IOP Physics Education Phys. Educ. 52 P A P ER Phys. Educ. 52 (2017) 034001 (9pp) iopscience.org/ped 2017 Let’s have a coffee with the © 2017 IOP Publishing Ltd Standard Model of particle PHEDA7 physics! 034001 Julia Woithe1,2, Gerfried J Wiener1,3 J Woithe et al and Frederik F Van der Veken1 1 CERN, European Organization for Nuclear Research, Geneva, Switzerland Let’s have a coffee with the Standard Model of particle physics! 2 Department of Physics/Physics Education Group, University of Kaiserslautern, Germany 3 Austrian Educational Competence Centre Physics, University of Vienna, Austria Printed in the UK E-mail: [email protected], [email protected] and [email protected] PED Abstract The Standard Model of particle physics is one of the most successful theories 10.1088/1361-6552/aa5b25 in physics and describes the fundamental interactions between elementary particles. It is encoded in a compact description, the so-called ‘Lagrangian’, which even fts on t-shirts and coffee mugs. This mathematical formulation, 1361-6552 however, is complex and only rarely makes it into the physics classroom. Therefore, to support high school teachers in their challenging endeavour Published of introducing particle physics in the classroom, we provide a qualitative explanation of the terms of the Lagrangian and discuss their interpretation based on associated Feynman diagrams. 5 1. Introduction fundamental interactions in nature, all except grav- 3 The Standard Model of particle physics is the most ity are described by the Standard Model of particle important achievement of high energy physics to physics: particles with an electric charge are infu- date. This highly elegant theory sorts elementary enced by the electromagnetic interaction (quant um particles according to their respective charges and electrodynamics, or QED for short), particles with a weak charge are infuenced by the weak inter- describes how they interact through fundamental action (quantum favour dynamics or QFD), and interactions. In this context, a charge is a property those with a colour charge are infuenced by the of an elementary particle that defnes the funda- strong interaction (quantum chromodynamics or mental interaction by which it is infuenced. We QCD). Contrary to the fundamental interactions, then say that the corresponding interaction particle the Brout Englert Higgs (BEH) feld acts in a couples to a certain charge. For example, gluons, – – ‘ ’ special way. Because it is a scalar feld, it induces the interaction particles of the strong interaction, spontaneous symmetry-breaking, which in turn couple to colour-charged particles. Of the four gives mass to all particles with which it interacts Original content from this work may be (this is commonly called the Higgs mechanism). used under the terms of the Creative In addition, the Higgs particle (H) couples to any Commons Attribution 3.0 licence. Any further distri- bution of this work must maintain attribution to the other particle which has mass (including itself). author(s) and the title of the work, journal citation and Interactions are mediated by their respec- DOI. tive interaction particles: photons (γ) for the 1361-6552/17/034001+9$33.00 1 © 2017 IOP Publishing Ltd J Woithe et al QED (electromagnetic) matter particles: q,q ν,ν QFD(weak) QCD (strong) interaction particles: g γ W ,Z0 H BEH (Higgs) Figure 1. Matter particles can be divided into three groups: quarks (q) and antiquarks (q); electrically charged leptons (ℓ) and antileptons (ℓ); neutrinos (ν) and antineutrinos (ν). Gluons (g) couple to colour charge, which only quarks, antiquarks, and gluons themselves, have. Photons (γ) couple to electric charge, which is found in (anti)quarks and electrically charged (anti)leptons. The weak bosons (W−, W+ , Z0) couple to the weak charge, which all matter particles have. Weak bosons can also interact with the photon (but this is a pure weak interaction, not an electromagnetic one). And fnally, the Brout–Englert–Higgs feld interacts with particles that have mass (all particles except the gluon and the photon). electro magnetic interaction, the weak bosons particle physics. Hence, any signs of irregularities (W −, W + , and Z 0) for the weak interaction, and between the predictions of the Standard Model of gluons (g) for the strong interaction. Furthermore, particle physics and experimental results would an elementary particle can be infuenced by more spark tremendous excitement. After all, this would than one fundamental interaction, in which case enable the physics community to update and mod- it has several charges (see fgure 1). For example, ify the current description of nature. due to its electric and weak charges, a muon is infuenced both by the electromagnetic interac- tion and the weak interaction. 2. The Lagrangian The development of the Standard Model of The mathematical formulation of the Standard particle physics started in the early 1970s and has Model of particle physics is complex. However, so far withstood every experimental test. The latest all information is encoded in a compact descrip- success was the verifcation of the Brout–Englert– tion—the so-called ‘Lagrangian’. Nonetheless, Higgs feld by ATLAS and CMS at CERN’s Large this ‘compact’ formulation still flls several pages Hadron Collider in 2012. Both experiments suc- [1]. That is why an ultra-short, four-line version cessfully detected the quantised excitation of the of the Lagrangian is also commonly shown. This BEH feld—the so-called Higgs boson. This con- par ticular formula draws a lot of attention and frmed the Higgs mechanism, which associates everyone who visits CERN will come across it elementary particles with their respective mass. at some point. For example, the CERN gift shop One might think that, given this great success sells t-shirts and coffee mugs (see fgure 2) featur- story, the particle physics community is happy and ing this four-line version of the Lagrangian. This content. But, as a matter of fact, the exact opposite can be especially challenging for physics teachers, is the case! While the Standard Model of particle who might then be asked by interested students to physics provides a unique and elegant description explain the meaning and the physics behind the of fundamental interactions between elementary Lagrangian. Therefore, we want to give a quali- particles, it is assumed that this quantum feld tative description of the individual terms of the theory is only part of a broader theory. Indeed, the Lagrangian, explain the fundamental processes Standard Model of particle physics describes only behind them, and associate them to their respective about 5% of the universe. It does not explain dark Feynman diagrams. matter, which accounts for approximately 25% of Feynman diagrams are pictorial representa- the universe—not to speak of dark energy, which tions of the underlying mathematical expressions supposedly adds the remaining 70% of the uni- describing particle interactions. Even though parti- verse. Their description can only be achieved by cle physicists will use a set of ‘Feynman rules’ to theories which go beyond the Standard Model of translate a diagram into a mathematical expression, May 2017 2 Phys. Educ. 52 (2017) 034001 Let’s have a coffee with the Standard Model of particle physics! the diagram on its own is a useful tool to visualise and understand what is happening in a certain inter- action without the need for mathematics. Every line in a Feynman diagram represents a particle, with different styles of line for the various types of par- ticles. In this article, we additionally use different colours to indicate the associated interactions (see fgures 1 and 3). Thus, a straight black line with an arrow denotes a matter particle, a wavy yellow line represents either a photon or a weak boson, a coiled green line corresponds to a gluon, and a dashed blue line indicates a Higgs boson. The time axis of a Feynman diagram is often oriented horizontally. Figure 2. Lagrangian on a coffee mug. However, the reading direction is only important abbreviations and derivatives mean, and when to for the physical interpretation, since all vertices consider each of the fundamental interactions. In can be rotated arbitrarily. Hereafter, we will read all the physics classroom, however, it is very diffcult Feynman diagrams from left to right with a hori- to achieve a deep-level understanding because the zontal time axis: lines starting on the left represent required mathematics skills go far beyond high- particles present before the interaction, and lines school level. Hence, we will only treat the ultra-short ending on the right represent particles present after Lagrangian in fgure 2 on a term-by-term basis, the interaction. The arrow for matter particle lines without detailing how different felds are combined should not be mistaken as an indicator of the direc- inside these terms. tion of movement, since it only indicates whether the line belongs to a particle (with an arrow point- ing to the right) or an anti-particle (with an arrow 3.1. What does the L stand for? pointing to the left). Every vertex, where three or L stands for the Lagrangian density, which is the den- four lines meet, represents an interaction between sity of the Lagrangian function L in a differ ential vol- particles. There are different possible vertices for ume element. In other words, L is defned such that QED, QFD, QCD, and BEH interactions, and these form the elementary building blocks of a Feynman the Lagrangian L is the integral over space of the den- 3 diagram. In addition, Feynman diagrams are ‘fex- sity: Lx= ∫ d L. In 1788, Joseph–Louis Lagrange ible’: lines should not be understood as rigid, but as introduced Lagrangian mechanics as a refor mulation a combination of all possible paths a particle can of classical mechanics.