Table of Contents

• Difference in W+jets and Z+jets events
• Difference in W+jets and QCD events
• VBS
• Event
• Trigger
• Custodial Symmetry
• Hadrons
• Elementarity test of electron

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Difference in W+jets and Z+jets events

1. $W \rightarrow l \nu$, $Z \rightarrow l^+ l^-$
2. In case of leptonic decay, reconstruction of W-boson is difficult because of MET.
3. Z-boson has higher mass than W-boson, which leads to higher multiplicity, a higher jet-pT and a higher lepton pT.
4. Z-boson is mostly produced from $u\bar{u}$, while $W^+$ is mostly produced from $u\bar{d}$ and $W^-$ from $d\bar{u}$. That affects the rapidity distribution of the bosons because of PDFs for the valence quarks up and down are different.
5. The coupling of W- and Z-bosons are different. The W-boson couples to left handed particles with universal V-A coupling while Z-boson couples through V+A coupling as well as V-A to both left and right handed particles. This influence the angular distribution of the final state particles, especially leptons.

Difference in W+jets and QCD events

1. W+jets events generally contain two hard sub-jets, while QCD jets usually has 1 hard sub-jets.

2. W is a color singlet particle, i.e. all QCD radiation from boosted W-boson decay is confined in a small cone around W-boson momentum direction.

   While, QCD jet initiated by color triplet or octet, which is color connected to the beam or the other side of event. So, the radiation from QCD jet is usually much more diffuse.

VBS

1. Two class of physical process give rise to VVjj final states ¹ :
   1. VBS contribution, involves exclusively weak interactions at Born level and is referred to as electroweak production.
   2. The process which involves both the strong and electroweak interactions at Born level and is referred to as strong production.
   3. In case of same-sign charge WW production (i.e. $W^{\pm}W^{\pm}jj$), the strong production cross-section does not dominates the electroweak cross-section. So, the same-sign WW VBS studies is easier to perform.

Event

An event is set of signals in the detector resulting from a PP collision, or several such coincident collisions. It includes raw signal (e.g. tracker hits, calorimetric energy deposits, etc.) and derived quantities (e.e. tracks, jets, etc.)

Trigger

Trigger is a combination of hardware and software system that uses certain criteria (based on physics algorithms) to rapidly decide to keep (record) or drop a pp collision event in the CMS detector.

Custodial Symmetry

• Before the breaking of $SU(2)L x U(1)_Y$, the Higgs potential as a global $SU(2)_L x SU(2)_R$ symmetry which reduces to $SU(2)_v$ when symmetry is broken. This remanent global symmetry is called the “_Custodial Symmetry”[^Ref:Custodial]
• If the gauge symmetry of the electroweak model is broken by the Higgs doublet, there is a custodial symmetry which protects the mass relation of the W and Z gauge fields, i.e. \(\rho = \frac{M^2_{w}}{ {M_Z}^2 Cos^2(\theta) } \sim 1\), here, $\theta$ is the weak mixing angle.

This relation is also valid after the radiative corrections if the custodial symmetry is not broken. Experimentally, this relation is satisfied at the 1% level, which restricts the new physics beyond SM and allows us to distinguish among different models.

• When the SM symmetry is broken by Higgs doublets, there is a global symmetry that protects the mass relation of the W and Z fields, which transforms as the components of a triplets. This relation is violated when this symmetry is not exact. If the isospin symmetry or custodial symmetry is broken, then $\rho$ parameter may get radiative corrections different from zero. To look for new physics beyond the SM it is important to know if this symmetry is still exact.

Hadrons

Hadrons interacts via strong interaction and categorized into two category. They are

• Meson: Mesons are the hadrons that are formed via a quark and an anti-quark pair. It falls into the boson category. There are approximately 140 types of mesons and the lightest meson is pion.
• Baryon: Baryons are the hadrons that are formed via the combinations of three quarks. It falls into the fermion category. There are approximately 120 types of baryons and the lightest baryon is proton. Proton is the only hadron which is stable in free space. All baryons other than nucleons decay with mean lives of less than $10^{-9}$ s in a variety of ways, but the end result is always a proton or neutron.

Elementarity test of electron

Electron is one of the elementary particle. One of the elementarity test is to measure particles magnetic moment value. A charged particle with spin necessarily has an intrinsic magnetic moment $\vec{\mu}$.

The Dirac equation for a point like spin-$\frac{1}{2}$ particle of charge q and mass m has a magnetic moment \(\vec{\mu} = (\frac{q}{m})\vec{s},\) where $\vec{s}$ is its spin vector, and hence $\vec{\mu}$ has magnitude \(\mu = \frac{qh}{4\pi m}.\) The magnetic moment of the electron very accurately obey this relation, confirming that electrons are elementary.