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The Higgs Boson Jim Branson Phase (gauge) Symmetry in QM • Even in NR Quantum Mechanics, phase symmetry requires a vector potential with gauge transformation. Schrödinger Equation invariant under global change of the phase of the wavefunction. x,t e x,t i There is a bigger symmetry: local change of phase of wfn. We can change the phase of the wave function by a different amount at every point in space-time. x,t e i (x,t) x,t Extra terms in Schrödinger Equation with derivatives of . We must make a related change in the EM potential at every point. hc A A e One requires the other for terms to cancel in Schrödinger equation. Electron’s phase symmetry requires existence of photon. 2 QuantumElectroDynamics An A Fn j Fn xn x xn ieA m 0 x • QED is quantum field theory (QFT) of electrons and photons. • Written in terms of electron field and photon field A. • Fields and A are quantized. Able to create or annihilate photons with E=hn. Able to create or annihilate electron positron pairs. • Gauge (phase) symmetry transformation 3 Phase (Gauge) Symmetry in QED x,t ei(x,t) x,t • Phase symmetry in electron wavefunction corresponds to gauge symmetry in vector potential. One requires the other for terms to cancel in Schrödinger equation. Electron’s phase symmetry requires existence of photon. • The theory can be defined from the gauge symmetry. • Gauge symmetry assures charge is conserved and that photon remains massless. 4 Relativistic Quantum Field Theory • Dirac Equation: Relativistic QM for electrons Matrix () eq. Includes Spin Negative E solutions understood as antiparticles • Quantum Electrodynamics ieA m 0 Field theory for electrons and photons x Rules of QFT developed and tested Lamb Shift Vacuum Polarization Renormalization (fixing infinities) Example of a “Gauge Theory” Very well tested to high accuracy 5 Strong and Weak Interactions were thought not to be QFT • No sensible QFT found for Strong Interaction; particles were not points… Solved around 1970 with quarks and Negative function which gave Confinement Decreasing coupling constant with energy • Weak Interaction was point interaction Massive vector boson theory NOT renormalizable Goldstone Theorem seemed to rule out broken symmetry. Discovery of Neutral Currents helped 6 Higgs Mechanism Solves the problem • Around 1970, WS used the mechanism of Higgs (and Kibble) to have spontaneous symmetry breaking which gives massive bosons in a renormalizable theory. • QFT was reborn 7 2 Particles With the Same Mass... 1 2 • Imagine 2 types of electrons with the same mass, spin, charge…, everything the same. • The laws of physics would not change if we replaced electrons of type 1 with electrons of type 2. • We can choose any linear combination of electrons 1 and 2. This is called a global SU(2) symmetry. (spin also has an SU(2) sym.) • What is a local SU(2) symmetry? Different Lin. Comb. At each space-time point 8 Angular Momentum and SU(2) 0 1 • Angular Momentum in QM also follows x the algebra of SU(2). 1 0 Spin ½ follows the simplest representation. 0 i Spin 1… also follow SU(2) algebra. y • Pauli matrices are the simplest operators i 0 that follow the algebra. 1 0 z 0 1 x , y 2i z 9 SU(2) Gauge Theory n i n x,t e e e • The electron and neutrino are massless and have the same properties (in the beginning). • Exponential (2X2 matrix) operates on state giving a linear combination which depends on x and t. • To cancel the terms in the Schrödinger equation, we must add 3 massless vector bosons, W. • The “charge” of this interaction is weak isospin which is conserved. 10 1 2 3 the Standard Model Massless vector U(1) (e) (q) ei(x,t) Local gauge transformation boson Bº n SU(2) triplet of n i n x,t Local gauge Massless vector e L e e bosons SU(2) e transformation W u (SU(2) rotation) 0 W d L W SU(3) Octet of u u u i x,t Local gauge massless vector SU(3) u u e u transformation bosons u u u (SU(3) rotation) gº 3 simplest gauge (Yang-Mills) theories 11 Higgs Potential • I symmetric in SU(2) but minimum energy is for non-zero vev and some direction is picked, breaking symmetry. • Goldstone boson (massless rolling mode) is eaten by vector bosons. 2 V( ) 2† † negative QuickTime™ and a TIFF (Un compressed) decompressor are neede d to see this picture. 1 0 (x)= 2 v+H(x) 12 The Higgs • Makes our QFT of the weak interactions renormalizable. • Takes on a VEV and causes the vacuum to enter a ‘‘superconducting’’ phase. • Generates the mass term for all particles. • Is the only missing particle and the only fundamental scalar in the SM. • Should generate a cosmological constant large enough to make the universe the size of a football. 13 Higgs Mrchanism Predictions • W boson has known gauge couplings to Higgs so masses are predicted. • Fermions have unknown couplings to the Higgs. We determine the couplings from the fermion mass. • B0 and W0 mix to give A0 and Z0. • Three Higgs fields are ‘‘eaten’’ by the vector bosons to make longitudinal massive vector boson. • Mass of W, mass of Z, and vector couplings of all fermions can be checked against predictions. 14 40 Years of Electroweak Broken Symmetry • Many accurate predictions Gauge boson masses Mixing angle measured many ways • Scalar doublet(s) break symmetry • 40 years later we have still never seen a “fundamental” scalar particle Certainly actual measurement of spin 1 and spin 1/2 led to new physics 15 SM Higgs Mass Constraints Experiment SM theory Indirect constraints from precision EW data : The triviality (upper) bound and MH < 260 GeV at 95 %CL (2004) vacuum stability (lower) bound as MH < 186 GeV with Run-I/II prelim. (2005) function of the cut-off scale L MH < 166 GeV (2006) (bounds beyond perturbation theory are similar) Direct limit from LEP: MH > 114.4 GeV 16 SM Higgs production pb NLO Cross sections M. Spira et al. gg fusion IVB fusion 17 SM Higgs decays When WW channel opens up pronounced dip in the ZZ BR For very large mass the width of the Higgs boson becomes very large (ΓH >200 GeV for MH ≳ 700 GeV) 18 CMS PTDR contains studies of Higgs detection at L=2x1033cm-2s-1 CERN/LHCC 2006-001 CERN/LHCC 2006-021 Many full simulation studies with systematic error analysis. Luminosity needed for 5 discovery Discover SM Higgs with 10 fb-1 Higgs Evidence or exclusion as early as 1 fb-1 (yikes) 2008-2009 if accelerator and detectors work… 20 HZZ (*)4 ℓ (golden mode) Background: ZZ, tt, llbb (“Zbb”) Selections : - lepton isolation in tracker and calo HZZee - lepton impact parameter, , ee vertex - mass windows MZ(*), MH 21 HZZ4ℓ • Irreducible background: ZZ production • Reducible backgrounds: tt and Zbb small after selection • ZZ background: NLO k factor depends on m4l • Very good mass resolution ~1% • Background can be measured from sidebands ee ee CMS at 5 sign. CMS at 5 sign. 22 HZZ4e (pre-selection) QuickTime™ and a TIFF (LZW) decompressor are neede d to see this picture. 23 HZZ4e (selection) QuickTime™ and a TIFF (LZW) decompressor are neede d to see this picture. 24 HZZ4e at 30 fb-1 QuickTime™ and a TIFF (LZW) decompressor are neede d to see this picture. 25 HZZ4 QuickTime™ and a QuickTime™ and a TIFF (LZW) decompressor TIFF (LZW) decompressor are neede d to see this picture. are neede d to see this picture. 26 HZZ4 QuickTime™ and a TIFF (LZW) decompressor are neede d to see this picture. 27 HZZee QuickTime™ and a TIFF (LZW) decompressor are neede d to see this picture. 28 HZZ4ℓ 29 HWW2ℓ2n In PTDR • Dominates in narrow mass range around 165 GeV Poor mass measurement Leptons tend to be collinear • New elements of analysis PT Higgs and WW bkg. as at NLO (re-weighted in PYTHIA) include box gg->WW bkg. NLO Wt cross section after jet veto • Backgrounds from the data (and theory) tt from the data; uncertainty 16% at 5 fb-1 after cuts: WW from the data; uncertainty 17% - ETmiss > 50 GeV at 5 fb-1 - jet veto in h < 2.4 Wt and gg->WW bkg from theor. - 30 <pT l max<55 GeV uncertainty 22% and 30% - pT l min > 25 GeV - 12 < mll < 40 GeV 30 Discovery reach with HWW2ℓ 31 Improvement in PTDR 4ℓ and WW analyses (compared to earlier analyses): VERY SMALL 32 SM Higgs decays WWllnn ZZ4l The real branching ratios! 33 HWW2ℓ2n • UCSD group at CDF has done a good analysis of this channel. Far more detailed than the CMS study • Eliot thinks that it will be powerful below 160 GeV because the background from WW drops more rapidly (in mWW) than the signal does! But you need to estimate mWW 34 Higgs Mass Dependence If WW is large compared to the other modes, the branching ratio doesn’t fall as fast as the continuum production of WW. WW fW WW BWW WW ZZ bb fW WW fZ ZZ bb 35 Likelihood Ratio for M=160 e Like sign Help measure background QuickTime™ and a TIFF (LZW) decomp resso r are neede d to see this picture. WW background is the most important Has higher mass and less lepton correlation 36 Likelihood Ratio for M=180 QuickTime™ and a TIFF (LZW) decomp resso r are neede d to see this picture. 37 Likelihood Ratio for M=140 QuickTime™ and a TIFF (LZW) decomp resso r are neede d to see this picture. At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100. 38 Could see Higgs over wider mass range. QuickTime™ and a QuickTime™ and a QuickTime™ and a TIFF (LZW) decomp resso r TIFF (LZW) decomp resso r TIFF (LZW) decomp resso r are neede d to see this picture. are neede d to see this picture. are neede d to see this picture. At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100. 39 H H → γγ MH = 115 GeV Very important for low Higgs masses. 80-140 GeV Rather large background. Very good mass resolution. 40 SM Higgs decays WWllnn ZZ4l The real branching ratios! 41 H→ γγ • Sigma x BR ~90 fb for MH = 110-130 GeV • Large irreducible backgrounds from gg→ γγ, qq → γγ, gq → γ jet → γγ jet • Reducible background from fake photons from jets and isolated π0 (isolation requirements) • Very good mass resolution ~1% • Background rate and characteristics well measured from sidebands 42 Tracker Material Comparison ATLAS CMS CMS divides data into unconverted and converted categories to mitigate the effect of conversions 43 r9 and Categories signal categories unconverted background • (Sum of 9)/ESC (uncorrected) • Selects unconverted or late converting photons. Better mass resolution Also discriminates against jets. 44 45 Backgrounds for 1 fb -1 46 H0→ has large background Higgs Mass Hypothesis • To cope with the large background, CMS measures the two isolated signal photons well yielding a narrow peak in mass. • We will therefore have a large sample of di-photon background to train on. background • Good candidate for aggressive, discovery oriented analysis. Di-photon Mass 47 New Isolation Variables Not just X isolation X X X Eff Sig./Eff. Bkgd Powerful rejection of jet background with ECAL supercluster having ET>40. 48 ETi/Mass (Barrel) Gluon fusion signal VBoson fusion signal Gamma + jet bkgd g+j (2 real photon) bkgd Born 2 photon bkgd Box 2 photon bkgd Signal photons are at higher ET. • since signal has higher di-photon ET • and background favors longitudinal momentum Some are in a low background region. 49 Separate Signal from Background Use Photon Isolation and Kinematics Background measured from sidebands 50 Understanding s/b Variation from NN Strong peak < 1% supressed Optimal cut at 1% Category 0 Signal is rigorously flat; A factor of b/s in 16 GeV Mass Window 2 in s/b is additional factor of 10 from Mass like the difference between Shashlik and crystals 1/10 of signal with 10 times better s/b halves lumi needed 51 S/b in Categories 5 4 3 2 1 0 52 Discovery potential of H SM light h in MSSM inclusive search Significance for SM Higgs MH=130 GeV for 30 fb-1 •NN with kinematics and isolation as input, s/b per event •CMS result optimized at 120 GeV 53 Luminosity needed for 5 discovery Discover SM Higgs with 10 fb-1 Higgs Evidence or exclusion as early as 1 fb-1 (yikes) 2008-2009 if accelerator and detectors work… 54 MSSM Higgs • Two Higgs doublets model 5 Higgs bosons: In the MSSM: 2 Neutral scalars h,H Mh ≲ 135 GeV 1 Neutral pseudo-scalar A 2 Charged scalars H± • In the Higgs sector, all masses and couplings are determined by two independent parameters (at tree level) • Most common choice: tanβ – ratio of vacuum expectation values of the two doublets MA – mass of pseudo-scalar Higgs boson • New SUSY scenarios Mhmax, gluophopic, no-mixing, small eff. 55 MSSM Search Strategies • Apply SM searches with rescaled cross sections and branching ratios. Mainly h searches when it is SM- like. • Direct searches for H or A ggbbH or bbA proportional to tan2 Decays to (10%) or (0.03%) • Direct searches for charged Higgs Decays to n or tb • Search for Susyh (not here) • Search for HSusy (not here) 56