Higgs physics

1
Higgs physics

• theory aspects
• experimental approaches
• Monika Jurcovicova
• Department of Nuclear Physics, Comenius
  University Bratislava

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Reasons for Higgs

• the presence of mass terms for gauge fields
  destroys the gauge invariance of Lagrangian
• no problem for gluons and photons
• serious problem for W?, Z0
• problems with origin of fermion masses

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Spontaneous Symmetry Breaking

• way to generate particle masses
• opposite of putting them by hand into Lagrangian

basic idea -- there is a simple world
consisting just of scalar particles
described by -- where
so not a usual mass term -- ground state
(vacuum) is not there are 2 minima
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Spontaneous Symmetry Breaking

• perturbative calculations involve expansions
  around classical minimum or
  one of them has
  to be chosen ( )
• then the reflection symmetry of Lagrangian is
  broken
• the mass is revealed

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The Higgs mechanism

• spontaneous breaking of a local gauge symmetry
  (simplest U(1) gauge symmetry)
• procedure add the Higgs potential to Lagrangian
  
  translate the field to a true ground state
• obtained particle spectrum 1 Higgs field with
  mass 1 massive vector A? - desired
  1 massless Goldstone boson
  - unwanted
• with a special choice of gauge the unwanted
  Goldstone boson becomes longitudinal polarization
  of the massive vector
  
  ?? the Higgs mechanism has avoided massless
  particles

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The EW Weinberg-Salam model

• formulation of Higgs mechanism
• W?, Z0 - become massive
• photon remains massless
• SU(2) x U(1) gauge symmetry
• ? must be an isospin doublet
• special choice of vacuum
• U(1)em symmetry with generator
  remains unbroken gt the photon remains
  massless
• W?, Z0 masses

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Fermion masses

• the fermion mass term is excluded from the
  original Lagrangian by gauge invariance
• the same doublet which generates W?, Z0 masses is
  sufficient to give masses to leptons and quarks
• however the value of mass is not predicted -
  just parameters of the theory
• nevertheless the Higgs coupling to fermions is
  proportional to their masses
  this can be tested

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Theory summary

• the existence of the Higgs field has 3 main
  consequences
• W?, Z0 acquire masses in the ratio
• there are quanta of the Higgs field, called Higgs
  bosons
• fermions acquire masses
• deficiencies of the theory
• fermion masses are not predicted
• the mass of the Higgs boson itself is not
  predicted either

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What do we know today about

• mass not predicted by theory except that mH lt
  1000 GeV
• from direct searches at LEP mH gt 114.4 GeV
• indirect limits from fit of SM to data from LEP,
  Tevatron (mW, mtop)

• Best fit (minimum ?2) mH 81 52-33 GeV
• mH lt 193 GeV 95 C.L.

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Higgs decays

• mH lt 130 GeV H ? dominates
• mH ? 130 GeV H ? WW(), ZZ() dominate
• important H ???, H ? ZZ ? 4?, H?WW ?????,
  etc.

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H ? gg
mH ? 150 GeV

• select events with 2 photons with pT 50
• measure energy and direction of each photon
• calculate invariant mass of photon pair
  
  m?? ((E1 E2 )2 -(p1 p2 )2 )1/2
• plot the m?? spectrum - Higgs should appear as a
  peak at mH

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Main backgrounds of H ? gg

• ?? production irreducible (i.e. same final
  state as signal)

• ? jet jet jet production where one/two jets
  fake photons reducible

? 60 mgg 100 GeV
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H ? ZZ() ? 4 ?
120 ? mH lt 700 GeV

• gold-plated channel for Higgs discovery at LHC
• select events with 4 high-pT leptons (t
  excluded) ee- ee-, mm- mm-, ee- mm-
• require at least one lepton pair consistent with
  Z mass
• plot 4? invariant mass distribution

Higgs should appear as a peak at mH
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Backgrounds of H ? ZZ() ? 4 ?

• irreducible pp ? ZZ () ? 4?

• reducible

Both reducible rejected by asking -- m??
mZ -- leptons are isolated -- leptons come
from interaction vertex ( B lifetime
1.5 ps ? leptons from B produced at ? 1
mm from vertex)
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How can one claim a discovery

• Signal significance

peak width due to detector resolution
NS number of signal events NB number of
background events
in peak region
if S gt 5 signal is larger than 5x
error of background probability that background
fluctuates up by more than 5s is 10-7
? discovery
mgg
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2 critical parameters to maximize S

• detector resolution S 1 /?sm
  detector with better resolution has larger
  probability to find signal
  (Note only valid if GH ltlt sm. If Higgs
  is broad, detector resolution is not relevant.)
• integrated luminosity S ?L
  numbers of events increase with luminosity

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Summary on Higgs at LHC

• LHC can discover Higgs over full mass range with
  S gt 5 in lt 2 years
• detector performance is crucial in most cases
• discovery faster for larger masses
• whole mass range can be excluded at 95 C.L.
  after 1 month of running

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What about the Tevatron

• for mH 115 GeV Tevatron needs
• 2 fb-1 for 95 C.L. in 2003-2004 ?
• 5 fb-1 for 3s observation in 2004-2005 ?
• 15 fb-1 for 5s discovery end 2007-beg 2008 ?
  Discovery possible up to mH 120 GeV

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Conclusions

• Standard Model Higgs can be discovered
• at the Tevatron up to mH 120 GeV
• at the LHC over the full mass region up to mH
  1 TeV
  final word about SM Higgs mechanism
• if SM Higgs is not found before/at LHC, then
  alternative methods for generation of masses will
  have to be found