1. Results and Comparison with Simple Effective Theory
Presenter: David Smith
Site: Nuclear Physics
Mentor: Dr. Richard Jones

2. The GlueX Experiment
The GlueX Experiment is an upcoming particle physics experiment which will take place at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia.
It carries the stated purpose of gaining a “quantitative understanding of the confinement of quarks and gluons in quantum chromodynamics (QCD).”
Quantum chromodynamics is the theory of strong interactions as relates to the quark color force. Confinement is the process of quarks being confined in color-neutral groups called hadrons (the force between quarks does not diminish with distance).
An artist's rendering of the complex which will contain the GlueX experiment.

3. In the GlueX set-up, electrons are passed through a diamond wafer to create linearly polarized photons. In turn, these photons are used to create low-energy mesons (quark/anti-quark composite particles), which will be used to probe the quarks and gluons.

4. GlueX Collaborators
Several institutions are lending their efforts to the GlueX experiment’s development, including:
Thomas Jefferson National Laboratory
Carnegie Mellon University
Indiana University
University of Athens (Greece)
Florida State University
University of Regina
University of Connecticut

5. The Diamond
In the GlueX experiment, the diamond wafer used to produce photons will be mounted within a frame, supported by two tungsten wires.
A mock set-up used in our experiment. The diamond wafer is replaced by a much larger piece of glass.

6. The Issue
During preliminary testing of the diamond and its mount, vibrations proved to be a significant issue.
These vibrations are believed to be translated through the tungsten wires to the diamond, originating in the environment surrounding the apparatus.
This poses a significant problem—if the electron does not strike the diamond at a very precise angle, the resulting photon will not have the correct polarization.

7. Our Experiment
Using the mock diamond set-up, and a laser beam, we will study the problematic vibrations.
This experiment will indicate the type of vibrations that the glass (the diamond’s stand-in) undergoes, and the frequencies of these vibrations.
Throughout our time at our mentorship site, we did a great deal of theoretical work on this problem.

8. Modes of Oscillation 7
Vibration along Z or X axis (these can be explained by the same mathematics)
Rotation about X axis
Rotation about Y axis
Rotation about Z axis

9. Results of Theoretical Analysis
Oscillation Along
Z-Axis
45.1 Hz
5060 Hz
10100 Hz
Rotation About
X-Axis
78.0 Hz
5060 Hz
10100 Hz
Rotation About
Y-Axis
55.5 Hz
5060 Hz
10100 Hz
Oscillation Along
Z-Axis
2560 Hz

10. Michelson Interferometer
The Actual Experiment
Michelson Interferometer

11. Results

12. Simple Effective Theory
An effective theory is an approximation of the physical world, which includes an appropriate number of degrees of freedom (the number parameters upon which the theory depends) for a chosen length or energy scale. Such a theory ignores degrees of freedom at higher energies or more extreme length scales. 8
Effective theory can be applied in explaining phenomena as varied as the vastly complex world of the quark and classical systems such as the vibrating diamond.

13. Effective Theory Applied
We can consider the utility of effective theory by applying it to our theoretical work on the vibrating diamond problem.
Actual Behavior of the System
-Frequencies Ranging from Low to Very High
-Wires Behave Like Sine Curve
Effective Theory
-Low Frequencies Only
-Wires Are Considered to Behave Like Rigid Rods

14. Diamond/Wire Diagrams
The diamond/wire system as viewed in the ZY coordinate plane (side-on).
Actual Behavior of the System
Effective Theory Approximation

15. Effect on Theoretical Analysis
If we assume the wires to be rigid, we must also imagine that they cannot stretch. Thus, through our effective theory, we can eliminate an entire mode of oscillation—rotation about z-axis, which depends on a change in length of the wires.
The glass rotates about the z-axis, as viewed in the XY coordinate plane. This form of rotation stretches the wires.

16. Comprehensive Equation Effective Theory
Our effective theory will also have an effect on our calculations. To observe this effect, we will consider our equation for the frequency of motion for oscillation along the z-axis.
Comprehensive Equation Effective Theory 1
______
4ωTcot(wω/v) 4 ω T
cot ( w ω / v )
___________________
ω2=
___________________
_______
ω = 2 2 vm v m
In our original equation, we included the original trigonometric cotangent (cot) function to account for the fact that the wire behaves like a sine wave. In our rigid-wire effective theory, this can be removed, making for a much simpler equation.

17. Comprehensive Equation
Lowest order frequency prediction:
45.11 Hz
Effective Theory Equation
Lowest order frequency prediction:
45.07 Hz

18. GlueX and Effective Theory
In reality, calculations of systems such as the diamond/tungsten wire system do not require effective theory, because we can create more comprehensive theories.
However, incredibly complex systems, such as the interactions between quarks and gluons, require such effective theories.
Even the standard model is an effective theory.
Therefore, the work being conducted in the GlueX project will, if successful, contribute to an effective theory of the interactions between quarks via the color force.

19. That concludes my presentation!
Special Thanks To:
-Mentor: Dr. Richard Jones
-Students: Igor, Woody, Chris, and Mike
-My Fellow Physics Students, Ryan and Austin
-Mentor Connection Staff

20. Sources
1 "The GlueX Experiment." gluex.org. 14 Apr Thomas Jefferson National Accelerator Facility. 26 Jul 2009 <
2 Meyer, Curtis A.. "Carnegie Mellon GlueX experiment makes a big step forward with the Department of Energy groundbreaking." curtismeyer.com. Carnegie Mellon University. 27 Jul 2009 <
3 "quantum chromodynamics." The Columbia Encyclopedia, Sixth Edition Encyclopedia.com. 27 Jul <
4 "Quark Confinement." The Particle Adventure. Lawrence Berkeley National Laboratory. 26 Jul 2009 <
5 Chaplin, Steve. " IU GlueX experiment advances with Department of Energy groundbreaking." IU News Room. 15 April Indiana University. 27 Jul 2009 <

21. Sources (Continued)
6 Meyer, Curtis A. "The GlueX Collaboration." gluex.org. Thomas Jefferson National Accelerator Facility. 27 Jul 2009 <
7 "3D coordinate system." Wikimedia Commons. 26 Jul Wikimedia. 27 Jul 2009 <
8 "Effective field theory." Absolute Astronomy. AbsoluteAstronomy.com. 28 Jul 2009 <