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

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: particle identification based on peaks 2

C OMPACT M UON S OLENOID (CMS) D ETECTOR A general purpose LHC detector 3

T HE L AYERS OF CMS 4

CMS S PECS • Heaviest LHC detector • 2 nd 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 5

M Y D AT ATA Cosmic muon data Co Mon Monte ca carlo Si Simul ulati tions ns of f collect co cted from m CMS in si simul ulati tions ons of of cosm osmic co collision eve vents 2015 2015 mu muons generated i ge d in Py Pythia8 6

C OSMIC E NDPOINT M ETHOD Measuring uncertainty in p T 7

W HAT K IND OF M EASUREMENTS ? These variables can be used to • calculate virtually every property of the particle we’re interested in! Physicists also like to use η • 𝜃 = − ln tan 𝜄 2 In my study, I studied distributions • of p T 8

T HE S TUDY • Assume: detector has systematic error or bias that causes p T to be scaled up by factor that depends on p T ⎻ p T’ = α p T where α depends linearly on p T , ±0 • This is equivalent to a constant shift in curvature 𝜆 = - . = - . • Procedure 1. Make p T histograms 2. Calculate and make κ histograms 3. Apply shift to κ of simulation 4. Compare data and simulation 5. Rinse and repeat 9

χ ∆ κ 2 vs. (MANUAL0) for 16 bins (CRAFT/ASYMP) 2 χ 40 35 R ESULTS Uncertainty = ± 0.07 C/TeV 30 Min Χ 2 = 25.56 25 The bias in the detector is very small! 20 Bias = 0.01 C/TeV ...but now we have uncertainty... 15 − − 0.2 0.1 0 0.1 0.2 ∆ κ bias (C/TeV) 10

R ELATIVE D IFFERENCE S TUDY Propagating uncertainty in p T to the mass spectrum 11

Q UARK C OMPOSITENESS Drell-Yan (DY) Contact Interaction (CI) 2 → 𝑚 9 𝑚 : 𝑟𝑟 2 → 𝑎 / 𝛿 ∗ → 𝑚 9 𝑚 : 𝑟𝑟 No Z boson intermediate Z boson intermediate 12

I NVARIANT M ASS • 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 13

D RELL -Y AN VS . C ONTACT I NTERACTION Dimuon Invariant Mass Spectrum 5 10 Number Drell-Yan Λ Compositeness ( = 10 TeV) Λ Compositeness ( = 16 TeV) Λ 4 Compositeness ( = 100000 TeV) 10 3 10 2 10 1000 1500 2000 2500 3000 3500 4000 4500 5000 mass (GeV) 14

T HE S TUDY • Recalculate the masses using a shifted value of p T ⎻ shifting κ → shifted p T → 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 15

R ESULTS ∆ κ ∆ κ Relative Difference for DY ( = 0.05 C/TeV) Relative Difference for DY ( = 0.05 C/TeV) Relative Difference Relative Difference 0.35 0.025 both p 's scaled up one p scaled up, one p scaled down T T T 0.3 0.02 both p 's scaled down T 0.25 0.015 0.2 0.01 0.15 0.005 0.1 0 1000 1200 1400 1600 1800 2000 2200 2400 1000 1200 1400 1600 1800 2000 2200 2400 Minimum Mass (GeV) Minimum Mass (GeV) 16

D RELL -Y AN VS . C ONTACT I NTERACTION Scaling down One up, one down Scaling up Λ ∆ κ Λ ∆ κ Relative Difference for DY vs. CI after Scaling Down ( = 16 TeV, = 0.05 C/TeV) Λ ∆ κ Relative Difference for DY vs. CI after Curvature Scaling ( = 16 TeV, = 0.05 C/TeV) Relative Difference for DY vs. CI after Scaling Up ( = 16 TeV, = 0.05 C/TeV) 0.4 0.4 Relative Difference Relative Difference 0.025 Relative Difference Drell-Yan Drell-Yan Drell-Yan 0.35 0.35 Compositeness Compositeness Compositeness 0.02 0.3 0.3 0.25 0.25 0.015 0.2 0.2 0.01 0.15 0.15 0.1 0.1 0.005 0.05 0.05 0 1000 1200 1400 1600 1800 2000 2200 2400 1000 1200 1400 1600 1800 2000 2200 2400 1000 1200 1400 1600 1800 2000 2200 2400 Minimum Mass (GeV) Minimum Mass (GeV) Minimum Mass (GeV) 17

C ONNECTING THE DOTS Use the Λ Λ Relative Difference vs. Minimum Mass for DY Relative Difference vs. Minimum Mass for DY Relative Difference vs. Minimum Mass for CI ( Relative Difference vs. Minimum Mass for CI ( = 16 TeV) = 16 TeV) 0.7 0.7 uncertainty in p T Relative Difference Relative Difference ∆ κ ∆ κ scaled up, = 0.08 C/TeV scaled up, = 0.08 C/TeV ∆ κ ∆ κ obtained by the 0.6 scaled down, = 0.06 C/TeV 0.6 scaled down, = 0.06 C/TeV Cosmic Endpoint 0.5 0.5 Method to get an 0.4 0.4 uncertainty band 0.3 0.3 in the dimuon 0.2 0.2 mass spectrum 0.1 0.1 0 0 1000 1200 1400 1600 1800 2000 2200 2400 1000 1200 1400 1600 1800 2000 2200 2400 Minimum Mass (GeV) Minimum Mass (GeV) 18

A CKNOWLEDGEMENTS • 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! 19

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B ACKUP S LIDES 21

P ROCEDURE 1. Calculate and make histograms of p T P Histogram for Data P Histogram for Monte Carlo Simulation T T Number Number 400 6000 350 5000 300 4000 250 200 3000 150 2000 100 1000 50 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 p (TeV) p (TeV) T T 22

P ROCEDURE 2. Calculate and make histograms of κ Curvature Histogram for Data Curvature Histogram for Monte Carlo Simulation Number Number 250 3500 3000 200 2500 150 2000 1500 100 1000 50 500 0 0 − − − − − − − − − − 10 8 6 4 2 0 2 4 6 8 10 10 8 6 4 2 0 2 4 6 8 10 κ κ Curvature (C/TeV) Curvature (C/TeV) 23

P ROCEDURE 3. Apply shift to κ Shifted Curvature Histograms Number ∆ κ = -2.0 C/TeV 2500 ∆ κ = 0.0 C/TeV ∆ κ = 2.0 C/TeV 2000 1500 1000 500 0 − − − − − 5 4 3 2 1 0 1 2 3 4 5 curvature 24

C OMPARING D ATA AND S IMULATION χ ∆ κ 2 vs. (MANUAL0) for 16 bins (CRAFT/ASYMP) 2 χ 500 400 300 200 100 0 − − − − 2 1.5 1 0.5 0 0.5 1 1.5 2 ∆ κ bias (C/TeV) 25

C OMPOSITENESS • 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 26

Q UARK C OMPOSITENESS • At some energy scale Λ , can essentially “break apart” quarks without a Z intermediate and get some fraction of 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 Additional terms for CI events 27