Standard Model Higgs

1
Standard Model Higgs

• at the LHC

Peter Z. Skands Fermilab Theoretical Physics
Department (Significant parts taken from TASI
PASI lectures by M. Carena (Fermilab), S. Dawson
(BNL), D. Rainwater (U Rochester) )
2
The Role of Particle Physics

• To discover what the Universe is made of and how
  it works.
• Particle Accelerators reproduce in a controlled
  lab environment forms of matter and energy last
  seen in the early universe.
• Elementary particles are the ultimate
  constituents of matter
• Five basic forces act between these elementary
  matter particles
• GRAVITATION (couples to energy)
• ELECTROMAGNETISM (couples to electromagnetic
  charge)
• THE STRONG FORCE (couples to colour charge)
• THE WEAK FORCE (couples to weak isospin)
• MASS rest energy (where does it come from?)

Relativity
Gauge Forces
?
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What we Know

• The photon and gluon appear to be massless
• The W and Z bosons are very heavy
• MW 80.404 GeV 0.030 GeV
• MZ 91.1875 GeV 0.0021 GeV
• There are 6 quarks (actually 36)
• Mt 171.4 2.1 GeV (CDFDØ July 2006)
• Expected ? 1.5 GeV at end of Run II
• Mt gtgt other fermion masses
• There appear to be 3 neutrinos
  with small but non-zero masses
• The pattern of fermions appears to replicate
  itself 3 times

Dec 8 2006 DØ Reported 3.4s Evidence for
single top
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The Higgs Mechanism

• Spontaneous Symmetry Breaking

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Why is the photon massless?

• U(1) gauge theory with spin-1 photon Aµ
• Local gauge invariance
• Could we put in a mass term for A?
• Not gauge invariant!
• So charge conservation ? ? massless

?
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Adding a charged scalar

• U(1) gauge theory with spin-1 Aµ and charged
  scalar f
• V(f) Most general renormalizable potential
  allowed by U(1) invariance
• ? L is still invariant under U(1) rotations

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Two solutions

• U(1) gauge theory with spin-1 Aµ and charged
  scalar f

• µ2 gt 0
• QED with m?0 and mfµ
• Unique minimum at f0

• µ2 lt 0
• Minimum energy state at
• Vacuum breaks U(1) symm.

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A closer look at µ2 lt 0

• µ2 lt 0 Minimum energy state at
• Write complex f in (Mod,Arg) notation
• v constant offset ? minimum-energy (vacuum)
  state
• h modulus d.o.f. ? Higgs field, with mass mh
  -2µ2 gt 0
• ? argument d.o.f. ? massless Goldstone boson

m?ev
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What happens to the Goldstone boson?

• What happens to the ? field?
• After gauge transformation (unitary gauge)
• L becomes
• ? disappears, enslaved to longitudinal part of A
  (eaten)
• Physical degrees of freedom
• before SSB massless A (2 d.o.f) complex scalar
  f (2 d.o.f.)
• after SSB massive A (3 d.o.f.) real Higgs
  scalar (1 d.o.f.)

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Abelian Higgs Mechanism

• Spontaneous breaking of a gauge symmetry by the
  non-zero VEV of a charged scalar field
• ?The Goldstone degree of freedom of the scalar is
  enslaved (eaten) to serve as the longitudinal
  component of the gauge field
• ?On this background, the gauge field propagator
  appears to be massive
• In QED, this is what happens in a superconductor
• For the weak force it happens in free space.

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SM Higgs Mechanism

• SU(2)WxU(1)Y gauge symmetry.
• Add a scalar doublet with Y1
• For µ2lt0 there is a minimum at
• (direction not fixed)
• ?One massive Higgs scalar
• And 3 Goldstone bosons
• (same for charged components)

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SM Mass Spectrum

• When replacing H by its vev HVV ? masses
• LHiggs
• This mass matrix has one zero eigenvalue and 3
  others g2, g2, and g2g2
• Fermions acquire mass due to Yukawa (Hff)
  couplings

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Current Status

• Brief Summary

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Unitarity

• WLWL scattering
• Pertubative scattering P gt 1for s 1 TeV2
• Need something (e.g. Higgs) to unitarize theory
• If SM Higgs, then mH lt 800 GeV

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Perturbativity and Stability

• The Higgs quartic coupling determines the Higgs
  mass
• Running due to self-coupling and top quark loops

from M. Carena, TASI 2006
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? Theoretical Constraints

• Self-coupling can become non-perturbative ? 8 ?
  upper bound
• Radiative corrections ? deeper minima at large
  values of f ? lower bound

from M. Carena, TASI 2006
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Precision Tests of the Standard Model

• The Standard Model has been tested to very high
  precision (one part in a thousand) at experiments
  around the world
• Although the Higgs has not been seen and its mass
  is unknown, via quantum corrections it enters
  electroweak observables (masses, decay rates, )
• All electroweak parameters have at most
  logarithmic dependence on mh, however, a
  preferred value of mh can still be determined

Fermilab, SLAC, CERN,
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The Blue Band Plot
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LEP and Tevatron

• Precise measurements of W and top masses can rule
  out SM above TeV
• Tevatron shooting for top mass at or below 1.5
  GeV uncertainty

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Before LHC

• Run II search ultimately depends on combination
  of many weak channels, impaired by low lumi, but
  still interesting window remains

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Higgs at the LHC

• Discovery and Measurement Strategies

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Higgs at Hadron Colliders
Much progress recently in computing NLO (and even
NNLO) QCD corrections, see http//maltoni.home.ce
rn.ch/maltoni/TeV4LHC/SM.html
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SM Higgs Decay Modes

• Uncertainties due to uncertainties in as, mt, mb,
  and mc
• At low mh, mostly bb, tt, but also cc and gg can
  be important.
• At large mh, H?VV
• h?gg, h???, h?Z? generated at one loop, but due
  to heavy particles in loop ? relevant
  contributions

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Choosing a Channel

• What channel works best at a hadron collider
  isnt so obvious
• Tevatron uses multiple channels
• If H?bb dominant then (light Higgs)
• If H?WW/ZZ dominant then (heavy Higgs)
• Requiring leptons in the final state help reject
  QCD but not ttbar
• Jet-jet mass resolution 15 GeV seriously
  impairs search for a narrow resonance

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Signal Cross Sections

• While gg?H rises QCD-like, the VH channels
  become relatively quite small

Tevatron
LHC
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Backgrounds
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Higgs at the LHC

• The story of ttH
• H? ?? and H? tt
• Weak Boson Fusion
• Heavy Higgs, H? VV

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Light Higgs ttH at LHC

• Idea ttH coupling is large and ttH final state
  should be easy to distinguish ? Little
  Background?
• However, original studies did not treat QCD
  carefully, especially ttbb and ttjj were
  underestimated

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Light Higgs ttH current outlook

• Now ttH looks marginal at best
• S/B now about 1/6 for mh 120 GeV
• Shape only differs very slightly ? any shape
  uncertainty will make 5s impossible, even if L?8

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Heavy Higgs ttH

• ttH, H?WW is viable!
• Complicated final states WWWWbb ? multileptons
• Best channels same-sign dilepton, trilepton
• LOTS of nasty never-before-calculated bkgs
• tt Z /? (jj) , ttWjj, ttWW, tttt
• lots of diagrams, large QCD uncertainties
• If HWW coupling known ? only direct Yt measurement

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Heavy Higgs ttH _at_ ATLAS

• Works over large mh range

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Light Higgs gg?H?photons

• Idea rare decay might win because bkg is also
  EW, not QCD.
• BR(H?photons) 0.2 for light 110ltmhlt140 GeV
• Might not be discovery but gets mass to 1
• Requires very good jet (fake photon) rejection
  j? , jj bkgs non-trivial detector sim estimates
  still range over factor 2

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Light Higgs What about H?tt?

• Problem taus not observed directly
• Problem lots of missing energy, how to
  reconstruct mass?
• Important taus must not be back-to-back
• ?Limited usefulness for gg?H?tt

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Weak Boson Fusion

• Use the LHC as a W/Z collider
• Quarks get scattered forward in detector, and no
  QCD current over central rapidity region

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WBF H?tt

• WBF ? H ? tt ? one or two leptons

Backgrounds
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WBF H?tt _at_ LHC

• ATLAS and CMS say it works very well!
• For 110 lt mh lt 150 GeV (100 fb-1)

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WBF H?WW

• For WW recall angular correlation
• At threshold, Ws at rest ? mll m??, construct
  transverse mass
• Works well even away from threshold
• Detector effects smear things out

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WBF H?WW _at_ LHC

• ATLAS and CMS say Jacobian peak still there!
• May even work down to mh 120 GeV (but serious
  backgrounds ? more study needed, e.g. ttj at NLO)

mh 140 GeV
mh 160 GeV
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WBF Remaining Issues

• So WBF turns out to be great, but how well do we
  understand it?
• Minijet Veto (QCD radiation, underlying event)
  currently at primitive stage, but can be tested
  on data, e.g. WBF Zjj
• tt jets (off-shell effects, normalization and
  shape changes at NLO)
• Contamination from gluon fusion jets.
  Partially understood
• real experimental issues tagging,
  calibrations, underlying event,

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The Combination Machine

• mh lt 120 GeV
• 200 700 GeV
• Inclusive H?ZZ?4l
• gt 800 GeV
• WBF H?WW? l?jj
• WBF H?ZZ?ll??

NO ESCAPE ROUTE FOR SM HIGGS AT LHC!
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Putting it together
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The LHC Potential

• ATLASCMS total sensitivity combining all
  channels ? 5s discovery possible for all masses
  with 5fb-1 (?)
• For mh 120 GeV, combination of many different
  channels necessary, hence requires a good
  understanding of the detectors
• Note mh 120 GeV is simultaneously most
  sensitive region for Tevatron

• Mass resolution for 300 fb-1
• 0.1 to 1 from H?ZZ?4l or H???