First, I ’ d like to look ahead to the Standard Model. This is the chart from CPEP.

1. A journey through time with the Higgs particleGordon J. Aubrecht, IIColumbus Science Pub, 2 October 2012

2. Sometime in the fall of 1967 that I attended a seminar by a brash young physicist from MIT. From the way the senior physicists at Princeton (where I was a graduate student at the time) treated Steven Weinberg, it was clear that this was someone who had a future in theoretical physics. It wasn’t clear they thought he would go on to win the Nobel Prize (in 1979, with Abdus Salam) for his contributions to building what is now called the Standard Model, but I and the other graduate students there knew he was considered special.

3. That afternoon, I learned about spontaneous symmetry breaking. I recall Weinberg talking about a scalar particle and how this scalar particle could give mass to the vector bosons. I remember him doing calculations on the blackboard and coming out with a mass parameter μ from the symmetry breaking. The idea is that the ground state equilibrium is unstable, and any perturbation results in the particle falling to the lower potential energy. It was my first introduction to what has been called the “wine-bottle” or “Mexican-hat” potential.

4. First, I’d like to look ahead to the Standard Model. This is the chart from CPEP.

5. I am the former chair of the Contemporary Physics Education Project (CPEP). We created this chart in the late 1980s, as it became clear to all of us that there was such a thing as a “Standard Model.”

7. The frantic 1970sGoing back to the 1930s, there was a weak interaction theory that was originally developed by Enrico Fermi for beta decay. In fact, it is still known to physics students as Fermi’s Golden Rule: that the probability of a transition from initial to final state depends on the density of states and the square of the interaction matrix element between initial and final states.

8. Of course, in 1934, people didn’t know the matrix element; it would take until the 1950s to develop the ideas that led to the proper beta-decay spectrum. The Fermi model of weak interactions had problems when applied beyond relatively low energies—the prediction extrapolated more generally led to a growing transition probability because the 1950s constant matrix element and the growing density of states. The matrix element, as we have since learned, is simply a low-energy approximation in the bigger model.

9. Theorists showed that one could calculate real values through a process of renormalization reminiscent of Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga and many others’ work on quantum electrodynamics (QED).

10. The development of QED during the 1940s showed how renormalization could work to eliminate the infinities in electromagnetism. Electromagnetism can be explained in terms of exchange of photons. Of course, photons are massless and their exchange—through matrix elements that involved propagators that are the inverse of the square of the four-momentum, 1/p2—led to calculations that found infinite values for physical parameters.

11. The general idea of exchange of particles came from what is known as gauge invariance in electromagnetism, and the particles exchanged could be referred to generally as gauge particles.Photons are gauge particles for electromagnetism.

12. A way to get rid of the pesky infinities in theories of interactions is to realize that interactions are mediated by gauge particles. This is an old idea in particle physics. Nuclear physicists considered exchange of virtual (massive) pions and other virtual particles as the way the strong interaction worked inside nuclei.

13. a) A neutron and a proton at time t1. b) At time t2 > t1, the proton emits a virtual positively charged pion and becomes a neutron. c) At time t3 > t2, the neutron absorbs the pion, becoming a proton. d) At time t4 > t3, there is again a neutron and a proton.

14. Feynman developed a graphical method of calculation for QED. The exchange on the last slide could be calculated from this diagram (with appropriate rules).

15. The idea that interactions could proceed by exchange of particles that were massive was applied to the weak interactions. Simplifying the situation immensely, if there were massive gauge particles similar to the photon, the infinities would go away.

16. If this idea were to work, for example in the case of the 1930s “poster child” for the weak interaction, nuclear beta decay, this would mean that nuclear beta decay and scattering of a neutrino from a neutron to produce a proton and an electron would be related.

17. a) The Feynman diagram describing the process in which a neutron (symbolized by d) and a neutrino scatter through the weak interaction producing a proton and an electron. b) The Feynman diagram for nucleon beta decay, in which a constituent of the neutron (d) is changed by the weak interaction into a constituent of a proton (u) and produces a W-, which then decays into an electron and an antineutrino (note that the antineutrino line points to the right). The u and d are quark constituents of the nucleons. There is a propagator for the W- and there are two vertices (u-d-W- and e--e-W-) included in each of these Feynman diagrams.

18. In the 1970s, such an interaction would be labeled a charged-current interaction (the W- being charged and being exchanged; we could instead have drawn the diagrams for electron plus proton to neutron and electron neutrino and for positron emission, which proceed through exchange of the W+).

19. The exchanged virtual particles’ propagators would be of the form 1/(pp – m2), and the m2 term would mean approximately constant matrix elements at low energy (compared to the m2), while the p2 part of term would make them vanishingly small at high energy by tending the denominator toward zero.

20. There must also be indications not simply of exchange of a charged gauge boson as in nuclear beta decay. In other instances of the weak interaction, there could possibly be exchange of a neutral gauge boson, similar to the photon in its lack of electric charge, but having a nonzero mass. In the parlance of the 1970s, the former would be called a charged current interaction and the latter a neutral-current interaction (the currents form the matrix element).

21. Such a particle could be produced by sending electrons and positrons colliding together and seeing, for example, +-- pairs emerge or scattering an electron neutrino from an electron and producing the same thing or producing a - and . The first experimental evidence for the electroweak theory was the discovery of weak neutral currents, first seen in 1973 in by the Gargamelle collaboration at CERN in –nucleon scattering and anti-muon-neutrino-electron scattering, and immediately thereafter by the Harvard-Penn-Wisconsin collaboration at Fermilab. The exchanged gauge particle is known as the Z.

22. Thus, the experimental result supported electroweak theory, in which the photon, the W±, and the Z are the gauge bosons. The mystery was why the photon was massless, while the W± and Z had masses. This is where the spontaneous symmetry breaking comes in. Massless particles have two states of polarization, which we usually label clockwise and counterclockwise. Massive particles also have a longitudinal polarization, for a total of three states of polarization.

23. The “extra” state is supplied through the acquisition of mass by the Higgs mechanism.This gives mass to the W± and Z particles.To trust the model, the W± and Z would have to be found experimentally.They were found in experiments at the CERN SPS (super proton synchrotron) in the early 1980s and the 1984 Nobel Prize was given for their discovery.

24. The “normal” massive particles’ masses arise largely through the kinetic energy of the bound constituent quarks. This is very different from the idea of the Higgs mechanism.

25. Consider a field  for a particle whose original value puts it on an extremum of the potential. We named particles like these Higgs particles, which are represented by the fields, spontaneously move away from their original wavefunction to a new wavefunction at  =  having a lower potential energy.

26. A three-dimensional vision of the potential. V(ϕ) = λ(ϕ∗ϕ – μ2)2

27. In this process, known as the Higgs mechanism, the fields disappear when they “fall” into the lower potential and through their disappearance become responsible for creating the masses and thus the longitudinal polarizations of the gauge bosons. Thus, a key part of verification of electroweak unification is the appearance of Higgs bosons in experiments.

28. A new field is made from the Higgs …ϕ = H + μthere is an interaction term ϕ∗ϕA2 = μ2A2 + . . .That acts like a mass term (1/2 m2 = μ2).Also, the Higgs field also has a mass that comes from the potential V(ϕ).

29. From the 1970s to now, the Higgs was a “holy grail” of experimental searches. Up until Independence Day 2012, no such scalar particle had been found.A particle accelerator (the LHC) was built to try to find it.

30. LHC stands for Large Hadron Collider.What do we mean by the “hadron” in the Large Hadron Collider?

31. There are two sorts of particles shown on the chart I hope I gave you—leptons and hadrons. They are completely different in their properties from one another, but all leptons have spin n + 1/2 and do not interact strongly. All hadrons interact strongly and can have have either integer spin or spin n + 1/2.Leptons interact gravitationally, electromagnetically, and via the weak interaction.Hadrons are the only particles that interact via the strong interaction. Quarks are hadrons.

34. This is important: the hadrons act over really short distances—distances of a femtometer (10-15 m).

35. The Large Hadron Collider (LHC) is a place where interactions can occur through particle collisions. According to Wikipedia, “The Large Hadron Collider (LHC) is the world’s largest and highest-energy particle accelerator, intended to collide opposing particle beams, protons at an energy of 7 TeV/particle or lead nuclei at 574 TeV/particle.”

36. The LHC is a circular accelerator ring 27 km around. Particles are steered in both directions using superconducting magnets and made to collide in several regions loaded with detectors like the Atlas detector.Because the ring is so big, the particles’energies are immense—10 TeV—and the particles are traveling at essentially the speed of light: E =  mc2 =  1 GeV, so 10 TeV/(1 GeV) = 10,000, givingv = c - 1.5 m/s.

37. Let’s think a bit.The resolution of objects depends on the wavelength of the probing object. A wave of wavelength  bends around objects of size d. Waves and particles are not more than different evocations of some underlying reality. Particles have momentum p that is related to the wavelength : p = h/.

38. Becausep = h/,  is comparable in size to the object (d),and the energy of a particle is given byE = (p2c2 + m2c4)1/2 = mc2, we see that to “see” a small object (d very small), p must be very large, and so in turn E must be very large.

39. This means that particle physicists are always searching to increase the energy of collisions. They do this by accelerating the particles in an accelerator.The first accelerators were designed in the 1920s—Cockroft and Walton designed a linear accelerator (linac), and E. O. Lawrence designed a circular accelerator (cyclotron).

40. Lawrence’s machine was called a cyclotron (not prefix), and today particle physicists use both linacs and synchrocyclotrons to study particle physics.The synchronization is necessary due to the effects of special relativity.

41. LHC preacceleratorsp and Pb: Linear accelerators for protons (Linac 2) and Lead (Linac 3) (not marked) Proton Synchrotron BoosterPS: Proton Synchrotron SPS: Super Proton SynchrotronLHC experimentsATLAS A Toroidal LHC ApparatusCMS Compact Muon SolenoidLHCb LHC-beautyALICE A Large Ion Collider ExperimentTOTEM Total Cross Section, Elastic Scattering and Diffraction DissociationLHCf LHC-forward

43. ATLAS is about 45 meters long, more than 25 meters high, and has a mass of about 7,000 tonnes.

44. The Compact Muon Solenoid (CMS) is 21 meters long and 15 meters wide and high. It has a mass of 12,500 tonnes.

45. The Standard Model (the chart I showed) has been the most successful model ever in describing the actions of particles.The Standard Model explains all the particle physics of the past 30 years. Explorations of the Standard Model have been responsible for 32 Nobel Prizes over the last 30 years.

46. The Higgs boson gives mass to the four colorless gauge bosons (g, W+, W-, Z) in the Standard Model.

47. In the Standard Model chart, we now have the Higgs.

48. There are other bosons besides the gauge bosons. In the standard model, they are made of quark-antiquark pairs.

50. As already noted, constituent mesons get their masses mainly from their enclosed constituents’ kinetic energy. (Note the smallness of the quark masses.)