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01. project date 8/19/2011. Conceptual Studies for the π 0 Hadronic Calorimeter. Rob Macedo and Katya Gilbo Catholic University of America. Under the Direction of Dr. Tanja Horn. Paul the Pion. 02. Outline. Intro Goals/Motivations The π 0 Experiment Kinematics and Programming

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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



  • Intro

  • Goals/Motivations

  • The π0 Experiment

  • Kinematics and Programming

  • Challenge: Special Relativity

  • Results

  • Outlook

  • Extra: Amazing Aerogel



  • six flavors of quarks: up, down, top, bottom, charm, strange

  • six leptons: electron, muon, tau with corresponding neutrinos

  • Gauge bosons (force carrier particles)


  • 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

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.

The π0 Experiment


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


Proton surrounded by virtual pions

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

Our Task:


  • 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




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)



Inv. Dist.

We input in function:

Average: Hypothetical Values (Above)

Standard Deviation (for each): 0.1 GeV

Kinematics continued


Kinematics (continued)

4. The “Missing Mass” is affected by the three inversely distributed quantities.




Gaussian Distribute these “Realistic” Missing Mass Values

Results the necessary detector accuracy


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


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.

Special relativity fresh perspectives
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!

Checking Aerogel Index of Refraction


  • 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


where n is the index, p is density


  • 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!