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Elementary Particles And Fields
One of the great triumphs of twentieth century physics was the elucidation of the structure of matter and the forces that govern it. The language describing this subnuclear world is the language of quantum field theory. Field theory is central to understanding the extreme quantum and relativistic phenomena at this level of structure. Our improved understanding of field theory has also provided us with the tools to go beyond the standard model. Its interrelation with mathematical ideas from modern geometry and topology have broadened our horizons and led to physics beyond the Standard Model. Supersymmetry and string theory have deep and important roots in our modern understanding of field theory. Physicists at Syracuse are actively engaged in consolidating and extending our understanding of this level of structure in our world using quantum field theory and its modern developments.
Beyond Standard Model and Extra Dimensions (Kaustubh Agashe) Prof. Agashe's research is in the field of theoretical particle physics. Agashe works on ideas going beyond the standard model (SM) of particle physics, a theory developed over the past couple of decades which accounts for the interactions of the elementary particles. Such extensions of the SM are motivated to solve many of the problems of the SM such as existence of enormous mass hierarchies or the nature of dark matter of the universe. Agashe is interested in both building models along these lines and also their phenomenology, i.e., connecting these ideas to experiments. Specifically, his work has focused on two such extensions of the SM: supersymmetry (SUSY), which is a symmetry relating particles whose spins differ by 1/2 unit, and the existence of extra spacetime dimensions.
Agashe's recent work has been on the framework of a "warped" extra dimension. Agashe and his collaborators have shown that this idea solves many of the puzzles of nature: it provides an explanation for the mass hierarchies and a candidate for dark matter and also unifies the three forces of the SM. Hence, this framework is a worthy competitor to the more popular idea of SUSY which also enjoys some of the same successes. Currently, Agashe is working on making predictions for this framework which can be tested in ongoing and upcoming experiments, especially the large hadron collider (LHC) which will be operational at the CERN laboratory in Europe in a few years.
Effective Lagrangians (J. Schechter) Professor J. Schechter and co-workers have been actively investigating effective chiral Lagrangians to describe strong interactions at low energies. The underlying idea is to see how far one can get using the symmetry structure of QCD, including the various quantum anomalies, and the observed low energy spectrum. This approach has become increasingly accepted as a valuable tool for studying the phenomenology of strong and weak interactions. It is rich in consequences and, perhaps surprisingly, in no danger of being soon exhausted. In fact, the general approach seems to have become a paradigm for treating theories in which either the exact behavior is too difficult to obtain or the theory, away from a low energy region, is actually unknown. A related important feature of interest is the treatment of baryons as solitons (Skyrmions) associated with this Lagrangian.
Of particular interest to the Syracuse group has been the description of the low-lying scalar mesons. Effective Lagrangians incorporating scalar and vector mesons have been constructed and examined in detail to expose the structure of this mysterious nonet. Detailed calculations of scattering, starting from the proposed effective Lagrangians, are an important tool in this project. In ongoing studies it is planned to investigate different approaches to its unitarization and to account for channels opening at higher energies.
Evidence from these studies indicates that the conventional nonet has strong four quark components. The low lying scalar meson sector is then a jumble of two and four quark states. Professor Schechter and collaborators will be studying the symmetry breaking patterns, scattering and decay properties involving scalar states in order to shed light on these issues. Unraveling the structure of these states is an ongoing project.
Fuzzy Physics and Noncommutative Geometry (A. P. Balachandran) Conventional discretizations of quantum fields on a manifold replace the latter by a lattice of points. This is the basis for the important work on lattice gauge theory. An alternative discretization, which leads to fuzzy physics treats the manifold as a phase space and quantizes the manifold. The manifold becomes a fuzzy manifold. Continuum physics emerges as a classical limit of the fuzzy manifold. Fuzzy physics provides an alternative to the standard methods of lattice field theory. Functions on the original manifold commute, but they become non-commutative on quantization. The fuzzy path thus leads to noncommutative manifolds and their geometries.
In the recent past Balachandran and coworkers have made substantial contributions to the theory of quantum field theories on fuzzy spaces. They have formulated gauge theories, developed a precise theory of monopoles and instantons, formulated chiral fermions without fermion doubling and proved the axial anomaly in the framework of fuzzy physics. Balachandran and coworkers have published a book on this subject entitled "Lecture Notes on Fuzzy and Fuzzy SUSY Physics".
These investigations suggest many directions for research. With few exceptions existing literature treats fuzzy physics in 2 dimensions. Balachandran and coworkers are making progress in extending these studies to more realistic 4 dimensional spaces. When completed this will be an alternative to the standard lattice discretization. Supersymmetry can be formulated on fuzzy spaces. The full formulation of supersymmetry including topological states remains to be done and is a focus of the Syracuse group.
A related development concerns the formulation of quantum field theories on noncommutative spacetime. Such spacetimes are suggested by quantum gravity and string physics. Balachandran and coworkers have published extremely in this field and proved such fundamental results as the breakdown of Pauli principle in such spacetimes. Application to low energy phenomena such as quantum Hall effect have also been found. Work is now on progress applying these ideas to cosmic microwave background and exploring their consequences to experimental particle physics.
Lattice Supersymmetry and Technicolor (Simon Catterall)
Prof. Catterall is currently interested in theoretical and computational lattice studies of theories which attempt to go beyond the Standard Model of particle physics.
In the past he has worked on discrete theories of quantum gravity and string theory but more recently has been interested in studying supersymmetric theories on the lattice. He has developed new lattice formulations which allow an element of supersymmetry to be preserved exactly at non-zero lattice spacing and has begun studying these theories using Monte Carlo simulation. Such studies can potentially cast light on conjectured dualities between supersymmetric gauge theories and gravity and have impact and application in string and M-theory.
He has also recently begun investigations of lattice gauge theories with fermions in higher dimensional representations. Such models are conjectured to develop conformally invariant phases as the number of fermion flavors is increased. Close to these points the theory exhibits a slow evolution of the coupling with energy scale -- the theory walks. We have been examining the minimal model with 2 colors and 2 flavors which can form the basis of a technicolor model for breaking the electroweak theory with a light composite Higgs.
Prof. Catterall is a member of the USQCD collaboration and has access to multi Teraflop scale supersomputers at Fermilab and Jlab for carrying out these studies.
Neutrinos (Schechter) Recent experimental results from super Kamiokande and Sudbury strongly suggest the existence of neutrino oscillations and neutrino masses. Schechter and students introduced a so-called complementary ansatz for the mass matrix which, when taken together with the experimental information, would be sufficient to determine the neutrino masses themselves. It will be of interest to consider more extensive fits giving precedence to certain experiments.
Recently it has been suggested that our universe corresponds to a 3+1 dimensional membrane embedded in a higher dimensional compactified space. Particles with nontrivial standard model quantum numbers are postulated to propagate only on the membrane. This opens up interesting possibilities for the neutrino sector since possible right-handed neutrino fields and some Higgs fields do not carry standard model quantum numbers. Schechter with students and Sannino are investigating possible experimental consequences of a Higgs singlet which can propagate in the bulk outside the membrane.
Non-commutative Geometry (Kameshwar Wali) Noncommutative geometry provides a mathematical framework to study the interplay of elementary particle interactions and gravity. Along with Einstein gravity the action functional that emerges from these considerations involves scalar and vector interactions. If we ignore the vector interactions we have a model that has a well-specified scalar potential that can account for inflation. The scalar field has a mass and hence it does not face the usual problem of a dilaton. Wali and collaborators are investigating the implications of these ideas for cosmology. A cosmological constant with adjustable magnitude is possible.
There are indications that the field theories constructed with non-commutative geometries have improved high energy behavior. Wali is investigating whether this leads to improved renormalizability in realistic models of the standard model.
Quark Gluon Plasma (Carl Rosenzweig) Professor Rosenzweig has a program to study the possible utility of the Upsilon particle as a probe of the Quark Gluon Plasma (QGP). In work with a graduate student, Golumbeano, he showed that Upsilons with shifted masses may survive the formation and subsequent cooling of the plasma. Studies are currently underway to test the robustness of the mass shift to changes in potential and screening mechanism. In addition they will look at correlations between the mass shift in Upsilon states and suppression of J particles and higher ( 1P, 2S etc.) bottomonium states for more detailed information of the conditions of the original QGP.
Another area of research involves the color superconducting phase of QCD. Although the observability of this phase is still not clear, the theoretical case for its existence is strong. The phase bears a strong resemblance to the hadronic phase with prominent diquarks, chiral symmetry breaking etc. It is possible that we can glean insight into the confined phase by studying properties of the superconductor phase. In particular the diquark model has been unexpectedly successful in describing hadron spectroscopy and fragmentation. The analogous prominence in the superconducting phase may shed light on the hadronic phase.
Spin and Statistics (Balachandran) A fundamental theorem in Quantum Field Theory (for flat background metrics) concerns the relation between spin and statistics. For n identical particles the 2p rotation of a particle is exactly the same as the exchange of any two particles. In canonical quantum gravity there is strong evidence from previous work at Syracuse that this result can be falsified for the Friedman-Sorkin geons unless topology change is allowed. Balachandran and coworkers have been studying this theorem using an approach based on certain algebras. They reflect the diffeomorphism invariance of the theory, allow for topology change and serve to select a family of vector bundles to define the quantum Hilbert space. A program is underway to understand the spin-statistics theorem in this more general setting. Novel spin-statistics relations have already been established for geons in (2+1) dimensions.
Supersymmetry-inspired QCD (Schechter) It is natural to hope that information obtained from the more highly constrained supersymmetric gauge theories can be used to learn about ordinary gauge theories, notably QCD. Sannino (a former student now at Nordita) and Schechter proposed a speculative toy model to illustrate how the effective Lagrangian for super-QCD might go over to the one for QCD. The implementation of this approach involves a suitable choice of possible supersymmetry breaking terms. The exploration and exploitation of this model offers much insight into how super-QCD and QCD might be related. The dominant piece of the QCD Lagrangian possesses a kind of tree level holomorphicity. Physically this corresponds to the explicit realization of the axial and trace anomalies. In fact, the holomorphic piece of the Lagrangian was derived on this basis by Hsu, Sannino and Schechter. They suggested a decoupling procedure when a flavored quark becomes massive and mimics the one employed by Seiberg for supersymmetric gauge field theories. It is seen that, after decoupling, the QCD potential naturally converts to the one with one less flavor. These studies will be extended to studies of chiral phase transitions. These models can continue to give us insight into supersymmetry and QCD.
Topological Defects / Branes in Field Theory and Supersymmetry (Mark Trodden) Professor Trodden and coworker Sean Carroll (U. Chicago) introduced a new class of topological defects in ordinary field theories. These configurations consist of topological solitons which end on others of equal or higher dimension. In such models, the higher dimensional defect provides Dirichlet boundary conditions for the lower dimensional one. We therefore term these configurations Dirichlet topological defects, since they are the field theory analogues of string theory D-branes.
A natural extension of this work was to the behavior of brane junctions in supersymmetric Yang-Mills theories. Trodden, Carroll and Simeon Hellerman (Stanford) were able to show that intersecting domain walls in such theories are 1/4-BPS states, and as such are important tools for probing the nonperturbative structure of these theories. Further, they were able to derive mass bounds on BPS junctions, and relate these to the behavior of the Kahler potential of the theory. In a second study, they included gravity. By examining a class of supergravity-like theories, they demonstrated a set of important results relevant to Randall-Sundrum type models in which the 3+1 dimensional universe exists at the intersection of two or more higher dimensional branes.
Trodden, with Anne-Christine Davis and Steven Davis (Cambridge) has also investigated the particle physics and cosmological properties of topological defects in supersymmetic theories. Their first study, dealing with abelian theories demonstrated that all spontaneously broken abelian supersymmetric theories admit cosmic string solutions which are superconducting due to fermion zero modes. Further, by using supersymmetry transformations, they showed how to calculate the supercurrents in terms of the background String fields. The second paper extended these results to nonabelian theories and investigated the effects of soft supersymmetry breaking. Such defects lead to strong cosmological constraints, and these techniques should prove powerful tools with which to constrain proposed particle physics models using cosmological arguments.
