A T ALE OF T WO U NCERTAINTIES : Analyzing P T Bias and its Effects - - PowerPoint PPT Presentation

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A T ALE OF T WO U NCERTAINTIES : Analyzing P T Bias and its Effects - - PowerPoint PPT Presentation

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A T ALE OF T WO U NCERTAINTIES : Analyzing P T Bias and its Effects on the Dimuon Mass Spectrum Tamra Nebabu, Duke University Dr. Pushpalatha Bhat, Dr. Leonard Spiegel Fermilab, CMS W HY U NCERTAINTY M ATTERS It changes conclusions! Ex:

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SLIDE 1

A TALE OF TWO UNCERTAINTIES:

Tamra Nebabu, Duke University

  • Dr. Pushpalatha Bhat, Dr. Leonard Spiegel

Fermilab, CMS

Analyzing PT Bias and its Effects on the Dimuon Mass Spectrum

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SLIDE 2
  • It changes conclusions!

⎻Ex: particle identification based on peaks

WHY UNCERTAINTY MATTERS

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SLIDE 3

COMPACT MUON SOLENOID (CMS) DETECTOR

A general purpose LHC detector

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SLIDE 4

THE LAYERS OF CMS

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SLIDE 5
  • Heaviest LHC detector
  • 2nd largest general purpose detector in volume
  • 100 meters underground
  • 14 million kgs = 14,000

= 5,000

  • 4 T magnet = 100,000

= 2.7

  • 5 layers – silicon tracker, EM calorimeter, hadron

calorimeter, solenoidal magnet, muon detection layer

CMS SPECS

5

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SLIDE 6

Co Cosmic muon data co collect cted from m CMS in 2015 2015 Mon Monte ca carlo si simul ulati tions

  • ns of
  • f cosm
  • smic

mu muons Si Simul ulati tions ns of f co collision eve vents ge generated i d in Py Pythia8

MY DAT

ATA

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SLIDE 7

COSMIC ENDPOINT METHOD

Measuring uncertainty in pT

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SLIDE 8

WHAT KIND OF MEASUREMENTS?

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  • These variables can be used to

calculate virtually every property

  • f the particle we’re interested in!
  • Physicists also like to use η

𝜃 = − ln tan 𝜄 2

  • In my study, I studied distributions
  • f pT
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SLIDE 9

THE STUDY

  • Assume: detector has systematic error or bias that causes pT to

be scaled up by factor that depends on pT ⎻ pT’ = α pT where α depends linearly on pT

  • This is equivalent to a constant shift in curvature 𝜆 =

,

  • . =

±0

  • .
  • Procedure
  • 1. Make pT histograms
  • 2. Calculate and make κ histograms
  • 3. Apply shift to κ of simulation
  • 4. Compare data and simulation
  • 5. Rinse and repeat

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SLIDE 10

(C/TeV) κ ∆ bias

0.2 − 0.1 − 0.1 0.2

2

χ

15 20 25 30 35 40

(MANUAL0) for 16 bins (CRAFT/ASYMP) κ ∆ vs.

2

χ

RESULTS

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The bias in the detector is very small! ...but now we have uncertainty...

Bias = 0.01 C/TeV Min Χ2 = 25.56 Uncertainty = ±0.07 C/TeV

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SLIDE 11

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RELATIVE DIFFERENCE STUDY

Propagating uncertainty in pT to the mass spectrum

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SLIDE 12

𝑟𝑟 2 → 𝑎 / 𝛿∗ → 𝑚9𝑚: Z boson intermediate

𝑟𝑟 2 → 𝑚9𝑚: No Z boson intermediate

QUARK COMPOSITENESS

Drell-Yan (DY) Contact Interaction (CI)

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SLIDE 13

INVARIANT MASS

  • Is the rest mass of the two-muon system

⎻NOT the sum of the rest masses!!

  • By conservation of mass-energy, should be more or less

equivalent to the mass of the parent Z boson

  • Derived from 𝐹< = 𝑛>𝑑< < + 𝑞𝑑< <
  • In the highly relativistic (E >> m) case, approximates to

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SLIDE 14

DRELL-YAN VS. CONTACT INTERACTION

mass (GeV) 1000 1500 2000 2500 3000 3500 4000 4500 5000 Number

2

10

3

10

4

10

5

10 Drell-Yan = 10 TeV) Λ Compositeness ( = 16 TeV) Λ Compositeness ( = 100000 TeV) Λ Compositeness (

Dimuon Invariant Mass Spectrum

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SLIDE 15

THE STUDY

  • Recalculate the masses using a shifted value of pT

⎻ shifting κ → shifted pT → shifted mass

  • Perform a counting experiment!

1. Pick a minimum mass 2. Count up the number of entries above that mass value in the unshifted spectrum 3. Count again for the shifted spectrum 4. Calculate the relative difference between the shifted and unshifted mass spectra

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SLIDE 16

RESULTS

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.005 0.01 0.015 0.02 0.025

scaled down

T

scaled up, one p

T

  • ne p

= 0.05 C/TeV) κ ∆ Relative Difference for DY (

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.1 0.15 0.2 0.25 0.3 0.35

's scaled up

T

both p 's scaled down

T

both p

= 0.05 C/TeV) κ ∆ Relative Difference for DY (

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SLIDE 17

DRELL-YAN VS. CONTACT INTERACTION

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Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Drell-Yan Compositeness

= 0.05 C/TeV) κ ∆ = 16 TeV, Λ Relative Difference for DY vs. CI after Scaling Up (

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Drell-Yan Compositeness

= 0.05 C/TeV) κ ∆ = 16 TeV, Λ Relative Difference for DY vs. CI after Scaling Down (

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.005 0.01 0.015 0.02 0.025

Drell-Yan Compositeness

= 0.05 C/TeV) κ ∆ = 16 TeV, Λ Relative Difference for DY vs. CI after Curvature Scaling (

Scaling up Scaling down One up, one down

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SLIDE 18

CONNECTING THE DOTS

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Relative Difference vs. Minimum Mass for DY

= 0.08 C/TeV κ ∆ scaled up, = 0.06 C/TeV κ ∆ scaled down,

Relative Difference vs. Minimum Mass for DY

Minimum Mass (GeV) 1000 1200 1400 1600 1800 2000 2200 2400 Relative Difference 0.1 0.2 0.3 0.4 0.5 0.6 0.7

= 16 TeV) Λ Relative Difference vs. Minimum Mass for CI (

= 0.08 C/TeV κ ∆ scaled up, = 0.06 C/TeV κ ∆ scaled down,

= 16 TeV) Λ Relative Difference vs. Minimum Mass for CI (

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Use the uncertainty in pT

  • btained by the

Cosmic Endpoint Method to get an uncertainty band in the dimuon mass spectrum

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SLIDE 19

ACKNOWLEDGEMENTS

  • My supervisors Dr. Pushpa Baht and Dr. Leonard Spiegel
  • Shawn Zaleski
  • My office buddy Amanda
  • Dr. Elliott McCrory, Sandra Charles, and the entire SIST

committee and staff

  • My SIST mentors William Freeman and Jodi Coghill
  • You guys!

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SLIDE 20

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SLIDE 21

BACKUP SLIDES

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PROCEDURE

  • 1. Calculate and make histograms of pT

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(TeV)

T

p 0.2 0.4 0.6 0.8 1 1.2 1.4 Number 50 100 150 200 250 300 350 400

Histogram for Data

T

P

(TeV)

T

p 0.2 0.4 0.6 0.8 1 1.2 1.4 Number 1000 2000 3000 4000 5000 6000

Histogram for Monte Carlo Simulation

T

P

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SLIDE 23

PROCEDURE

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(C/TeV) κ Curvature 10 − 8 − 6 − 4 − 2 − 2 4 6 8 10 Number 50 100 150 200 250

Curvature Histogram for Data

(C/TeV) κ Curvature 10 − 8 − 6 − 4 − 2 − 2 4 6 8 10 Number 500 1000 1500 2000 2500 3000 3500 Curvature Histogram for Monte Carlo Simulation

  • 2. Calculate and make histograms of κ
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SLIDE 24

PROCEDURE

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  • 3. Apply shift to κ

curvature 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 Number 500 1000 1500 2000 2500 = -2.0 C/TeV κ ∆ = 0.0 C/TeV κ ∆ = 2.0 C/TeV κ ∆

Shifted Curvature Histograms

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SLIDE 25

COMPARING DATA AND SIMULATION

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(C/TeV) κ ∆ bias

2 − 1.5 − 1 − 0.5 − 0.5 1 1.5 2

2

χ

100 200 300 400 500

(MANUAL0) for 16 bins (CRAFT/ASYMP) κ ∆ vs.

2

χ

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SLIDE 26

COMPOSITENESS

  • Theory that all elementary particles are actually made up

the same fundamental building blocks, which are called preons

  • If true, would observe compositeness effects at some

energy scale Λ ⎻So far, not observed up to 9.5 TeV in one model of compositeness, and 13.1 TeV in another model

“The finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a 10,000 dollar fine.”

  • -Willis Lamb

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SLIDE 27

QUARK COMPOSITENESS

  • At some energy scale Λ , can essentially “break apart”

quarks without a Z intermediate and get some fraction

  • f DY events and some fraction of CI events
  • However, if Λ is infinite (i.e. it takes infinite energy to

break the preons apart) that means the quarks are effectively the smallest indivisible particle ⎻ In this case, all of the events would be DY

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Additional terms for CI events