Brontekst bekijken van Electroweak and Strong Interactions

==Samenvattingen==
[[Elektrozwakke en sterke interacties/Samenvattingen| Klik hier om de samenvattingen te bekijken]]

==Algemene informatie==
Dit is eigenlijk een vak van de VUB, maar dat wel vaak gevolgd wordt door Leuvense studenten. Dit is een vervolg op kwantumveldentheorie; ook gegeven door prof. Sevrin, en ook in dezelfde stijl. Dit jaar stonden er 5 punten op een taak die je moest maken tegen ergens in de blok, over een bepaald onderwerp dat we gezien hadden in de les (of niet), en dat uitspitten en wat in detail bespreken (5-10 blz).

==Informatie over het examen==
Het exaam bestond uit 2 vragen. Het "uiterst maximum" was 4,5 uur om ze op te lossen, maar uiteindelijk liep het mondeling e.d. uit tot een goeie 5-5,5 uur. Tegen dan zou je wel best iets hebben, anders zul je het wel niet zo goed gekund hebben...

Voor de rest: zie bij kwantumveldentheorie voor meer uitleg; dit vak en exaam is volledig analoog!

==De afgelopen examens==

===28 May 2021===
* Explain hierarchy problem
  - Is it also a problem for the electron mass?
  - …
*Explain why W decays into 2/3 hadrons and only 1/3 leptons?
*What experimental observation let to the introduction of non-diagonal Yukawa couplings?
*Explain how LEP calculated there are only 3 generations of neutrinos. 
*Explain running coupling constants
  - What’s the difference for abelian vs non-abelian theory?
  - …


Discuss the figure about decay channels of Higgs Boson:
  - At low Higgs-mass: why is the branching ratio to bb- about 10 times bigger than tau+tau-? 
  - How can a Higgs-particle decay into 2 photons?
  - How is it possible that Higgs decays into WW starting from 80GeV, even though their mass is bigger than that of Higgs?
  - Explain the dip of ZZ at +-160GeV?

And many more little questions I’ve already forgotten…

===27 May 2021===
Credit to Students of UGent
[[Media:Examenvragen-Electroweak-and-strong-interaction.pdf]]
====Question 1====
Consider the figure below:
* Give a qualitative explanation for relative strength of the branching ratio to bb with respect to <math> \tau\tau </math>  for low BEH masses
* Give an explanation with Feynman diagrams of leading order decay of a scalar boson to a gluon-gluon pair and a photon-photon pair.
* Define the concepts of partial decay width, total decay width and branching ratio of a decay process and explain the dip in the ZZ producing process branching ratio
* Discuss the production of a WW and ZZ boson pair from the decay of scalar boson
and explain when these modes are possible and give the respective decay process. Justify why the WW branching ratio is significantly higher than the ZZ branching ratio.

[[Bestand:Decay channels higgs.png]]

====Question 2====
Explain what the Hierarchy problem  is for the Higgs Boson.

====Question 3====
What are the running couplings? And why does one constant increases with increasing energy and the other constant become smaller?

===28 juni 2019===

The exam had similar questions as the exams of the previous years. Professor Sevrin considered this as the easiest exam he made during this examination period, compared to the exams in Gent and Brussels and the other exam in Leuven.

[[Media:EWS-2019-06-28.pdf]]

====Question 1====

Consider a Higgs triplet

<math>\Phi(x) = \left(\begin{matrix} \phi_1(x) \\ \phi_2(x) \\ \phi_3(x) \end{matrix}\right), </math>

where the lagrangian density in the scalar sector is given by

<math> \mathcal{L} = \partial_\mu \Phi^\dagger \partial^\mu \Phi + m^2 \Phi^\dagger \Phi - \lambda (\Phi^\dagger \Phi)^2, </math>

and where <math> \Phi  </math> transforms under the three dimensional representation of <math>SU(2)</math> with the <math>SU(2) \times U(1) </math> gauge transformation given by 

<math> \Phi(x) \to \Phi'(x) = \exp(i g \, t_a \alpha^a(x)) \exp(i g' q_S \beta(x)) \Phi(x). </math>

The matrices <math> t_a </math> obey the usual <math> SU(2) </math> commutation relations and are given by

<math> t_1 = \frac{1}{\sqrt{2}} \left(\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}\right), \qquad t_2 = \frac{i}{\sqrt{2}} \left(\begin{matrix} 0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \end{matrix}\right), \qquad t_3 = \left(\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{matrix}\right). </math>


1) Discuss the groundstate(s) of the system.

2) Take as groundstate for the system

<math> \Phi = \frac{1}{\sqrt{2}} \left(\begin{matrix} 0 \\ 0 \\ v \end{matrix}\right), </math>

with <math> v = \sqrt(m^2/\lambda) </math>. Determine the weak hypercharge <math> q_S </math> such that the photon remains massless.

3) Give the Higgs multiplet in the unitairy gauge. An extra question on the oral part of the exam was to determine the electrical charge of the <math> \phi_1 </math> part of the the Higgs multiplet.

4) Determine the masses of the W and the Z gauge bosons.

5) Can you write down Yukawa couplings in this representation?

====Question 2====

We consider now the theory as it is used in the standard model and as we built it during the lectures. The coupling of the Brout-Englert-Higgs particle <math>\sigma</math> to the leptons and the quarks <math>\psi</math> is given by

<math> \mathcal{L}_{HF} = -\frac{1}{v} m_{\psi} \sigma \bar{\psi}\psi, </math>

and the coupling to the W- and Z-bosons is given by

<math> \mathcal{L}_{HVB} = \frac{vg^2}{2} \sigma W_{\mu}^{\dagger}W^{\mu} + \frac{g^2}{4} \sigma^2 W_{\mu}^{\dagger}W^{\mu} + \frac{vg^2}{4\cos^2\theta_W} \sigma Z_{\mu}Z^{\mu} + \frac{g^2}{8\cos^2\theta_W} \sigma^2 Z_{\mu}Z^{\mu}. </math>

The fermion masses are given by

<math>m_e = 0.51\cdot 10^{-3} \quad m_{\mu}=0.11 \quad m_{\tau}=1.8 \quad m_u = 1-5\cdot 10^{-3} \quad m_d = 3-9\cdot 10^{-3}</math>
<math>m_c=1.15-1.35 \quad m_s= 0.075-0.17 \quad m_t=170 \quad m_b=4.0-4.4</math>

A plot of the braching ratios of the decay of the Higgs particle was given similar to that on the last page of the exam of 2011.

1) Compare the Higgs-fermion coupling strenght to the electromagnetic coupling strength of the fermions. Use <math> g \sin\theta_W = e = g' \cos\theta_W </math>.

2) Consider the <math> b \overline{b} </math> and <math> \tau \tau </math> decay channels and explain.

3) Consider the <math> g g </math> and <math> \gamma \gamma </math> decay channels and explain. It is not necessary to explain the detailed form of the curves but a few Feynman diagrams would be nice.

4) Explain the form of the curves of the decay to WW and ZZ. The masses are approximately <math> m_W = 80 \, GeV/c^2 </math> and <math> m_Z = 90 \, GeV/c^2 </math>. An extra question on the oral part was to explain why the branching ratio of the Higgs decaying to the W boson is bigger than the branching ratio of the decay to the Z-boson, since the later is heavier so one could expect the opposite situation.

===31 May 2019===

Very similar questions as the previous years. An extra question on the oral part was to explain why the branching ratio of the Higgs decaying to the W boson is bigger than the branching ratio of the decay to the Z-boson, since the later is heavier so one could expect the opposite situation.

===8 juni 2015===

Identiek hetzelfde examen als 11 juni 2012.

===11 juni 2012===

[[Media:EWS11juni.pdf]]

===22 juni 2009===
====Vraag 1====
Toepassing van het Higgs mechanisme.

Gegeven zijn twee scalaire velden <math>\Phi_1</math> en <math>\Phi_2</math> die als doubletten onder <math>SU(2)_L</math> transformeren en beide hebben zwakke hyperlading <math>Q_Y=1/2</math>. We gebruiken de notatie:
<math>\Phi_1=\left( \phi_{11} \quad \phi_{12} \right)^T \quad \Phi_2 = \left( \phi_{21} \quad \phi_{22}\right)^T</math>
met alle <math>\phi</math>kes complexe getallen.
* Stel dat de vacuumsverwachtingswaarden van de scalaire velden door
<math>\Phi_1 = 1/\sqrt{2}\left(0 \quad v_1\right)^T</math> en <math>\Phi_2 = 1/\sqrt{2}\left(0 \quad v_2\right)^T</math>
gegeven worden met v1 en v2 reeel. Wat zijn de massa's van de W, de Z, en het foton?
* Veronderstel dat de Lagrange dichtheid voor de scalairen door
<math>\mathcal{L} = \partial_{\mu}\Phi_1^{\dagger}\partial^{\mu}\Phi_1 + \partial_{\mu}\Phi_2^{\dagger}\partial^{\mu}\Phi_2 + m_1^2\Phi_1^{\dagger}\Phi_1 + m_2^2\Phi_2^{\dagger}\Phi_2 - \lambda_1 (\Phi_1^{\dagger}\Phi_1)^2 - \lambda_2 (\Phi_2^{\dagger}\Phi_2)^2 - \lambda_3 (\Phi_1^{\dagger}\Phi_1)(\Phi_2^{\dagger}\Phi_2) </math>
gegeven is waar m1, m2 reeel en lamda_j>0 voor j in {1,2,3}. Bepaal v1 en v2 als functie van de diverse koppelingsconstantes.
* Bespreek de fysische vrijheidsgraden van de scalaire velden (maw geef een bondige analyse van de unitaire ijk). Toon bv aan dat het fysische elektrisch geladen veld door <math>-\sin\beta \phi_{11}+\cos\beta \phi_{21}</math> gegeven wordt met <math>\tan\beta=v_2/v_1</math>.
====Vraag 2====
Op zoek naar het Brout-Englert-Higgs deeltje. (een grote grafiek van de verschillende branching ratios is gegeven: [http://pdg.lbl.gov/2009/reviews/rpp2009-rev-higgs-boson.pdf], fig. 3 op p.8 - de figuur voor het exaam was ietsje anders, maar kwam op hetzelfde neer.)

De koppeling van het Higgs (<math>\sigma</math>) aan leptonen of quarks (<math>\psi</math>) heeft de vorm
<math>\mathcal{L}_{HF} = -(1/v)m_{\psi} \sigma \bar{\psi}\psi</math>
en deze van de Higgs aan de W en Z velden
<math>\mathcal{L}_{HVB} = (vg^2/2) \sigma W_{\mu}^{\dagger}W^{\mu} + (g^2/4)\sigma^2 W_{\mu}^{\dagger}W^{\mu} + (vg^2/4\cos^2\theta_W) \sigma Z_{\mu}Z^{\mu} + (g^2/8\cos^2\theta_W) \sigma^2 Z_{\mu}Z^{\mu}</math>
Hierin worden de massa's gegeven door (alle massa's werden uitgedrukt in GeV/c^2 en komen van PDG)
<math>m_e = 0.51\cdot 10^{-3} \quad m_{\mu}=0.11 \quad m_{\tau}=1.8 \quad m_u = 1-5\cdot 10^{-3} \quad m_d = 3-9\cdot 10^{-3}</math>
<math>m_c=1.15-1.35 \quad m_s= 0.075-0.17 \quad m_t=170 \quad m_b=4.0-4.4</math>
* Op het volgend blad vind je de branching ratios voor het Higgs verval als functie van de Higgsmassa (<math>m_H=v\sqrt{2\lambda}</math>). Geef een kwalitatieve bespreking van de bb, tautau, gammagamma, gg, WW en ZZ kanalen.

[[Categorie:mf]]