The history of the Standard Model - University of Helsinki · University of Southampton & Rutherford Appleton Laboratory Autumn 2018 H. Waltari The history of the Standard Model

Particle physics in early 1960sHadron structure and QCD

Weak interactions and electroweak unification

The history of the Standard Model

Harri Waltari

University of Helsinki & Helsinki Institute of PhysicsUniversity of Southampton & Rutherford Appleton Laboratory

Autumn 2018

H. Waltari The history of the Standard Model



The timeframe of this course goes from early 1960’s to1980’s

The first part of the course dealed mostly things invented in the1920’s (QM, Dirac equation) to 1950’s (symmetries of stronginteractions) or even 1960’s (deep inelastic scattering)

Most of the theoretical ideas presented in the second part wereinvented in 1960’s or 1970’s

Some of the particles were discovered experimentally a lot later, W-and Z-bosons in the 1980’s, the top quark in 1990’s and the Higgsboson in 2012

Next-to-leading order quantum corrections were computed bymid-1990s, some higher order computations have existed from early2000’s (notable exception: ge − 2, where three-loop correctionscomputed in 1980’s, five-loop computation finalized in 2012)




In 1964 the book for this course would have been Kallen’s

The main contents are the same but the details of the course differradically












Some of the ingredients were available

Kallen’s book was based on lectures given in 1961. Back then there was

quite a lot of scattering data, especially πN scattering

data on particle decay modes and lifetimes

knowledge of the finite size of nuclei, but incorrectly interpreted

a QFT for electrodynamics that worked at the quantum level (i.e.with loop corrections)

a QFT for (charged) weak interactions1 that worked at the Born(tree) level

no good idea as the theory of strong interactions — isospininvariance the only one that worked approximately

ingredients for non-Abelian gauge theories, but no idea of how tohave a finite range of force in that case

a question of whether QFT is a reasonable way of describing particlephysics, maybe one could derive a mathematical theory for theproperties of the S-matrix

1Neutral weak interactions weren’t observed yet.H. Waltari The history of the Standard Model



Advance 1: Hadron classification with SU(3)f

Gell-Mann and Zweig proposed that hadrons can be classifiedaccording to the irreducible representations of SU(3) — Gell-Manncalled the fundamental units quarks

For a long while quarks were considered as a mathematicalconstruction that needed not to be related to a possible internalstructure of hadrons




Advance 2: Deep inelastic scattering shows point-likeconstituents within the proton

ep scattering experiments at large momentum transfers compatiblewith scattering from point sources coined partons

Analysis of form factors show that proton constituents have spin-1/2

νN scattering confirms that parton charges are compatible withfractional charges of quarks

Partons were identified as quarks, further analysis showed also theexistence of sea quarks and gluons




Advance 3: Color charge leads to a QFT for stronginteractions

As quarks were real, the Pauli principle should have forbidden theexistence of the corners of the baryon decuplet (∆++, ∆−, Ω−),since there three identical particles would have had the same spinstate and their wave function was symmetric (parity)

Proposition: New quantum number called color, three possiblevalues, only color singlet states allowed

Gave correct predictions for σ(e+e− → hadrons)/σ(e+e− → µ+µ−)

Possible to formulate a QFT for quarks based on SU(3)c (Fritzsch,Gell-Mann, Leutwyler 1973)

Mediators later dubbed as gluons, the adjoint representation gave 8different color combinations




Advance 4: Asymptotic freedom explains why quarks werenot observed

Gross, Politzer and Wilczek show that strong interactions are strong(nonperturbative) in the infrared and rather weak (perturbative) inthe ultravioletResult depends on the number of quark flavors ⇒ upper limit forquark generations (8)From data the confinement scale was deduced to be around200 MeVThe hadronic spectra fits (and lattice computations later) show thatthe potential for strong force ∼ r at large distancesOn the other hand it became possible to factorize the hard collisionand soft hadronization as separate processesSince the lightest strongly interacting color neutral particle was thepion, the finite range of strong interactions got an explanationComputing the predictions of QCD still a tedious task, matchingexperimental precision requires either lattice computations or atleast two-loop computations in perturbation theory




The starting point for weak interactions wasFermi-Feynman-Gell-Mann theory

Fermi formulated the first theory for β-decay: Take two probabilitycurrents from the Dirac equation, multiply them together and fix thestrength of the interaction by a constant (Fermi constant)

In 1957 parity violation in weak interactions was observed by Wu et.al.

Feynman and Gell-Mann improved the Fermi theory by making itchiral: only left-handed particles and right-handed antiparticlesinvolved

Tree-level results agreed with experiment (±2%), loop correctionsinfinite (naive reason [GF ] = GeV−2)




Advance 1: Spontaneous breaking of symmetries borrowedfrom superconductivity

If a QFT were to be the solution, it needed to be non-Abelian, butthe short range was problematic

If gauge bosons were massive, they gave a finite range, but spoiledthe gauge invariance

In superconductivity the Ginzburg-Landau theory produced solutionswith effective mass, Nambu was the first to apply this to particlephysics

Problem: Goldstone showed that if the vacuum state broke thesymmetry of the Lagrangian, massless scalars (Goldstone bosons)should exist — none were seen




Advance 2: The Brout-Englert-Higgs mechanism got rid ofGoldstone bosons

Brout and Englert and, independently, Higgs noted in 1964 that asuitable choice of gauge could eliminate the Goldstone bosons fromthe spectrum

The gauge essentially made the would-be-Goldstone the longitudinalpolarization state of the gauge boson

This procedure created a mass term to the gauge boson

Also a physical scalar in the spectrum: the Higgs boson

Brout, Englert and Higgs considered only massive QED, thegeneralization to non-Abelian theories was due to Kibble in 1967




Advance 3: Finding the right symmetry group

Glashow proposed already in 1961 SU(2)× U(1) as a symmetrygroup for electromagnetic and weak interactions

Weinberg and, independently Salam applied Kibble’s results toGlashow’s idea and showed that in addition to gauge boson masses,the theory could produce masses to electrons and muons and leaveneutrinos massless

Lower limit for gauge boson masses around 38 GeV, out of the reachof colliders at that time

The theory predicted neutral weak currents, which were discoveredin 1973 by the Gargamelle experiment

Veltman and ’t Hooft showed in 1971-72 that the theory wasrenormalizable — the theory worked also at quantum level




Advance 4: Quark mixing with three generations explainedhadron lifetimes and CP violation

Once the quark/parton model became accepted, quark mixing(Cabibbo 1963) in weak interactions became the explanation for thelifetimes of heavier hadrons (decays of strange hadrons wereCabibbo-suppressed)

Anomaly cancellation required full doublets of quarks and leptons,GIM mechanism gave tools to predict masses (discovery of charm in1974)

Kobayashi and Maskawa predicted the existence of the thirdgeneration, since quark mixing with three generations was theminimal model allowing CP violation from the quark sector (otheroptions, see e.g. Montonen and Roos, Phys. Lett. B66 (1977) 61)

In the Standard Model a single CP violating parameter, recentmeasurements (> 10) can be explained with one source of CPviolation (highly nontrivial constraint!)




Essential features of the Standard Model wereexperimentally confirmed

The third fermion generation was found (τ 1975-76, bottom 1977,top 1995, ντ 2000)

The weak gauge bosons were found in 1983-84

The predictions of the SU(2)×U(1) invariance were tested at highprecision in the first phase of LEP: The Standard Model survived ata level where one-loop effects were needed

The search for the Higgs also successful in 2012, so far no deviationsfrom the Standard Model predictions (and it fixed the last freeparameter)




Some lessons to learn

Although not discussed here in detail, there were a number of otherideas and the ones that are currently accepted were not always themost favored ones

The main theoretical ideas were there already, but choosing the rightones required experimental input

Compared to the situation in 1960, Nature looks surprisingly simple


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The history of the Standard Model - University of Helsinki · University of Southampton & Rutherford Appleton Laboratory Autumn 2018 H. Waltari The history of the Standard Model