STANDARD MODEL PHENOMENOLOGY
Transcript of STANDARD MODEL PHENOMENOLOGY
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Standard Model Phenomenology N. Rius TAE 2011
STANDARD MODELPHENOMENOLOGY
• Review of the SM• SM: where are we?• Higgs search• Radiative corrections• Flavoured SM• Open problems of the SM
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Standard Model Phenomenology N. Rius TAE 2011
3. Higgs search Interaction ∝ mass (MZ
2, MW2, mf) Higgs couples to
heavy particles
- Top-Higgs coupling plays special role?
- No Higgs coupling to neutrinos
- No tree level couplings tophotons (γ) nor gluons (g)
-MH2= 2λv2 large MH is
strong coupling regime
-MH is parameter whichseparates perturbative/non-perturbative regimes
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Standard Model Phenomenology N. Rius TAE 2011
Higgs decay modes
The Higgs also couples at higher orders with other gaugebosons: Hγγ, HZγ, Hgg
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Standard Model Phenomenology N. Rius TAE 2011
Higgs branching ratios• 95 GeV < MH < 130 GeV , ΓH < 10 MeV
• MH > 130 GeV
• MH ≈ 500 GeV
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Standard Model Phenomenology N. Rius TAE 2011
Higgs searches at LEP2
• LEP2 searched for e+e- → Z → Z H• Rate turns on rapidly after threshold, peaks just above
threshold• Measure recoil mass of Higgs; result independent of Higgs
decay pattern• Momentum conservation:
• LEP2 limit: MH > 114.4 GeV
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Standard Model Phenomenology N. Rius TAE 2011
Higgs searches at hadron colliders• At proton - (anti)proton collisions, the Higgs is produced via:
- Gluon fusion: p p → g g → H - VV fusion: p p → V V → H
• Tevatron direct limit: MH ∈ [158, 173] GeV excluded (95% CL)
H → W+ W-
CDF + DO (July 2010)
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Standard Model Phenomenology N. Rius TAE 2011
But precision data prefer light Higgs:
LEP EWWG (July 2010)
114.4 GeV < MH < 158 GeV
MH > 185 GeV excluded by precision ew data (95% CL)
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Standard Model Phenomenology N. Rius TAE 2011
LHC?• No limits for 3 generations, yet …• In the SM with 4 generations, Higgs-gluon-gluon vertex
enhanced a factor 3 (2 extra heavy quarks running in theloop)
• Higgs branching ratios modified:
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Standard Model Phenomenology N. Rius TAE 2011
Limits from Tevatron and LHC
• 131 GeV < MH < 204 GeV at 95% CL Tevatron
• 144 GeV < MH < 207 GeV at 95% CL LHC
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Standard Model Phenomenology N. Rius TAE 2011
4. Radiative corrections - ρ parameter - Oblique corrections: S,T,U formalism
• ρ = 1 at tree level consequence of an unbroken globalSU(2) symmetry of the Higgs sector, custodial SU(2)symmetry
• Higgs doublet (complex) = 4 real scalars O(4) global symmetry
The vev of φ breaks this symmetry down to O(3), that is, SU(2)
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Standard Model Phenomenology N. Rius TAE 2011
• At one loop:
• Top quark contributes to W and Z 2-point functions:
qµqν piece connects to light (massless) fermions, anddoesn’t contribute here
top quark doesn’t decouple
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Standard Model Phenomenology N. Rius TAE 2011
In QED, running of α at scale µ not affected byheavy virtual particles with M >> µ
Decoupling theorem doesn’t apply to particleswhich couple to mass (longitudinal modes of gaugebosons in the SM)
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Standard Model Phenomenology N. Rius TAE 2011
Oblique corrections: S,T,U formalism [Peskin & Takeuchi, PRD46 (1992) 381]
• Suppose “new physics” contributes primarily to gauge bosontwo point functions
- cf Δr where vertex and box corrections are small
i,µ j,ν
Also assume new physics is at scale M >> MZ
Two point functions for γγ, WW, ZZ, γZ
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Standard Model Phenomenology N. Rius TAE 2011
piece connects to light (massless) fermions, anddoesn’t contribute
Taylor expand 2-point functions:
Keep first two terms
QED Ward identity requires any amplitude involving EMcurrent vanish at q2=0
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Standard Model Phenomenology N. Rius TAE 2011
• Recall that JZ ∝ J3 - sW2 JQ
• To order q2 there are 6 coefficients:
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Standard Model Phenomenology N. Rius TAE 2011
• Three combinations of parameters absorbed in α, GF, MZ
• Three independent coefficients that can be extractedfrom data:
SM contributionsin α, GF and MZ
Advantages: - Easy to calculate - Valid for many models - Experimentalists can provide model independent fits
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Standard Model Phenomenology N. Rius TAE 2011
Limits on S & T
• A model with a heavyHiggs requires a source oflarge (positive) ΔT
• Fit assumes MH = 150 GeV
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Standard Model Phenomenology N. Rius TAE 2011
• SM values of S, T, U are defined for a reference MH0
• αT = δρ
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Standard Model Phenomenology N. Rius TAE 2011
• Radiative corrections necessary to fit LEP and Tevatrondata
• Radiative corrections strongly limit new physics:
• Allowed quark mass splitting of a fourth generation
From Tevatron:
Large and negative S in technicolor models
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Standard Model Phenomenology N. Rius TAE 2011
4. Flavoured SM
Except for masses,the generations lookidentical
Fermions come in generations:NG= 3 identical copies Why ?
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Standard Model Phenomenology N. Rius TAE 2011
Need complete generations
• Sensible gauge theories can’t have anomalies (see M.A. Vázquez-Mozo lectures)
• Triangle diverges; grows with energy
• Anomaly independent of mass; depends only on gaugeproperties
group generator• Complete generations needed for anomaly cancellation
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Standard Model Phenomenology N. Rius TAE 2011
Anomalies, 2
• Standard Model generators:• Three W’s or one W and two B’s cancel because Tr(σa ) = 0
Contributions only from two W’s and one B or three B’s:
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Standard Model Phenomenology N. Rius TAE 2011
Fermion masses• For 3 generations, α,β=1,2,3 (flavour indices):
• After SSB:
• Arbitrary non-diagonal complex mass matrices:
• Unitary matrices diagonalize mass matrices:diagonal
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Standard Model Phenomenology N. Rius TAE 2011
• Mass eigenstates ≠ weak eigenstates• Yukawa couplings are diagonal in mass basis:
• Neutral currents remain flavour diagonal• Not necessarily true in models with extended Higgs
sector
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Standard Model Phenomenology N. Rius TAE 2011
• Neutral current:
- Flavour conserving neutral currents (GIM)
• Charged current:
- Flavour changing charged currents
CKM matrix
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Standard Model Phenomenology N. Rius TAE 2011
Lepton mixing
• Minimal SM without νR
- Separate lepton number conservation
If νR exists and lepton flavour violation, conserved If neutrinos are Majorana lepton flavour and total lepton
number L violation Present bounds:
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Standard Model Phenomenology N. Rius TAE 2011
Quark mixing
• Unitary NG x NG matrix NG2 parameters
• 2 NG - 1 arbitary phases:
• Vij physical parameters:
Moduli: Phases:
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Standard Model Phenomenology N. Rius TAE 2011
• NG=2: 1 angle (Cabibbo), 0 phases
No CP violation
• NG=3: 3 angles, 1 phase (CKM)
CP violation
• NG=4: 6 angles, 3 phases
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Standard Model Phenomenology N. Rius TAE 2011
• We measure decays of hadrons (no free quarks) important QCD uncertainties
• Also data from hadronic decays of W
• Hierarchical pattern Wolfenstein parametrization
CP violation
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Standard Model Phenomenology N. Rius TAE 2011
• C, P : violated maximally in weak interactions
• CP : symmetry of nearly all observed phenomena
• CP violation in meson - antimeson systems - 0.2 % CP violation in K0 decays (1964) - Sizeable CP violation in B0 decays (2001) - Hope we don’t need to wait other 30 years …
• Huge Matter-Antimatter asymmetry in our Universe Baryogenesis
• CPT theorem: CP violation ⇔ T violation
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Standard Model Phenomenology N. Rius TAE 2011
• In the SM, meson - antimeson mixing and CP violationgenerated by diagramas like phases + interferences
• Unitarity triangle
• An area ≠ 0 means CP violation
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Standard Model Phenomenology N. Rius TAE 2011
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Standard Model Phenomenology N. Rius TAE 2011
Standard Model CP violation
• Complex phases only in Yukawa couplings
• After SSB and diagonalization of quark’s mass matrix:
• The CKM matrix Vij is the only source of CP violation not sufficient to explain the baryon asymmety of the
Universe
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Standard Model Phenomenology N. Rius TAE 2011
Neutrino oscillationshttp://hitoshi.berkeley.edu/neutrino
- Lepton mixing- Neutrino masses- νR ?- New physics!
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Standard Model Phenomenology N. Rius TAE 2011
• Evidence for lepton flavour change from: - Solar neutrino oscillations, confirmed by reactor
experiment (KamLAND) - Atmospheric neutrino oscillations, confirmed by
accelerator experiment (K2K) - LSND and MiniBOONE ?
If ν’s are massive, mass eigenstates are not flavoureigenstates,
U PMNS mixing matrix, unitary
After traveling a distance L, time evolution gives (p>>mi)
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Standard Model Phenomenology N. Rius TAE 2011
• Then,
• For only 2 flavours:
Δm2 in eV, L in Km, E in GeV
• Sizeable transition probability if E/L ≈ Δm2
• Tiny neutrino masses lead to unobservable flavourchanging in charged lepton decays
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Standard Model Phenomenology N. Rius TAE 2011
• PMNS mixing matrix:
• Dirac phase δ
• 2 physical phases φi if neutrinos are Majorana particles
• CP violating phase δ may be observable only if s13 big
• Upper limit from CHOOZ ( reactor experiment, no evidenceof disappearance): sin2(2θ13) < 0.2 at 90% CL
• DOUBLE CHOOZ underway: limit down to 0.03
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Standard Model Phenomenology N. Rius TAE 2011
Global fit to neutrino oscillation dataMarch, 2011 (new reactor fluxes)
Recent indications of appearance in T2K andMINOS long-baseline accelerator experiments
non zero θ13 ?
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Standard Model Phenomenology N. Rius TAE 2011
• Mixing pattern close to tribimaximal, very different fromquarks:
• Only mass differences can bedetermined from oscillations
• Absolute neutrino mass scale unkown; best bound fromcosmology mν < 1 eV
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Standard Model Phenomenology N. Rius TAE 2011
Neutrino masses
• Two types of mass terms:
• Indistinguisable in oscillations• Majorana ν’s violate lepton number (accidental symmetry
of the SM) neutrinoless double beta decay• If νR exists, and lepton number is conserved
Yν ≈ 10-12
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Standard Model Phenomenology N. Rius TAE 2011
Seesaw mechanism
• But νR can have a Majorana mass term (not forbiden bygauge symmetry, because it is a SM singlet)
• After SSB, neutrino mass matrix in (νL, νRc) basis is
• If M >> MD : NG heavy Majorana neutrinos, ∼ νR with masses ∼ M NG light Majorana neutrinos, ∼ νL with masses ∼ MD
2/M
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Standard Model Phenomenology N. Rius TAE 2011
• If there is CP violation in the leptonic sector
Generation of the matter - antimatter asymmetry of theUniverse via Leptogenesis : CP-violating out of equilibriumdecay of the heavy neutrino in the Early Universe
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Standard Model Phenomenology N. Rius TAE 2011
5. Open problems of the SM• Theoretical: - Hierarchy problem (SUSY, Xdim, composite Higgs ) - Flavour structure
• Experimental: - Neutrinos - Dark matter - Dark energy - Baryon asymmetry of the Universe - Find the Higgs ?
Stay tuned: Exciting times ahead !