Abstract
The constituent fields/particles of the Standard Model (“matter” fields: quarks and leptons; “force” fields: gluons, weakons and photons; Higgs boson) are described with their masses, spins and charges with respect to strong, weak and electromagnetic interactions. The change in the interpretation of the SU(N) symmetries in the history of particle physics is described up to the culmination of the SU(6) flavor and SU(3) color symmetry in the Standard Model. Separate sections deal with quantum chromodynamics for strong interactions and the Glashow-Weinberg-Salam model for electro-weak interactions. The current algebra description of weak interactions is expounded as it is still an appropriate means to organize the leptons and quarks into chiral multiplets and to understand the Cabbibo-Kobayashi-Maskawa mass mixing. A further section deals with the conceptual weaknesses of the Standard Model, its generalization to massive neutrinos, various manifestations of anomalies, and the \(\beta \) functions of the color SU(3), the weak isospin SU(2), and the weak hypercharge U(1) component.
Lynda Williams: “Quark Sing-a-long”
(Refrain) Up, Down, Charm, Strange, Top and Bottom! The World is made up of Quarks and Leptons! Up, Down, Charm, Strange,Top and Bottom! Yum! Yum!
Quarks come in six flavors. They live in families of two. Up Down, Charm Strange, Top and Bottom! They come in anti-flavors too!
Each family makes a generation between which is a mass gap. The up quark is the lightest and the top quark is the most fat!
The second and third generations do not live for very long. That’s why everything in the Universe is made up of Ups and Downs!
Quarks carry a color charge. They come in red, green and blue. You’ll never see a quark all by itself cuz they stick together with a strong force glue.
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- 1.
On July 4th, 2012, CERN announced at first the discovery of a scalar boson with mass around 126 GeV identified by its decays and having properties of the Higgs. Further data collection and data evaluation for another year led to the opinion that indeed it was the long sought after Higgs boson. This prompted the Nobel prize committee to award the physics prize for the year 2013 to F. Englert and P.W. Kibble, two of the theoreticians that worked back in the 1960’s on what became known as the Higgs mechanism.
- 2.
the last to be established were the top-quark in 1995 and the \(\tau \)–neutrino in the year 2000
- 3.
I dispense with giving the full references of the authors in the following list since these approaches are now of historical interest only. But I mention them here to show how keen particle physicists have been in symmetry argumentation.
- 4.
1969 Nobel prize in appreciation “for his contributions and discoveries concerning the classification of elementary particles and their interactions”.
- 5.
This example of a “charmonium” is the only particle carrying two names: It is the \(J/\psi \), the letters standing for the discovery of the US East coast team with S. Ting and the West coast team with B. Richter.
- 6.
Of course you realize that the names of the quarks are not at all representatives of their attributes. I suppose that the naming of new phenomena and new entities in physics is a very interesting cultural and sociological theme to investigate.
- 7.
Conceiving the strong interaction as a YM-theory is going back to 1972 with work of M. Gell-Mann, H. Fritzsch, and H. Leutwyler, see e.g. [199].
- 8.
These were known even prior to bounds from experiments in particle physics.
- 9.
If you succeed in delivering a proof, this would earn you a 1 Million Dollar Clay Prize.
- 10.
Note that an apparently non-conservation of hitherto established conserved quantities related to basic symmetries of nature initiates the postulation of previously unobserved particles.
- 11.
Glashow, Salam and Weinberg received the Nobel price in 1979, although the massive vector bosons predicted by their model were found only in 1983 at CERN.
- 12.
If you read Fermi’s original article, you can appreciate how progress in physics is connected with the development of adequate mathematical notions.
- 13.
Generically it is a \((\frac{N_f}{2}\times \frac{N_f}{2})-\)matrix. However, as stated above, the discovery of more than six flavors would spoil both results in particle physics and in cosmology.
- 14.
They received the Nobel prize in 2008 “for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature”.
- 15.
Here we observe anew the belief and trust of physicists in symmetries.
- 16.
Nobel prize conferred in 1979: “For their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current”.
- 17.
I try to be consistent in this book in distinguishing the symmetry-breaking scalar field from the Higgs boson which survives the symmetry.
- 18.
Once again the assumption of further symmetries will improve our understanding of physics.
- 19.
There are only upper bounds, the most stringent one coming from the results on the microwave background radiation due to which the sum of the masses of the three neutrinos is smaller than roughly 1 eV.
- 20.
It would be out of the scope of this book on symmetries to derive this here. The derivation requires a lot more “meat” from quantum field theory.
- 21.
This “magical” cancellation could give rise to the philosophical statement that a world either without leptons or without quarks is inconsistent.
- 22.
The only possible dim-5 operator represents a Majorana mass term for the left-handed neutrinos. I thank A. Blum for pointing this out to me.
- 23.
Here I put “more fundamental” into quotation marks because the effective field-theory philosophy throws doubts on the meaning of this very conception.
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Sundermeyer, K. (2014). Particle Physics. In: Symmetries in Fundamental Physics. Fundamental Theories of Physics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-06581-6_6
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