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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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Under the Direction of Dr. Tanja Horn

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Under the direction of dr tanja horn


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

Under the direction of dr tanja horn



  • Intro

  • Goals/Motivations

  • The π0 Experiment

  • Kinematics and Programming

  • Challenge: Special Relativity

  • Results

  • Outlook

  • Extra: Amazing Aerogel

Under the direction of dr tanja horn



  • 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

Under the direction of dr tanja horn

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.

Under the direction of dr tanja horn

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

Under the direction of dr tanja horn


Under the direction of dr tanja horn

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

Under the direction of dr tanja horn

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!

Under the direction of dr tanja horn

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

Under the direction of dr tanja horn


  • 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!

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