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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:. Exercises Lecture 5:. Exercises Lecture 5:. Exercises Lecture 5:.

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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:**Niels Tuning (4)**Exercises Lecture 5:**Niels Tuning (5)**Exercises Lecture 5:**Niels Tuning (6)**Exercises Lecture 5:**Niels Tuning (7)**Plan**11 Feb • Intro: Relativity and accelerators • Basis • Atom model, strong and weak force • Scattering theory • Hadrons • Isospin, strangeness • Quark model, GIM • Standard Model • QED • Parity, neutrinos, weak inteaction • QCD • e+e- and DIS • Higgs and CKM 1900-1940 18 Feb 1945-1965 4 Mar 1965-1975 18 Mar 1975-2000 22 Apr 2000-2013 13 May Niels Tuning (8)**Outline for today:**• Higgs mechanism • Higgs discovery at ATLAS • CKM-mechanism • CP violations at LHCb Niels Tuning (9)**Lecture 1: Accelerators & Relativity**• Theory of relativity • Lorentz transformations (“boost”) • Calculate energy in collissions • 4-vector calculus • High energies needed to make (new) particles Niels Tuning (11)**Lecture 2: Quantum Mechanics & Scattering**• Schrödinger 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 • Described by 4-component spinors • Prediction of anti-matter Niels Tuning (12)**Lecture 2: Quantum Mechanics & Scattering**• Scattering Theory • (Relative) probability for certain process to happen • Cross section • Fermi’s Golden Rule • Decay: “decay width” Γ • Scattering: “cross section” σ Scattering amplitude in Quantum Field Theory Classic a → b + c a + b → c + d Niels Tuning (13)**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 (14)**Lecture 4: Gauge symmetry and Interactions**• Arbitrary “gauge” • Physics invariant • Introduce “gauge” fields in derivative • Interactions! • QED • Weak interactions • QCD 1 photon 3 weak bosons 8 gluons Niels Tuning (15)**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 (16)**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 (17)**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 (20)**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 (21)**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 (22)**Higgs mechanism**• Let’s give the photon a mass! • Introduce a complex scalar field: • with: • and: • Then: Niels Tuning (23)**Higgs mechanism**e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (24)**Higgs mechanism**• What about this field ? e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (25)**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 (26)**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 (27)**Higgs mechanism in the Standard Model**• Let’s give the W,Z a mass! • Introduce a doublet of complex scalar fields: Niels Tuning (28)**Spontaneous symmetry breaking**• Mass terms! • How about the physical fields? Niels Tuning (29)**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 (30)**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)**Weak mixing angle (or Weinberg angle):W**Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (33)**Rewriting in terms of physical gauge bosons**• W1, W2 : • W3, B: Niels Tuning (34)**Spontaneous symmetry breaking**(Keep the vacuum neutral) • Massterms! • How about the physicalfields? Niels Tuning (35)**Spontaneous symmetry breaking**Physical fields: Mass term Mass Niels Tuning (36)**Summary:**• Introduce doublet of scalar fields: • With potential: • S.S.B.: • Mass terms for gauge fields: Niels Tuning (37)**Boson masses?**• Photon couples to e: • Prediction for ratio of masses: • Veltman parameter: • Higgs mass: Niels Tuning (38)**Fermion masses?**• Add ad-hoc (!?) term to Lagrangian: Niels Tuning (39)**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

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