SectionSection XX TheThe StandardStandard ModelModel andand BeyondBeyond The Top The predicts the existence of the ⎛ u ⎞ ⎛c⎞ ⎛ t ⎞ + 2 3e ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝d ⎠ ⎝ s⎠ ⎝b⎠ −1 3 e which is required to explain a number of observations.

Example: Absence of the decay K 0 → µ+ µ− W − d µ − 0 0 + − −9 K u,c,t + ν B(K → µ µ )<10 W µ s µ + The top quark cancels the contributions from the u, c .

Example: Electromagnetic anomalies This diagram leads to infinities in the f γ theory unless Q = 0 γ f ∑ f f f γ where the sum is over all (and colours) 2 1 ∑Q f = []3×()−1 + []3×3× 3 + [3×3×(− 3 )]= 0 244 f 0 At LEP, mt too heavy for Z → t t or W → tb

However, measurements of MZ, MW, ΓZ and ΓW are sensitive to the existence of virtual top quarks b t t t W + W + Z 0 Z 0 Z 0 W t b t b Example: Standard Model prediction

Also depends on the Higgs mass

245 The top quark was discovered in 1994 by the CDF experiment at the worlds highest energy p p collider ( s = 1 . 8 TeV ), the Tevatron at Fermilab, US. q b Final state W +W −bb g t W + Mass reconstructed in a − t W similar manner to MW at q LEP, i.e. measure jet/ b energies/momenta.

mtop = (178 ± 4.3)GeV

Most recent result 2005

246 The Standard Model c. 2006 : Point-like ½ Dirac fermions. Charge/e Mass e− -1 0.511 MeV st 1 Generation Electron νe 0 0? d -1/3 0.35 GeV u +2/3 0.35 GeV µ- -1 0.106 GeV Muon neutrino 0 0? 2nd Generation νµ s -1/3 0.5 GeV c +2/3 1.5 GeV τ -1 1.8 GeV 3rd Generation ντ 0 0? b -1/3 4.5 GeV and Top quark t +2/3 178 GeV ANTI- 247 FORCES: Mediated by spin 1 Force (s) Mass Electromagnetic 0 Strong 8 0 Weak (CC) W± 80.4 GeV Weak (NC) Z0 91.2 GeV

¾ The Standard Model also predicts the existence of a spin 0 HIGGS which gives all particles their masses via its interactions.

¾ The Standard Model successfully describes ALL existing data, with the exception of one

⇒ Neutrino Oscillations ⇒ have mass

First indication of physics BEYOND THE STANDARD MODEL

248 Atmospheric Neutrino Oscillations In 1998 the Super-Kamiokande experiment announced convincing evidence for NEUTRINO OSCILLATIONS implying that neutrinos have mass. Cosmic Ray π π → µ ν DOWN π µ π → e ν ν e µ µ µ µ e- e- e-

N ν µ UP νµ ν νµ ν ν νµ ν νµ ν Expect ≈ 2 µ e µ e e N ν e

Super-Kamiokande results indicate a deficit of νµ from the upwards direction.

¾ Interpreted as ν µ → ν τ OSCILLATIONS ¾ Implies neutrino MIXING and neutrinos have MASS 249 Detecting Neutrinos Neutrinos are detected by observing the lepton produced in CHARGED CURRENT interactions with nuclei. − + e.g. νe + N → e + ν µ + N → µ + X

Size : ¾ Neutrino mean free path in water ~ light-years. ¾ Require very large mass, cheap and simple detectors ¾ Water Cherenkov detection

Cherenkov radiation ¾ Light is emitted when a charged particle traverses a dielectric medium ¾ A coherent wavefront forms when the velocity of a charged particle exceeds c/n (n = refractive index) ¾ Cherenkov radiation is emitted in a cone i.e. at fixed angle with respect to Cerenko v the particle. ct ring n Particle θ β c 1 c ct cosϑ = = ν e- C e nv nβ ν e 250 Super-Kamiokande

Super-Kamiokande is a water Cherenkov detector sited in Kamioka, Japan

¾ 50,000 tons of water ¾ Surrounded by 11,146, 50 cm diameter, photo-multiplier tubes 251 Example of events:

− − νe + N → e + X ν µ + N → µ + X

252 sub-GeV multi-GeV 250 50 DOWN75 e-like e-like e-like > < > 200 pe -like 0.4 GeV/c 40 p 2.5 GeV/c 60 p 2.5 GeV/c θ 150 30 45

100 20 30

50 10 UP 15 0 0 0 300 100Expect 125 µ-like µ-like Partially Contained > ¾ Isotropic (flat) distributions in cosθ 240 pµ -like 0.4 GeV/c 80 100 ¾ N (νµ) ∼ 2 N (νe) 180 60 75

120 40Observe 50 ¾ Deficit of νµ from BELOW 60 20 25 Interpretation 0 0 0 0.61 -1 -0.6 -0.2 0.2 0.6 1 -1 -0.6 -0.2 0.2 0.6 1 -1 -0.6 -0.2 0.2 0.6 1 Θ ¾ νµ→ντ OSCILLATIONSΘ Θ cos cosθ cos cos ¾ Neutrinos have MASS 253 Neutrino Mixing The quark states which take part in the (d’, s’) are related to the flavour (mass) states (d, s) ′ Weak Eigenstates ⎛d ⎞ ⎛ cosϑC sinϑC ⎞ ⎛d ⎞ Mass Eigenstates ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎝ s′ ⎠ ⎝− sinϑC cosϑC ⎠ ⎝ s ⎠ ϑC = Cabibbo angle Assume the same thing happens for neutrinos. Consider only the first two generations.

⎛ νe ⎞ ⎛ cosϑ sinϑ⎞ ⎛ ν ⎞ Mass Eigenstates Weak Eigenstates ⎜ ⎟ = ⎜ ⎟ ⎜ 1 ⎟ ⎜ν ⎟ ⎜ ⎟ ⎜ ⎟ ϑ = Mixing angle ⎝ µ ⎠ ⎝− sinϑ cosϑ⎠ ⎝ν2 ⎠

+ + ¾ e.g. in π decay produce µ and νµ i.e. the state that couples to the weak interaction. The νµ corresponds to a linear combination of the states with definite mass, ν1 and ν2

νe = +cosϑ ν1 + sinϑν2 ν = −sinϑ ν + cosϑν µ 1 2 254 or expressing the mass eigenstates in terms of the weak eigenstates

ν1 = +cosϑ νe − sinϑνµ

ν2 = +sinϑ νe + cosϑνµ Suppose a muon neutrino with momentum pv is produced in a WEAK + + decay, e.g. π → µ νµ

At t = 0, the wavefunction v v v v ψ()p,t = 0 = νµ (p)(= cosϑν2 p)− sinϑν1 (p) The time dependent parts of the wavefunction are given by v v −iE1 t ν1 (p,t)= ν1 (p)e

v v −iE2 t ν2 ()p,t = ν2 (p)e After time t, v v −iE2 t v −iE1 t ψ()p,t = cosϑν2 (p)e − sinϑν1 (p)e

v v −iE2 t v v −iE1 t = cosϑ[]sinϑνe ()p + cosϑνµ ()p e − sinϑ[]cosϑνe ()p − sinϑνµ ()p e

2 −iE2 t 2 −iE1 t v −iE2 t −iE1 t v = []cos ϑe + sin ϑe νµ ()p + []sinϑcosϑ()e − e νe ()p v v = cµνµ ()p + ceνe ()p 255 Probability of oscillating into νe 2 2 −iE2 t −iE1 t P()νe = ce = [sinϑcosϑ(e − e )] 1 = sin2 2ϑ()e−iE2 t − e−iE1 t (eiE2 t − eiE1 t ) 4 1 = sin2 2ϑ()2 − ei()E2 −E1 t − e−i()E2 −E1 t 4

2 2 ⎡()E2 − E1 t ⎤ = sin 2ϑsin ⎢ ⎥ ⎣ 2 ⎦

1 1 ⎛ m2 ⎞ 2 m2 E = ()p2 + m2 2 = p⎜1+ ⎟ ≈ p + But ⎜ 2 ⎟ for m << E ⎝ p ⎠ 2p m2 − m2 m2 − m2 E ()p − E ()p ≈ 2 1 ≈ 2 1 2 1 2p 2E

2 2 2 2 ⎡(m2 − m1 )t ⎤ P()νµ → νe = sin 2ϑsin ⎢ ⎥ ⎣ 4E ⎦ 256 Equivalent expression for νµ → ντ

2 2 2 2 ⎡1.27 ()m3 − m2 L⎤ P()νµ → ντ = sin 2ϑsin ⎢ ⎥ ⎣ Eν ⎦

2 2 2 where L is the distance travelled in km, ∆ m = m 3 − m 2 is the mass 2 difference in (eV) and Eν is the neutrino energy in GeV. Interpretation of Super-Kamiokande Results E =1GeV For ν µ (typical of atmospheric neutrinos)

DOWN UP

257 Results are consistent with ν µ → ν τ oscillations:

2 2 −3 2 m3 − m2 ~ 2.5×10 eV sin 2 2θ ≈1 Comments: ¾ Neutrinos almost certainly have mass ¾ only sensitive to mass differences ¾ More evidence for neutrino oscillations Solar neutrinos (SNO experiment) See Reactor neutrinos (KamLand)

2 2 −5 2 suggest m2 − m1 ≈10 eV

¾ IF mass states ν 3 > ν 2 > ν 1 , then

m ~ 2.5×10−3 eV ~ 0.05 eV ν3 m ~ 10−5 eV ~ 0.003 eV ν2 258 Problems with the Standard Model The Standard Model successfully describes ALL existing particle physics data (with the exception of neutrino oscillations).

BUT: many input parameters: Quark and lepton masses Quark charges 2 Couplings αem , sin ϑW ,αs Quark generation mixing

AND: many unanswered questions:

¾ Why so many free parameters ? ¾ Why only 3 generations of quarks and ? ¾ Where does mass come from ? (?) ¾ Why is the neutrino mass so small and the top quark mass so large ? ¾ Why are the charges of the p and e identical ? ¾ What is responsible for the observed matter-antimatter asymmetry ? ¾ How can we include ? etc 259 The Higgs Mechanism The Higgs mechanism introduces a NEW (Higgs) field into the vacuum which interacts with particles that propagate through it.

Classical Vacuum Boundary conditions at ±∞

Higgs Vacuum Particle induces currents in the Higgs xxx xxx xxx xxx xxx xxx xxx xxx field which modifies the form of the xxx xxx xxx xxx xxx xxx xxx xxx particle wavefunction and hence its xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx propagation. Particle appears to have xxx xxx xxx xxx xxxHiggsxxx xxx Fieldxxx MASS due to interaction. xxx xxx xxx xxx xxx xxx xxx xxx Local boundary conditions.

The combined massless particle + Higgs system behaves identically to a MASSIVE particle in a classical vacuum. 260 The Higgs Potential Higgs Potential At HIGH temp, average Higgs field in vacuum is zero. Massless particles. E Higgs Field Strength At LOW temp, Higgs field is non-zero everywhere. Ground State Particles acquire MASS.

Consequences ¾ Particles travelling through the Higgs field acquire MASS via their interactions with it. ¾ The quantum associated with the Higgs field is a neutral spin 0 boson ⇒ HIGGS BOSON ¾ For the theory to be calculable, requires the Higgs boson to be discovered with an energy scale ≤ 1 TeV 261 ANALOGY: Photon in a waveguide.

¾ Consider a plane polarized photon in vacuum. Boundary conditions at ∞. The wavefunction has the form ψ ~ ei(ωt-kx) ¾ When the photon enters a waveguide, need to satisfy local boundary conditions v ¾ E sets up current I in walls and Ev I v I induces a B field which oscillates v Bv B′ along direction of motion. x

¾ The form of the photon wavefunction becomes ψ ~ e-k′x and the photon no longer propagates beyond ~ 1 k′

¾ For a massive , range ~ 1 m

⇒ Photon behaves like a MASSIVE particle 262 Higgs at LEP Higgs Production at LEP

IF M H < s − M Z e- Z0 Z∗

+ e H In 2000, LEP operated with s ≈ 207 GeV , therefore had the potential to discover Higgs boson IF M H <116 GeV

Higgs Decay ¾ The Higgs boson couples to mass ¾ Hence, partial widths proportional to m2 of particle involved ¾ The Higgs boson decays preferentially to the most massive particle kinematically allowed ¾ b For M H < 116 GeV this is the quark 263 At LEP search for f e- Z0 f Z∗ e+e− → H 0 Z 0 → bb f f b e+ H b

4 possible e + e − → H 0 Z 0 events observed in the final year of LEP operation, consistent with

M H =115 GeV

The evidence is tantalizing BUT FAR FROM conclusive

⇒ LARGE COLLDER (2007) 264 The Large Hadron Collider The LHC is a new -proton collider being constructed in the LEP tunnel at CERN. 7 TeV + 7 TeV : s =14 TeV ATLAS General purpose ALICE Heavy ions Quark- plasma

10T superconducting magnets

LHCb B Physics Matter-Antimatter CMS asymmetries General purpose 265 ATLAS

266 Higgs at LHC Higgs Production at the LHC The dominant Higgs production mechanism at the LHC is g t “gluon fusion” t H g t

Higgs Decay at the LHC Depending on the mass of the Higgs boson, it will decay in different ways γ b Z0

H H H 0 γ b Z Low Mass Medium mass High mass 267 ATLAS Barrel Inner Detector Ð H→bb

H → γγ ATLAS b H → bb Higgs Events

ATLAS Barrel Inner Detector → * → µ+µ- + - H ZZ e e ( mH = 130 GeV )

- e H → Z 0 Z 0 → e+e− µ+ µ−

µ+ Ð b

µ-

e+ 268 Future Higgs signals in ATLAS ? (by Graduate student currently in 2006 Part II course?) H → γγ H → Z 0 Z 0 → e+e− µ+ µ− 1500 M H =120 GeV 20000 15 M H = 300 GeV 15

1000 ∫ L dt = 10 fb-1 Events / 2 GeV Events / 17500 (no K-factors) Events/7.5 GeV Events/7.5 GeV 10 10

500 15000

5 5 12500 0 Signal-background, events / 2 GeV

10000 0 0 105 120 135 105 120 135 200 400 mγγ (GeV) mγγ (GeV) m4l (GeV) ¾ LHC CAN discover the Higgs boson up to a mass of ~ 1 TeV. ¾ PHYSICS BEYOND THE STANDARD MODEL LHC MAY also discover 269 Beyond the Standard Model Grand Unification Theories (GUTs) aim to unite the strong interaction with the electroweak interaction.

The strength of the interactions depends on energy: α αs (QCD) 10−1 1 42 α αw (EW) G 10−2 α (QED)

102 GeV ~ 1015 GeV

¾ Unification of all forces at ~1015 GeV. ¾ Strength of Gravity only significant at the Planck Mass ~1019 GeV 270 (SUSY) Supersymmetry (SUSY) is a Grand Unified Theory that links fermions and bosons ⇒ SUPERFAMILY

It predicts that every known particle has a SUPERSYMMETRIC partner which is identical except for its SPIN

Spin 1/2 Spin 1 SUSY

Fermion Boson

¾ Linked to Gravity through a theory called SUPERGRAVITY ¾ Mass of Sparticles not predicted, but MUST be < 1 TeV 271 The SupersymmetricThe Standard StandardModel Model

SPIN 0 SPIN 1/2 SPIN 1

SQUARKS QUARKS ~ ~ ~ ~u, d, ~~s, c, b, t u, d, s, c, b, t

SLEPTONS LEPTONS MATTER ~e,~ν , µ,~ ν~ , ~τ, ~ν e µ τ e, νe, µ, νµ, τ, ντ

GAUGE BOSONS ~ ~γ, ~W,Z, ~g γ, W,Z, g FORCES

HIGGS BOSON S ~H

MASS 0 0 0 ± h , H A ,H 272 ¾ In the Standard Model, the interaction strengths are not quite unified at very high energy. ¾ Add SUSY: unification much improved. 60

50 −1 α1 SM 40 −1 α 30 −1 α2 20 MSSM

−1 10 α3 0 246810 12 14 16 18 log10(E/GeV) 273 SUSY at LHC The LHC will search for SUSY sparticles with masses < 1 TeV. e.g. SUSY events will have “missing energy” plus ℓ+ℓ-

274 Summary At this point my story about particle physics ends……

¾ Over the past 30 years our understanding of the fundamental particles and forces of nature has changed beyond recognition.

¾ The Standard Model of particle physics is an enormous success. It has been tested to very high precision and describes ALL experimental observations.

¾ However, we are beginning to get hints that physics beyond the Standard Model is at work (e.g. neutrino oscillations).

¾ We expect that the next few years will bring many more (un)expected surprises (Higgs boson, SUSY, etc).

275 Simulation of a “Mini Black-Hole” at the LHC

276