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Evidence for the gauge More generations The

Introduction to physics Lecture 7

Frank Krauss

IPPP Durham

U Durham, Epiphany term 2009

F. Krauss IPPP Introduction to Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Outline

1 Evidence for the gauge bosons

2 More generations

3 The Standard Model

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Finding the

TASSO (1979) @ DESY (Petra collider) Obvious question: Is there a (like the in QED) acting as carrier of the strong interactions? Yes! The gluon ...... manifests itself 1979 in “three-” events

For colour reasons: Cannot be interpreted as three events, & qqq¯ ′q¯′ production is suppressed.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Finding the

Some more weak theory The massive, observable W ± are directly related to the original SU(2) massless bosons, acquire mass during breaking. The massive Z 0 boson and the massless γ are linear combinations of the original W 0 and the B0 of the original U(1):

0 A = W sin θW + B cos θW 0 Z = W cos θW B sin θW . − Masses related by

MW ± MZ = . cos θW

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Some more theory (cont’d)

Coupling gW of gauge bosons to fermions related with electromagnetic coupling as e gW = sin θW

and with Fermi’s constant through the mass of the W ±:

8G g 2 M F = W g W , 2 W GeV √2 MW ⇐⇒ ≈ 124

where GF taken from lifetime ( 1/GF ). ∝ Weak interactions by definition should be perturbative, therefore gW 1. Assuming a maximum of roughly 1/2, this fixes the W mass≪ at around 60 GeV and the Z mass at around 80 GeV.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Designing the experiment Due to their large masses, the lifetimes of the weak gauge bosons are too short for direct observation: Must deduce their existence and properties from their decay products. The Z couples to -position pairs, therefore the best and cleanest place for its study should be e+e−-annihilations at c.m.-energies identical to its mass (resonant production!). In the 1970’s this was far away (LEP became operational in 1989). Instead people, among them C.Rubbia, realised that - collisions would give enough qq¯ annihilations to enable a search for W ’s and Z’s. They used the 400 GeV SPS (super proton synchrotron), which hitherto delivered to a fixed target experiment. The catch was that they realised that the same ring could simultaneously accelerate protons and in opposite directions. Design was 270 GeV per beam, i.e. 540 GeV c.m.-energy of the pp¯ pairs.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Discovery at UA1/UA2 at CERN (1983) Two experiments at the SPS: UA1 and UA2.

A typical thing in particle physics: Friendly competition - a quality control. 54 qq¯′ W eν events and 4 qq¯ Z e+e− events at UA1, similar→ numbers→ at UA2. → → Signatures: A high-energetic electron, unbalanced in transverse momentum (because of the being missed by the detector) for the W and well-balanced electron- pairs.

First mass measurements: mW = 80.3 GeV and mZ = 95.5 GeV.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The November revolution 1974 A charming quark

Notable asymmetry: One u quark with qu = 2/3, but a down and a with charge qd,s = 1/3 each. − Discovery of the J/Ψ (November, 1974): S.C.C.Ting at Brookhaven AGS proton synchrotron in the reaction − p + Be → J(→ e+e ) + , m = 3.1 GeV. − B.Richter at SLAC/Spear e+e -collider with Mark-I detector in the reaction − − e+e → Ψ → e+e , m = 3.105 GeV. The two states have been identified to be the same, dubbed J/Ψ - a cc¯.

Properties of the : qc = 2/3, weak currents with both the d and the s quark, again parametrised by Cabibbo angle.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The next generation

The discovery of the τ- Discovery of the τ (M.Perl, 1975): Found at SLAC/Spear at 4 GeV in the reaction + − + − e + e τ + τ , mτ 1.8 GeV. → ≈ Interpretation: A new lepton! 24 events out of 35000 yield signature e+ + e− e± + µ∓+ invisible. → Easy to interpret invisible as ν’s. Is there some mechanism breaking lepton type number conservation? Interesting signature, due to decay τ ± ℓ±+ invisible, where ℓ = e, µ. →

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The discovery of beauty/bottom L.Ledermann (1977) at Fermilab: Observation of a di-muon Resonance at 9.5 GeV in 400 GeV Proton-Nucleus − Collisions: Υ(1s) → µ+µ . Interpretation (again): bound state of a new quark (beauty or bottom, mb ≈ 4.5 GeV). There must be another quark (top). Also: good for theoretical reasons (anomalies) to have complete generations.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The discovery of truth/top CDF and D0 (1995) at Fermilab

CDF: 37 events over est. 12, D0: 17 events over 4. First mass measurements agreed with indirect evidence:

mt = 176 8 10 GeV (CDF) mt = 199 20 22 GeV (D0) ± ± ± ±

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The number of generations At LEP the width of the Z boson ] has been measured very accurately. 2ν nb [

3ν Its invisible width, given by had 30 ALEPH σ DELPHI in the Standard Model, is L3 4ν OPAL consistent with exactly three open 20 average measurements, neutrino channels. error bars increased by factor 10 As a consequence, if there is a 10 further generation, we know that

0 its neutrino must be very heavy - 86 88 90 92 94 E [GeV] much as half as heavy as the Z cm boson. In addition, there’s further constraints on 4th generation from direct searches etc..

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

The Standard Model sector -1/2 fermions in three generations (families), coming as leptons and .

In addition, a scalar as remainder of spontaneous symmetry breaking that has not been seen yet.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Matter sector (cont’d) The fermions of each generation come in left-handed iso-doublets and right handed singlets; the quarks come in colour triplets.

Example: The first generation (u, d, νe and e):

u uR νe − .  d L dR  e L eR In the Standard Model, there are no right-handed neutrinos, and they are, by definition, massless. Other fermion masses:

mu 5 MeV mc 1.5 GeV mt 175 GeV ≈ ≈ ≈ md 5 MeV ms 200 MeV mb 4.5 GeV ≈ ≈ ≈ me 0.511 MeV mµ 105 MeV mτ 1.75 GeV ≈ ≈ ≈ Neutrinos experience only weak interactions, leptons have weak and electromagnetic interactions, and quarks enjoy strong, electromagnetic and weak interactions.

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Carriers of the interactions Interactions in the Standard Model are related to gauge invariance: Invariance of the Lagrangian under global gauge transformations ensures conserved charges (electrical charge, , colour), the demand for local gauge invariance generates the interactions, mediated by spin-1 gauge bosons (may carry charge themselves). mγ = mg = 0. Spontaneous symmetry breaking generates masses for the weak gauge bosons (mW ≈ 80.4 GeV, mZ ≈ 91.2 GeV).

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Feynman rules in the Standard Model Fermion-fermion- interactions (1st generation only):

e−, u, d νe,e−, u, d u, d

e−, u, d νe,e−, u, d u, d

γ Z0 g

e−, d νe, u

νe, u e−, d

W ( ) W + ( ) − ↓ ↓ Important note: The charged bosons (W ±) only allow for inter-generation mixing of the quarks (us, ub, dc, dt, cb, st).

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Gauge boson self-interactions: + W W − g g

γ, Z0 g

Interactions of the Higgs boson:

Interactions proportional to mass, therefore only heavy . 0 W ±, Z τ, b, t 0 W ±, Z τ, b, t

H H

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Precision tests of the Standard Model There are many relations between the parameters of the Standard Model, especially in the (weak) gauge sector: For example, the masses of the bosons are directly related with the Weinberg angle by MZ = MW / cos θW , also related with the Fermi-constant governing the muon decay, loop corrections in addition include quark masses, especially the heaviest one, the . Therefore relations between, e.g. mW , mt and mH . These relations have very precisely been measured and calculated, the agreement is astonishing! However, despite this apparent success, the building rests on the existence of the to give a mass to the particles. Its ultimate test is the existence of the Higgs boson, not yet found. Note also: Neutrino oscillations indicate that neutrinos have masses - a first sign that the Standard Model is not complete!

F. Krauss IPPP Introduction to particle physics Lecture 7 Evidence for the gauge bosons More generations The Standard Model

Summary Recapitulated the theory behind weak gauge bosons in brief. Discussed the discoveries of the weak gauge bosons, the gluon, and the third generation. Put constraints on the number of generations. Brief discussion of the construction of the Standard Model: Elementary particles and their properties, Feynman rules. To read: Coughlan, Dodd & Gripaios, “The ideas of particle physics”, Sec 35-38.

F. Krauss IPPP Introduction to particle physics Lecture 7