1. radius To use a Compton polarimeter, the possible range of the backscattered photons’ energy should be calculated. Applying the laws of conservation of energy and momentum, we get three equations that can find the energy of the backscattered photon, the momentum of the scattered electron, and the scattering angles.,, The Q-weak Experiment The Q-weak experiment is a precision Test of the Standard Model and Determination of the Weak Charges of quarks through Parity-Violating Electron Scattering. The spin of electrons in the electron beam is altered 30 times per second. The beam acts with the weak interaction differently when it is left-handed and when it is right-handed. Due to the parity violation of the weak interaction, it acts differently on left-handed and right-handed electrons. Therefore, measuring the difference of the energy of scattered particles between two type of electron spins, we will be able to measure the weak charge of proton precisely. Any significant deviation of the weak charge from the Standard Model prediction would be a signal of new physics, whereas agreement would place new and significant constraints on possible Standard Model extensions. Assuming that the 1GeV electron beam interacts with a 500nm green laser, we solved these equations. Below is the actual graph and logarithmic graph of the backscattered photon’s energy as the scattering angle of the photon changes. Problem 1 : Energy of backscattered photon Compton Scattering For the experiment, the polarization of the electron beam should be measured precisely. To measure it, we will use a Compton polarimeter. Compton scattering is used by the polarimeter to determine polarization. If the electron has its spin angular momentum in the same direction as its momentum, it will have a greater Compton scattering probability. The Compton effect is the interaction between electrons and photons when they collide with each other. This phenomenon shows the particle-like behavior of light. In the interaction, the photon and electron exchange energy and momentum. During the interaction, the total energy and momentum are conserved, which is a fundamental law of physics. Above is the equation for Compton scattering when an gamma ray collides with a stationary electron. A Feynman diagram for Compton scattering With the graph, we can easily realize that the backscattered photons could get lots of energy from electrons, compared to the other photons. The maximum energy gained from electrons is ~37 MeV; only about 3.7% of the initial energy of the electrons. Problem 2 : Positioning the mirrors Detectors For the Compton polarimeter to work, the thick laser light should be guided and focused correctly to collide with thin electron beam. Below is a simple model for the mirror arrangement. 1) Cherenkov detector – to measure the velocity of charged particles Cherenkov radiation results when a charged particle, most commonly an electron, exceeds the speed at which light is propagating in a dielectric (electrically insulating) medium through which it passes. In a similar way to the ‘sonic boom,’ a charged particle can generate a photonic shockwave as it travels through an insulator. By measuring the angle of radiation, we can get the velocity of the charged particle. 2) Calorimeter – to measure the Energy of photons The detector works by sensing the energy deposited by photons when they are absorbed. The total amount of energy deposited is directly proportional to the photon energy. This picture of an X-ray calorimeter shows a simple model of modern photon-calorimeters. 3) Magnetic field – to measure the Momentum of charged particles According to Electromagnetism, a charged particle moving in a magnetic field feels the ‘Lorentz force’ that makes it to move in a circle. If one knows the charge of the particle, he or she can get the momentum of the particle by measuring the radius of the circle. The electron beam is curved twice by magnetic fields, and goes parallel to its initial direction, but below its initial height. After it collides with the laser source, it is curved again, and returned to the initial height. This is done to prevent damage the detectors for photons and electrons that would be inevitable if they had to be placed in the electron beam. The thick laser light is reflected by four identical mirrors, with a focus length equal to the distance from the colliding point to itself, at the corners. The laser then goes to the ‘dump.’ During this one cycle, the light collides with the electron beam twice. In the case that the angle between electron beam and laser light is very small(0~1 degree), we can ignore the effect of angle and use our calculation for Problem 1. However, to achieve this effect, the size of mirror should be small in order not to be damaged by the 1GeV electron beam. Then, some parts of light would be reflected at the edge of the mirrors, and we will have to predict the effect of this, In this whole cycle, only a few of photons can collide with electron beam because the beam is very thin. If a photon collides with an electron and backscattered, the detectors will catch the photon and electron to measure the energy, velocity, momentum, etc.. Conclusion Structure of the Compton Polarimeter In conclusion, Q-weak experiment’s goal is to find out the accurate value of a proton’s weak charge and possibly discover new physics. This experiment depends heavily on the polarization of an electron beam because the weak charge can be separated from the electric charge due to parity violation (only left- handed electrons can be affected by the weak neutral nuclear interaction). The Q-weak experiment needs a polarimeter that can measure the beam’s polarization exactly without interrupting the beam itself. That is a Compton polarimeter, which applies the property of Compton scattering to measure the polarization. In this project, we solved two problems relating to the design of the polarimeter: 1. The range of the energy that scattered photons can have and 2. Positioning the mirrors that guide the laser light to collide with electron beam. The first problem was solved using the laws of conservation of momentum and energy. It was obvious that the energy of scattered photons increases greatly as the scattered angle goes close to Pi; however, the maximum energy of the completely backscattered photons was only 3.7% of the initial energy of an electron. To solve the second problem, we designed a mirror system that aims the approximately parallel laser light beam at the electron beam. Also, convex mirrors were used to focus the relatively ‘fat’ laser beam to about 50 microns (the width of the electron beam). With the beams positioned and focused correctly, Compton scattering can take place, and the weak charge can be measured from data collected about the backscattered photons and electrons. Time Below is a simple model of a complete Compton polarimeter. First, the electron beam curves and goes below its initial height. The laser light collides with the beam and, due to the Compton effect, some of the photons are scattered. The photons are then sent to the detectors and their properties are measured. With the energy data, we can calculate the polarization of the electron beam. Detectors This graph shows the number of ‘Compton events’. A Compton event is when either a scattered photon or electron is detected. As the electron beam’s polarization changes 30 times per second, the number of Compton events also changes 30 times per second, due to the effects of spin on Compton scattering. Designing a Compton Polarimeter Lee Hyun Seok, Matthew Harrigan Advisor: Richard Jones Physics Department, University of Connecticut, Storrs