The Higgs Boson

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The Higgs Boson

• Jim Branson

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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.
• Electrons phase symmetry requires existence of
  photon.

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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 Ehn.
• Able to create or annihilate electron positron
  pairs.
• Gauge (phase) symmetry transformation

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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.
• Electrons 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.

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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

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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

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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

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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

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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.

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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.

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

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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.

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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.

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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

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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 lt 260 GeV at 95 CL (2004) MH lt 186 GeV
with Run-I/II prelim. (2005) MH lt 166 GeV
(2006)
Direct limit from LEP MH gt 114.4 GeV
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SM Higgs production
pb
NLO Cross sections
M. Spira et al.
gg fusion
IVB fusion
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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 (GH gt200 GeV for MH ? 700 GeV)
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CMS PTDR contains studies of Higgs detection at
L2x1033cm-2s-1

• CERN/LHCC 2006-001 CERN/LHCC
  2006-021
• Many full simulation studies with systematic
  error analysis.

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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
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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
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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.
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H?ZZ?4e (pre-selection)
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H?ZZ?4e (selection)
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H?ZZ?4e at 30 fb-1
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H?ZZ?4?
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H?ZZ?4?
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H?ZZ?ee??
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H?ZZ?4l
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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-gtWW 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-gtWW bkg from theor. uncertainty 22
  and 30

after cuts - ETmiss gt 50 GeV - jet
veto in h lt 2.4 - 30 ltpT l maxlt55 GeV -
pT l min gt 25 GeV - 12 lt mll lt 40 GeV
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Discovery reach with H?WW?2l
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Improvement in PTDR 4l and WW analyses (compared
to earlier analyses)VERY SMALL
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SM Higgs decays
WW?ll??
ZZ?4l
The real branching ratios!
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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

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Higgs Mass Dependence
If ?WW is large compared to the other modes, the
branching ratio doesnt fall as fast as the
continuum production of WW.
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Likelihood Ratio for M160
e? Like sign Help measure background WW
background is the most important Has higher mass
and less lepton correlation
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Likelihood Ratio for M180
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Likelihood Ratio for M140
At LHC, the WW cross section increases by a
factor of 10. The signal increases by a factor
of 100.
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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.
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H?gg
H ? ?? MH 115 GeV
Very important for low Higgs masses. 80-140
GeV Rather large background. Very good mass
resolution.
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SM Higgs decays
WW?ll??
ZZ?4l
The real branching ratios!
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H? ??

• Sigma x BR 90 fb for MH 110-130 GeV
• Large irreducible backgrounds from gg? ??, qq ?
  ??, gq ? ? jet ? ?? jet
• Reducible background from fake photons from jets
  and isolated p0 (isolation requirements)
• Very good mass resolution 1
• Background rate and characteristics well measured
  from sidebands

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

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Backgrounds for 1 fb-1
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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
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New Isolation Variables
Eff Sig./Eff. Bkgd
Powerful rejection of jet background with ECAL
supercluster having ETgt40.
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ETi/Mass (Barrel)
Gluon fusion signal VBoson fusion signal Gamma
jet bkgd gj (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.

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Separate Signal from Background
Use Photon Isolation and Kinematics
Background measured from sidebands
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Understanding s/b Variation from NN
Strong peak lt 1 supressed Optimal cut at 1
Category 0
A factor of 2 in s/b is like the difference
between Shashlik and crystals
Signal is rigorously flat b/s in 16 GeV Mass
Window ? additional factor of 10 from Mass
1/10 of signal with 10 times better s/b halves
lumi needed
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S/b in Categories
5
4
3
2
1
0
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Discovery potential of H?gg
SM
light h?gg in MSSM inclusive search
Significance for SM Higgs MH130 GeV for 30 fb-1

• NN with kinematics and g isolation as input, s/b
  per event
• CMS result optimized at 120 GeV

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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
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MSSM Higgs

• Two Higgs doublets model
• 5 Higgs bosons
• 2 Neutral scalars h,H
• 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
• tanß 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.

In the MSSM Mh ? 135 GeV
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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 ?? or tb
• Search for Susy?h (not here)
• Search for H?Susy (not here)