A Higgs-bozon keresése: a kizárás és felfedezés statisztikus kalandja

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 1 A Higgs-bozon keresése: a kizárás és felfedezés statisztikus kalandja Search for the Higgs Boson: A Statistical Adventure of Exclusion and Discovery CCP-2013, XXV IUPAP Conference on Computational Physics, Moscow, 21-24 August 2013 Dezső Horváth on behalf of the CMS Collaboration horvath.dezso@wigner.mta.hu Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, Budapest, Hungary & ATOMKI, Debrecen, Hungary

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 2 Outline The Higgs boson of the Standard Model Statistical Methods of the Search Exclusion at LEP Observation at LHC Is it the SM Higgs? What next? With the support of the Hungarian OTKA Grants K103917, K109703

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 3 References The CMS Collaboration: Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30-61. Long version: arxiv:1303.4571 submitted to JHEP The CMS Collaboration: Measurements of the properties of the new boson with a mass near 125 GeV CMS Physics Analysis Summary HIG-13-005, 14 March 2013 The ATLAS Collaboration: Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 29 The ATLAS Collaboration: Combined coupling measurements of the Higgs-like boson with the ATLAS detector using up to 25 fb 1 of proton-proton collision data ATLAS NOTE, ATLAS-CONF-2013-034

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 4 The Zoo of the Standard Model The elementary particles 3 fermion families: 1 pair of quarks and 1 pair of leptons in each 3 kinds of gauge bosons: the force carriers All identified and studied! + the Higgs boson (?) Color: the charge of the strong interaction colored quarks colorless composite hadrons of 2 kinds hadrons = mesons (qq) + baryons (qqq)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 5 The Standard Model Derive 3 interactions of local U(1), SU(2) and SU(3) symmetries Unify and separate e-m U(1) and weak SU(2) interactions using spontaneous symmetry breaking: Anderson-Englert-Brout-Higgs- Guralnik-Hagen-Kibble (BEH) mechanism, 1963-64 Add a 4-component, symmetry breaking field to vacuum. Separate a good U(1) local symmetry from the ruined U(1) SU(2) electromagnetism + zero-mass photon, OK! Turn 3 d.f. of Higgs-field to create masses for Z, W +, W, get a correct weak interaction with 3 heavy gauge bosons. 4th degree of freedom: heavy scalar boson.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 6 Glory Road of the Standard Model Status in 2013 Includes hundreds of measurements of all experiments Expt theory expt. uncertainty Slightly deviating quantity used to change Now it is forward-backward asymmetry of e + e Z b b LEP Electroweak Working Group: http://lepewwg.web.cern.ch/ Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02750 ± 0.00033 0.02759 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4959 σ 0 had [nb] 41.540 ± 0.037 41.478 R l 20.767 ± 0.025 20.742 A 0,l fb 0.01714 ± 0.00095 0.01645 A l (P τ ) 0.1465 ± 0.0032 0.1481 R b 0.21629 ± 0.00066 0.21579 R c 0.1721 ± 0.0030 0.1723 A 0,b fb 0.0992 ± 0.0016 0.1038 A 0,c fb 0.0707 ± 0.0035 0.0742 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1481 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.385 ± 0.015 80.377 Γ W [GeV] 2.085 ± 0.042 2.092 m t [GeV] 173.20 ± 0.90 173.26 March 2012 0 1 2 3

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 7 The Higgs boson of the Standard Model Spinless, neutral, heavy particle The scalar particle needed for renormalisation Does it really exist? SM: it must! Many jokes of the Higgs boson on internet... The Higgs boson walks into a bar. The bartender says "Watch out, there were some guys looking for you." The Higgs boson walks into a church. The priest says Your kind is not welcome here. The boson replies: But without me how can you have mass?

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 8 Viccek a Higgs-bozonról, előtte A bárba besétál egy Higgs-bozon. A csapos nem érti... Szeretnék végre látni egy jó Higgs-bozonos viccet. Biztosan létezik, de évekbe telhet, amíg rátalálunk.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 9 Viccek a Higgs-bozonról, utána A bárba besétál egy Higgs-bozon. A csapos megkérdezi: Mi van? mire ő: Én!! A Higgs-bozon felfedezése után a fizikusok tömegesen ünnepeltek. Nem tudom, mi a csuda az, de klassz, hogy felfedezték! Ellenőrizni kell. A múltkor is azt hittem, Higgs-bozont találtam az ágyam alatt, de csak egy üveggolyó volt. Jó, hogy megvagy, Isten-részecske. Én csak egy átlagember vagyok, aki nem ért téged.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 10 Spontán szimmetriasértés A történet: Mechanizmus: Anderson javasolja 1963-ban Kidolgozzák: F. Englert és R. Brout, 1964 P. Higgs, 1964 G.S. Guralnik, C.R. Hagen és T.W.B. Kibble, 1964 Skalár bozon: Peter Higgs, 1964-65 Bozon megfigyelve: ATLAS és CMS, 2012 Nobel-díj: F. Englert és P. Higgs, 2013 Az elnevezés (vitatéma) Igazságos: Higgs-bozon, BEH-mechanizmus Igazságtalan: Higgs-mechanizmus, -potenciál, -tér

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 11 tatistical Concepts of Particle Physicists are far from those of official math statistics! LHC Statistics for Pedestrians by Eilam Gross in PHYSTAT-LHC Workshop on Statistical Issues for LHC Physics, CERN-2008-001, p. 205: A pedestrians guide... to help the confused physicist to understand the jargon and methods used by HEP Phystatisticians. A Phystatistician is a Physicist who knows his way in Statistics and knows how Kendalls advanced theory of statistics book looks like... Every collaboration has phystatistician experts and they all have quite different ideas how to analyse data...

Last 2 PHYSTAT-LHC Workshops Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 12

Statistics Committees Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 13

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 14 Likelihood Poisson distribution (n i events in bin i): P(n i µ i ) = µn i i e µ i n i! Poisson likelihood: L = Π i P(n i µ i ) Expected < n i >: µ i = j Lσ jǫ ji L: luminosity ( collision rate), σ j : cross section of source j, ǫ ji : efficiency (Monte Carlo) of source j in bin i.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 15 Luminosity: collision rate Luminosity: L = fn N 1N 2 A [L] = s 1 cm 2 ( flux) f: circulation frequency; n: nr. of bunches in ring; N 1,N 2 particles/bunch; A: spatial overlap Rate of reaction with cross section σ at ǫ efficiency R = ǫσl Integrated luminosity: t 2 t 1 Ldt measured in units of inverse cross-section: [pb 1, fb 1 ]

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 16 Exclusion and Discovery General convention in accelerator experiments: Exclusion of a given phenomenon at 95% confidence level. ε/2 ε/2 Observation of something new: > 5σ above background. (x x 0 )/ σ One-sided exclusion: X > X 0 at 95% CL if X obs X 0 > 1.64σ

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 17 And what isσ? The total uncertainty of the physics parameters P according to the best honest guess of the experimentalist. It has a statistical component (from the number of observed events) and systematic ones from various sources: Monte Carlo statistics and inputs, calibration factors, efficiencies, etc. (nuisance parameters Θ) could be added up with correlations accounted for with a final uncertainty roughly: σ = σstat 2 + σ2 syst However, we derive the final uncertainty via marginalizing (integrating out) the nuisance parameters in likelihood L using the related probability distributions W: L(P;x) = W(x P) = W(x P,Θ)W(Θ P)dΘ

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 18 Blind Analysis A blind analysis is a measurement which is performed without looking at the answer. Blind analyses are the optimal way to reduce or eliminate experimenter s bias, the unintended biasing of a result in a particular direction. A. Roodman: Blind Analysis in Particle Physics, http://arxiv.org/abs/physics/0312102, SLAC, 2003 Originally coming from medicine Basic analysis method of Higgs search at LHC: Optimize, prove and publish your analysis technique using simulations and earlier data only before touching new data in the critical region CMS, 2012: 110 < M H < 140 GeV blinded because of 3σ excess observed in 2011 Simultaneous unblinding for all analysis channels

The Large Electron Positron collider Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 19

Accelerators at CERN, LEP era Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 20

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 21 The LEP Collider Year E(e + e ), GeV Ldt/4, pb 1 main goal 1989 94 91 140 Z 0 1995 130 136 5 1996 161 172 20 W + W 1997 184 60 WW, ZZ 1998 189 190 WW, ZZ 1999 192 202 220 Higgs 2000 204 209 220 Higgs

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 22 Search for the SM Higgs boson at LEP Dominant formation: Higgs-strahlung e e + ZH Dominant decay: H bb Various analyses for different Z decays

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 23 What is observed: resonance τ = Γ 1 lifetime exp. decay: N(t) = N 0 e Γt Probability distribution: χ(e) 2 = 1 (E M) 2 +Γ 2 /4 Breit-Wigner equation M Γ resonance centre width ( = 1,c = 1) Lorentz curve New particle discovery: resonance at decay energy corresponding to the particle mass

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 24 Hunting the Higgs boson Compose a complete SM background using Monte Carlo simulation taking all types of possible events normalized to their cross-sections. Higgs signal: simulation of all possible production and decay processes with all possible Higgs-boson masses Put all these through the detector simulation to get events analogous to the measured ones. Optimize the event selection: reduce B background, enhance S signal via maximizing e.g. N S / N B or N S / N S + N B or 2 ( N S + N B N B ) Calculate at experimental luminosity expected nr. of events for signal and background at various conditions. SM background experiment? (YES / NO ). Bityukov and Krasnikov, 1999

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 25 Hypothesis Testing: Test Statistic Likelihood ratio: signal+background/background Q = L s+b /L b Usually analysed and plotted: 2lnQ(m H ) = 2 N ch k=1 [ s k (m H ) n k j=1 ln ( )] 1 + s k(m H )S k (x jk ;m H ) b k B k (x jk ) n k : events observed in channel k, k = 1...N ch s k (m H ) and b k : signal and background events in channel k for Higgs mass m H S k (x jk ;m H ) and B k (x jk ): probability distributions for events for Higgs mass m H at test point x jk x jk : position of event j of channel k on the plane of its reconstructed Higgs mass and cumulative testing variable constructed of various features of the event like b-tagging, signal likelihood, neural network output, etc.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 26 No Higgs at LEP: M H > 114.4 GeV 1-CL b 1 10-1 10-2 10-3 10-4 10-5 ALEPH Observed Expected signal+background Expected background 100 102 104 106 108 110 112 114 116 118 120 m H (GeV/c 2 ) 2σ 3σ 4σ 1-CL b 1 10-1 10-2 10-3 10-4 10-5 DLO Observed Expected signal+background Expected background 100 102 104 106 108 110 112 114 116 118 120 m H (GeV/c 2 ) 2σ 3σ 4σ Expected and observed signal confidence level assuming background only (ALEPH, DELPHI, L3 and OPAL: Phys. Lett. B 565 (2003) 61-75.) Excess in ALEPH s 4-jet events at 115 GeV: E LEP2000 = 206 GeV m H (115) + m Z (91) = 206 GeV!!

LEP: exclusion by experiment Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 27

LEP: exclusion by channel Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 28

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 29 ALEPH event (e + e bbqq) b quark: long lifetime secondary vertex

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 30 LEP: spaghetti diagrams Event weights vs. Higgs mass for 17 selected LEP events The LEP Collaborations, Search for the Standard Model Higgs Boson at LEP Phys. Lett. B 565 (2003) 61.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 31 Accelerators of CERN now LHC: Large Hadron Collider SPS: Super Proton Synchrotron AD: Antiproton Decelerator ISOLDE: Isotope Separator On Line DEvice PSB: Proton Synchrotron Booster PS: Proton Synchrotron LINAC: LINear ACcelerator LEIR: Low Energy Ion Ring CNGS: Cern Neutrinos to Gran Sasso

LHC and its main experiments Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 32

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 33 Steering magnets of LHC 1232 superconducting magnets (before installation) (L = 15 m, M = 35 t, T = 1.9 K, B = 8.3 T)

Dipole magnets of LHC in the tunnel Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 34

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 35 CMS: Compact Muon Solenoid 14000 ton digital camera: 100 M pixel, 20 M pictures/sec, 1000 GB/sec data Processes max 400 pictures/sec intelligent filter!!

The (Compact Muon) Solenoid itself Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 36

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 37 The CMS Collaboration (2013) 181 institutions of 42 countries 3275 physicists (incl. 1535 students) 790 engineers and technicians Participants by countries of institutes: USA: 1426, Italy: 545, Germany: 349, Russia: 270 Participants by nationality: USA: 861, Italy: 697, Germany: 375, Russia: 353 390 publications since 2010, the start of LHC data taking Huge joint effort: 3000 people worked on it for 20 years!

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 38 Formation of the SM Higgs boson in p-p collisions at LHC g q H g gluon fusion q q _ q W,Z _ q H vector boson fusion

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 39 Decay of the SM Higgs boson March 2012 Not excluded by 2011 CMS data: 114 < M H < 127 GeV (at 95% CL) (where many decay processes contest) Best identified: H γγ; H ZZ l + l l + l (l ± = e ±,µ ± ) Excess observed 2 3σ at 125 GeV!

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 40 CMS: elektromagnetic calorimeter optimized for studying H γγ 75,848 PbWO 4 single crystal scintillators

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 41 Eseményregisztrálás, trigger Esemény (event) Valamilyen érdekes észlelés (trigger) indítja Minden jellemző adatot tartalmaz, de csak a megszólalt detektorelemekét Egyidejűleg többfélét figyelünk (és regisztrálunk) Fizikai, kalibrációs, ellenőrző Triggertől függ, milyen adatokat olvasunk/tárolunk Ami az érdekes Trigger Elektronikus és számítógép-generált CMS: 2 trigger-szint 0: 20 MHz (2009-12); 1: 20 khz; 2: 400 Hz eseményhozam

A CMS event: H γγ candidate Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 42

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 43 CMS: 78 identified vertices! Many p-p collisions can be in the same event (same bunch collision). Record: 78 identified vertices. This increases data taking speed and makes life hard.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 44 MINOS-bizonytalanság Nem-lineáris becslésnél rengeteg elhanyagolás eredmény torzítása szimmetrikus szórás nem életszerű MINUIT MINOS-hibája χ 2 n m 1 Paramétert változtatni, amíg χ 2 χ 2 + 1 p = p σ exp + σ 1 2 többi paraméter optimalizálásával χ 2 min+1 χ 2 min p ~ σ1 p ~ p ~ + σ 2 p

Szisztematikus bizonytalanság Minden bizonytalanság, amely nem az észlelt eseményszámból ered Becslése: Valamennyi bevitt információ ésszerű változtatásának hatása az eredményre Összegzés korrelációk figyelembevételével Eredeti illesztési munka sokszorosa Később korrigálható korábbi mérések eredménye elméleti számítás globális kalibráció (E LEP ) Nem korrigálható szimuláció eredménye adott méréstechnika eleme aldetektor kalibrációja Ésszerű változtatás: (Mért szimulált) érték Bemenő paraméter ± szórás Különböző algoritmusok (fragmentáció, jet-keresés) Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 45

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 46 Teljes bizonytalanság Felfedezés: +5σ tot. σ tot =? A P fizikai paraméterek teljes bizonytalansága a kísérletező legjobb becsületes becslésével meghatározva. Durva becslés: összeadni, σ = σstat 2 + σ2 syst Korrelációkat figyelembe kell venni. Szimulációból? LHC-nál: sziszt. bizonytalanság eltüntetése a likelihoodból a zavaró (nem fizikai) Θ paraméterek marginalizációjával (kiintegrálás) a megfelelő W eloszlásokkal: L(P;x) = W(x P) = W(x P,Θ)W(Θ P)dΘ

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 47 Fizikatörténet I: mérés vs. év Review of Particle Physics, K. Nakamura et al, J. Phys. G 37, 075021 (2010)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 48 Fizikatörténet II: mérés vs. év Review of Particle Physics, K. Nakamura et al, J. Phys. G 37, 075021 (2010)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 49 4 July 2012: we have something! ATLAS and CMS, at LHC collision energies 7 and 8 TeV, in two decay channels H γγ and H ZZ l + l l + l, at invariant mass of m 126 GeV see a new boson at a convincing statistical significance of 5σ conf. level each with properties corresponding to those of the SM Higgs boson. H γγ J H = 0 or 2 Data analysis was optimized for SM Higgs search... Nevertheless, it has to be shown to be the SM Higgs, e.g. J H = 0: H ZZ and H WW angular distribution of decay products H XY... cross sections follow the SM predictions There is one Higgs boson only (no charged or more neutral ones)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 50 2012 július 4: valami van! ATLAS és CMS, 7 és 8 TeV ütközési energián, H γγ és H ZZ l + l l + l csatornában, m 126 GeV tömegnél statisztikusan jelentősen (kísérletenként 5σ szignifikanciával) lát egy új H részecskét a SM Higgs-bozonjának megfelelő tulajdonságokkal. François Englert és Peter Higgs első találkozása

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 51 CMS: H γγ (VBF) Vertex for measuring the γγ invariant mass: two hadron jets from vector boson fusion.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 52 CMS and ATLAS: A new boson ATLAS: 2931 authors CMS: 2899 authors

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 53 CMS: H γγ mass distribution 2012 (2011 + 25% of 2012 data) 2014 (2011 + all 2012 data) +0.09 σ expt /σ SM = 1.14 ± 0.21(stat) 0.05 (syst) +0.13 0.09 (theo) CMS Collaboration, Eur. Phys. J. C (2014) 74:3076

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 54 ATLAS: H γγ mass distribution 2012 (2011 + 25% of 2012 data) 2014 (2011 + all 2012 data) ATLAS Collaboration, arxiv.org:1408.7084, 2014

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 55 CMS: H ZZ l + l l + l 2012 (2011 + 25% of 2012 data) 2014 (2011 + all 2012 data) +0.26 σ/σ SM = 0.93 0.23 (stat) +0.13 0.09 (syst) CMS Collaboration, Physical Review D 89, 092007 (2014)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 56 CMS: H ZZ l + l l + l CMS : H ZZ l + l l + l animated

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 57 p-value The probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. Higgs search: The probability that random fluctuation of the measured background could give the observed excess. Discovery: excess above 5σ p-value: how much above

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 58 The Look Elsewhere effect Looking for something with threshold p value p < α? If you did not find it you will look elsewhere (e.g. at different simulated Higgs-masses). n df (degrees of freedom) independent tests should give probability p = 1/n df possibly leading to false discovery. CMS recommendation: quote 2 p-values local (discovery place) and global (whole region) No such effect in exclusion

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 59 CMS: p distributions (4 July 2012) The probability that random fluctuation of the measured background could give the observed excess. γγ and ZZ: 5.0σ γγ, ZZ and WW: 5.1σ All together: 4.9σ ATLAS got the same: γγ and ZZ: 5.0σ Adding WW increased the ATLAS excess to 6.0σ

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 60 CMS, Dec. 2012: significance Doubling 8 TeV statistics increased CMS excess to 6.9 σ Sharp peak, close to SM exp. at 126 GeV, far less elsewhere

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 61 CMS 2014: mass vs. x-sec m H = 125.03 +0.26 0.27 (stat) +0.13 0.15 (syst) GeV (CMS Physics Analysis Summary HIG-14-009, 2014)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 62 CMS, March 2013: spin, parity CMS data favor + parity for S X = 0 CMS Physics Analysis Summary HIG-13-005

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 63 CMS: is it the SM Higgs boson? Branching ratios of different decay channels as compared to SM predictions for a 125.03 GeV Higgs boson CMS Physics Analysis Summary HIG-14-009, 3 July 2014

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 64 Signal strengths vs. SM expectations CMS preliminary results Relative signal strengths for various production and decay channels 68% confidence level contours All agree with the SM CMS Physics Analysis Summary HIG-14-009, 3 July 2014

CMS vs. ATLAS: masses Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 65

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 66 CMS vs. ATLAS: mass (determined consistently, in various ways) Mass averaged for both channels and all decay modes CMS, 2013: 125.7 ± 0.3(stat) ± 0.3(syst) GeV/c 2 +0.26 CMS, 2014: 125.03 ± 0.27 (stat) ± +0.13 (syst) GeV/c2 0.15 ATLAS, 2013: 125.5 ± 0.2(stat) ± +0.5 (syst) GeV/c2 0.6 ATLAS, 2014: 125.36 ± 0.37(stat) ± 0.18(syst) = 125.36 ± 0.41 GeV/c 2 High gain in systematics with some loss of statistics.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 67 CMS vs. ATLAS: signal strength Total cross section for all production and decay channels as compared to the SM prediction for M H = 125 GeV (µ = σ obs /σ SM ): CMS, 2013: 0.80 ± 0.14 CMS, 2014: 1.00 ± 0.09(stat) ± 0.07(syst) ± ATLAS, 2013: 1.43 ± 0.16(stat) ± 0.14(syst) +0.08 0.07 (theo) All agree with the Standard Model (unfortunately)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 68 Fizikai Nobel-díj, 2013 The Nobel prize was awarded to François Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN s Large Hadron Collider." Rolf-Dieter Heuer, a CERN főigazgatója, bejelenti a Nobel-díjat az ATLAS és CMS közös irodaépületében.

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 69 CMS, H γγ: mass and cross section All results (ATLAS & CMS, properties of various production and decay channels) agree within uncertainties. Mass: m γγ = 124.70 ± 0.31(stat) ± 0.15(syst)GeV = 124.70 ± 0.34 GeV Signal strength as compared with SM prediction: +0.09 σ expt /σ SM = 1.14 ± 0.21(stat) 0.05 (syst) +0.13 0.09 (theo) +0.26 = 1.14 0.23 CMS Collaboration, Eur. Phys. J. C (2014) 74:3076

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 70 CMS, H ZZ: mass and cross section H ZZ l + l l + l (l = e, µ) +1.5 m 4e = 126.2 1.8 m +0.9 2e2µ = 126.3 0.7 +0.6 m 4µ = 125.1 0.9. Mass average: m ZZ = 125.6 ± 0.4(stat) ± 0.2(syst) GeV Signal strength as compared with SM prediction: +0.26 σ/σ SM = 0.93 0.23 (stat) +0.13 0.09 (syst) CMS Collaboration, Physical Review D 89, 092007 (2014)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 71 CMS, 2014: mass and cross section Combination of all channels: H γγ, H ZZ l + l l + l, H WW lνlν, H ττ, WH, ZH;H bb, tth, H hadrons, leptons. (CMS Physics Analysis Summary HIG-14-009, 2014) m H = 125.03 Measured mass: +0.26 0.27 (stat) +0.13 (syst) GeV 0.15 Signal strength as compared to SM prediction at the measured mass: σ/σ SM = 1.00 ± 0.09(stat) ± 0.07(syst) +0.08 0.07 (theo)

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 72 OR: What does M H = 126 GeV mean? Conference Why M H = 126 GeV?, Madrid, 25-27 Sep. 2013 M H vs. M top is critical, at vacuum stability border Need very precise M H, M top and α s. SM may be valid until Planck energy (10 18 GeV)! New physics anywhere?? Somebody is pulling our leg??? Anthropic principle??? S. Alekhin et al., arxiv:1207.0980, 2012

Horváth Dezső: Higgs-keresés StatFiz Szem., ELTE, 2014.11.19. p. 73 Conclusion We very probably observed the Standard Model Higgs boson or (unfortunately, less probably) a Higgs boson of a more general model. The LHC will restart in 2015 with much higher energy and luminosity. Let us hope for some deviation from the Standard Model (although none seen yet). Thanks for your attention!