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

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.

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.

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

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.

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.

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.

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

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

Michelson Interferometer The Actual Experiment Michelson Interferometer

Results

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.

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

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

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.

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.

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

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.

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

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>.

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>.