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“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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**“Elementary Particles”Lecture 6**Niels Tuning Harry van der Graaf Niels Tuning (1)**Thanks**• Ik ben schatplichtig aan: • Dr. Ivo van Vulpen (UvA) • Prof. dr. ir. Bob van Eijk (UT) • Prof. dr. Marcel Merk (VU) Niels Tuning (2)**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)**Did I miss anything?**• Received homework sets: Niels Tuning (5)**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)**Prof.dr. J. Ellis**Half-way there?!**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)**Higgs mechanism in the Standard Model**• Let’s give the W,Z a mass! • Introduce a doublet of complex scalar fields: Niels Tuning (26)**Spontaneous symmetry breaking**• Mass terms! • How about the physical fields? Niels Tuning (27)**Rewriting in terms of physical gauge bosons**• W1, W2 : • W3, B: • Let’s do a ‘trick’ and ‘rotate’ the W3 and B fields to get the Z and A fields Niels Tuning (28)**Rewriting in terms of physical gauge bosons**• W1, W2 : • W3, B: Niels Tuning (29)**Rewriting in terms of physical gauge bosons**• W1, W2 : • W3, B: Niels Tuning (30)**Weak mixing angle (or Weinberg angle):W**Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (31)**Rewriting in terms of physical gauge bosons**• W1, W2 : • W3, B: Niels Tuning (32)**Spontaneous symmetry breaking**(Keep the vacuum neutral) • Massterms! • How about the physicalfields? Niels Tuning (33)**Spontaneous symmetry breaking**Physical fields: Mass term Mass Niels Tuning (34)**Summary:**• Introduce doublet of scalar fields: • With potential: • S.S.B.: • Mass terms for gauge fields: Niels Tuning (35)**Boson masses?**• Photon couples to e: • Prediction for ratio of masses: • Veltman parameter: • Higgs mass: Niels Tuning (36)**Fermion masses?**• Add ad-hoc (!?) term to Lagrangian: Niels Tuning (37)**Prof.dr. J. Ellis**Done**Prof.dr. J. Ellis**Let’s tackle the Yukawa couplings**First:**Higgs discovery**LHCb**ATLAS CMS ALICE**How are discoveries made?**New ? Normal muon muon ? muon muon**l+**Higgs ZZ 4 leptonssmall number of beautiful events Z l- higgs l- Z 120.000 Higgs bosons l- HZZ l+l-l+l- Only 1 in 1000 Higgs bosons decays to 4 leptons 50% chance that ATLAS detector finds them 60 (Higgs 4 lepton) events peak !? ‘other’ 52 events with Higgs 68 events**Higgs 2 photons**photon higgs photon Hγγ decay peak !?**Interpretation of excess**Claim discovery if: Probability of observing excess smaller than 1 in 1 milion Throwing 8 times 6 in a row**Discovery in slow-motion**jul/11 jul/11 mar/12 mar/12 dec/11 dec/11 Time-line higgs discovery jul/12 aug/12 jul/11 jul/11 mar/12 dec/11 dec/11 jul/12**What is mass ?? Anno 1687**Mass is de ‘exchange rate’ between force and acceleration: Does not describe what mass is ... F = m x a Newton**What is mass ?? Anno 1905**Mass is energy Describes what mass is ! But not where it comes from … E = m x c2 Einstein**What is mass ?? Anno 1964**Mass of elementary particles is due to “friction” of ubiquitous‘Higgs field’ m: ψψH Higgs

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