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Mathis Dubau · Scheme bank

Schemes

The 99 schemes I drew in TikZ for my thesis, to download as PDF or SVG. Reuse them freely, citing the thesis.

Click a scheme to open it full size; under each one, PDF and SVG download it. To reuse a scheme, cite the thesis with the figure number shown under it (one click on the box selects all of it for copying):

@phdthesis{Dubau:thesis,
  author = "M. Dubau",
  title  = "{Multivariate study of polarisation states in electroweak vector boson scattering WZ events using ATLAS data at the LHC}",
  school = "Universit\'{e} Savoie Mont Blanc",
  year   = "2026",
  doi    = "10.17181/cw32k-7w243",
  url    = "https://repository.cern/records/cw32k-7w243",
  type   = "PhD thesis"
}

The Standard Model

The Standard Model in Lego bricks: quarks, leptons and bosons, coloured by the interactions they take part in. — The Standard Model in Lego bricks: quarks, leptons and bosons, coloured by the interactions they take part in. Thesis Fig. 1.5

The 18 bricks, one by one

Legend — Legend
PDF · SVG

W boson — W boson
PDF · SVG

Z boson — Z boson
PDF · SVG

Photon — Photon
PDF · SVG

Gluon — Gluon
PDF · SVG

Higgs boson — Higgs boson
PDF · SVG

Electron neutrino — Electron neutrino
PDF · SVG

Muon neutrino — Muon neutrino
PDF · SVG

Tau neutrino — Tau neutrino
PDF · SVG

Electron — Electron
PDF · SVG

Muon — Muon
PDF · SVG

Tau — Tau
PDF · SVG

Down quark — Down quark
PDF · SVG

Strange quark — Strange quark
PDF · SVG

Bottom quark — Bottom quark
PDF · SVG

Up quark — Up quark
PDF · SVG

Charm quark — Charm quark
PDF · SVG

Top quark — Top quark
PDF · SVG

The Higgs potential: the field rolls from the unstable top to the circle of minima and breaks the symmetry. — The Higgs potential: the field rolls from the unstable top to the circle of minima and breaks the symmetry. Thesis Fig. 1.2

The three helicity states of a vector boson: spin -1, 0 and +1 along its direction of motion. — The three helicity states of a vector boson: spin $-1$ , $0$ and $+1$ along its direction of motion. Thesis Fig. 1.6

Feynman diagrams

Vertices and scalar scattering

The QED vertex: a photon couples to a fermion–antifermion pair with strength -iQe. — The QED vertex: a photon couples to a fermion–antifermion pair with strength $-iQe$ . Thesis Fig. 1.1

5 more schemes

The electroweak vertex: a W or Z boson couples to a pair of fermions. — The electroweak vertex: a W or Z boson couples to a pair of fermions. Thesis Fig. C.1

Quartic scalar interaction, the contact term of scalar scattering. — Quartic scalar interaction, the contact term of scalar scattering. Thesis Fig. A.1(a)

Scalar scattering through an s-channel Higgs exchange. — Scalar scattering through an s-channel Higgs exchange. Thesis Fig. A.1(b)

Scalar scattering through a t-channel Higgs exchange. — Scalar scattering through a t-channel Higgs exchange. Thesis Fig. A.1(c)

Scalar scattering through a u-channel Higgs exchange. — Scalar scattering through a u-channel Higgs exchange. Thesis Fig. A.1(d)

Vector boson scattering

Vector boson scattering: two quarks radiate a W and a Z that scatter, leaving two forward jets. — Vector boson scattering: two quarks radiate a W and a Z that scatter, leaving two forward jets. Thesis Fig. 6.4

2 more schemes

Electroweak ZZjj production through vector boson scattering. — Electroweak ZZjj production through vector boson scattering. Thesis Fig. 6.17(h)

Corrections to WZjj: NLO QCD and NLO electroweak emissions, virtual and real. — Corrections to WZjj: NLO QCD and NLO electroweak emissions, virtual and real. Thesis Fig. 6.16

Backgrounds

Show the 10 schemes

QCD-induced WZjj production, the main irreducible background. — QCD-induced WZjj production, the main irreducible background. Thesis Fig. 6.5(a)

Another QCD-induced WZjj diagram. — Another QCD-induced WZjj diagram. Thesis Fig. 6.5(b)

QCD-induced ZZjj production. — QCD-induced ZZjj production. Thesis Fig. 6.17(i)

Triboson production, a background with three leptons. — Triboson production, a background with three leptons. Thesis Fig. 6.17(e)

Z + jets, a background when a jet fakes the third lepton. — Z + jets, a background when a jet fakes the third lepton. Thesis Fig. 6.17(f)

Zgamma production, a background when the photon converts. — $\mathrm{Z}\gamma$ production, a background when the photon converts. Thesis Fig. 6.17(g)

tZj production, a background with three leptons and jets. — tZj production, a background with three leptons and jets. Thesis Fig. 6.17(d)

tbartW production. — $\mathrm{t\bar{t}W}$ production. Thesis Fig. 6.17(b)

tbartZ production. — $\mathrm{t\bar{t}Z}$ production. Thesis Fig. 6.17(c)

tbart production, a background with a non-prompt lepton. — $\mathrm{t\bar{t}}$ production, a background with a non-prompt lepton. Thesis Fig. 6.17(a)

Beyond the Standard Model

Show the 1 schemes

The one-loop diagram that gives neutrinos a Majorana mass in the scotogenic model. — The one-loop diagram that gives neutrinos a Majorana mass in the scotogenic model. Thesis Fig. Z.1

Vector boson scattering and the WZ analysis

History

Show the 2 schemes

Diboson and triboson measurements at LEP, the Tevatron and the LHC over time.

Vector boson scattering measurements over time, from searches to observations.

Events and selection

A WZjj vector boson scattering event in ATLAS. — A WZjj vector boson scattering event in ATLAS. Thesis Fig. 6.15

Discriminant plane

Output of the signal-versus-background network: background near 0, WZjj-EW near 1. — Output of the signal-versus-background network: background near 0, WZjj-EW near 1. Thesis Fig. 6.19(a)

The discriminant plane: background bottom left, the targeted polarisation state top right. — The discriminant plane: background bottom left, the targeted polarisation state top right. Thesis Fig. 6.23

3 more schemes

Output of a polarisation network for the targeted state and the others. — Output of a polarisation network for the targeted state and the others. Thesis Fig. 6.19(b)

Binning the discriminant plane: 1, 2times2 or 3times3 bins. — Binning the discriminant plane: $1$ , $2\times2$ or $3\times3$ bins. Thesis Fig. G.1(a)

The four polarisation states of the WZ pair, longitudinal (0) or transverse (T). — The four polarisation states of the WZ pair, longitudinal (0) or transverse (T). Thesis Fig. G.1(b)

Statistics

From a p-value to a significance Z: the tail of a unit Gaussian. — From a $p$ -value to a significance $Z$ : the tail of a unit Gaussian. Thesis Fig. O.1

A profile-likelihood scan and the intervals read where

-2\Delta\ln L

crosses

1

and

2.71

. Thesis Fig. O.2

Machine learning

Neural networks

An artificial neuron: weighted inputs, a sum and an activation. — An artificial neuron: weighted inputs, a sum and an activation. Thesis Fig. 4.1

A fully connected neural network with two hidden layers. — A fully connected neural network with two hidden layers. Thesis Fig. 4.2

Under- and overfitting: training and validation loss against the epochs. — Under- and overfitting: training and validation loss against the epochs. Thesis Fig. 4.5

A ROC curve: background rejection against signal efficiency. — A ROC curve: background rejection against signal efficiency. Thesis Fig. 4.8

5 more schemes

Training a network: forward pass, loss against the truth, back-propagation.

The ReLU activation. — The ReLU activation. Thesis Fig. 4.4(a)

The sigmoid activation. — The sigmoid activation. Thesis Fig. 4.4(b)

The softmax activation. — The softmax activation. Thesis Fig. 4.4(c)

The softplus activation. — The softplus activation. Thesis Fig. 5.13

Decision trees

Show the 3 schemes

A decision tree and the cuts it makes. — A decision tree and the cuts it makes. Thesis Fig. 4.9(a)

The regions a decision tree cuts the plane into. — The regions a decision tree cuts the plane into. Thesis Fig. 4.9(b)

Boosting: each weak tree learns from the residuals of the previous ones. — Boosting: each weak tree learns from the residuals of the previous ones. Thesis Fig. 4.10

Active learning

The active-learning loop: a network chooses which points the expensive oracle computes. — The active-learning loop: a network chooses which points the expensive oracle computes. Thesis Fig. Z.2

Simulation

A simulated proton–proton collision: hard scattering, parton showers, underlying event and hadronisation. — A simulated proton–proton collision: hard scattering, parton showers, underlying event and hadronisation. Thesis Fig. 4.13

CERN and the LHC

Accelerators

The CERN accelerator complex, from LINAC 4 to the LHC. — The CERN accelerator complex, from LINAC 4 to the LHC. Thesis Fig. 2.3

The injection chain: the magnet cycles of the PS Booster, PS and SPS that fill the LHC. — The injection chain: the magnet cycles of the PS Booster, PS and SPS that fill the LHC. Thesis Fig. 2.4(a)

The LHC ring and its eight sectors, with the four large experiments. — The LHC ring and its eight sectors, with the four large experiments. Thesis Fig. 2.5

An LHC fill: injection, ramp, squeeze, stable beams and dump. — An LHC fill: injection, ramp, squeeze, stable beams and dump. Thesis Fig. 2.4(b)

The LHC timeline, from Run 1 to the High-Luminosity LHC. — The LHC timeline, from Run 1 to the High-Luminosity LHC. Thesis Fig. 2.6

Coordinates

The LHC ring and the ATLAS axes. — The LHC ring and the ATLAS axes. Thesis Fig. 3.2(a)

The ATLAS coordinate system and the pseudorapidity eta. — The ATLAS coordinate system and the pseudorapidity $\eta$ . Thesis Fig. 3.2(b)

The ATLAS detector

Whole detector

Electromagnetic showers of electrons and photons in the ATLAS calorimeter. — Electromagnetic showers of electrons and photons in the ATLAS calorimeter. Thesis Fig. 5.1

Hadronic showers in the ATLAS calorimeters. — Hadronic showers in the ATLAS calorimeters. Thesis Fig. 6.7(a)

A muon crossing the whole of ATLAS. — A muon crossing the whole of ATLAS. Thesis Fig. 6.7(b)

Inner detector

Quarter view of the ATLAS Inner Detector: pixels, strips and straw tubes. — Quarter view of the ATLAS Inner Detector: pixels, strips and straw tubes. Thesis Fig. 3.3(b)

Quarter view of the ITk and HGTD, which reach |eta| = 4 at the HL-LHC. — Quarter view of the ITk and HGTD, which reach $|\eta| = 4$ at the HL-LHC. Thesis Fig. 3.16(b)

6 more schemes

A pixel sensor and its bump-bonded readout. — A pixel sensor and its bump-bonded readout. Thesis Fig. 3.4(a)

An IBL pixel sensor. — An IBL pixel sensor. Thesis Fig. 3.4(b)

An SCT strip sensor. — An SCT strip sensor. Thesis Fig. 3.4(c)

A TRT straw: ionisation and transition radiation in a gas-filled tube. — A TRT straw: ionisation and transition radiation in a gas-filled tube. Thesis Fig. 3.5

An ITk strip sensor. — An ITk strip sensor. Thesis Fig. 3.17(a)

An HGTD low-gain avalanche sensor, which times each track. — An HGTD low-gain avalanche sensor, which times each track. Thesis Fig. 3.17(b)

Calorimeters

Quarter view of the ATLAS calorimeters. — Quarter view of the ATLAS calorimeters. Thesis Fig. 3.6(b)

The accordion geometry of the ATLAS liquid-argon electromagnetic calorimeter. — The accordion geometry of the ATLAS liquid-argon electromagnetic calorimeter. Thesis Fig. 3.7(a)

4 more schemes

Sampling in liquid argon: lead absorbers, argon gaps and readout electrodes. — Sampling in liquid argon: lead absorbers, argon gaps and readout electrodes. Thesis Fig. 3.8(a)

Sampling in the Tile calorimeter: steel and scintillator, read through wavelength-shifting fibres. — Sampling in the Tile calorimeter: steel and scintillator, read through wavelength-shifting fibres. Thesis Fig. 3.8(b)

A Tile calorimeter module. — A Tile calorimeter module. Thesis Fig. 3.7(b)

A forward calorimeter electrode: a rod in a tube, with a thin liquid-argon gap. — A forward calorimeter electrode: a rod in a tube, with a thin liquid-argon gap. Thesis Fig. 3.9

Muon spectrometer

Quarter view of the ATLAS muon spectrometer. — Quarter view of the ATLAS muon spectrometer. Thesis Fig. 3.10(b)

5 more schemes

A monitored drift tube: the muon ionises the gas and the electrons drift to the anode wire. — A monitored drift tube: the muon ionises the gas and the electrons drift to the anode wire. Thesis Fig. 3.11(a)

A cathode strip chamber. — A cathode strip chamber. Thesis Fig. 3.11(b)

A resistive plate chamber. — A resistive plate chamber. Thesis Fig. 3.12(a)

A thin gap chamber. — A thin gap chamber. Thesis Fig. 3.12(b)

A Micromegas chamber of the New Small Wheel. — A Micromegas chamber of the New Small Wheel. Thesis Fig. 3.11(c)

Trigger and luminosity

Show the 2 schemes

The ATLAS trigger and data acquisition chain. — The ATLAS trigger and data acquisition chain. Thesis Fig. 3.14

LUCID, the luminosity monitor: Cherenkov light in quartz read by photomultipliers. — LUCID, the luminosity monitor: Cherenkov light in quartz read by photomultipliers. Thesis Fig. 3.15

Reconstruction

Tracks

The perigee parameters of a track. — The perigee parameters of a track. Thesis Fig. 5.3

1 more scheme

Track reconstruction in the inner detector. — Track reconstruction in the inner detector. Thesis Fig. 5.4

Electrons and photons

Electron and photon reconstruction in ATLAS, step by step. — Electron and photon reconstruction in ATLAS, step by step. Thesis Fig. 5.2

8 more schemes

Superclusters: a seed cluster gathers its satellites, for electrons and converted photons. — Superclusters: a seed cluster gathers its satellites, for electrons and converted photons. Thesis Fig. 5.6

Electron or photon? How the ambiguity is resolved. — Electron or photon? How the ambiguity is resolved. Thesis Fig. 5.7

The electron and photon energy calibration chain. — The electron and photon energy calibration chain. Thesis Fig. 5.8

Calorimeter isolation: the energy in a cone around the electron, its core removed. — Calorimeter isolation: the energy in a cone around the electron, its core removed. Thesis Fig. 5.10

The calorimeter and track variables used to identify electrons.

A forward electron shower and its cluster moments. — A forward electron shower and its cluster moments. Thesis Fig. 5.11

Decorrelation: a variable replaced by its residual from a linear fit in p_T. — Decorrelation: a variable replaced by its residual from a linear fit in $p_{\text{T}}$ . Thesis Fig. 5.16

The forward-electron calibration and identification workflow. — The forward-electron calibration and identification workflow. Thesis Fig. 5.18

Jets, muons, taus and missing momentum

k_t and anti-k_t jet clustering: anti-k_t grows round jets around the hard particles. — $k_t$ and anti- $k_t$ jet clustering: anti- $k_t$ grows round jets around the hard particles. Thesis Fig. 6.9(a)

The ATLAS jet energy calibration chain. — The ATLAS jet energy calibration chain. Thesis Fig. 6.10

Missing transverse momentum: minus the vector sum of every reconstructed object. — Missing transverse momentum: minus the vector sum of every reconstructed object. Thesis Fig. 6.12

6 more schemes

The k_t clustering algorithm, step by step. — The $k_t$ clustering algorithm, step by step. Thesis Fig. 6.9(b)

A b-jet: the b hadron flies before decaying at a secondary vertex. — A b-jet: the b hadron flies before decaying at a secondary vertex. Thesis Fig. 6.11(a)

A tau lepton decaying to a lepton at a displaced vertex. — A $\tau$ lepton decaying to a lepton at a displaced vertex. Thesis Fig. 6.11(b)

Prompt and non-prompt leptons: a lepton from a secondary vertex is displaced from the primary one. — Prompt and non-prompt leptons: a lepton from a secondary vertex is displaced from the primary one. Thesis Fig. 5.5

Muon momentum corrections: the simulation is matched to the data on the Z peak. — Muon momentum corrections: the simulation is matched to the data on the Z peak. Thesis Fig. 6.6

Particle flow: tracks are matched to calorimeter clusters and their expected energy is subtracted. — Particle flow: tracks are matched to calorimeter clusters and their expected energy is subtracted. Thesis Fig. 6.8

Drawn with the thesis, not printed in it

Show the 9 schemes

What the signal region is made of: the WZjj signal and each background.

The information budget: what the inputs x tell about the label y, I(x;y), and what is left, H(y|x). — The information budget: what the inputs $x$ tell about the label $y$ , $I(x;y)$ , and what is left, $H(y|x)$ .

A cross-entropy gives a lower bound on the mutual information: I(x;y) geq H(y) - CE(q). — A cross-entropy gives a lower bound on the mutual information: $I(x;y) \geq H(y) - \mathrm{CE}(q)$ .

The toy model used to check the information measurements against the analytic truth.

Ionisation: a charged particle passing by knocks an electron out of the atom.

Bremsstrahlung: an electron deflected by the nucleus radiates a photon.

Photoelectric effect: a photon is absorbed and ejects a bound electron.

Compton scattering: a photon scatters off an atomic electron and loses energy.

Pair creation: near a nucleus, a photon turns into an electron–positron pair.