The Discovery of the Higgs Boson

Jake Xuereb

May 22, 2021

Abstract 1 In the majority of this document, I will describe the theoretical discovery of the Higgs boson emphasising the notions of spontaneous symmetry breaking and Goldstone’s Theorem. As a result, we will see how the 1964 PRL Papers [2, 3, 4] discovered the Higgs boson and solved the mass acquisition problem. After this, I will brieﬂy describe how this particle was discovered experimentally by CMS [5] and ATLAS [6] at the LHC, CERN via the statistically inferred obser- vance of a number of its decay processes. 1Cover Image due to Lucas Layton (CMS) showing a simulation of a Higgs boson detection event at the CMS [1].

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Abbreviations

ATLAS A Toroidal LHC ApparatuS

CERN Conseil Europeen´ pour la Recherche Nucleaire´

CMS Compact Muon Solenoid

LHC Large Hadron Collider

QED Quantum Electrodynamics

Contents

1 The Theoretical Discovery of the Higgs Boson 3 1.1 The need for the Higgs Mechanism ...... 3 1.2 Spontaneous Symmetry Breaking and Goldstone’s Theorem ...... 4 1.3 The Higgs Mechanism - Two Massless theories give One Massive theory ...... 7

2 The Experimental Discovery of the Higgs Boson 10 2.1 The Decay Processes of the Higgs Boson ...... 10 2.2 Detecting the Higgs boson using the CMS & ATLAS Detectors ...... 11

A Schematics of Particle Detectors 14

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1 The Theoretical Discovery of the Higgs Boson

1.1 The need for the Higgs Mechanism Following the success of quantum electrodynamics (QED) [7], theoretical physicists began to look to explain the short-range nuclear forces, starting with the weak interaction that models the physics of radioactive decay. Here the problem of establishing a model for how particles acquire mass started to become abundantly clear and central. The key issue as pointed out by Glashow [8] and Schwinger [9] was the mass of the gauge bosons. The photon is the gauge boson that mediates the electromagnetic field and corresponds to the generator of U(1). This boson is evidently massless and created a puzzle for Glashow and Schwinger. In [8], Glashow argues that the weak interaction gauge bosons (corresponding to the generators of SU(2)) need be massive, ostensibly breaking the correspondence with the other gauge boson, the photon which is massless. This incongruence between these two gauge theories was the key stumbling block electroweak theory needed to overcome to become unified later on [10, 11]. Schwinger [9] makes an even more foundational argument by pointing out that the massless nature of the photon cannot be explained dynamically. Beyond this, we also have a mathematical problem. We cannot na¨ıvely add a mass term to the La- grangian modeling our weak interaction to satisfy Glashow’s argument in [8]. The weak interaction and elctromagnetism have gauge bosons given by field strength tensors [12, 13]

a a a abc b c Wµν = ∂µWν − ∂µWµ + ge WµWν Bµν = ∂µBν − ∂νBµ (1) where g is the weak interaction coupling strength and e is the Levi-Civita tensor. The Langrangians of these interactions respect the gauge symmetries, SU(2) and U(1) respectively, meaning that local gauge invariance is observed by their transformations as 1 1 B → B + ∂ λ(x) Wa → Wa + ∂ λ(x) + eabcWbλc(x) (2) µ µ g0 µ µ µ g µ µ where g0 is the coupling strength of the hypercharge interaction and λ(x) is an arbitrary function. 2 2 µ Clearly, adding a mass term m FµF to the Lagrangian would break the gauge invariance observed by these transformations. Meaning that gauge bosons are massless. . . or at least that this mass cannot appear within the gauge sector of their Lagrangian as one would expect. These issues pointed to a fundamental lack of understanding of the elementary nature of mass in our particle physics, or at least in bosonic theories. In fermionic gauge theories, the addition of mass terms does not spoil gauge invariance, possibly pointing to why the need for the Higgs mechanism was not felt during the development of QED. That being said, the mechanism through which fermions acquired mass was unknown3 As such, developing a model for the acquisition of mass was of clear importance and this is the problem which the Higgs mechanism and the Higgs ﬁeld solves. Before this we must understand the main driver of the Higgs mechanism, spontaneous symmetry breaking and its main constraint, Goldstone’s Theorem [15].

2F is being used as a placeholder for either ﬁeld strength tensor. 3And is still somewhat contentious [14] despite an explanation as we will see through Yukawa interaction with the Higgs ﬁeld.

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1.2 Spontaneous Symmetry Breaking and Goldstone’s Theorem

(a) Z2 Symmetry Breaking (b) An O(N) Symmetry Breaking potential for N = 2 Figure 1: Symmetry breaking potentials visualised by the author using Mathematica.

Let’s begin with a simple example. Consider the symmetric double potential well in Fig. 1(a). Placing a classical particle in such a double well we evidently have Z2 symmetry for V(x) = V(−x) but at the ground state energy of this system we run into an issue. We must make a choice to discern the position of the particle and so the symmetry is broken by the ground state. That is the ground state is degenerate whilst the potential is symmetric. State in the system break the systems own symmetry and in this sense, we call it spontaneous, as symmetry breaking states are always accessible.

The Linear Sigma Model Spontaneous symmetry breaking [12, 16] can occur in ﬁeld theories where Lagrangians are often invariant under continuous global gauge symmetries. Consider the Lagrangian

1 2 1 2 λ 22 L = ∂ φi + µ2 φi − φi (3) 2 µ 2 4 where we have i ∈ {1, . . . , N} real Klein-Gordon scalar ﬁelds φi interacting through some quartic interaction. This is known as the linear sigma model and serves as an effective ﬁeld theory for pions4 This Lagrangian is invariant under the rotations in O(N), known as the orthogonal group, which result in gauge transformations

φi → Rijφj (4)

4Preempting myself a bit, this is because they are pseudo goldstone bosons.

4 PHY3232 - Nuclear Physics Assignement Jake Xuereb which are clearly observed by the whole system, globally. But taking a closer look at the potential

1 2 λ 22 V(φi) = − µ2 φi + φi : λ, µ ∈ R (5) 2 4 we see that the situation becomes a bit more complicated. This potential is minimised by a static ﬁeld conﬁguration

2 µ2 φi = . (6) 0 λ We require that λ > 0 for the system to be physical for the energy to be bounded below. This creates two cases for µ2 < 0 and µ2 > 0. In the ﬁrst case, the potential is a conventional multi-dimensional well with the ground state being the bottom of the well at the origin. For the second case, we see the situation depicted in Fig 1b) for N = 2. Here we have a ground state degeneracy since as we can visualise for N = 2 we have an arbitrary number of minimum energy points along the circle at the bottom of the potential before the dimple. These points break the symmetry of the system whilst together they respect it. Upgrading back to the N dimensional case, we see that the symmetry can be broken in N − 1 directions so examining the Nth direction we have

i µ φ0 = 0 0 . . . v where v = √ (7) λ so the groundstate has a non-zero value, this is called a vacuum expectation value. To appreciate the dynamics of this system in the continuous symmetry breaking case we consider a small energy ﬂuctuation away from a degenerate ground state making use of a coordinate transformation to a shifted ﬁeld.

i k φ0 = π (x) v + σ(x) (8) where k = 1, . . . , N − 1 and π(x) and σ(x) are some arbitrary ﬁelds. Rewriting (3) we have the effective Lagrangian

2 1 2 1 2 1 √ √ 2 λ λ 2 λ 2 L = ∂ πk + ∂ σ − 2µ2 σ2 − λµσ3 − λµ πk σ − σ4 − πk σ2 − πk . (9) 2 µ 2 µ 2 4 2 4

Sitting with this, we appreciate that we have N − 1 massless fields highlighted in blue, which together observe O(N − 1) symmetry, and one massive field highlighted in purple with the other terms being higher order interactions. This makes sense physically. The massive field corresponds to an excitation in the vertical axis where there is a cost associated manifested by the curvature in the potential. The massless fields represent excitations that require no energy cost because we are creating excitations tangentially along the degenerate ground states available in N − 1 directions. Such massless excitations are an instance of a more general structure known as Goldstone bosons.

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Goldstone’s Theorem If a bosonic ﬁeld is invariant under a continuous global symmetry then for every spontaneously broken symmetry this theory will contain a massless boson.

This was proven by Salam, Weinberg and Goldstone in [17]. Adapting presentations from [12, 16] we can understand this proof as follows. Consider a theory with some interacting ﬁelds φa(x) with a generic Lagrangian L = (derivative terms) − V(φ) (10)

a and let φ0 be the constant ﬁeld leading to the minimum potential such that ∂V a | a a = 0. (11) ∂φ φ (s)=φ0 We can now examine the vacuum ﬂuctuations by taking a taylor series about this minimum giving

1 ∂2V V(φ) = V(φ ) + (φ − φ )a (φ − φ )b + . . . (12) 0 2 0 0 ∂φa∂φb φ0 Analysing this series we see that the coefﬁcient of the second term

∂2V = m2 (13) ∂φa∂φb ab φ0 corresponds to a symmetric matrix whose eigenvalues are the masses of the excitations of this field theory. Thus, we wish to show that gauge transformations under which the Lagrangian is invariant but φ0 is not, lead to zero eigenvalues. To begin with, we can appreciate that generally we cannot have negative eigenvalues since φ0 is a minimum. Moving on, consider a general gauge transformation φa → φa + λ∆a(φ) (14) where λ is an infinitesimal parameter and ∆α is a function of all the contributing fields. Constant fields have no derivative terms in their Lagrangian meaning that only the potential must be invariant under (14). This is manifest in two equivalent conditions. ∂V V(φa) = V(φa + α∆a(φ)) ∆a(φ) = 0. (15) ∂φa

b Letting φ = φ0 and differentiating with respect to φ we have ∂∆a ∂V ∂2V + ∆a (φ ) = 0 (16) ∂φb ∂φa 0 ∂φa∂φb φ0 φ0 φ0

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by the product rule. The ﬁrst term disappears as a result of φ0 being a minimum of V so we have

∂2V ∆a (φ ) = m2 ∆a (φ ) = 0. (17) 0 ∂φa∂φb ab 0 φ0

a In we have gauge invariance this would imply ∆ (φ0) = 0 which is a trivial relation. But in the a a symmetry breaking case we have ∆ (φ0) 6= 0 which implies that ∆ (φ0) must be an eigenvector of the mass tensor with a corresponding zero eigenvalue. So all symmetry breaking ﬂuctuations in the ground state lead to massless excitations!

1.3 The Higgs Mechanism - Two Massless theories give One Massive theory We have now shown that the gauge bosons of the weak interaction are massless so as to respect local gauge invariance and also introduced massless Goldstone bosons which arise when global symmetries are spontaneously broken by ground state degeneracy. Surprisingly, it turns out that if we put these two massless ideas together, mass becomes manifest in the weak interaction gauge bosons and we can explain the massless nature of the photon. This was the key realisation of the 1964 PRL papers [3, 2, 4] and what the Higgs mechanism is about. Let us see the Higgs Mechanism at work leading to mass acquisition in electromagnetism and the weak interaction allowing us to understand it.

An Example - Abealian Gauge Theory with Spontaneous Symmetry Breaking Following presentations in [12, 16] and using the notation of [16] consider a complex scalar ﬁeld coupled to itself and an electromagnetic ﬁeld, represented by the Lagrangian

1 2 2 L = − F + D φ − V(φ) (18) 4 µν µ where the covariant derivative is

Dµ = ∂µ + ieAµ (19)

which is enforcing a local U(1) gauge invariance 1 φ(x) → eiα(x)φ(x) A (x) → A (x) − ∂ α(x) (20) µ µ e µ where α(x) is an arbitrary function imposing inﬁnitesimal change. Now, we choose a potential a quartic scalar potential similar to that which we examined in the linear sigma model λ V(φ) = −µ2φ?φ + (φ?φ)2 . (21) 2 As in section 1.2, we see that for µ2 > 0 in a quartic potential with these parameters we have spontaneous symmetry breaking in the ground state. But this time the global symmetry U(1) is being

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broken as opposed to O(N) as we encountered earlier. This means that we expect one massless goldstone boson to appear according to Goldstone’s Theorem, let’s examine this. The symmetry breaking degenerate ground states will have a vacuum expectation value r µ2 hφi = φ = (22) 0 λ

where φ0 is one of a set of static scalar fields related by U(1) as in (20). Since, the field is a complex scalar field we can decompose it as the complex sum of two real scalar fields 1 φ(x) = φ + √ (φ1(x) + iφ2(x)) . (23) 2

Now as in (12), we take a taylor series about φ0 we examine low-energy vacuum ﬂuctuations −1 1 V(φ) = µ4 + · µ2φ2 + O(φ3) (24) 2λ 2 1 i √ it’s evident that φ1 has acquired a mass of m = 2µ and φ2 is a massless Goldstone boson. Examining the the kinetic energy up to second order, we achieve a fuller understanding of the picture √ 2 1 2 1 2 D φ = ∂ φ + ∂ φ + 2eφ · A ∂µφ + e2φ2 A Aµ + . . . (25) µ 2 µ 1 2 µ 1 0 µ 2 0 µ where we have found that the non-zero vacuum expectation value admitted through the global symmetry breaking has resulted in a photon mass as the last term in (25) 1 2 ∆L = − m2 Ai : m2 = 2e2φ2 (26) 2 A A 0 with correct physical spacelike components and sign in the potential energy, solving Schwinger’s worries in [9]. But how did this happen mechanically? Well, if we investigate the 3rd term in (25) we notice that we have coupling between the gauge boson and the goldstone boson √ √ µ µ µ 2eφ0 · Aµ∂ φ2 =⇒ i 2eφ0 (−ik ) = mAk (27)

leading to the colloquialism that gauge bosons eat goldstone bosons to become massive through the Higgs mechanism. Having seen it in action, we can now summarise the Higgs mechanism as the addition of a scalar field to a gauge theory wherein spontaneous symmetry breaking occurs in the ground state resulting in Goldstone bosons that couple to the gauge bosons allowing them to acquire mass. This scalar field is known as the Higgs field and its excitation, the Higgs boson. It is worth mentioning that outside of a particle physics context, condensed matter physicist Philip Anderson working on superconductivity had discovered the same mechanism for mass acquisition, two years before the 1964 PRL papers in [18]. The human story of the theoretical discovery of the Higgs mechanism is just as rich as the physics behind it.

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Mass Acquisition in Electroweak Unification To answer the question that this document initiates at its outset and find the masses of the weak interaction bosons we would add a scalar field to the weak interaction Lagrangian which is invariant under SU(2). This a non-Abelian quantum field theory so the Higgs mechanism calculations, whilst they follow the same path as presented above, are a bit more involving and out of scope for this document5 What we can do is summarise them. As in (25) we examine the covariant derivative which for the electroweak theory with a couple Higgs scalar field is given by [12] as 1 D φ = ∂ − igAa τa − i g0B φ (28) µ µ µ 2 µ a a 1 where Aµ and Bµ are the gauge bosons of the SU(2) and U(1) gauge theories, τ = 2 σa the Pauli matrices and φ is the coupled scalar field. Since the gauge bosons are commutative we also have two coupling constants, g and g0. Representing the vacuum expectation as 1 0 hφi = √ = (29) 2 v we evaluate the covariant derivative for the ground state giving T 1 0 1 1 0 ∆L = gAa τa + g0B gAbµτb + g0Bµ . (30) 2 1 µ 2 µ 2 1 Evaluating this explicitly using the Pauli matrices the masses of the electroweak gauge bosons are given as

± 1 1 2 v Wµ = √ Aµ ∓ iAµ mW = g (31) 2 2 q 0 1 3 0 v 2 02 Zµ = p gAµ − g Bµ mZ = g + g (32) g2 + g02 2

1 3 0 Aµ = p gAµ + g Bµ mA = 0. (33) g2 + g02 This evidences the power of the Higgs Mechanism and how it solves the problem presented at the start of this document. It is good to remark the the photon is massless because showing a reductive view of the Lagrangian evaluated for the vacuum expectation i 1 0 0 1 0 −i 1 0 β + α1 + α2 + α3 hφi (34) 2 0 1 1 0 i 0 0 −1 where α is the isospin and β is the hypercharge, we see that the combination corresponding to the photon, β = α3 gives 1 0 0 0 ≡ (35) 0 0 v 0

5A thorough overview can be found in Chapter 20 of [12].

9 PHY3232 - Nuclear Physics Assignement Jake Xuereb resulting in the massless photon of this theory. The inclusion of the Higgs Mechanism to an SU(2) = SU(2) × U(1) gauge theory is what led to the celebrated electroweak uniﬁcation theory of Salam, Glashow and Weinberg [11, 19] for which they were awarded a Nobel prize in 1979. This uniﬁcation theory is based on the work summarised above.

Mass Aquisition in Fermions Fermions do not acquire mass via the Higgs Mechanism but rather acquire mass through a Yukawa interaction [12] with the Higgs scalar field [19] that was causing spontaneous symmetry breaking in the bosonic gauge theories. This gave more of a precedent to think that the Higgs field was mediated by an observable particle. I will briefly characterise this particle and its experiemental discovery in Section 2. As mentioned earlier in passing, mass acquisition in fermions is not a closed case and arguments have been made for mass acquisition in certain fermionic sectors which would not explicitly involve coupling with the Higgs field [14].

2 The Experimental Discovery of the Higgs Boson

The Higgs boson was experimentally detected at two independent experiments at CERN, ATLAS and CMS. This was achieved through the observation of vastly large numbers of scattering events where the distribution of particles observed can be correlated to the decay or scattering of particles of interest. In this short section, I will brieﬂy introduce the Higgs boson and outline the decay and scattering processes it contributes to which were observed in [5, 6] commenting on how these observations were possible.

2.1 The Decay Processes of the Higgs Boson Recalling the Lagrangian for a scalar ﬁeld wherein spontaneous symmetry breaking occurs we see that an explicit renormalizable Lagrangian that provides a vacuum expectation value is given [12]

2 2 2 † † L = |Dµφ| + µ φ φ − λ φ φ (36) where the minimum of the potential energy occurs at r µ2 v = . (37) λ In the unitarity gauge we have

1 1 λ 1 L = −µ2h2 − λvh3 − λh4 = − m2h2 − m h3 − λh4 (38) V 4 2 h 2 h 4 where the quantum of the ﬁeld h(x) is a scalar particle which is called the Higgs boson with mass mh.

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From the kinetic energy terms of this Lagrangian and by examining the Yukawa interaction with fermions we arrive at the following interactions for gauge bosonsf and fermions [12]

2 1 2 2 µ+ − 1 2 µ h ¯ h L f = ∂µh + mWW Wµ + mZZ Zµ · 1 + L f = −m f f f 1 + (39) 2 2 v h v h which give the following Feynman diagrams.

Figure 2: Feynman diagrams for the Higgs boson decay processes [13]. f¯ (a) h → f f (b) h → W+W− + f Wµ

h h h h

f¯ Wν−

hh h h

Wν−

2.2 Detecting the Higgs boson using the CMS & ATLAS Detectors Since I’ve focused mainly on the theoretical discovery of the Higgs boson I must be quite brief in talking about the experimentalh detectionh to abide by the scope of the document, so I will not distin- guish between the CMS and ATLAS.Instead I will review the process to detecting the Higgs boson in general. Schematics of these particle detectors are given in Appendix A. At the LHC, we begin by producing hadrons by colliding very many protons together at very high energies using an electromagnetic ring. In particular, such collisions can produce the Higgs boson in the following ways [13, 5, 6]. After the particle is produced it will decay in one of the ways presented in the Feynman diagrams of Figure 2 with different associated probabilities. Of course 5 the Higgs boson is not the only particle produced from the collision of two protons4 so a gargantuan number of different decay processes occur within each experiment. The existence of the Higgs must

h 11

4 5

5 g

g q j

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Figure 3: Feynman diagrams for the production of the Higgs boson at LHC [13]. g g (a) Gluon fusion, 1st order (b) Gluon fusion, 2nd order term. term (c) Weak boson fusion. g q j q j

W, Z

h h h

W, Z

g g q j

q j q j q¯ W, Z then be inferred from the distribution of the decay products such that if the Higgs were produced it ought to be reﬂected in that this distribution. This is whatW, Z was achieved at CMS and ATLAS allowing humanity to verify that our model for mass acquisition reﬂects the nature of nature and that we had discovered a new particle. h h W, Z References g q j q h [1] Lucas Taylor. “CMS: Simulated Higgs to two jets and two electrons”. Oct. 1997. URL: https: //cds.cern.ch/record/628469. q j q¯ W, Z 7 [2] Peter W. Higgs. “Broken Symmetries and the Masses of Gauge Bosons”. In: Phys. Rev. Lett. 13 (16 Oct. 1964), pp. 508–509.W, Z DOI: 10.1103/PhysRevLett.13.508. URL: https://link.aps.org/ doi/10.1103/PhysRevLett.13.508. h [3] F. Englert and R. Brout. “Broken Symmetry and the Mass of Gauge Vector Mesons”. In: Phys. Rev. Lett. 13 (9 Aug.W, 1964), Z pp. 321–323. DOI: 10 . 1103 / PhysRevLett . 13 . 321. URL: https : //link.aps.org/doi/10.1103/PhysRevLett.13.321. q j q [4] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble. “Globalh Conservation Laws and Massless Particles”. In: Phys. Rev. Lett. 13 (20 Nov. 1964), pp. 585–587. DOI: 10.1103/PhysRevLett.13. 585. URL: https://link.aps.org/doi/10.1103/PhysRevLett.13.585. q¯ W, Z 7 [5] S. Chatrchyan et al. “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC”. In: Physics Letters B 716.1 (Sept. 2012), pp. 30–61. ISSN: 0370-2693. DOI: 10.1016/j.physletb.2012.08.021. URL: http://dx.doi.org/10.1016/j.physletb.2012. 08.021. [6] G. Aad et al. “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC”. In: Physics Letters B 716.1 (Sept. 2012), pp. 1–29. ISSN: q 0370-2693. DOI: 10.1016/j.physletb.2012.08.020h . URL: http://dx.doi.org/10.1016/j. physletb.2012.08.020.

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[7] F. J. Dyson. “The Radiation Theories of Tomonaga, Schwinger, and Feynman”. In: Phys. Rev. 75 (3 Feb. 1949), pp. 486–502. DOI: 10.1103/PhysRev.75.486. URL: https://link.aps.org/doi/ 10.1103/PhysRev.75.486. [8] S. L. Glashow. “Partial Symmetries of Weak Interactions”. In: Nucl. Phys. 22 (1961), pp. 579– 588. DOI: 10.1016/0029-5582(61)90469-2. [9] Julian S. Schwinger. “Gauge Invariance and Mass”. In: Phys. Rev. 125 (1962). Ed. by J. C. Taylor, pp. 397–398. DOI: 10.1103/PhysRev.125.397. [10] Sheldon L. Glashow. “The renormalizability of vector meson interactions”. In: Nucl. Phys. 10 (1959), pp. 107–117. DOI: 10.1016/0029-5582(59)90196-8. [11] Abdus Salam and John Clive Ward. “Weak and electromagnetic interactions”. In: Nuovo Cim. 11 (1959), pp. 568–577. DOI: 10.1007/BF02726525. [12] Michael E. Peskin and Daniel V. Schroeder. An Introduction to quantum field theory. Reading, USA: Addison-Wesley, 1995. ISBN: 978-0-201-50397-5. [13] Heather E. Logan. TASI 2013 lectures on Higgs physics within and beyond the Standard Model. 2017. arXiv: 1406.1786 [hep-ph]. [14] “Is the Higgs mechanism of fermion mass generation a fact? A Yukawa-less first-two-generation model”. In: Physics Letters B 755 (2016), pp. 504–508. ISSN: 0370-2693. DOI: https://doi.org/ 10.1016/j.physletb.2016.02.059. [15] J Goldstone. “Field theories with ”superconductor” solutions”. In: Nuovo Cimento 19 (Aug. 1960), pp. 154–164. DOI: 10.1007/BF02812722. URL: https://cds.cern.ch/record/343400. [16] A. Zee. Quantum field theory in a nutshell. 2003. ISBN: 978-0-691-14034-6. [17] Jeffrey Goldstone, Abdus Salam, and Steven Weinberg. “Broken Symmetries”. In: Phys. Rev. 127 (3 Aug. 1962), pp. 965–970. DOI: 10.1103/PhysRev.127.965. URL: https://link.aps.org/ doi/10.1103/PhysRev.127.965. [18] P. W. Anderson. “Plasmons, Gauge Invariance, and Mass”. In: Phys. Rev. 130 (1 Apr. 1963), pp. 439–442. DOI: 10.1103/PhysRev.130.439. URL: https://link.aps.org/doi/10.1103/ PhysRev.130.439. [19] Steven Weinberg. “A Model of Leptons”. In: Phys. Rev. Lett. 19 (21 Nov. 1967), pp. 1264– 1266. DOI: 10.1103/PhysRevLett.19.1264. URL: https://link.aps.org/doi/10.1103/ PhysRevLett.19.1264. [20] Tai Sakuma. “Cutaway diagrams of CMS detector”. In: (May 2019). URL: https://cds.cern. ch/record/2665537. [21] “The ATLAS Data Acquisition and High Level Trigger system”. In: Journal of Instrumentation 11.06 (June 2016), P06008–P06008. DOI: 10 . 1088 / 1748 - 0221 / 11 / 06 / p06008. URL: https : //doi.org/10.1088/1748-0221/11/06/p06008.

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A Schematics of Particle Detectors

Figure 4: Cutaway diagram of the CMS particle detector from [20].

Figure 5: Cutaway diagram of the ATLAS particle detector from [21].