“Elementary Particles” Lecture 6. Niels Tuning Harry van der Graaf. Thanks. Ik ben schatplichtig aan: Dr. Ivo van Vulpen (UvA) Prof. dr. ir. Bob van Eijk (UT) Prof. dr. Marcel Merk (VU). Homework. Exercises Lecture 5:. Time was a bit short (1 week + Pinksteren) …

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“Elementary Particles” Lecture 6

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Exercises Lecture 5: • Time was a bit short (1 week + Pinksteren) … • I propose to shift the deadline to next week. • I might add one extra exercise: look at blackboard Niels Tuning (4)

Plan 12 Feb • Intro: Relativity and accelerators • Basis • Quantum mechanics, Radioactivity • Scattering theory • Hadrons • Strangeness, quark model • Symmetries, Isospin • Standard Model • Gauge invariance, QED: EM interaction • Parity, neutrinos: Weak interaction • QCD: Strong interaction • e+e- and DIS • Higgs and CKM 1900-1940 26 Feb 1945-1965 12 Mar 1965-1975 26 Mar 1975-2000 14 May 2000-2013 21 May Niels Tuning (6)

Outline for today: • Higgs mechanism • Higgs discovery at ATLAS • CKM-mechanism • CP violations at LHCb Niels Tuning (7)

Lecture 1: Accelerators & Relativity • High energies needed to make (new) particles • Theory of relativity • Lorentz transformations (“boost”) • Calculate energy in collissions • 4-vector calculus Niels Tuning (9)

Lecture 2: Quantum Mechanics & Scattering • Schrodinger equation • Time-dependence of wave function • Klein-Gordon equation • Relativistic equation of motion of scalar particles • Dirac equation • Relativistically correct, and linear • Equation of motion for spin-1/2 particles • Prediction of anti-matter • Scattering Theory • (Relative) probability for certain process to happen • Cross section dq Niels Tuning (10)

Lecture 3: Quarkmodel & Isospin • “Partice Zoo” not elegant • Hadrons consist of quarks • Observed symmetries • Same mass of hadrons: isospin • Slow decay of K, Λ: strangeness • Fermi-Dirac statistics Δ++,. Ω: color • Combining/decaying particles with (iso)spin • Clebsch-Gordan coefficients Niels Tuning (11)

Lecture 4: Gauge symmetry and Interactions • Arbitrary “gauge” • Physics invariant • Introduce “gauge” fields in derivative • Interactions! • QED • Weak interactions • QCD Niels Tuning (12)

Lecture 4: QED and QCD QED QCD • Local SU(3) gauge transformation • Introduce 8 Aμa gauge fields • Non-“Abelian” theory, • Self-interacting gluons • Gluons have (color) charge • Different “running” • Local U(1) gauge transformation • Introduce 1 Aμ gauge field • “Abelian” theory, • No self-interacting photon • Photons do not have (electric) charge • Different “running” Niels Tuning (13)

Lecture 5: e+e- scattering and DIS • e+e- scattering:QED at work: R • e+e-→μ+μ- • e+e-→cc • e+e-→qq g • e+e-→Z • e+e-→WW • e+p scattering:QCD at work: F2 • Quarkmodel: do quarks exist?? • Substructure • Bjorken-x, sum rules • Scaling • ‘Parton density functions’ (pdf) and ‘structure functions’ • Scaling violations: more quarks at higher Q2 due to QCD Niels Tuning (14)

Standard Model Todo-list: • No masses for W, Z !? • (LHC/ATLAS) Higgs mechanism, Yukawa couplings • Interactions between the three families !? • (LHC/LHCb) CKM-mechanism, CP violation Niels Tuning (15)

Higgs mechanism • Let’s give the photon a mass! • Introduce a complex scalar field: • with: • and the Lagrangian is invariant under: Niels Tuning (18)

Scalar potential V(φ) If 2 > 0: • φ will acquire a vaccumexpectation value v, • “spontaneously” ! • System not any more “spherical” symmetric SSB vev • Spontaneous Symmetry Breaking Niels Tuning (19)

Complex scalar field φ If 2 > 0: • φ will acquire a vaccum expectation value v • Parameterize φ as: • h: Higgs boson • : Goldstone boson • Both real scalar fields h Niels Tuning (20)

Higgs mechanism • Let’s give the photon a mass! • Introduce a complex scalar field: • with: • and: • Then: Niels Tuning (21)

Higgs mechanism e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (22)

Higgs mechanism • What about this field ? e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (23)

Higgs mechanism • Unitary gauge: • Goldstone boson has been “eaten” by the photon mass e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ (24)

Higgs mechanism • Unitary gauge: • Degrees of freedom • Before: massless photon: 2, complex scalar field φ: 2 Total: 4 • After: massive photon: 3, one real scalar field h: 1 Total: 4 • Goldstone boson has been “eaten” by the photon mass e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ (25)