1. Under the Direction of Dr. Tanja Horn 01 Conceptual Studies for the π 0 Hadronic Calorimeter project date 8/19/2011 Rob Macedo and Katya Gilbo Catholic University of America

2. Outline 02  Intro  Goals/Motivations  The π 0 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. 04 The π 0 Experiment Electron from electron beam emits a virtual photon, and is scattered. The Scattered electron’s angle, momentum and energy can be measured. Proton surrounded by virtual pions Pion gains enough energy to become real, and is recoiled Proton is also recoiled Pion decays into two photons. Angle between photons, photon energy and momentum can be measured using a calorimeter – giving us details about the pion.

7. 05 Physical Motivation 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. 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) Our Task: A Hadronic Calorimeter 06

9. Kinematics The Steps: 1.Modifying a Fortran based program’s charged pion kinematic equations to build an Excel spreadsheet for the neutral pion equations 2.Calculate all kinematics (ex. energies) in our hypothetical experiment => perfect values 3. Simulate real life, using inverse distribution function: – USE Probability (RANDOM), Average, and Standard Deviation (for each column) DETECTED VALUES Hypothetical θpicm Ppilab (GeV)Epi (GeV) 02.8602.863 DETECTED VALUES Real Life (Simulated) θpicm Ppilab (GeV) Epi (GeV) -0.092.993.02 -0.062.89 -0.102.892.97 0.062.972.99 0.142.692.61 -0.042.772.75 Inv. Dist. We input in function: Average: Hypothetical Values (Above) Standard Deviation (for each): 0.1 GeV 07

10. Kinematics (continued) 4. The “Missing Mass” is affected by the three inversely distributed quantities. Perfect Missing Mass (GeV) 0.938 Missing Mass with Inv. Dist. Pion Values (GeV) 1.37 2.44 1.88 1.62 0.76 2.05 5. RESULTS: Gaussian Distribute these “Realistic” Missing Mass Values 08

11. Results- the necessary detector accuracy Proton mass Mean: 0.938 GeV Calorimeter STDEV: 0.1 GeV Proton Missing Mass STDEV: 0.14 GeV 09 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. Extra: n=1+0.21(p), where n is the index, p is density  Silica Oxide  Cherenkov detector  Photoshop Statistic Application For Accurate Volume Measurement (applying a biological technique) Aerogel Top Pixel Num. Drawn Square 17.9 cm 2 Drawn Square 17.9 cm 2

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!