Graduate Student Research

Research opportunities for graduate students abound. In addition to working directly with a Physics Department faculty member, graduate students also have access to research taking place in Astronomy & Astrophysics, Chemistry, Mathematics, Geophysical Sciences, Biological Sciences, Medical Physics, Computer Science, as well as at Fermilab, Argonne, CERN, and many other departments, facilities, observatories, and laboratories.

In many cases, graduate students can get involved in research immediately upon, and sometime before, beginning his or her first quarter in our program; this is especially true for students interested in experimental research. Theory students, depending on the area, may need to take a few courses before settling down into a research project.

The best way for graduate students to get involved in the research of his or her choice is to talk to the faculty members working in their area(s) of interest and find out how to best proceed based on his or her background and specific situation. A great way to explore an experimental research group early-on is to satisfy the experimental physics requirement by doing a year-long research project with that group.

Below, you will find a sampling of some of the fore-front-level research being done by our graduate students. You may also view the graduate research archive for previous profiles. Enjoy…

eric

Eric Feng

B.S., University of California, Berkeley, 2003 (Engineering Physics)
B.A., University of California, Berkeley, 2003 (Mathematics)
M.S., University of Chicago, 2007 (Physics)
Graduate Student (2005), Dept. of Physics, Enrico Fermi Institute
Experimental High-Energy Physics
Awards: Robert Sachs Fellow (Physics), Robert McCormick Fellow (Physics), GAANN Fellow (Dept. of Ed), US LHC Award (NSF), Best Poster Prize (USLUO), Gaurang & Kanwal Yodh Prize (Physics)
Research Advisor: James Pilcher

My research involves the investigation of fundamental interactions between elementary particles at the world's highest man-made energies -- or equivalently, the shortest distances -- using data collected by the ATLAS experiment at the Large Hadron Collider (LHC). I am resident at the European Center for Particle Physics (CERN) in Geneva, Switzerland, where the LHC is located. The LHC is a proton-proton collider with the highest center-of-mass energy (7 TeV) in the world; it began operation in 2008 and produced its first collisions at 900 GeV in 2009.

The primary goal of my research is to probe quantum chromodynamics (QCD) as predicted by perturbative calculations in the Standard Model, as well to search for deviations from QCD that may arise due to new physical phenomena. As a member of the ATLAS Collaboration, I have played a leading role in the world's first cross-section measurements at a center-of-mass energy of 7 TeV of inclusive jet and dijet production, which involve final states containing at least one or two jets, respectively. Each "jet" is the result of a quark or gluon that hadronizes due to quark confinement, such that only the spray of hadrons (quarks bound together by the strong force) constituting the "jet" can be measured. Our jet measurements form the foundation for future precision tests of QCD at the LHC, including the precise measurement of the strong coupling constant, the determination of parton distribution functions (which describe the density of partons within hadrons), and constraints on non-perturbative QCD where the strong coupling constant becomes large and cannot be calculated analytically.

By performing searches using the invariant mass and angular distribution in dijet final states, we have also set the world's best limit on the possible existence of dijet resonances arising from excited quarks, as well as the best limit for contact interactions that may arise from quark compositeness. These analyses probe QCD in a new kinematic regime -- at high jet transverse momentum and large dijet mass -- that has never been investigated before, yielding sensitivity to exotic physics scenarios that may appear at these very short distance scales.

My hardware work has included substantial responsibilities for optimizing the performance, simulation, and operation of photo-electronics for the Minimum Bias Trigger Scintillator (MBTS) system, which was used to trigger the vast majority of the 2009 data that was collected and analyzed. I have also been involved in studies using both cosmic ray muons and collision data to commission the Tile Calorimeter, which measures hadronic energy depositions for jet measurements. In addition, I pioneered software for the remote monitoring system that is now used globally by the experiment, allowing collaborators worldwide to take remote shifts for detector operation and data quality.

To improve the detector performance, I have investigated a technique to remediate calorimeter failures using tracks reconstructed from charged particles passing through the detector. I have also studied a scheme to calibrate the absolute jet energy scale (JES) of the calorimeter using transverse momentum balance between a photon and a jet in the final state. The latter issue arises primarily due to the non-compensation of the hadronic calorimeter and is of critical importance for jet analyses, where the JES uncertainty is usually the dominant systematic uncertainty.

Publications

  • ATLAS Collaboration. "Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at sqrt{s_NN}=2.76 TeV with the ATLAS detector at the LHC." Phys. Rev. Lett. 105, 252303 (2010). Cover of Vol. 105, Issue 25.
  • ATLAS Collaboration. "Measurement of inclusive jet and dijet cross sections in proton-proton collisions at 7 TeV centre-of-mass energy with the ATLAS detector." Eur. Phys. J. C 71, 1512 (2011). Cover of Vol. 71, Issue 2.
  • ATLAS Collaboration. "Search for Quark Contact Interactions in Dijet Angular Distributions in pp Collisions at sqrt(s) = 7 TeV Measured with the ATLAS Detector." Phys. Lett. B 694, 327-345 (2011).
  • ATLAS Collaboration. "Search for New Particles in Two-Jet Final States in 7 TeV Proton-Proton Collisions with the ATLAS Detector at the LHC." Phys. Rev. Lett. 105, 161801 (2010).
  • E. Feng (for the ATLAS Collaboration). "Observation of Energetic Jet Production in pp Collisions at sqrt(s) = 7 TeV using the ATLAS Experiment at the LHC." Proceedings of Physics at the LHC 2010, DESY, 241-245 (2010).

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imai

Imai Jen-La Plante

B.S., University of Washington 2005 (Physics)
M.S., University of Chicago 2006 (Physics)
PhD (2011), Dept. of Physics
Experimental High-energy Physics
Awards: LHC Graduate Student Award (NSF), Gaurang & Kanwal Yodh Prize (Dept. of Physics), Nathan Sugarman Award (Enrico Fermi Institute)
Research Advisor: James Pilcher

The start of proton-proton collisions at the Large Hadron Collider (LHC) has opened a new era in particle physics. My research with Prof. James Pilcher uses the ATLAS detector to look at these collisions, which have the highest center-of-mass energies ever produced in a laboratory. Together with 3000 collaborators from all over the world, we reconstruct particles from data collected with the 7000 ton detector located in Geneva, Switzerland.

Among the first things to be measured at the LHC are properties of the W± bosons, mediators of the weak force in the Standard Model of particle physics. Observing these particles verifies our understanding of the detector performance and physics modeling at the new collision energies. They often decay to a lepton, such as an electron, and a neutrino, which passes through the ATLAS detector without depositing measurable energy. This gives a clear event signature, as the neutrino is identified by an imbalance of energy in the plane perpendicular to the direction of the colliding protons.

Finding such missing transverse energy particularly relies on the ATLAS calorimeters. The calorimeters are massive layers of the detector that stop electromagnetic and hadronic particles and measure their energy. During my early years in graduate school, I worked to prepare the hadronic calorimeter, especially by calibrating the front-end readout electronics, which were designed and built at the University of Chicago.

My current focus is to measure the associated production of W± bosons with quarks or gluons. The additional particles are mainly detected in the calorimeters as narrow sprays of energetic particles called jets. Measuring the production rates and properties of the jets in these events gives a precise test of Standard Model predictions that rely on sophisticated theoretical and numerical techniques. These predictions have not yet been proven at LHC energies and are essential to understanding our observations there.

One exciting possibility is that the data could contain evidence of new physics beyond the Standard Model. Many models of new physics predict particles that escape from the detector like neutrinos and can only be observed through missing transverse energy. Events where W± bosons decay to a lepton and neutrino are a key background in such models. Measuring the rate of these events and using them to understand the ATLAS detector and physics at the LHC is an important step toward potential discoveries.

Publications

  • ATLAS Collaboration, Measurement of the production cross section for W-bosons in association with jets in pp collisions at sqrt(s)=7 TeV with the ATLAS detector, Phys. Lett. B 698, 325-45 (2011).
  • I. Jen-La Plante for the ATLAS and CMS Collaborations, QCD Studies with W and Z Measurements at the LHC. PoS (EPS-HEP 2009) 305.

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jonathan Jonathan Logan

B.S., University of Florida 2004 (Physics)
M.S., University of Chicago 2006 (Physics)
Graduate Student (2004), Dept. of Physics, James Franck Institute
Experimental Condensed Matter Physics
Awards: Laboratory-Graduate Research Appointment (Argonne)
Research Advisor: Eric Isaacs

The microscopic structure and dynamics of magnetic domains underlie many properties of materials important for both fundamental science and technology. In the research group of Professor Eric Isaacs I have studied the physics of antiferromagnetic domain walls in both bulk and thin film Chromium. Antiferromagnetic domain dynamics are of great interest because they are implicated in basic problems in condensed matter physics such as high temperature superconductivity and ‘heavy’ fermions. Additionally, as antiferromagnets begin to find applications in areas such as pinning layers in spintronics, there is an increasing need for a more thorough understanding of the properties of their domains.

Chromium is an elemental antiferromagnet that displays magnetic and charge order common to considerably more complex materials. Below its Néel temperature of 311K, bulk Chromium exhibits an incommensurate spin-density wave characterized by a spin polarization wave vector S and propagation wave vector Q. We have investigated the slow domain dynamics naturally present in bulk Chromium even at low temperatures. Quantum dynamics have emerged in recent years as playing a critical role in the ground state properties of many modern condensed matter systems such as high-Tc superconductors, spin glasses and CMR manganites. Time-resolved coherent x-ray diffraction patterns may be used to measure spin and charge dynamics in bulk materials with sensitivity to the mesoscale dimensions. When microscopic spin or charge domains are present in the sample, coherent x-ray diffraction produces a speckle pattern that serves as a “fingerprint” of particular domain wall configuration.

We performed coherent x-ray speckle measurements of slow dynamics of domain walls separating microscopic regions with different orientations of the spin- (charge-) density waves in bulk Chromium samples [1]. By following the time evolution of speckle pattern, our measurements reveal a cross-over from thermally assisted domain wall motion to quantum tunnelling of domain walls below a temperature of 40 K. The dynamic behaviour provides insight into the free energy landscape of domain wall configurations and reveals that even at the lowest temperatures quantum fluctuations provide a path for the system to continue to explore alternate ground states.

To facilitate more precise measurements on individual antiferromagnetic domain walls, we have also devised a method for producing artificial domains of predefined size, number, and location [2]. This method uses a proximity effect of ferromagnetic layers to rotate Q in predetermined locations of Chromium thin film samples. We grew high quality single crystal Cr films which were covered by a layer of Fe. By combining photolithography and wet etching techniques, desired parts of an Fe cap layer are selected and then etched away to expose the underlying Cr film. When the process is complete, Q lies parallel to the film plane in the Fe-covered areas and perpendicular to the film in the Fe-etched areas. We then have a single film with Q domain boundaries at the border marking the presence or absence of the Fe cap layer. X-ray diffraction was performed on the uncapped and the Fe capped regions of the Chromium film confirming the creation of the antiferromagnetic domain boundary. We also performed an x-ray microprobe experiment with a submicron beam and showed that the artificial domain boundary has a width of less than our step size of 1 micron. The ability to engineer and control well defined and temporally stable antiferromagnetic domains is an important step forward for future studies of their physical properties as well as for the viability of their technological applications.

Publications:

  1. O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan and A. R. Sandy. Direct measurement of antiferromagnetic domain fluctuations. Nature 447, 68–71 (2007).
  2. J. M. Logan, H. C. Kim, D. Rosenmann, Z. Cai, R. Divan and E. D. Isaacs. Antiferromagnetic Domain Wall Engineering in Chromium Thin Films. (to be published).

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ying Ying Li

B.S., Peking University 2005 (Physics)
M.S., University of Chicago 2006 (Physics)
PhD (2011) Dept. of Physics
Theoretical Biological Physics
Awards: Robert Sachs Fellow (Dept. of Physics)
Research Advisor: Aaron Dinner

A lot of simple biological functions are well understood through experiments. However, it is still challenging to turn our knowledge about key molecular players in a complex system into a system-level understanding that is capable of making reliable predictions. So the first aim of my studies is to develop and apply computational models to understand how complex biological behaviors arise from physical and chemical features. Another feature of biological systems is out of equilibrium (irreversible). Although many theorems have been developed for the equilibrium, there are not many for non-equilibrium. The second aim of my studies is to improve our understanding of non-equilibrium theories through studies of biological systems. My research is in collaboration with Prof. Aaron Dinner.

Force transmission by focal adhesion

Cytoskeleton is a dynamic structure and has important functions in maintaining cell shape, enabling cellular motion, intracellular transport and cellular division. Actin filament, a type of cytoskeleton, is beneath the cell membrane and under retrograde flows. Structurally, actin filament is connected to extracellular matrix (ECM) through assemblies of proteins called focal adhesions (FAs). Stresses are generated in this structure by the relative motion between actin filaments and ECM. My study was to understand how the flow of actin filament affects the traction stress on the ECM. In the computational model, I simplified the structure into three layers (actin filaments, FAs and ECM from top to bottom) and molecular bonds between layers into springs. Under steady states, traction stress was found to be consistent with experimental observations, first increase and then decrease with the speeds of actin flows. Physics underneath is the competition between a decrease in protein bonds and an increase in stress per bond. Further extension into a multiple-layer model predicted two scenarios of collective motions. At small actin flows, the structure behaves as a whole and proteins move at progressively slower speeds from the actin-end to the ECM-end. At large actin flows, breakage occurs in the structure; proteins above the breakage move with the same speeds as the actin filaments and those below the breakage are immobile. The experiment was done by Prof. Gardel in Phys. Dept.

Cell fates in the immune system

B cells are an essential component of the adaptive immune system. The principal function of B cells is to make antibodies against antigens and such capability is affected by cells’ affinities to antigens. In doing so, B cells differentiate into antibody-secreting cells either directly or through an intermediate state, where they mutate intensively and modify their affinities. My study was to explain how a gene regulatory network enables B cell to select between two competing pathways to become antibody secreting cells. Five key proteins and their interactions were identified on the gene level, e.g., activation or repression of the expression of a protein by another one. Ordinary Differential Equations with noise terms were used to model the production and degradation of proteins in a single cell level. Kinetic Monte Carlo was used to model behaviors in a population level, e.g., division, death and mutation. The key discovery was the ghosting effect, which states a control parameter (initial affinity to antigen) determines the time for a system to go through a particular region in the phase space (intermediate state). The biological rationale is that B cells whose initial responses to antigen are poor need editing in their surface receptor to improve the effectiveness (affinity) in eliminating antigens. The ghosting effect also enabled me to distinguish between two similar mechanisms (dynamic control v.s. bistability), which is beyond steady-state analysis, e.g., bifurcation diagrams. This work was in collaboration with a recent physics graduate in my group and the Prof. Singh in Immunology.

Single molecule trajectories of RNA folding

This part of research focuses on non-equilibrium dynamics. The plan was to periodically drive the system and observe the responses. Experimentally, our collaborators fluorescently labeled two positions in RNA molecules, put them in a magnesium solution whose concentration varied over time in a controlled fashion and recorded the trajectories of the efficiency of fluorescence resonance energy transfer (FRET). FRET informed us the distance between two labels and the conformational changes (folding). There are two challenges: 1) Only distances in one or two coordinates are recorded such that the observed dynamics are usually non-Markovian due to the projection from high dimensions; 2) the non-equilibrium nature of the measurement limits the choice of theoretical tools.

I studied the problem from two directions, the microscopic schemes that controls transitions between RNA folding states and the Fluctuation theorem for a projected system. In the first direction, I represented the stable folding states as wells in the phase space and transitions between states as barrier crossing. The function of magnesium ion was to change the relative positions and the chemical potentials of the stable folding states as well as the friction of motion in the hidden dimensions. I developed a hybrid approach that modeled the motions in the observed dimension as a discrete stochastic process by using a discrete Master equation and the motions in the unobserved dimensions as a continuous stochastic process by using a Langevin equation. This phenomenological model attributed the non-Markovian dynamics and a wiggled relaxation to an approximately oscillatory and slow motion in the hidden dimensions driven by the changing magnesium concentration. In the second direction, I extended the study to derive a general Fluctuation Theorem for non-equilibrium systems that are both stochastic and projected. In the second law of thermodynamics, irreversible processes result in an increase in entropy. However, microscopic events can deviate from ensemble expectation and consume rather than produce entropy. Fluctuation Theorem constrains the statistics of observing such events and presents a general mechanism capable of describing processes arbitrarily far from equilibrium, including those in living systems. People have derived fluctuation theorems for systems in steady state or stable limit cycle. However, in these works, all the microscopic states are observed (no projection). So understanding how projection of a dynamics impacts the application of fluctuation theorems is of interest for interpreting experiments. My study has shown that entropies of single trajectories can change sign under projection and projection also makes systems appear closer to equilibrium to an extent determined by the dimension of the driving. That is, if the driving impacts transitions in the hidden dimensions, the systems appear more equilibrated because the driving is washed out by projection.

Publications:

  • A network architecture that translates signal strength into gene expression duration to diversity a cellular state. Sciammas, R.*, Warmflash, A.*, Li, Y.*, Dinner, A.R. and Singh, H., submitted to Cell (* equal contribution).
  • Model for how retrograde actin flow regulates adhesion traction stresses. Li, Y., Bhimalapuram, P. and Dinner, A.R., J. Phys.: Condens. Matter, 22, 194113 (2010).
  • Models of single-molecule experiments with periodic perturbations reveal hidden dynamics in RNA folding. Li, Y., Qu, X., Ma, A., Smith, G.J., Scherer, N.F. and Dinner, A.R., J. Phys. Chem. B, 113, 7579 (2009).
  • How focal adhesion size depends on integrin affinity. Zhao, T., Li, Y. and Dinner, A.R., Langmuir, 25, 1540 (2009).
  • How the nature of an observation affects single-trajectory entropies. Li, Y., Zhao, T., Bhimalapuram, P. and Dinner, A.R., J. Chem. Phys., 128, 074102 (2008).

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ibrahim Ibrahim Sulai

B.S., Allegheny College 2004 (Physics)
M.S., University of Chicago 2006 (Physics)
PhD (2011), Dept. of Physics, Enrico Fermi Institute
Experimental Atomic & Nuclear physics
Awards: Nathan Sugarman Award (Enrico Fermi Institute), David W. Grainger Fellowship (Dept. of Physics)
Research Advisor: Zheng-Tian Lu

Working under the supervision of Zheng-Tian Lu, I have been involved in studies whereby the tools of precision atomic physics are applied to atoms with interesting nuclei in order to test nuclear structure theories and to search for the possible violation of discrete symmetries.

For the first couple of years, I worked on a project to measure the nuclear charge radius of the helium-8 isotope. This is a very neutron - rich system, and has a so called neutron halo. Current advances in microscopic nuclear structure theories allow for the description of such few-body nuclear systems with increasing precision. An equally precise determination of the charge radius therefore serves as a test of these theories.

Because of the short half life of helium - 8 (119 ms), a traditional probe of the nuclear charge distribution using electron scattering on a fixed target could not be readily applied. Instead, our approach relied on determining the charge radius by performing precision atomic spectroscopy such that in effect, the bound electrons probed the nucleus--yielding information about the finite nuclear size. The measurements were made on single helium atoms which were trapped in a magneto-optical trap. This was performed at GANIL, a cyclotron facility in Normandy, France where the isotopes were produced.

Back in Chicago, at Argonne National Laboratory, I worked on laser cooling and trapping radium atoms in preparation for a search for the permanent electric dipole moment (EDM) of radium-225. A permanent EDM necessarily vanishes as a consequence of the discrete symmetries of parity (P) and time-reversal symmetry (T). A non-zero EDM would therefore signify the violation of these two symmetries. Radium-225 is believed to be particularly sensitive to interactions which are odd under P and T. This experiment is still underway.

Publications:

  • Trimble et al. Phys. Rev. A 80, 054501 (2009).
  • Holt et al. Nuc. Phys. A 844, 53c (2010).
  • Sulai et al. Phys. Rev. Lett. 101, 173001 (2008).
  • Mueller et al. Phys. Rev. Lett. 99, 252501 (2007).

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arun Arun Thalapillil

B.E., Birla Institute of Technology and Science - Pilani 2005 (Electrical & Electronics Engineering)
M.Sc., Birla Institute of Technology and Science - Pilani 2005 (Physics)
M.S., University of Chicago 2006 (Physics)
Graduate Student (2005), Dept. of Physics, Enrico Fermi Institute
Elementary Particle Theory
Awards: Sidney Bloomenthal Fellowship (Dept. of Physics), Subrahmanyan Chandrasekhar Memorial Fellowship (Dept. of Physics)
Research Advisor: Jonathan L. Rosner

My research interests lie broadly in theoretical particle physics. All phenomena we have encountered to date in nature may ultimately be reduced to four fundamental interactions- gravitational, electromagnetic, weak and strong force. Particle physics deals mainly with the last three of these interactions. We currently have a very successful theory of elementary particles and their interactions, prosaically called the `Standard Model’ (SM). This is based on a quantum field theory and has been quite well tested experimentally over the past many years. In spite of its remarkable success though, there are compelling reasons to suspect that it’s incomplete. Generation of particle masses, the hierarchy among these masses, matter-antimatter asymmetry in the universe, presence of dark matter are among the open questions. My time in graduate school has been spent preparing for the next generation of collider and non-collider experiments, where some of these questions will be probed.

The Large Hadron Collider (LHC) at CERN, Geneva is the world’s highest energy particle accelerator, one aim of which is to discover the Higgs boson which is believed to give masses to all other elementary particles. The production and decay mechanisms of the Higgs boson in a collider has been extensively studied in the context of the SM and the Minimal Supersymmetric Standard Model (MSSM). But if the Higgs boson is relatively light and has some exotic decays, for instance to 4 jets, then the backgrounds would completely swamp the signal and a detection at the LHC would be almost impossible. Along with my collaborators, we recently studied such a case of a relatively light-higgs boson decaying into 4-jets. We were able to show that using jet-substructure techniques we can reduce the background sufficiently to enable detection.

Another aim of the LHC is to look for hints of new physics beyond the SM. A promising candidate in this direction is Supersymmetry, which predicts ‘superpartners’ for all particles in the SM (squarks for quarks, gluinos for gluons etc.). My collaborators and I studied search strategies for associated squark and gluino production at the LHC, using jet-shape variables, in the case when the squark is heavy. The discovery of such a scenario is complicated because heavy squarks decay primarily into a jet and boosted gluino, yielding a dijet-like topology with missing energy (MET) pointing along the direction of the second hardest jet. The result is that many signal events are removed by standard jet/MET anti-alignment cuts designed to guard against jet mismeasurement errors. We suggested in the work that replacing these anti-alignment cuts with a measurement of jet substructure can significantly extend the reach of this channel while still removing much of the background.

The possibility of light scalar/pseudo-scalar particles in the GeV mass-range has received renewed attention recently in the context of certain experimental anomalies and dark matter searches. We explored the consequences of a fermiophobic (i.e. no coupling to fermions) sector in the context of bound states and astrophysics/cosmology. To make our treatment as general and comprehensive as possible we looked at fermiophobic Unparticles (which in the limit of the scaling dimension tending to 1, give scalar and axion-like particles). Apart from pointing out theoretical aspects of the Unparticle-Uehling potential, energy level ordering and astrophysical constraints, we commented that if there is improvement in the Nuclear/QED theory of high-Z muonic-atoms then muonic-atom spectroscopy can potentially be complementary to collider based searches. This is especially pertinent in the context of many upcoming and proposed experiments to look for coherent muon-electron conversion (lepton-flavor violation) in muonic atoms.

Recently, a novel parametrization and framework to study gauge mediation models (GM) was introduced in the literature, termed general gauge mediation (GGM), which showed that the actual space of possibilities in GM are larger than what was once thought. We looked at features (for instance the NLSP topography) and constraints in the MSSM/NMSSM with GGM, in the context of low-energy observables like muon anomalous magnetic moment and flavor observables. It was found that there are strong constraints on the GGM space from these low-energy observables as well as interesting relations among the various quantities.

Publications:

  • J. Fan, D. Krohn, P. Mosteiro, A. M. Thalapillil, and L. T. Wang, Heavy Squarks at the LHC, JHEP 1103, 07(2011) [arXiv:1102.0302[hep-ph]].
  • A. M. Thalapillil, Low-energy Observables and General Gauge Mediation in the MSSM and NMSSM, JHEP 1106, 059 (2011) [arXiv:1012.4829 [hep-ph]].
  • A. Falkowski, D. Krohn, L. T. Wang, J. Shelton and A. Thalapillil, Unburied Higgs, [arXiv:1006.1650 [hep-ph]].
  • A. M. Thalapillil, Bound states and fermiophobic Unparticle oblique corrections to the photon, Phys. Rev. D 81, 035001 (2010) [arXiv:0906.4379 [hep-ph]].

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