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- . 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. It allows the description of take. Therefore, both individual lines and Feynman the dynamics of a given classical system using only diagrams as a whole can be freely rotated. one (scalar) function L = T − V, where T is the kinetic energy and V the potential energy of the sys- tem. The Lagrangian is used together with the prin- 3. The elements of the Lagrangian ciple of least action to obtain the equations of motion The Standard Model of particle physics is a of that system in a very elegant way. quant um feld theory. Therefore, its fundamental When handling quantum felds, instead of elements are quantum felds and the excitations of the discrete particles of classical mechanics, the these felds are identifed as particles. For exam- Lagrangian density describes the kinematics and ple, the quantised excitation of the electron feld dynamics of the quantum system. Indeed, the is interpreted as an electron. From our viewpoint, Lagrangian density of quantum feld theory can it is not only permissible, but even advisable to be compared to the Lagrangian function of classi- speak directly of elementary particles instead of cal mechanics. Hence, it is common to refer to L feld excitations when discussing basic principles simply as ‘the Lagrangian’. of particle physics qualitatively in high school. A word of warning: as mentioned before, 3.2. Term 1: − 1 FFµν the Lagrangian is an extremely compact nota- 4 µν tion. Theoretical particle physicists normally know This term is the scalar product of the feld strength when to sum over which indices, what different tensor Fµν containing the mathematical encoding
May 2017 3 Phys. Educ. 52 (2017) 034001 J Woithe et al
g g g W+ W+ γ
g g g W− W− Z0
Figure 3. Some examples of Feynman diagrams that are included in − 1 FFµν: gluon gluon-interaction (3-gluon 4 µν – vertex and 4-gluon vertex), weak–weak interaction, and weak-photon interaction. of all interaction particles except the Higgs boson, featuring all the interaction particles (except the where µ and ν are Lorentz indices representing the Higgs), but this time without self-interactions. spacetime components4. It contains the necessary The beauty of this term is that it contains the formulation for these particles to even exist, and description of the electromagnetic, weak, and strong describes how they interact with each other. The interactions. Indeed, while all three fundamental contents differ depending on the properties of the interactions are different, the basic vertices by which interaction particles. For example, photons, the inter- they can be visualised look quite similar. We will action particles of the electro magnetic interaction, start by discussing the most important interaction cannot interact with each other, because they have of our daily lives, the electro magnetic interaction. no electric charge. Therefore, the contribution of the Here, pair production or annihilation of electrons electromagnetic interaction consists only of a kinetic and positrons, and the absorption or emission of term, the basis for the existence of free photons. photons by electrons, are prominent examples. All The description of gluons and the weak bosons also four of these processes can be represented using includes interaction terms in addition to the kinetic Feynman diagrams with the same basic vertex. For terms. Gluons, for example, are colour-charged example, the left part of fgure 4(a) shows the anni- themselves and can therefore also interact with each hilation of an electron and a positron (remember that other (see fgure 3). This leads to an exciting con- we use a reading direction from left to right). The sequence: the Standard Model of particle physics next diagram is produced by rotating the frst dia- predicts the existence of bound states consisting only gram by 180°, and is now a representation of pair of gluons, so-called ‘glueballs’. However, no experi- production. Rotating the vertex further, we arrive at ment has detected glueballs thus far. the third diagram, which describes the absorption of a photon by an electron. Last, the fourth permutation of the vertex gives the diagram for photon emission, 3.3. Term 2: iψψD/ also known as ‘Bremsstrahlung’. This term describes how interaction particles inter- If we now look at the basic vertex of the act with matter particles. The felds ψ and ψ describe strong interaction (see fgure 4(b)), we notice that (anti)quarks and (anti)leptons5. The bar over ψ it looks very similar to the vertex of the electro- means that the corresponding vector must be trans- magnetic interaction. For example, an anti-quark posed and complex-conjugated; a technical trick to and a corresponding quark transforming into a ensure that the Lagrangian density remains scalar gluon can be described as an annihilation process. and real. D is the so-called covariant derivative, In the reverse reading direction, this process can also be interpreted as pair creation, where a gluon 4 In this case, one has to sum over the indices according to transforms into a quark and an associated anti- the Einstein summation convention. quark. Additionally, by rotating the vertex fur- 5 The symbol ψ is also used to represent a wave function in classical quantum mechanics. Although this is related to the ther, we obtain the Feynman diagrams for gluon feld representation we use, the two are not exactly the same. absorption and gluon emission.
May 2017 4 Phys. Educ. 52 (2017) 034001 Let’s have a coffee with the Standard Model of particle physics!
(a) e+ e− γ γ
γγ e− e− e− e−
e− e+ (b) q q g g
g g qqqq
(c) − − − νe e W W
W− W− νe e− e− νe
− e νe
Figure 4. Basic vertices of the electromagnetic interaction (a), strong interaction (b), and weak interaction (c). From left to right: examples of annihilation, pair production, absorption, and emission.
Last but not least, the transformation pro- positron as ‘fragments’ of the original neutron or cesses of the weak interaction can be illustrated in proton. Instead of using the word ‘beta radiation’, a similar way as well (fgure 4(c)). Again, depend- we also recommend referring directly to emitted ing on the orientation, the example represents electrons (or positrons) to focus more strongly on annihilation or pair production of an electron and the particle aspect of the transformation process. an anti-electron-neutrino, and absorption or emis- Overall, this second term of the Lagrangian sion of a W− boson. The weak interaction differs is of special importance for our everyday life, and from the electromagnetic and the strong interac- therefore merits discussion in the physics class- tions in that it transforms one matter particle into room. Indeed, apart from gravity, all physical another, for example an electron into an electron- phenomena can be described on a particle level by neutrino and vice versa. We consider processes the basic vertices of the strong, weak, and electro- of the weak interaction involving a W boson to magnetic interaction. Furthermore, given that the be particularly interesting for introduction in strong and weak interactions play a minor role in the classroom. For example, the transformation high-school curricula, almost all physical phe- of a down-quark into an up-quark by emission nomena can be described using the basic vertex of a virtual W− boson, which itself transforms of the electromagnetic interaction (fgure 4(a)). into an electron and an anti-electron-neutrino: However, as discussed above, once this basic ver- 0 +− n → pe++νe is already part of many phys- tex is introduced, it is possible to draw connec- ics curricula [2–4] (see fgure 5). In many phys- tions to the basic vertices of the strong interaction ics textbooks this process is called ‘beta-minus (fgure 4(b)) and the weak interaction (fgure 4(c)) ++0 decay’ (or in the case of pn→ ++e νe: ‘beta- as well. plus decay’). The emitted electron (or positron) is then introduced as ‘beta radiation’. Here, we rec- 3.4. Term 3: h.c. ommend using the term ‘transformation’ instead of ‘decay’, as this more accurately describes the This term represents the ‘hermitian conjugate’ physical process. In addition, doing so can prevent of term 2. The hermitian conjugate is neces- the triggering of misconceptions of the electron or sary if arithmetic operations on matrices produce
May 2017 5 Phys. Educ. 52 (2017) 034001 J Woithe et al complex-valued ‘disturbances’. By adding h.c., such disturbances cancel each other out, thus the u u Lagrangian remains a real-valued function. n0 d d p+ Actually, the addition of h.c. is not required for u term 2, since term 2 is self-adjoint. Therefore, this d e− term is often omitted. Anyway, h.c. should not be W− taken literally. Theorists often use it as a reminder: νe ‘If a term changes when conjugating it, then add h.c.! If nothing changes (because it is self-adjoint), then add nothing . This term does not have a physi- Figure 5. Beta transformation: a neutron’s down-quark ’ transforms into an up-quark, emitting a virtual W− cal meaning, but it ensures that the theory is sound. boson. The virtual W− boson then transforms into an Tip: we recommend the CERN-wide interpre- electron and an anti-electron-neutrino. Macroscopically, tation of term 3: h.c. = hot coffee. After all, the a neutron (n0) becomes a proton (p+ ). Note: the weak Lagrangian is printed on a coffee mug for a good interaction allows only particle transformations between reason. It is therefore advisable to take a break at two specifc elementary particles, so-called ‘weak isospin doublets’. Prominent examples are the electron- half time with a mug of coffee. Afterwards, it will − neutrino and electron doublet ()νe, e , and the up-quark be easier to enjoy the full beauty of terms 4 to 7, and down-quark doublet ()ud, . which we explain next.
3.5. Term 4: ψiyijψφj – This term describes how matter particles couple τ to the Brout–Englert–Higgs feld φ and thereby obtain mass. The entries of the Yukawa matrix yij H represent the coupling parameters to the Brout– Englert–Higgs feld, and hence are directly τ + related to the mass of the particle in question. These parameters are not predicted by theory, but have been determined experimentally. Parts of this term still cause physicists head- Figure 6. A Higgs boson transforms into a pair of aches: it is still not clear why neutrinos are so tauon and anti-tauon. much lighter than other elementary particles, in relatively more massive particles and anti-parti- other words, why they couple only very weakly cles. Measurements by the ATLAS detector show, to the BEH feld. In addition, it is still not pos- for example, evidence of the direct coupling of sible to derive the entries of the Yukawa matrix in the Higgs boson to tauons , see fgure 6. a theoretically predictive way. It is known that particles with high mass, 3.6. Term 5: h.c. in other words with a strong coupling to the Brout–Englert–Higgs feld, also couple strongly See term 3, but here this term is really necessary, to the Higgs boson. This is currently being veri- since term 4 is not self-adjoint. While term 4 fed experimentally at the LHC, where Higgs bos- describes the interaction between a Higgs particle ons are produced in particle collisions. However, and matter particles, term 5, the hermitian con- Higgs bosons transform into particle–antiparticle jugate of term 4, describes the same interaction, pairs after about 10−22 s. Depending on their but with antimatter particles. Depending on the mass, i.e. their coupling parameter, certain par- interpretation, however, we recommend at least ticle–antiparticle pairs are much more likely, and one more mug of hot coffee. thus easier to observe experimentally, than others. This is because the coupling parameter, which 3.7. Term 6: ||D φ 2 describes the coupling to the Higgs boson, is sim- µ ply the mass of the particle itself. The Higgs boson This term describes how the interaction particles is thus more likely to be transformed into pairs of couple to the BEH feld. This applies only to the
May 2017 6 Phys. Educ. 52 (2017) 034001 Let’s have a coffee with the Standard Model of particle physics!
W− H H H
W+ H H H
Figure 7. One example of a Feynman diagram that is 2 encoded in ||Dµφ . A Higgs boson transforms into a pair Figure 9. Diagrams of Higgs self-interaction (3-Higgs of W+ and W− bosons. vertex and 4-Higgs vertex) that originate from −V()φ . different and leads to spontaneous symmetry- d d breaking (when choosing one of the minima). p+ u u As discussed for terms 4 and 6, matter particles and interaction particles couple differently to this u d background feld and thus obtain their respec- + ‘ ’ W tive masses. Term 7 also describes how Higgs H bosons couple to each other (see fgure 9). The W− Higgs boson, the quantised excitation of the BEH d u feld, was experimentally confrmed at CERN in p+ u u 2012. In 2013, François Englert and Peter Higgs u u were awarded the Nobel Prize in Physics for the development of the Higgs mechanism.
Figure 8. Possible vector-boson fusion process from two colliding protons. A down-quark emits a W− boson 4. Conclusions, and what about and an up-quark emits a W+ boson. The two W bosons the second mug? transform into an electrically neutral Higgs boson. Our experience at CERN is that both high school interaction particles of the weak interaction, which students and teachers are greatly fascinated by the thereby obtain their mass. This has been proven Lagrangian. Hence, introducing it in the class- experimentally, because couplings of W bosons room can contribute positively when discussing to Higgs bosons (fgure 7) have already been particle physics. However, due to the complex verifed. Photons do not obtain mass by the Higgs level of mathematical formalism used in the mechanism, whereas gluons are massless because Lagrangian, it is probably not favourable to aim they do not couple to the Brout–Englert–Higgs for a complete, in-depth discussion. Instead, we feld. Furthermore, rotating the process depicted recommend starting with an introduction to the in fgure 7 by 180° leads to an important produc- individual terms of the Lagrangian by focusing on tion mechanism of Higgs bosons in the LHC: their general interpretation (see fgure 10). Based the so-called ‘vector-boson fusion’ in which, for on this frst glimpse into the world of quantum example, a W+ boson and a W− boson transform feld theory, the associated Feynman diagrams into a Higgs boson (see fgure 8). can be discussed, which allow students to gain insight into the precise prediction power of the Standard Model of particle physics. This can even 3.8. Term 7: V − ()φ be done in a playful way: by taking conserva- This term describes the potential of the BEH feld. tion of charge (electric, weak, and colour) into Contrary to the other quantum felds, this poten- account, fundamental vertices can be attached to tial does not have a single minimum at zero but each other like dominoes. This enables students has an infnite set of different minima. This makes to determine which processes and interactions the Brout–Englert–Higgs feld fundamentally between elementary particles are possible. For
May 2017 7 Phys. Educ. 52 (2017) 034001 J Woithe et al
interaction particles hot coffee (can be omitted)
1 − F Fµν = 4 µν interactions between matter particles
iψDψ h.c. + + mass for antimatter particles
+ ψiyijψjφ + h.c.
mass for matter particles 2 + Dµφ −V(φ)
mass for interaction particles Higgs self-interactions
Figure 10. Short version of the Lagrangian. The terms coloured in red are governed by the electromagnetic, weak, and strong interactions, while those that are coloured blue are governed by interactions with the Brout– Englert–Higgs feld. Most everyday phenomena, such as light, electricity, radioactivity, and sound, are described by the second term, ‘interactions between matter particles’. instance: ‘Start with a muon. Is it possible for the muon to transform in such a way that at the end of this process, among other particles, an electron exists?’ When discussing Feynman diagrams in the classroom, however, it is important to point out that these diagrams are only visualisations of the Standard Model of particle physics. The interpre- tation of Feynman diagrams is strictly limited to fundamental processes and care should be taken to avoid any notion of misleading interpretation of Feynman diagrams as 2D motion diagrams. Once Feynman diagrams are established, an addi- tional step can be the introduction of Feynman Figure 11. Standard Model of particle physics and rules  and the coupling parameters of the Einstein’s theory of general relativity. respective interaction particles. Together with conservation of energy and momentum, one can Although the Standard Model of particle then make full use of Feynman diagrams, which physics is an extremely successful theory, it is even allow determinations of the probabilities of far from being a complete description of the uni- transformation processes. For instance, this tech- verse: according to today’s models, the universe nique is used to calculate the production rates consists only of 5% visible matter, which can be of Higgs bosons at the Large Hadron Collider, described by the Standard Model of particle phys- which are then compared with measurements ics. This means future generations of physicists from CMS and ATLAS. As mentioned above, any will still have plenty of new physics to discover! deviation between the two would open the door Currently, the hunt is on for theories which go to new physics and even more exciting times in beyond the Standard Model of particle physics to particle physics. incorporate dark matter and dark energy.
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Another shortcoming of the Standard Model  ATLAS Collaboration 2015 Evidence for the of particle physics is the absence of a description Higgs–Boson Yukawa coupling to tau leptons of gravity. The search for a unifcation of all four with the ATLAS detector J. High Energy Phys. JHEP04(2015)117 fundamental interactions through a single the-  Tanedo F 2010 Feynman diagrams and rules ory—the so-called Theory of Everything—can (quantum diaries) (http://quantumdiaries. be seen as the quest for the Holy Grail of our org/2010/02/14/lets-draw-feynman-diagams) times. It is probably a safe bet to say that this Julia Woithe is a high school teacher ambition will keep supersymmetry researchers for physics and mathematics. She is and string-theorists busy for quite some time. In currently working on her PhD project the meantime, there are two coffee mugs in the in physics education research at CERN, Geneva, Switzerland in cooperation with offces at CERN: one for the Standard Model of the University of Kaiserslautern and particle physics and one for Einstein’s theory of the University of Geneva. Her project general relativity (see fgure 11). We hope that is S’Cool LAB, a hands-on particle with the help of further hot coffees we will soon physics learning laboratory at CERN. She is interested in hands-on/minds-on need only one mug... learning activities in particle physics, students’ conceptions, and 3D-printing. Received 14 December 2016, in fnal form 9 January 2017 Gerfried Jeff Wiener worked as Accepted for publication 20 January 2017 a high school teacher for physics, https://doi.org/10.1088/1361-6552/aa5b25 philosophy, and psychology in Vienna, Austria. He is currently pursuing his PhD in physics education research in cooperation with the University of Vienna through the Austrian Doctorate References Programme at CERN, Geneva,  Cottingham W N and Greenwood D A 2007 Switzerland. His research goals Standard Model Lagrangian An Introduction are focused on how to adequately to the Standard Model of Particle Physics integrate particle physics into modern (Cambridge: Cambridge university curricula. Aside from his doctoral Press) (https://doi.org/10.1017/ work he is now managing CERN’s national and international CBO9780511791406) teacher training programmes.  Next Generation Science Standards (NGSS) 2013 HS-PS1-8 matter and its interactions (http:// Frederik Van der Veken is a theoretical physicist working at CERN. He has a nextgenscience.org/) PhD in mathematical aspects of QCD,  International Baccalaureate Organization (IBO) which he conducted at the University 2007 Diploma programme. Physics—guide of Antwerp, Belgium. He is currently a (http://ibo.org) fellow in the beams department at CERN,  Department for Education 2014 National participating in the design of the High curriculum in England. Science programmes Luminosity upgrade of the Large Hadron of study: key stage 4 (https://gov.uk/ Collider. He likes to approach science, government/publications/national- nature, and the universe from a theoretical curriculum-in-england-science-programmes- viewpoint, trying to understand what of-study) makes the world go round.
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