Invariant Mass, Missing Mass, jet reconstruction and jet flavour tagging

Transcription

1 1 Experimentelle Methods of Particle Physics HS Wednesday and Thursday Invariant Mass, Missing Mass, jet reconstruction and jet flavour tagging Dr. Michael Dittmar/ETH Zurich Introduction and examples the decay of unstable particles and their detection. Missing energy, momentum and mass Invariant mass and detector calibration jet reconstruction the so called tagging of b-flavoured jets

2 2 Introduction M 2 System = (ΣE i) 2 (Σ P i ) 2 Two body decays: M 2 System = (E 1 + E 2 ) 2 ( P 1 + P 2 ) 2 M 2 System = E2 1 + E E 1 E 2 P 2 1 P P 1 P 2 cos Θ 12 M 2 System = m2 1 + m E 1 E 2 2 P 1 P 2 cos Θ 12 m 1 = m 2 = m γγ = 2 P 1 P 2 (1 cos Θ 12 )

3 3 Example I: M(K ± π ± ) OPAL Collaboration, CERN-PPE/ Zeit. für Physik C56 (1992) entries/2 MeV 12 8 (a) entries/ 5 MeV 8 6 (b) Mass(Kπ) (GeV) Mass(KK) (GeV) entries/2 MeV 1 75 (c) entries/ 5 MeV 2 (d) Mass(Kπ) (GeV) Mass(KK) (GeV) entries/2 MeV 4 3 (e) entries/ 5 MeV 6 4 (f) Mass(Kπ) (GeV) Figure Mass(KK) (GeV)

4 4 Example II: the search of D (cū) K π + OPAL Collaboration, CERN-PPE/ Zeit. für Physik C6 (1993)

5 5 Example III: the D ± trick OPAL Collaboration, CERN-PPE/ Zeit. für Physik C67 (1995) Number of entries per.5 MeV/c OPAL x D* < M(D*)-M(D ) (GeV/c 2 ) OPAL.2<x D* < OPAL.1<x D* < M(D*)-M(D ) (GeV/c 2 ) OPAL x D* > M(D*)-M(D ) (GeV/c 2 ) M(D*)-M(D ) (GeV/c 2 )

6 Example IV: the decay π γγ L3 Collaboration, CERN-EP/21-63; August 31, 21. L3 preprint (a) L3.15 N γγ / N event / 3.75 MeV (b) Data Fit result Background L3.5 Data MC m γγ [GeV] 6

7 7 Example V: the decay π, η γγ ALEPH Collaboration, CERN-EP Entries / 2 MeV/c Data π M γγ Fit Bkg Jet 3.1 x <.14 Entries / 1 MeV/c Data η M γγ Fit Bkg Jet 3.14 x < M γγ [GeV/c 2 ] M γγ [GeV/c 2 ] Figure 1: Example of a fitted γγ invariant mass distribution in jet 3 for inclusive π production in three-jet events. 2 Figure 2: Example of a fitted γγ invariant mass distribution in jet 3 for inclusive η production in three-jet events.

8 8 Example VI: a Missing Mass Peak (e + e γx) ALEPH Collaboration, Eur. Phys. J., C 28 (23) Entries/(3 GeV/c 2 ) 2 15 ALEPH s = GeV Missing mass (GeV/c 2 )

9 9 Example VII: a three body decay (Λ c pkπ) ALEPH Collaboration, hep-ex/ Λ c ALEPH Candidates / 6 MeV/c M(pKπ) (GeV/c 2 ) Figure 6: pk π + invariant mass distribution with the fit result.

10 1 Example VIII a: B Hadron Peaks from CDF CDF Collaboration, Homepage 26 2 Events/5 MeV/c CDF Run II Preliminary 22 pb N(ψ )=6429.3± ψ(2s) J/ψ π J/ψππ candidate mass [GeV/c π - ] 2 Events/5 MeV/c CDF Run II Preliminary 22 pb ± ± B J/ψ K N(Bu)=2264.1±52.6 Fit Prob: 52.% B u candidate mass [GeV/c ]

11 11 Example VIII b: B Hadron Peaks from CDF CDF Collaboration, Homepage 26 2 Events/5 MeV/c CDF Run II Preliminary 22 pb 6 B N(Bs)=184.6±12.5 s J/ψφ Fit Prob: 75.% Events/6 MeV/c CDF Run II Preliminary 22 pb Λ B J/ψ Λ N(Λ b )=88.6 ±1.3 Fit Prob: 23.3% B s candidate mass [GeV/c ] Λ b candidate mass [GeV/c ]

12 12 Example IX: CDF W( µν) transverse mass CDF Collaboration, Homepage 26

13 13 Example IX: CDF Z e + e Mass CDF Collaboration, Homepage 26

14 14 Example X: CMS di-muon mass spectrum 21 CMS Collaboration, the first LHC Data: summer 21 Events/GeV ρ,ω φ J/ ψ η ψ ' Υ(1,2,3S) Z CMS Preliminary s = 7 TeV, L int -1 = 4 pb µ + µ - mass (GeV/c 2 )

15 15 Particle- (mass) reconstruction: summary good decay channels with charged stable particles in the decay K s π + π Λ pπ, Λ pπ + J/Ψ µ + µ Z µ + µ other decay channels π, η γγ cascade decays: Ω ΛK, D + D π + three body decays: D + K π + π + four body decays: H ZZ µ + µ µ + µ

16 16 Invariant mass determination: measurement and measurement error? Particle identification: Pion, Kaon or Proton Mass (m i ) momentum vector (px,py,pz): tracking detectors for neutral particles (γ s) practically only with the calorimeter (angular measurement error) Tricks?! kinematic selection criteria (different kinematics between signal and background) long lifetimes (decay products are not coming from the event vertex! using kinematic/geometric regions with best accuracy. For decay cascades: analyse only relative mass measurements, kinematic constraints (e. g. D D π Kππ D mass is known exactly!). Attention of phase space reflections!

17 17 The search for B s µµ (I) with many details and plots py/access?resid=&materialid=slides&confid=216344

18 18 The search for B s µµ (II) November 212 result: Clear indication of a signal! First evidence for the decay B s µµ with many details and plots py/access?resid=&materialid=slides&confid=216344

19 19 Searching for mass peaks: with known branching ratios? LHC Higgs search with CMS and ATLAS: H γγ, H ZZ and/or H W + W Which W and Z decays should be used? How large is the background (mass measurement error)? Can one find additional kinematic selection criteria (and tricks?) an optimisation problem!

20 2 Missing energy, momentum and mass I Neutrino like particles in the decay (like W eν): Signature? Missing momentum and missing transverse momentum. Required: hermetic detector combined with well understood even kinematic! L3 Monte Carlo: b e ν X events E ν reconstructed E ν generated 1 Entries / GeV Neutrino Energy [ GeV ] E ν reconstructed E ν smeared Neutrino Energy [ GeV ]

21 21 Missing energy, momentum and mass II measuring neutrinos in Z b b Zerfällen: Lett. B 351 (1995) 375.) b lνx (L3 Collaboration, Phys. 1 2 a) L3 b e ν X Data MC V-A MC V+A 1 Entries / GeV Neutrino Energy Spectrum [ GeV ] 1 3 b) L3 b µ ν X Data MC V-A MC V+A Neutrino Energy Spectrum [ GeV ]

22 22 Missing energy, momentum and mass III Acoplanar and acolineare events events with 2 and more missing neutrino like particles: e + e W + W lνlνx

23 23 Missing Mass kinematics can (not) be described with just one massless particle. Example 1: an energetic γ disappears in the beam pipe e + e Zγ γq q Example 2: searching for the Higgs with a future linear collider e + e HZ b bz und Z X

24 e + e Zγ γq q Run # 788 Event # 286 Total Energy : 15.6 GeV Transverse Imbalance :.86 Longitudinal Imbalance : Thrust :.7935 Major :.5396 Minor :.1163 Event DAQ Time :

25 25 e + e HZ b bz and Z X Chapter 2 Figure 2.4: Higgs reconstruction in the process e + e Z h for various Higgs boson masses, using l + l, νν, and hadronic Z decays, for a 3 fb 1 event sample at 3 GeV, from [63]. The background is dominated by the process e + e Z Z, which produces the missing-mass peak at m Z. The unshaded solid histogram gives the background if a b-tag is applied to the Higgs candidate. The dashed histograms in (a) and (b) show the background with no b-tag. 32

26 26 Invariant mass and detector calibration Yesterdays discovery is todays calibration tool and tomorrows background (origin unknown but Quoted by many) Mass peaks from particles with known mass Teilchen allow to calibrate your detector (tracking and energy measurement)! Which decays can be used? high detectable cross section with small background (K s π + π, J/Ψ we(µµ), Z ee(µµ))! Electromagnetic calorimeter (π, η γγ).

27 27 Jet reconstruction and calibration I What are jets? Energetic quarks and gluons (High Q 2 ) will be transformed in the fragmentation process (low Q 2 ) in observable mesons and baryons. experimentally one observes bundles of hadrons: many particles within a small cone quantitative description is difficult and Modell dependent. (ask yourself: what is the goal of the measurement?)

28 28 Jet reconstruction and calibration II How to determine 4-vectors of jets? measurement of all associated hadrons is difficult. Which hadrons should be added in a multi-jet environment? which jet-algorithm? (For me) The most important is a consistent definition in the experimental and modelled reconstruction of theorie (QCD) jets. Calibration of jets at the LHC (what is the goal?) pp γ jet final states and pp t t with t bw and W q q.

29 29 The tagging of b-flavoured Jets I from the jet 4-vector to the jet initiating parton 4-vector. (what was the original quark flavour?) Assumptions? during the jet-fragmentation practically only light quarkantiquark pairs are produced (uū,d d und s s). The hadron with the original quark contains on average the largest momentum

30 3 The tagging of b-flavoured Jets II How can we learn something about the primary quark production mechanism? some methods: b (beauty) flavoured jets? long lifetime, combined with high p t B-hadron decay products (partial mass reconstruction using inclusive electrons and muons)! Up to 5% of the b-jets in t t events can be tagged in modern LHC detectors. jets with the charm-flavour? Rekonstruction of Charmed hadrons (D etc) Identification of u, d, s and gluon jets is practically impossible! some statistical enrichment with anti b and c criteria!