The Higgs Boson

1. The Higgs Boson Jim Branson

2. 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. • 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. • Extra terms in Schrödinger Equation with derivatives of . • We must make a related change in the EM potential at every point. • One requires the other for terms to cancel in Schrödinger equation. • Electron’s phase symmetry requires existence of photon.

3. QuantumElectroDynamics • QED is quantum field theory (QFT) of electrons and photons. • Written in terms of electron field y and photon field A. • Fields y 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

4. Phase (Gauge) Symmetry in QED • 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.

5. Relativistic Quantum Field Theory • Dirac Equation: Relativistic QM for electrons • Matrix (g) eq. Includes Spin • Negative E solutions understood as antiparticles • Quantum Electrodynamics • Field theory for electrons and photons • Rules of QFT developed and tested • Lamb Shift • Vacuum Polarization • Renormalization (fixing infinities) • Example of a “Gauge Theory” • Very well tested to high accuracy

6. 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

7. 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

8. 2 1 2 Particles With the Same Mass... • 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

9. Angular Momentum and SU(2) • Angular Momentum in QM also follows the algebra of SU(2). • Spin ½ follows the simplest representation. • Spin 1… also follow SU(2) algebra. • Pauli matrices are the simplest operators that follow the algebra.

10. SU(2) Gauge Theory • 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.

11. 1 2 3 the Standard Model 3 simplest gauge (Yang-Mills) theories

12. 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.

13. 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.

14. 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.

15. 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

16. SM Higgs Mass Constraints Experiment SM theory The triviality (upper) bound and vacuum stability (lower) bound as function of the cut-off scale L (bounds beyond perturbation theory are similar) Indirect constraints from precision EW data : MH < 260 GeV at 95 %CL (2004) MH < 186 GeV with Run-I/II prelim. (2005) MH < 166 GeV (2006) Direct limit from LEP: MH > 114.4 GeV

17. SM Higgs production pb NLO Cross sections M. Spira et al. gg fusion IVB fusion

18. 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)

19. 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.

20. 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…

21. HZZ(*)4ℓ (golden mode) • Background: ZZ, tt, llbb (“Zbb”) • Selections : • lepton isolation in tracker and calo • lepton impact parameter, mm, ee vertex • mass windows MZ(*), MH HZZee mm

22. eemm CMS at 5s sign. HZZ4ℓ • 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 eemm CMS at 5s sign.

23. HZZ4e (pre-selection)

24. HZZ4e (selection)

25. HZZ4e at 30 fb-1

26. HZZ4

27. HZZ4

28. HZZee

29. HZZ4ℓ

30. 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 WW from the data; uncertainty 17% at 5 fb-1 Wt and gg->WW bkg from theor. uncertainty 22% and 30% HWW2ℓ2n In PTDR after cuts: - ETmiss > 50 GeV - jet veto in h < 2.4 - 30 <pT l max<55 GeV - pTl min > 25 GeV - 12 < mll < 40 GeV

31. Discovery reach with HWW2ℓ

32. Improvement in PTDR 4ℓ and WW analyses (compared to earlier analyses):VERY SMALL

33. SM Higgs decays WWll ZZ4l The real branching ratios!

34. HWW2ℓ2n • 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

35. 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.

36. Likelihood Ratio for M=160 e Like sign Help measure background WW background is the most important Has higher mass and less lepton correlation

37. Likelihood Ratio for M=180

38. Likelihood Ratio for M=140 At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100.

39. Could see Higgs over wider mass range. At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100.

40. Hgg H →γγMH = 115 GeV Very important for low Higgs masses. 80-140 GeV Rather large background. Very good mass resolution.

41. SM Higgs decays WWll ZZ4l The real branching ratios!

42. 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

43. Tracker Material Comparison ATLAS CMS CMS divides data into unconverted and converted categories to mitigate the effect of conversions

44. 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.

46. Backgrounds for 1 fb-1

47. Higgs Mass Hypothesis H0→gg has large background • To cope with the large background, CMS measures the two isolated photons well yielding a narrow peak in mass. • We will therefore have a large sample of di-photon background to train on. • Good candidate for aggressive, discovery oriented analysis. signal background Di-photon Mass

48. Not just isolation X X X X New Isolation Variables Eff Sig./Eff. Bkgd Powerful rejection of jet background with ECAL supercluster having ET>40.

49. 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.

50. Separate Signal from Background Use Photon Isolation and Kinematics Background measured from sidebands