Download Effective Theory - Richard Jones

Results and Comparison
with Simple Effective
Theory
Presenter: David Smith
Site: Nuclear Physics
Mentor: Dr. Richard Jones
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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.
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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/antiquark composite particles), which will be used to probe the quarks and gluons.
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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





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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.
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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.

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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.

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Modes of Oscillation
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1.
2.
3.
4.
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
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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
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The
Actual Experiment
Michelson
Interferometer
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Results
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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.
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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
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Diamond/Wire Diagrams
The diamond/wire system as viewed in the ZY coordinate plane (side-on).
Actual Behavior of the System
Effective Theory Approximation
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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 zaxis, as viewed in the XY
coordinate plane. This form
of rotation stretches the wires.
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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
4ωTcot(wω/v)
___________________
2
ω=
vm
Effective Theory
1
______
4ω T cot
( wω /v )
2 ___________________
_______
ω= 2
vm
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.
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Comprehensive
Equation
Effective Theory
Equation
Lowest order
frequency prediction:
45.11 Hz
Lowest order
frequency prediction:
45.07 Hz
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GlueX and Effective Theory

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

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.
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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
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Sources
1 "The
GlueX Experiment." gluex.org. 14 Apr 2009. Thomas Jefferson National
Accelerator Facility. 26 Jul 2009 <http://www.gluex.org/>.
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
<http://www.curtismeyer.com/ground/ground_break.html>.
3 "quantum chromodynamics." The Columbia Encyclopedia, Sixth Edition.
2008. Encyclopedia.com. 27 Jul. 2009 <http://www.encyclopedia.com>.
4 "Quark Confinement." The Particle Adventure. Lawrence Berkeley National
Laboratory. 26 Jul 2009
<http://www.particleadventure.org/quark_confinement.html>.
5 Chaplin, Steve. " IU GlueX experiment advances with Department of Energy
groundbreaking." IU News Room. 15 April 2009. Indiana University. 27
Jul 2009 <http://newsinfo.iu.edu/news/page/normal/10607.html>.
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Sources (Continued)
6
Meyer, Curtis A. "The GlueX Collaboration." gluex.org. Thomas Jefferson
National Accelerator Facility. 27 Jul 2009 <http://www.gluex.org/>.
7
"3D coordinate system." Wikimedia Commons. 26 Jul 2007. Wikimedia. 27 Jul
2009
<http://commons.wikimedia.org/wiki/File:3D_coordinate_system.svg>.
8 "Effective field theory." Absolute Astronomy. AbsoluteAstronomy.com. 28 Jul
2009
<http://www.absoluteastronomy.com/topics/Effective_field_theory>.
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