The Basic Laws of Nature: from quarks to cosmos by K2Tytb9

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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
        Fn  j                                   Fn     
    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
          HZZ (*)4               ℓ (golden mode)




Background: ZZ, tt, llbb (“Zbb”)

Selections :
- lepton isolation in tracker and calo     HZZee 
- lepton impact parameter, , ee vertex
- mass windows MZ(*), MH                                21
                      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
                         ee                  ee




    CMS
    at 5 sign.                         CMS
                                        at 5 sign.
                                                      22
HZZ4e        (pre-selection)


             QuickTime™ and a
         TIFF (LZW) decompressor
      are neede d to see this picture.




                                         23
HZZ4e              (selection)


           QuickTime™ and a
       TIFF (LZW) decompressor
    are neede d to see this picture.




                                       24
HZZ4e                 at 30          fb-1




           QuickTime™ and a
       TIFF (LZW) decompressor
    are neede d to see this picture.




                                              25
                                   HZZ4




       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
HZZ4



        QuickTime™ and a
    TIFF (LZW) decompressor
 are neede d to see this picture.




                                    27
HZZee




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    TIFF (LZW) decompressor
 are neede d to see this picture.




                                    28
HZZ4ℓ




          29
           HWW2ℓ2n 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 HWW2ℓ




                               31
Improvement in PTDR 4ℓ and
 WW analyses (compared to
     earlier analyses):

   VERY SMALL


                             32
SM Higgs decays

                    WWllnn




                     ZZ4l

        The real branching ratios!

                                     33
              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


                                                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.



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      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

                    WWllnn




                     ZZ4l

        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
      ggbbH or bbA proportional to
       tan2
      Decays to  (10%) or  (0.03%)
• Direct searches for charged
  Higgs
      Decays to n or tb
• Search for Susyh (not here)
• Search for HSusy (not here)
                                          56

								
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