Under the Direction of Dr. Tanja Horn

01

Conceptual Studies for the π0

Hadronic Calorimeter

project date 8/19/2011

Rob Macedo and Katya GilboCatholic University of America

Outline02

Intro Goals/Motivations The π0 Experiment Kinematics and

Programming Challenge: Special

Relativity Results Outlook Extra: Amazing Aerogel

03

1. FUNDAMENTAL PARTICLESsix flavors of quarks: up, down, top, bottom, charm, strangesix leptons: electron, muon, tau with corresponding neutrinosGauge bosons (force carrier particles)

2. FUNDAMENTAL FORCES: electromagnetism, gravity, weak, strong

Subatomic Forces:STRONG controls quark interactions (via carrier particles, GLUONS), holds nucleus togetherWEAK 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.

04 The π0 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.

05Physical 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

• 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 H

adro

nic

Cal

orim

eter

06

KinematicsThe 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 VALUESHypothetical

θpicmPpilab (GeV) Epi (GeV)

0 2.860 2.863

DETECTED VALUESReal Life (Simulated)

θpicmPpilab (GeV)

Epi (GeV)

-0.09 2.99 3.02-0.06 2.89 2.89-0.10 2.89 2.970.06 2.97 2.990.14 2.69 2.61

-0.04 2.77 2.75

Inv. Dist.

We input in function: Average: Hypothetical Values (Above) Standard Deviation (for each): 0.1 GeV

07

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)

1.372.441.881.620.762.05

5. RESULTS:Gaussian Distribute these “Realistic” Missing Mass Values

08

Results- the necessary detector accuracy

Proton mass Mean: 0.938 GeVCalorimeter STDEV: 0.1 GeV Proton Missing Mass STDEV: 0.14 GeV

09

Eta mass mean:0.15 GeV

delta mass mean: 1.2 GeV

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.

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!

Extra:

n=1+0.21(p), where n is the index, p is density

Silica Oxide Cherenkov detector

Photoshop Statistic ApplicationFor Accurate Volume Measurement

(applying a biological technique)

Aerogel Top

Pixel Num.

Drawn Square

17.9 cm2

Drawn Square

17.9 cm2

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!