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Standard Model Lesson #3 Higgs boson searches at LEP1, LEP2 Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Higgs searches at LEP The coupling of the Higgs field to the vectorial bosons and fermions it’s fully defined in the Standard Model The cross section of the Higgs production and the decay modes as a function of it’s mass are predicted by the theory Z Z* H Z* Z H Padova, May 6th 2013 Ezio Torassa ECM=206 GeV XXVIII Ph.D in Physics ECM=206 GeV The dominating Higgs production mechanism at LEP1 and LEP2 is the “Higgs-strahlung” MH(GeV/c2) Higgs-strahlung WW fusion + interference Dominant mode m(H) s-m(Z) Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Higgs decay channels For mH 120 GeV, the most important decay chanel is H bb Hbb 85% “b-tagging” is relevant ! Reaserch topology: 4 jets 2 jets & missing energy 19% 60% Htt 8% 2 jet & 2 lepton 6% Padova, May 6th 2013 Ezio Torassa XXVIII in Physics Or a tPh.D instead of the b Higgs searches at LEP1 Neutrino decay channel The signature is one unbalanced hadronic event. 2 jets & The background is due to Z decay into b quarks missing energy Background reduction: • invariant mass of the two jets MZ • jets not in collinear directions • b-tagging b c uds c uds b Tracks impact parameters Padova, 6th 2013 Padova May 12 Aprile 2011 Ezio Torassa Ezio Torassa Leptons transverse momentum XXVIII Ph.D in Physics Data analysis example (1991-1992) Zqq Z H (55GeV)X (1) Preselection: Acollinearity > 8 0 Eff. ( Z HX) = 81.2% Eff. (Zqq) = 1.5 % 20 GeV < Minvariant < 70 GeV (2) Neural network: Z HX Zqq Neural network with 15 input variables. The output is a single quality variables: Q takes values between 0 and 1 Q > 0.95 Eff. ( Z HX) = 65.8% Eff. (Zqq) = 0.23 % ( to be multiplied with the previous Eff. ) Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Q( ) Results Sum of the tree decay channels: # observed events: 0 Z Zee Z # expected background events : 0 # expected signal events M (GeV) H Eventi (simulati HZ) 50 55 7.90.4 3.60.2 60 65 1.40.1 0.410.05 For MH = 55.7 GeV we have 3 expected signal events events. The expected number of event is a mean number (l=3) with a Poisson distribution: The probability to observe 0 events is 5%. l=3 e l ln (n | l ) n! Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics For MH larger than 55.7 GeV the probability to observe zero events il smaller than 5%. Your confidence level is 95%. DELPHI 1991-1992: Higgs mass limit: MH > 55.7 GeV al 95 % di C.L. 1 M hadronic events ~380 k events ee LEP1 : 1989-1995 4 detectors , all channels m(Higgs) > 65 GeV Padova, May 6th 2013 /c2 Ezio Torassa LEP1 1989-1995 at 95%CL 17 M hadronic events XXVIII Ph.D in Physics Exclusion and discovery Large number of events Gauss distribution approximation Small number of events Poisson distribution n = number of observed events e l ln (n | l ) ; n l ; n l ; m = mean number of events n! Contributions to the mean value l: background (b) and signal (s) : e (b s ) (b s) n (n | b s) ; n b s; n b s; n! n is the measurement; • Exclusion (at least at 95% CL): the probability to observe n events 5% • Discovery (5 significance): Padova, May 6th 2013 signal 5 times larger than the error Ezio Torassa XXVIII Ph.D in Physics EXCLUSION The observed small number of events could be due to a statistical fluctuation with prob. 5×10-2 DISCOVERY The observed large number of events could be due to a statistical fluctuation with prob. 5.7×10-5 Lexclusion Increasing the Integrated luminosity the background uncertainty decreases. When the difference between background and background+signal is 2 the Luminosity for the exclusion is reached. Ldiscovery Similar definition for the discovery Really observe n events and expect to observe n events at a given luminosity is not the same. At the exclusion (or discovery) Luminosity the probability to 2013 reach the goal is 50% Ezio Torassa Padova, May 6th XXVIII Ph.D in Physics Significance e ( b s ) ( b s ) n (n | b s ) ; n b s; n b s; n! S cP ScP s bs s b When the background b can be precisely estimated With high statistics, for few units of significance, the denominator is only √b The inclusion of the background error Db with a Gaussian distribution needs a specific calculation, with the Gaussian approximation for the number of events n the significance can be expressed with the following relation: S cl s b Db 2 Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics The “blind analysis” • With a large number of observed events (n>>n), the statistical fluctuations do not have a big impact in the final result; for small numbers is the opposite: small changes in the selection can produce big differences (i.e. 0 evts 2 evts) • None is “neutral” , good arguments can be found to modify a little bit the cuts to obtain a sensible change of the final result; • The selection criteria must be defined a priori with the MC to optimize the signal significance, only at the end we can open the box and look the impact on the real data. This method is called “blind analysis”. Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Higgs searches at LEP II The “Higgs-strahlung” is dominant production also at LEP II. At higher s - the diboson fusion increas the relative relevance; - higher Higgs masses can be produced. ECM=206 GeV Padova, May 6th 2013 MH Ezio Torassa XXVIII Ph.D in Physics Higgs decay channels at LEP II The most relevant decay channel is H bb like at LEP I Over 115 GeV (LHC region) other decay channels (WW e ZZ) becames relevant or dominant Research topology: Hbb 85% 4 jets 2 jets & LEP I missing energy LEP II 19% 60% Htt 8% 2 jet & 2 lepton 6% Padova, May 6th 2013 Ezio Torassa XXVIII in Physics Or a tPh.D instead of the b In addition to Zff we have also the WW , ZZ and production and decays. e+ W+ We- H e+ e- e+ Z e+e- → e+e-qq H Z f’ Z ee+ f W+, Z, ,e ePadova, May 6th 2013 e+ W-, Z, eEzio Torassa e+ e- q q XXVIII Ph.D in Physics mH=100 GeV mH=115 GeV Invariant mass distribution for MC and real data. Final LEP selections for 115 GeV search (Loose and Tight) Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Statistic approach for the global combination We need to combine the results from different channels (Hqq, H, Hll) and different energies Ecm. They are grouped in the same two-dimensional space (mH rec , G) G mH rec reconstruced invariant mass G discrimanant variable (QNN, b-tag) mHrec For every k channel we obtain: - bk estimanted background - sk estimated signal (related to mH) - nk number of Higgs candidate from the real data We build the Likelihood for two hypothesis: - candidates coming from signal + background - candidates coming from background Padova, May 6th 2013 Ezio Torassa Ls+b Lb XXVIII Ph.D in Physics We want to discriminate the number of observed events (n) w.r.t. the mean number of expected signal plus background (b+s) or only background (b) The following is the probability for b+s , s is a function related to mH : e (b s ( mH )) (b s(mH )) n P( n | b s ) n! The Likelihood is the product of the probability density (k channel density) nk L P(nk | bk sk (mH )) i 1 k Padova, May 6th 2013 Ezio Torassa sk Sik (mH ) bk Bik sk bk XXVIII Ph.D in Physics e (bk sk ( mH )) (bk sk (mH )) nk L nk ! k nk sk Sik (mH ) bk Bik sk bk i 1 The comparison between the two hypothesis is provided by the Likelihood ratio. Q ( mH ) Ln|b s (mH ) Ln|b (mH ) We choose to describe the results with the log of the ratio because it provides the 2 difference : 2 ln( Q(mH )) D 2 We look to the function -2ln(Q(mH)) (i) For the real data (ii) For the MC with n=b (iii) For the MC with n=b+s Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics green: 1 from the background yellow: 2 from the background background (higher 2 for b+s) signal+background (higher 2 for b) Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Over 114 GeV/c2 the real data line (red) is closer the the s+b line (brown) Finally we can estimate the exclusion at 95% of confidence level anyway the real data line is always (every mH ) within 2 from the background line (CLs = CLs+b / CLb) mH > 114.4 GeV/c2 at 95% CLs LEP I mH > 65 GeV/c2 Padova, May 6th 2013 LEP II mH > 114.4 GeV/c2 Ezio Torassa XXVIII Ph.D in Physics The “window” for MHiggs 171 GeV 114.4 GeV This exclusion window is at 95% of C.L. , masses outside this window are not forbidden, they have a smaller probability Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics Higgs searches at LEP I : Z Physics at LEP I CERN 89-08 Vol 2 – Higgs search (pag. 58) Search for the standard model Higgs boson in Z decays – Nucl Physics B 421 (1994) 3-37 Higgs searches at LEP II : Search for the Standard Model Higgs Boson at LEP – CERN-EP/2003- 011 Padova, May 6th 2013 Ezio Torassa XXVIII Ph.D in Physics