Vector Boson Scattering & Anomalous Quartic Gauge Coupling Final Presentation

Aobo Li University of Washington Outline

• Theory – Electroweak Symmetry Breaking – Higgs Field and VBS • Process – Madgraph & root environment – Wrtiting Proc Card – Generating Events based on different model – ROOT plot • Future Prospection • Q & A Electroweak Symmetry Breaking

• Goldstone Boson: Boson that appear necessarily in model exhibiting spontaneous breakdown of continuous symmetry. • At high enough temperature, Electromagnetic and weak interactions are unified(The symmetry is unbroken), all elementary particles are masless. • At a critical temperature the Higgs field become tachyonic. • Once the tachyonic field reaches its minimum potential, its quanta are no longer tachyonic, but with positive mass squared. • Higgs boson is a good example. • The tachyonic field goes through a spontaneous process called Tachyonic condensation, which grants mass to both W and Z boson. EWSB Higgs Field and VBS

• Higgs Field: a SU(2) doublet, a complex scalar with 4 real component. • U(1) : circle group corresponding to weak hypercharge. • The gauge group for electroweak part is SU(2) × U(1). During this, three of the four scalar mixed with 3 W and Z bosons, while one remains scalar as Higgs boson. • Vector Boson scattering(quartic gauge coupling) must be attributed to this process, if not: – Unitarity is broken. – Theory become non-perturbative, require lots of correction.

Outline

• Theory – Electroweak Symmetry Breaking – Higgs Field and VBS • Process – Madgraph & root environment – Wrtiting Proc Card – Generating Events based on different model – ROOT plot • Future Prospection • Q & A Madgraph & Root

• Madgraph: C language based Monte Carlo generator, used to simulate particle collision process. • Root: CERN published data analysis framework, also C language based. • Our goal is to use Madgraph to generate truth events for analysis purpose, then using root to implement cut & uncertainty propagation. Set up environment on Mac

• Mac X OS is not C language based. • Set up C environment with X code & XQuartz. – xcode-select --install • Take care of gfortran compiler. • Install root from source(Milen’s guide)

Process generation

• Generating particle collision process by writing Madgraph proc card. • This quarter, our goal is to simulate zajj final state process. – p p -> Z a j j • Proc cards are wiritten under different theory model. – SM,Heft, LT8 Generating Events

• After generating process, we can proceed to events generation • Turn on Pythia parton showering. • Turn on Delphes: a detecton simulation framework for truth study. • Generating collision events for different model. Standard Model

• Background

HEFT model

• Higgs Effective Field Theory model. • Effective Field Theory: approximation for underline physics theory. • Include appropriate degree of freedom to describe phenomenon occurred at chosen energy/length scale, while ignoring substructures and degrees of freedom at shorter distance(higher energy scale) • Under this model, triple gauge coupling (Vector boson fusion) events are found, but no quartic gauge coupling(Vector boson scattering) events exists.

Vector Boson Fusion Other coupling Z Boson Bremsstrahlung

• Braking radiation

LLT8 Model

• Generating events with dimension-8 operator on field terms. • Set dimension-8 anomalous input to amplitude 1e-12, while turn every other anomalous input off(Set amplitude to 0) • Quartic Gauge coupling(Vectro boson scattering) events starts to emerge. Vector Boson Scattering SLT8 NA model

• LT8 model with all anomalous operator set to 0 amplitude. • Are supposed to produce background events(identical to Standard Model) LT8 events ROOT Analysis

• Writing compact root macros for data analysis purpose. • Can do a lot of things with root: – Constructing & fitting histogram – Making plot – Implementing cut – More advanced stuff. ROOT Macro

• Reading Delphes tree by ExRootTreeReader • Loop through all events • Assigning interested object to proper type(eg particle to GenParticle, jet to Jet) • Loop through objects and filling histogram • Renormalize histogram with cross section to make the plot independent of the amount of events generated.

Making plot

• By calling macro in Mac terminal – Can either use .x Macro.C – Or .L Macro.C and call the function • Overlapping datas from 4 different event generation into single plot. – HEFT model:Green Line – LT8 model:Red Line – LT8NA model: Purple Line – Standard Model: Yellow Line

Outline

• Theory – Electroweak Symmetry Breaking – Higgs Field and VBS • Process – Madgraph & root environment – Wrtiting Proc Card – Generating Events based on different model – ROOT plot • Future Prospection • Q & A What’s Next

• The plots looks pretty much the same, so some event selection/cut implementation is needed • Doing more complicated analysis using root(e.g. cutflow) • Writing more advanced C code – Writing a Madgraph model – Constructing a plugin for Delphes

What’s Next

• Learning more Quantum theory – Going to Grad school! • Ingesting more Math for Theory • Reading Paper. • The fun has just start! QQuestion and Answer Thank You!

• Have a great summer!