Under the Direction of Dr. Tanja Horn

1. 01 project date8/19/2011 Conceptual Studies for the π0 Hadronic Calorimeter Rob Macedo and Katya Gilbo Catholic University of America Under the Direction of Dr. Tanja Horn Paul the Pion

2. 02 Outline • Intro • Goals/Motivations • The π0 Experiment • Kinematics and Programming • Challenge: Special Relativity • Results • Outlook • Extra: Amazing Aerogel

3. 03 • 1. FUNDAMENTAL PARTICLES • six flavors of quarks: up, down, top, bottom, charm, strange • six leptons: electron, muon, tau with corresponding neutrinos • Gauge bosons (force carrier particles) • 2. FUNDAMENTAL FORCES: • electromagnetism, gravity, weak, strong • Subatomic Forces: • STRONG controls quark interactions (via carrier particles, GLUONS), holds nucleus together • WEAK force controls neutron interaction and beta decay

4. Overall Goal of CUA Nuclear Physics Team:To study the proton's substructure, including the quarks inside a proton and the workings of the strong force. We want a better understanding of our universe.

5. The π0 Experiment 04 Pion decays into two photons. Angle between photons, photon energy and momentum can be measured using a calorimeter – giving us details about the pion. Pion gains enough energy to become real, and is recoiled Electron from electron beam emits a virtual photon, and is scattered. The Scattered electron’s angle, momentum and energy can be measured. Proton is also recoiled e- Proton surrounded by virtual pions

6. e-

7. Physical Motivation 05 • Why Pion Detection? • Analyzing the energy and momentum of the pion leads us to learn more about our target, the proton. • The pion’s detection allows us to study the proton’s substructure through General Parton Distributions (GPDs), which describe the movements, placements, and momenta of the quarks inside the proton. • The neutral pion one of the simplest and lightest particles! • We can identify what happened in our reaction by detecting the pion Ex. of GPDs

8. Our Task: 06 • In the experiment, the recoiled proton is NOT detected. • Need to identify this undetected particle through Conservation of Energy • Total Energy – All Detected Energies= “Energy of Undetected Particle” or “missing energy” • Through missing energy and missing momentum, we can calculate what the undetected particle is! • If it is 0.938 MeV, then it must be a proton! • Our Question: How accurately (or perfectly) should our calorimeter measure the energy and momentum of the pion’s two decay photons? (so that we can identify the undetected proton in our experiment) A Hadronic Calorimeter

9. 07 Kinematics The Steps: • Modifying a Fortran based program’s charged pion kinematic equations to build an Excel spreadsheet for the neutral pion equations • Calculate all kinematics (ex. energies) in our hypothetical experiment => perfect values • Simulate real life, using inverse distribution function: • USE Probability (RANDOM), Average, and Standard Deviation (for each column) TO From Inv. Dist. We input in function: Average: Hypothetical Values (Above) Standard Deviation (for each): 0.1 GeV

10. 08 Kinematics (continued) 4. The “Missing Mass” is affected by the three inversely distributed quantities. TO From 5. RESULTS: Gaussian Distribute these “Realistic” Missing Mass Values

11. 09 Results- the necessary detector accuracy Proton mass Mean: 0.938 GeV Calorimeter STDEV: 0.1 GeV Proton Missing Mass STDEV: 0.14 GeV Eta mass mean:0.15 GeV delta mass mean: 1.2 GeV

13. Outlook Where do we go now? • The accuracy of our calorimeter ( a standard deviation of 100 MeV) is enough to spot a difference between a calculated proton and the two more common particles (Delta Baryon and Eta). • Realistic accuracy for a not too expensive calorimeter. • More design aspects will have to calculated and simulated using programs (like fortran and excel), and detector materials must be chosen and designed. • Important step towards creating the pion detector – and discovering the inner working of the proton.

14. Special Relativity: Fresh Perspectives • Two Frames: since particles travel near speed of light! 1. Center of Mass (CM)- coordinate frame with zero net momentum, “frame from particle’s perspective” 2. Laboratory- coordinate frame with stationary proton target, “frame from detector’s perspectives” • CM calculations are converted to Lab. through the boost factor, gamma, where we can then simulate detected values and observe missing mass values. • Momentum and energy values are different when measured form different frames!

15. Checking Aerogel Index of Refraction Extra: • Silica Oxide • Cherenkov detector Aerogel Top • Photoshop Statistic Application • For Accurate Volume Measurement (applying a biological technique) Pixel Num. Drawn Square 17.9 cm2 17.9 cm2 Drawn Square n=1+0.21(p), where n is the index, p is density

16. Acknowledgements • Dr. Tanja Horn! • Nathaniel Hlavin, Mike, and Laura Rothgeb • Dr. Liam • Jefferson Lab • Dr. Muller • CUA • Thank you for teaching us bizarrely • incredible things and answering every single question!!!! • And thank you for this wondrous internship experience of direct scientific research!