Abstract
It is often said that the Standard Model (SM) is a theory of interactions. That means,that it describes the laws of nature by assigning its pieces a susceptibility to certain forces.This is modelled as a charge with respect to a field, which in this respect is nothing more than a quantum of how strongly it couples to the force carriers of that field.
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Notes
- 1.
For a general introduction to the Standard Model, see for instance the review in [1], and references therein.
- 2.
A net charge arises as the hair is stripped of or receives electrons—fundamental particles with electric charge \(-1e\). Unlike a compound object, a fundamental particle has an intrinsic, fixed charge.
- 3.
This could be an indication of a more fundamental theory than the SM.
- 4.
Here it is again, the elusive, seemingly fundamental, concept of mass.
- 5.
Electroweak as in the unification of electromagnetic and weak interactions.
- 6.
The electron being the first fundamental particle discovered, it set the standard for electric charge—as the name suggests.
- 7.
In the unified electroweak force, the charge is instead weak hypercharge, which takes both weak isospin and electric charge into account.
- 8.
We won’t need to discuss parity further in this work, but for a historical experiment, the interested reader is referred to Ref. [4].
- 9.
L denotes left-handed. The right-handed counterparts are flavour singlets, and thus stand alone: \(e_R, \mu _R, \ldots \).
- 10.
Flavour oscillations are a quantum mechanical subtlety, relating to the flavour eigenstate not being the same as the mass eigenstate. Oh, yes, there it is again.
- 11.
\(8 = 3^2 - 1\), QCD being an SU(3) symmetry group.
- 12.
Had the history of discovery been different, the electric charge of the electron had likely been defined as \(-3e\) instead.
- 13.
The relation between energy and velocity is given by \(E^2 = m^2 + \vec {p}^2\).
- 14.
This convention goes back to considering antiparticles as particles moving backwards in time, as introduced in [5].
- 15.
Anti-electron: also known as positron.
- 16.
The concept of hadrons is older than the quark model, so, they must have certain unique characteristics, evident already before.
- 17.
Colourless combinations thereof, such as pentaquarks, have also been observed [6].
- 18.
Virtual particles can “borrow” additional energy from the vacuum, but only for a short time.
- 19.
More strictly speaking: \(m_n > m_p + m_e + m_{\bar{\nu }_e}\).
- 20.
The idea is similar to the method of Taylor expansion.
- 21.
This discussion loosely follows Ref. [10], which gives an overview of the renormalisation idea that is worth a read!
- 22.
For QED the physically meaningful upper cut-off is the scale of unification with the weak interaction.
- 23.
In the natural units commonly used in particle physics, where the speed of light in vacuum \(c = 1\), distance has dimensions of 1/(energy).
- 24.
The electroweak theory is also non-Abelian, and W and Z bosons are self-interacting. Photons are not.
- 25.
Macroscopic—or even outside the proton radius.
- 26.
The colour field lines are not radial (as in electromagnetism) but compressed in a flux tube between the partons.
- 27.
Sign convention; confusing but true.
- 28.
Note that since they don’t interact in the SM, right-handed neutrinos are here not constrained to stay on the brane!
- 29.
The naming conventions and parameter choices vary between models. Here we choose the ADD representation.
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Bryngemark, L.K. (2017). The Standard Model and Beyond. In: Search for New Phenomena in Dijet Angular Distributions at √s = 8 and 13 TeV. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-67346-2_2
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