The Standard Model of Electroweak Physics. Christopher T. Hill Head of Theoretical Physics Fermilab

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1 The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab

2 Lecture I: Incarnations of Symmetry

3 Noether s Theorem is as important to us now as the Pythagorean Theorem Emmy Noether

4 Electricity and Magnetism Electric charge: Electric charge is conserved:

5 What is the Symmetry that leads, by Noether s Theorem to electric charge conservation?

6 In Five Easy Pieces

7 I. Local Gauge Symmetry of Electrodynamics electron = electron + gauge field

8

9 Electromagnetic force

10 Electromagnetic force Quark color force

11 Weak Force: SU(2) x U(1) d W nu What gives rise to masses of W and Z boson? u e SU(2)xU(1) is Spontaneously broken Symmetry Higgs Field?

12 U(1) Local Gauge Invariance on a Wallet Card covariant derivative

13 U(1) Local Gauge Invariance on a Wallet Card field strength invariants

14 Yang-Mills Local Gauge Invariance on a Wallet Card

15 Homework: Verify all of the transformations laws stated on the previous pages for U(1) and Yang-Mills gauge theories.

16 II. Can a gauge field have a mass?

17 Can a gauge field have a mass? Yes!

18

19 Superconductivity === Massive Gauge Field

20 Cartoon Feature: Gauge Boson Mass time light cone +z axis

21 Massless Photon time light cone +z axis

22 A massive photon time light cone +z axis

23 A massive photon oscillates through spacetime, colliding with the condensate and mixing with phase degree of freedom: Charge condensate spin is conserved

24 Superconductivity === Massive photon Field

25 Superconductivity === Massive photon Field Our vacuum is an electroweak superconductor Massive W and Z bosons

26 Homework: Consider a charged scalar field coupled to the photon and described the Lagrangian: Show that this is gauge invariant under: Show that if : then the photon acquires a gauge invariant mass:

27 III. Massless Fermions and Chiral Symmetry

28 Massless Fermions have Chiral Symmetry

29 Both currents are conserved when fermions are massless and chiral symmetry is exact (modulo anomalies)

30 Each chiral current corresponds to a different chiral charge e.g., L couples to W-bosons while R does not Standard Model is flavor chiral

31 Cartoon Feature: Fermion Mass and Chirality time light cone +z axis

32 A massless right-handed fermion s z = +1/2 time momentum spin +z axis

33 A massless left-handed fermion s z = +1/2 time momentum spin +z axis

34 Can couple fermions to gauge bosons and preserve chiral symmetry: time right-handed right-handed Chirality is conserved +z axis

35 e.g., couple electron to the photon in a L-R symmetric way time left-handed left-handed Chirality is conserved +z axis

36 The left-handed and right-handed electrons have the same electric charge QED is vectorlike

37 Standard Model is not vectorlike!!! Only left-handed fermions have electroweak charge and form doublets under SU(2) Right handed s are sterile under SU(2)

38 only L fermions couple to the W-boson time left-handed left-handed +z axis

39 Reflection Symmetry (parity) doublets singlets

40 Helicity of decay products in pion decay:? Mirror Images?

41 Parity is violated in pion decay: (Lederman)

42 Chiral symmetry is broken by mass

43 Chiral symmetry is broken by mass

44 Cartoon: a massive electron time light cone +z axis

45 A massive fermion oscillates in chirality through spacetime: right-handed left-handed right-handed electric charge is conserved left-handed right-handed spin is conserved Chirality nonconservation by the mass term

46

47 Homework: Verify that: Hint: use the Dirac equation

48 How do we make a massive fermion but conserve weak charge? left-handed right-handed left-handed mass violates weak charge!!! right-handed left-handed Mass Violates Electroweak Gauge Symmetry!!!

49 IV. Spontaneous Symmetry Breaking

50

51

52 Higgs Boson Nambu-Goldstone Boson

53

54 Engineer a Coupling to a Complex Scalar Boson that conserves chirality

55 Couple to a Complex Scalar time right-handed complex boson left-handed +z axis Chiral charge is conserved

56 Can we have a massive fermion but conserve chirality? left-handed right-handed left-handed right-handed left-handed

57 Boson Condenses in vacuum! time Complex boson vacuum expectation value = f +z axis Chiral charge is hidden in vacuum!!

58 Fermion Masses generated spontaneously left-handed right-handed left-handed right-handed left-handed

59 Ungauged Spontaneously Broken Chiral Symmetry

60 Gauged Spontaneously Broken Chiral Symmetry

61

62 V. Putting it all together: Gauged Spontaneously Broken Chiral Symmetry

63 We re ready for the Standard Model!!! Weak Force: SU(2) x U(1) u d W nu e What gives rise to masses of W and Z boson? SU(2)xU(1) is Spontaneously broken Symmetry Higgs Field?

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