Study of the Differential Luminosity Spectrum Measurement using Bhabha Events in 350GeV WANG Sicheng 王 思丞 Supervisor: André Sailer

Ultimate Goal Want to know how well the detector would be able to perform, how good physics processes can be reconstructed. Obtaining the Differential Luminosity Spectrum which is essential in center of mass energy related measurements Develop a method that can be applied later for the reconstruction of the Luminosity Spectrum when the detector is built.

Approach to the Problem ● Should extract the measurement of the Luminosity Spectrum out of the reconstructions ● Need a specific physics process ● Simulate interaction between beams of the future collider in computer ● Know the center of mass energy for each collision ● Start study form the simulated luminosity spectrum

Contribution to Lumi-Spectrum Beam Energy SpreadBeamstrahlung Initial State Radiation and Final State Radiation (ISR & FSR) ● Come from accelerator and beam-beam interaction ● Related to specific physics process

Simulation of the Lumi-Spectrum Fig: The simulated Lumi-Spectrum given by G UINEA P IG. ● Taking the Beam Energy Spread and Beamstrahlung into account, we simulates the interaction between the electrons and positrons at the collision point. ● The whole Luminosity Spectrum is complex in shape, unable to be described one single simple function.

Separate and Fit ● Separate into the smaller special regions which may be modeled separately with some basic functions. Peak Arm1 Arm2 Body

Separate and Fit Peak Arm1 ● Fit by beta distribution convoluted with a gauss ● with Beta Distribution:

Separate and Fit ● Cutting criteria: E1/E < ● Fit to the larger energy range again with linear combination of beta distributions ● This energy spread mainly caused by Beamstrahlung Body ● The fit with 3 beta distribution is better than the 1 beta-distribution, but 1 can do as good when applying the cut Arm2

The Model ● Use the model function constructed by S. Poss and A. Sailer to describe the behaviour ● BES and BB are convoluted functions

Reweighting Fit We use Reweighting Fit to fit the Luminosity Spectrum with the model Advantage: ● Computationally efficient because the numerical convolution do not have to be calculated ● Reuse the events to fit new set of parameters

● Blue – para1 (μ=0, σ=1) generate random event ● Red – para2 (μ=1, σ=2) reweight every event in para1 to get the new distribution with the weight: Reweighting Example Transform events from one Gaussian distribution to another

Fit Result Comparison between the fit result with the original G UINEA P IG output in 1D Histogram. MC model events

Fit Result Closer Look at the peak Variance between the GP and the fit at the peak

Include Bhabha Events ● The previous work has demonstrate the model worked well with Luminosity Spectrum itself Next Step, include Bhabha events to get closer to the real measurement ● Use BHWide to simulate Bhabha events for the GP events and the Model MC events separately ● Compare the luminosity spectrum after the BHWide simulation to see if the fit still work well Cross Section for the Bhabha events Bhabha Scattering

Effective Cross Section ● The effective Cross Section at the nominal energy should consider the whole energy spread by the Luminosity Spectrum. Fig: The effective Luminosity Spectrum for Bhabha events

Include Bhabha Events ● Width of the Peak region is calculated to about 3.42e-03 for both with statistical uncertainty 1.7e-06 ● The difference between width of the GP data and the fit is: 1.1e-06

Include Bhabha Events ● The parameter and uncertainty out of the fit change after applying Bhabha events

Detector Resolution ● Use Mokka to simulate detector reconstruction and compare with the original MC particle ● The energy resolution reconstructed from track is better than from clusters.

What I have learnt ● Luminosity Spectrum ● ROOT ● Many accelerating physics topics ● Concept of Reweighting Fit ● Keep record on the work done – Important!! – Use subversion – Well organize the data obtained

Thanks Thanks to Andre for helping me with everything on the project. Thanks to Samir for giving useful advice on the project and this presentation. Thanks to everyone for being here.