 49

Thank You All

A big Thank You to ◮ Esteban and Andr´ e for giving me this project and for their patient explanations and good advice during the last ten weeks ◮ once again Esteban for giving me the opportunity to present my work at the CLICdp Collaboration meeting ◮ the entire group for having me as a summer student ◮ the CERN summer student team for making everything possible