Research
I aim to make this discussion of my research broadly (if not universally) accessible. I have been publicly funded for most of my career, so I should explain to taxpayers the work they have made possible. I also hope to contribute to public understanding of science, an important issue in its own right. If you have any questions about my research, you are welcome to contact me. Experts may wish to skip straight to my publications or statement of research interests.
Contents
Overview: strong dynamics and lattice field theory
My research focuses on theories of particle physics that involve strong interactions. The most familiar strongly-interacting theory is quantum chromodynamics (QCD), the "color" theory of the strong nuclear force that binds quarks and gluons into composite particles such as protons. To understand why we say this interaction is "strong", imagine pulling apart two quarks: separating them by a femtometer (10-15 m) would require a force of roughly 10 tons to balance the attractive color force pulling the quarks together. That's strong.
Strongly-interacting theories are very challenging to study because they cannot be treated by the standard analytical approach known as perturbation theory. This method treats interactions as minor corrections ("perturbations") to simpler systems, and can only be applied when interactions are weak in strength. In the case of QCD, we have the benefit of decades of experiments to help guide our understanding. This is not yet an option for hypothetical strongly-interacting theories that may be discovered by the Large Hadron Collider at CERN, the European Organization for Nuclear Reserach. Experimental guidance may never be available for purely theoretical scenarios that we can consider in order to improve our understanding of strongly-interacting systems in general.
In order to study QCD and other strongly-interacting theories from first principles, I perform numerical lattice field theory calculations. In this approach, space and time are replaced by a regular, finite lattice of discrete sites connected by links. The fields described by the theory are likewise discretized, and defined on the lattice in such a way that we recover the original theory in continuous spacetime when the lattice is taken to be infinitely large, with its sites infinitesimally close together. The discretized theory involves "only" millions of degrees of freedom, which allows us to stochastically calculate observables through long-established numerical techniques known as Monte Carlo importance sampling. These techniques require large-scale supercomputing.
The great benefit of lattice calculations is that they provide non-perturbative means to study strongly-interacting systems. Lattice field theory is currently the only method that can provide quantitatively-reliable predictions for strongly-interacting theories from first principles, and this will remain the case for the foreseeable future. The disadvantage of the approach is that it is extremely computationally intensive, and continues to push the bounds of high-performance computing.
The active field of lattice QCD applies lattice techniques to study the strong nuclear force, from the level of individual quark and gluon fields to the level of (small) atomic nuclei. In addition to lattice QCD, I also research superficially similar theories that hypothesize new, strongly-interacting forces to explain the origin of elementary particles' masses. To make our research possible and practical, we must aggressively develop and apply novel computational algorithms, and make full use of all advances in technology, both hardware and software. These three topics -- lattice QCD, the origin of mass, and high-performance computing -- are discussed in more detail below.
Quantum chromodynamics and the strong nuclear force
As the fundamental theory of the strong nuclear force, quantum chromodynamics is responsible for quarks being confined into composite particles such as nucleons (protons and neutrons), through the quarks' interactions with gluons. The picture below illustrates where quarks and nucleons fit into the structure of matter, but you should not take it too literally: The mass of the proton is roughly 100 times the mass of the three quarks that the picture shows it being made out of. The vast majority of the mass of composite particles (and thus of the visible universe) comes from the energy of strong QCD interactions.
Lattice QCD dates back to the 1970s, although the first numerical lattice QCD computations were not performed until the 1980s. The field has advanced steadily since then, in parallel with the development of high-performance computing. Lattice QCD calculations are now able to predict the mass of the proton with percent-level accuracy, the culmination of decades of progress.
Predicting particle masses is only one of the many calculations that one can perform with lattice QCD, and in many ways it is one of the easiest. My own work in this field has focused on studying the strange quark content of nucleons [arXiv:1012.0562]. Although strange quarks are not among the "valence" quarks that determine the quantum numbers of the nucleons, the energy of the strong interaction allows pairs of strange quarks and antiquarks to be continually produced and annihilated through quantum processes. These "virtual" strange quark pairs account for a portion of the nucleon's mass, and affect its internal structure.
Determining the role of strange quark pairs in the nucleon may be crucial to understanding the nature of the dark matter that makes up the majority of the (visible and invisible) mass in the universe. Many models predict that the dark matter may couple more strongly to strange quarks than to the lighter (up and down) valence quarks. (It can couple even more strongly to heavier charm and bottom quarks, but there isn't enough energy in the nucleon to produce very many of those.) In order to predict how strongly the dark matter should couple to the nucleon as a whole (and thus to all the atoms and matter made out of nucleons), the strange quark content of the nucleon needs to be determined. Without this knowledge, it becomes more difficult to estimate which models of dark matter are still consistent with experimental constraints.
The fact that only strange quark pairs appear in the nucleon makes their contribution very difficult to evaluate on the lattice. In the mathematical shorthand of Feynman diagrams, strange quark pairs appear as closed loops that couple to the valence quarks of the nucleon only via gluon fields. In order to evaluate such "quark-line disconnected diagrams" exactly, the computation must be repeated with the strange quarks' closed loop beginning at every possible point in space and time (that is, every site on the lattice). This is not computationally feasible, so instead we are forced to develop methods to estimate the result. This still requires much more computing than does evaluating connected diagrams, and introduces a new source of statistical error.
Dynamical electroweak symmetry breaking and the origin of mass
While the energy of strong QCD interactions is responsible for the vast majority of the mass of composite particles, a small fraction comes from the masses of elementary particles themselves. The elementary particles, such as the quarks and electrons highlighted in the picture below, are those objects that do not yet exhibit any signs of substructure. So far as our best experiments can determine, elementary particles are points of zero size. Many of them possess nonzero masses, however, the origin of which is a longstanding mystery in particle physics.
More than 50 years ago, physicists realized that a fundamental symmetry of nature (the electroweak unification of electromagnetism and the weak nuclear force) appeared to be incompatible with the existence of massive elementary particles. This difficulty was overcome in the 1960s with the discovery that the electroweak symmetry can be hidden (or "spontaneously broken"), a process popularly known as the Higgs mechanism. While the generic picture of electroweak symmetry breaking (EWSB) has been strongly supported by experiments since the 1970s, the physics underlying this process remains unknown. Understanding EWSB is a central challenge in particle physics today, and is the main goal of the Large Hadron Collider at CERN, the European Organization for Nuclear Research.
A theoretically-elegant explanation of electroweak symmetry breaking relies on the existence of some new force (call it "technicolor") that becomes strongly-interacting at distance scales some 1000 times smaller than characteristic scale of QCD. That is, if we imagine pulling apart two hypothetical technifermions that feel this force, we would need 10 tons of force to separate them by as little as an attometer (10-18 m), compared to the femtometer scale of QCD mentioned in the first paragraph on this page.
As you can guess from the discussion above, theories of electroweak symmetry breaking through new strong dynamics are analytically intractable due to their reliance on strong interactions. As a result, although these theories were introduced in the 1970s, we do not yet know whether they can successfully explain the origin of mass. Using numerical lattice field theory to study new strong dynamics may seem intuitively obvious. However, lattice studies relevant to EWSB are more computationally demanding than the corresponding lattice QCD investigations, and have only started to become practical in the last few years.
My work in this field so far has been carried out as a member of both the Lattice Strong Dynamics (LSD) Collaboration and the US BSM Collaboration of USQCD. With the LSD Collaboration, I have explored how the behavior of strongly-interacting theories changes depending on how many types of light fermions feel the corresponding force [arXiv:0910.2224, arXiv:1002.3777]. Only two light quarks (the up and down quarks) feel the strong nuclear force, a very small number. As more fermions feel a force, the low-energy (long-distance) behavior of the corresponding interaction changes dramatically.
A particularly important observable to investigate this way is known as the S parameter [arXiv:1009.5967]. In the absence of direct evidence revealing the physics responsible for electroweak symmetry breaking (which the Large Hadron Collider may discover), decades of effort have been dedicated to using precise measurements of electroweak observables to constrain possible theories of EWSB. S parameterizes this information, and provides the tightest constraints on theories of new strong dynamics.
However, because physicists were previously unable to perform quantitatively-reliable non-perturbative calculations of strongly-interacting theories, they often studied theories of new strong dynamics by assuming that these theories closely resemble QCD, and therefore can be related to experimental measurements of the strong nuclear force. Because of how the behavior of strongly-interacting theories changes depending on how many types of light fermions feel the corresponding force, this approach is only applicable to a subset of possible models.
Experimentally, the S parameter is small and negative, S ≈ -0.15 ± 0.10. If QCD were used to model new strong dynamics, as discussed above, it would imply S > 0.3, in considerable disagreement with experiment. This corresponds to the red points in the plot below, which I calculated using lattice QCD and published in arXiv:1009.5967. The blue points come from calculations of new strong dynamics with three times as many light fermions as QCD. For this model, we find that S can be significantly smaller than for QCD, much closer to the experimental value.
High-performance computing: algorithms and machines
Both calculations of the strange quark content of the nucleon, and explorations of new strong dynamics on the lattice, share a common feature: they are extremely computationally demanding, even by the high standards of lattice field theory. The work discussed above was only possible thanks to steady advances in numerical algorithms complementing improvements in computing hardware, and this work will become even more important in the future.
A basic ingredient of lattice calculations is repeated solution of a linear system, Ax=b, where A is a large sparse matrix known as the Dirac operator. By "large", I mean that this matrix formally has millions of rows and millions of columns. Even though the matrix is sparse (most entries are zero), this is far too much data to store in a computer's memory. We use iterative techniques such as the conjugate gradient algorithm to solve this equation for x without explicitly writing down the full matrix A. It is this iterative calculation that must be performed repeatedly to evaluate the quark-line disconnected diagrams mentioned above.
In recent years, calculations involving disconnected diagrams have benefited greatly from the development and application of multigrid algorithms that dramatically decrease the computational cost of each solve. Multigrid algorithms represent the physical system on a succession of coarser grids with smaller systems to solve, adaptively determining the best representation of the system on the coarser levels. Applied to the studies reported in arXiv:1012.0562, multigrid algorithms can reduce costs by up to an order of magnitude, which made possible a new direction of research: performing disconnected diagrams calculations that involve the light (up and down) quarks in addition to strange quarks.
On the hardware side, graphics processing units (GPUs) have produced comparable performance improvements in certain calculations. GPUs can sustain enormous rates of computation, but memory and bandwidth constraints make it difficult to apply GPU computing to many common problems. These sorts of difficulties will likely become more severe as high-performance computing continues to evolve in coming years. Cheap and rapidly improving GPUs can be an ideal testbed for developing software that will get the most out of future computers.
In addition to working on projects (discussed above) that apply GPU computing and multigrid algorithms to reduce computational burdens, I have also performed research into the development of other improved algorithms [arXiv:0906.2813], though this work is a bit too specialized to discuss in detail here. A final interesting aspect of this line of research is that it can provide an ideal entry point into the field. We often use simple models to design and test improved techniques, including the two-dimensional systems such as graphene [arXiv:0902.0045, arXiv:1101.5131]. These smaller-scale computational projects can be more tractable for beginners, while still providing significant benefits to the field as a whole.
Last modified 1 September 2011.
