Mass Resconstruction with HEP detectors

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Information about Mass Resconstruction with HEP detectors
Education

Published on February 19, 2014

Author: yuanchao

Source: slideshare.net

Description

How to find mass resonances in collider experiments? How to reconstruct a colliding event from detector data?

Mass Reconstruction Yuan CHAO ( 趙元 ) (National Taiwan University, Taipei, Taiwan) Numerical Simulation in HEP 2012/02/15

Outlines Introduction Resonances Coordination system Four-vector conversion The W & Z bosons Z-boson (Ex. 1) Invariant mass Missing ET Transverse mass W-boson (Ex. 2) Tracks Jets Top reconstruction (cascade) ... 2

The Origin of the Universe 3

Goal of High Energy Physics LHC was built for the following purposes: To find the origin of mass... the Higgs boson. Looking for the unification.. Supersymmetry as well as other candidates of Dark Mater & Dark energy Investigate the mystery of anti-matter disappearance Physics at the early stage of the universe: Heavy Ion collisions and QGP 4

Introduction Accelerators & detectors LHC, CMS (hadron machine) 5

The Large Hadron Collider Four major experiments at LHC Atlas, Alice, CMS, LHCb LHC first beam in Sep. 2008 A technical trouble occurred 10 days after the start Physics restarted in Nov. 2009 CERN Energy starts at 0.9 TeV Pushed up to 2.36 TeV in Dec. New energy record in 2010 Collision at 7 TeV on Mar. 30 Delivered data ~36/pb in 2010 Reached ~5.7/fb in 2011 To increase to 8 TeV in 2012 LHC 6

The Large Hadron Collider Four major experiments at LHC Atlas, Alice, CMS, LHCb LHC first beam in Sep. 2008 A technical trouble occurred 10 days after the start Physics restarted in Nov. 2009 CERN Energy starts at 0.9 TeV Pushed up to 2.36 TeV in Dec. New energy record in 2010 Collision at 7 TeV on Mar. 30 Delivered data ~36/pb in 2010 Reached ~5.7/fb in 2011 To increase to 8 TeV in 2012 LHC 7

The Large Hadron Collider Four major experiments at LHC Atlas, Alice, CMS, LHCb LHC first beam in Sep. 2008 A technical trouble occurred 10 days after the start Physics restarted in Nov. 2009 Energy starts at 0.9 TeV Pushed up to 2.36 TeV in Dec. New energy record in 2010 Collision at 7 TeV on Mar. 30 13/12/11 dataset  max L≈ 3.54x1033cm-2s-1 LP11 dataset  EPS dataset  Delivered data ~36/pb in 2010 Reached ~5.7/fb in 2011 To increase to 8 TeV in 2012 8

Atlas Detector A Toroidal LHC Apparatus A general purposed detector 9

CMS Detector Compact Muon Solenoid A general purposed detector 3.8 10

CMS Detector Compact Muon Solenoid A general purposed detector 3.8 11

Introduction Accelerators & detectors KEK-B, BELLE (lepton machine) Tsukuba, Japan Lpeak=2.1 x 1034 /cm2/s2 Aerogel Cherenkov counter SC solenoid 1.5T CsI(Tl) 16X0 TOF counter n=1.015~1.030 3.5 GeV e+ 8 GeV e− EFC (online Lum.) Si vtx. det. 3/4 lyr. DSSD 3.5 GeV e+ on 8 GeV eWCM = M( Υ(4s) ) 3km circumference ~11mrad crossing angle BELLE Detector Central Drift Chamber small cell +He/C2H6 µ / KL detection 14/15 lyr. RPC+Fe 12

Long Lived Particles Most product of a collision decays before they reach the detectors Check the life-time on PDG handbook or web site: http://pdglive.lbl.gov/ Look for the value of cτ What we see in the detectors: e±, μ±, γ, π±,K±, KL, n, p± 13

Long Lived Particles Most product of a collision decays before they reach the detectors Check the life-time on PDG handbook or web site: http://pdglive.lbl.gov/ Look for the value of cτ What we see in the detectors: e±, μ±, γ, π±,K±, KL, n, p± Others can be found through resonances search Resonance mass is like the finger print of particles: unique Similar to line spectra analysis of lights 14

Resonance 15

Resonance Short life time particles Typical life-time of order 10-23 If flying at ~ speed of light → decay within 10-15 m Relationship between effective cross-section σ vs. the energy E, resonances often appear as bell-shaped E = m c2 Natural unit: c = ħ = 1 16

Resonance (cont.) Short life time particles Typical life-time of order 10-23 If flying at ~ speed of light → decay within 10-15 m Relationship between effective cross-section σ vs. the energy E, resonances often appear as bell-shaped Usually described as Breit-Wigner function (¡=2)2 ¾(E) = ¾0 (E0 ¡ E)2 + (¡=2)2 Relativistic Breit-Wigner distribution: 2 ¡2 M 2 ¾(m; M; ¡) = N ¢ ¢ ¼ (m2 ¡ M 2 )2 + m4 (¡2 =M 2 ) Natural units: c = ħ = 1 Experimentally often use Gaussian (for detector resolution) 17

Coordination System Most collider detectors built in barrel shape Detector build along the beam line Interesting particles have higher transverse momenta Symmetric shape to have uniform acceptance Special purpose detectors have different shapes LHCb 18

Coordination System Most collider detectors built in barrel shape Detector build along the beam line Interesting particles have higher transverse momenta Symmetric shape to have uniform acceptance Special purpose detectors have different shapes Coordination convention: Use cylindrical coordinate (r, θ, φ) Beam direction 19

Coordination System (cont.) Most collider detectors built in barrel shape Detector build along the beam line Interesting particles have higher transverse momenta Symmetric shape to have uniform acceptance Special purpose detectors have different shapes Coordination convention: Use cylindrical coordinate (r, θ, φ) Adopt Lorentz invariant variable: rapidity 1 y = ln 2 µ E + pL E ¡ pL ¶ jpj + pL jpj ¡ pL ¶ Pseudo-rapidity (approximation for m ≈ 0) 1 ´ = ln 2 µ · µ ¶¸ µ = ¡ ln tan 2 20

Four Vectors The key variables: 4-vectors Motion of particles can be described with (px, py, pz, E) in Cartesian More common used: (pT, η, Φ, m0) or (pT, η, Φ, E) q Conversions: px = pT cos Á py = pT sin Á pz = pT = tan µ = pT sinh ´ jpj = pT cosh ´ pT = p2 + p2 x y tan Á = py =px Implemented in ROOT, CLHEP, ... Will use through out the exercises One can use TLorentzVector with helper functions 21

The W & Z bosons The mediator of the weak interaction Known as weak bosons: W & Z A major success of Standard Model Predicted by Glashow, Weinberg, Salam in 1968 SU(2) gauge theory Discovery Neutral current interaction observed in 1973 Super Proton Synchrotron (SPS) at CERN W found Jan. 1983 at UA1 & UA2 Z was found a few months later The four gauge bosons of electroweak: W+, W-, Z0, γ 22

The Z boson Properties Charge = 0. Spin J = 1 Elementary particle Mass: 91.1876 ± 0.0021 GeV Full width Γ = 2.4952 ± 0.0023 GeV Decay modes l+l-: 3.3658 ± 0.0023 x 10-2 Invisible: 20.00 ± 0.06 x 10-2 Hadrons: 69.91 ± 0.06 x 10-2 We'll do exercise to find Z → e+e- or μ+μ- 23

Ex. 1 reconstruct Z D/L the provided sample ROOT: http://dl.dropbox.com/u/5196749/example.tgz Plain text: http://dl.dropbox.com/u/5196749/dump_top_cz.txt.gz EvtInfo_RunNo, EvtInfo_EvtNo, Leptons_Pt, Leptons_Eta, Leptons_Phi Leptons_Type (11: electron, 13: muon, and others) Leptons_Charge Identify an even: Check the RUN#, Event# The use of ROOT Check ROOT website: http://root.cern.ch Try TTree::MakeClass to generate a framework You can also use whatever you like with the plaint text ver. Make use of the pre-defined Lorentz vector class Add two vectors directly Get pT, eta, phi... 24 Calculate ΔR, ΔΦ...

Ex. 1 reconstruct Z Loop through all the leptons Find two leptons with the same flavor, opposite charge Sum up the four-vector and calculate the mass Draw a plot of the mass, pT, eta, phi... distribution for all combinations Check the result plot Where is the peak position? (try a fit!) How to improve the S/N? (re-fine the cuts) What's the width? Comparing with lifetime? Compare ee vs. mu mu 25

The W boson Properties Charge = ±1 e. Spin J = 1 Elementary particle Mass: 80.399 ± 0.023 GeV Full width Γ = 2.085 ± 0.042 GeV Decay modes l+-nu: 10.80 ± 0.09 x 10-2 Hadrons: 67.60 ± 0.27 x 10-2 We'll do exercise to find W → e±ν or μ±ν 26

How to find the invisibles? Neutrino detection at colliders No direct method due to its low interaction nature Relies on the knowledge of the whole event Basic idea: energy & momentum conservation To find the missing part Sum up all the particles → Transverse energy (calorimeter), momentum (tracks) Calculate the "miss ET" as negative of the sum Longitudinal component not considered: loss & background 27

The Transverse Mass Definition For the lack of longitudinal information of nu 2 MT = (ET;` + ET;º )2 ¡ (~T;` + ~T;º )2 p p = 2jpT;` jjpT;º j[1 ¡ cos(¢Á`;º )] MissET is the key here Relies on robust calorimeter detectors Usually poorer than direct measurements 28

Ex. 2 reconstruct W Use the same provided sample There's a special entry for computed MissET (type: 0) Go through all the leptons and MissET Find the best lepton to combine with MissET Calculate the transverse mass Draw a plot of the combinations Check the result plot Where is the peak position? (try a fit!) How to improve the S/N? (re-fine the cuts) Do you see the cut-off? 29

Tracks Charged particles can be detected as “tracks" So called "tracking system" Silicon, wired chamber, gas tubes... Magnetic filed for the momentum Curving direction for charge sign Parameterization Helix parameters 30

Calorimeters Calorimeter for energy measurement ElectroMagnetic Calorimeter Hadron Calorimeter To fully absorb the particle Heavy material Showers (see Chin-chen's) Convert into counts or light Granularity Used for electron & neutral particle detection Better energy resolution at very high pT Usually worse spatial resolution 31

Calorimeters EM Calorimeter ElectroMagnetic interactions Detecting e±, γ Showering Bremsstrahlung (low E: compton) Pair production Pair annihilation Shower size Moliere radius RM = 0:0265X0(Z + 1:2) Radiation length Shower length X = X0 ln(E0 =Ec ) ln 2 32

Jets Jets are products of out-going partons Including quarks and gluons Hadronization as strong interaction Particles pulled out of vacuum for colorless Detecting Jets Bunches of particles Including kaons, pions, leptons... Usually detected with "calorimeters" Various types and clustering algorithms 33

Jets in Hadron Machines TrackJet Charged Tracks are used for clustering Good for early data study CaloJet Uses ECal/HCal towers for clustering JPT (Jet Plus Tracks) Replace the avg. calo response with individual charged hadrons measured in tracker system Zero Supp. offset correction Correction for in-calo-cone tracks Adding out-of-calo-cone tracks Correction for track eff. & muons PFJet (Particle Flow Jet) New approach in CMS JME-09-002 34

Jets at LHC Several jet clustering algorithm available in CMS: Jet is the energy sum of a cluster p Cone algorithm: R = ¢´2 + ¢Á2 ' 0:5 Iterative cone, midpoint cone, SISCone 2p 2p Pairing distance: dij = min kT i ; kT j ´¢ ij D Kt: p=1, CA: p=0, Anti-Kt: p=-1 CMS uses FastJet package http://fastjet.fr Algorithm consideration Infrared & colinear safe Good performance (Energy, position ...) Robust to Piled-ups & UE CPU efficient: O( N2 ln(N) ) : O( N ln(N) ) G. Salam, “Jetography" Sequential recombination: ³ Priority needed on various jet algorithms Good to have many for cross checking The default jet algorithm is Anti-Kt 35

Resonance from Jets 36

The CDF Anomaly 37

Ways of Improvement Constrained Mass Using constraints to refine the distribution 38

Ways of Improvement Constrained Mass Using constraints to refine the distribution Re-fit on vertex, ex. Λ (cτ = 7.89 cm) ¤ ! p¼ 39

Ways of Improvement Constrained Mass Using constraints to refine the distribution Re-fit on vertex Mass constraints in cascaded decays, ex. ψ(2s) → J/ψ Ã(2s) ! J=Ã + ¼ + ¼ ¡ ; J=Ã ! e+ e¡ 40

Ways of Improvement Constrained Mass Using constraints to refine the distribution Re-fit on vertex Mass constraints in cascaded decays Energy constraint from accelerator info Mbc q 2 = Ebeam ¡ p2 B 41

Ways of Improvement Constrained Mass Using constraints to refine the distribution Re-fit on vertex Mass constraints in cascaded decays Energy constraint from accelerator info Be aware: could also destroy the shape... 42

Top Reconstruction Properties Charge = 2/3. Spin J = 1/2 Elementary particle Mass: 172.9 ± 1.5 GeV Full width Γ = 2.0 ± 0.7 GeV Decay modes Wb 0.99 ± 0.09 Lifetime so short (5 x 10-25) that no hadron forms before it decays: bare quark Theory: 1973 (K&M), Discovery 1995 Search Semi-leptonic ¹ pp ! tt ! W (qq )b; W (`0 º 0 )¹ ¹ b Di-leptonic ¹ pp ! tt ! W (`º)b; W (`0 º 0 )¹ b Di-jet ¹ pp ! tt ! W (qq )b; W (q q )¹ ¹ ¹b 43

Top Reconstruction Semi-leptonic search: Higher branching fraction Fully reconstruct by assigning W mass constraint p pz = 2 pz` (px` pxº + py` pyº + MW =2) § E` Di-leptonic search: 2 2 2 (px` pxº + py` pyº + MW =2)2 ¡ ET º (E` ¡ p2 ) z` 2 ¡ p2 E` z` Very clean mode as no extra jets Suffer from low branching fraction Cannot fully reconstructed due to two neutrinos An upper mass bound on mass combinations: h i (1) (2) mT 2 (minvis ) = min max[mT (minvis ; pT ); mT (minvis ; pT )] (1) (2) pT ;pT q vis invis ¡ pvis ¢ pinvis ) mT (minvis ; pinvis ) = m2 + m2 T vis invis + 2(ET ET T T 44

Summary Introduced the experiments Motivation & goals Accelerators & detectors Basics on data analysis The four-vector Mass reconstruction Missing ET Advance techniques More on detectors Constrained fits Cascaded decays Summary & conclusions Q&A 45

以上 Thank YOU! 謝謝 Remercie de Votre Attention

Higgs Limits on σ/σSM (CLs) 95% CL: obs. 127-600, exp: 117-543 GeV 47

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