Elementary Particles

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.

Effective Lagrangians (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. 

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.

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 (Balachandran)

Hints from quantum gravity and string theory suggest that the algebra of functions on spacetime may be noncommutative. In particular time and space coordinate functions may not commute, just as position and momentum in quantum theory do not commute. Consistent formulation of quantum theory on such spacetimes is of considerable conceptual and phenomenological interest. Qualitative considerations already suggest deep physical effects like violations of causality and the spin-statistics theorem. It is important to study these effects precisely. Balachandran and collaborators have undertaken a systematic formulation of quantum physics on noncommutative spacetime manifolds .Examples of violation of the spin-statistics theorem ,and even quantisation of time have been found. In the latter, energy is conserved only modulo a fixed unit E. Such models find concrete applications in quantum cosmology. They affect the black body spectrum including that of the cosmic microwave background as standard microcanonical and canonical ensembles are no longer valid. Systematic studies of these modifications are under way.

Related work concerns noncommutative deformations of conformal field theories. There exist systematic ways of deforming the algebra of functions on certain manifolds. Balachandran and coworkers have developed these ideas and constructed noncommutative deformations of well-known conformal field theories like the Wess-Zumino-Witten model.These deformations seem integrable.Current research concerns their detailed study including their renormalisation group equations.The possible existence of an analogue of the Zamalodchikov c-theorem is also being looked into.

Fuzzy Physics (Balachandran)

Conventional discretizations of quantum fields on a manifold replace the latter by a lattice of points. This is the basis for lattice gauge theory. An alternative discretization, which leads to fuzzy physics, treats the manifold as a phase space and quantizes the manifold. The manifold thus 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 noncommutative 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. The efficacy of this method of regulating quantum field theories have also been tested using numerical simulations.

These investigations suggest many directions for future research. In particular, with few exceptions, existing literature treats fuzzy physics in two dimensions. Balachandran and coworkers are making progress in extending these studies to more realistic four- dimensional spaces. When completed, this approach will be an alternative to the lattice discretization of the standard model.

Supersymmetry has also been formulated on fuzzy spaces. Numerical simulations on these supersymmetric models have now been initiated.

Non-commutative Geometry (Wali)

It is widely recognized that our present concepts space and time have proved inadequate for a unified description of elementary particle interactions. In recent years, Alain Connes has proposed a far reaching mathematical framework to explore non-commutative spaces and in so doing has provided an alternate approach to study the structure of space-time. Following the general ideas of Connes, Professor Wali (along with Nguyen Ai Viet) has developed a formalism that follows closely the Riemannian geometric approach to construct action functionals on a two sheeted space-time that can be looked upon as discretized version of Kaluza-Klein theory. The compact circle in the usual theory is replaced by two discrete points representing two copies of space-time. The resulting gravitational sector has a rich and complex structure with pairs of tensor, vector and scalar fields with one member of each pair having zero mass and the other massive. Matter fields living in such a space possess parity violating interactions originating from the generalized gravity sector. This could be of great significance in providing the much needed CP violation to explain baryon-anti-baryon asymmetry.

Quark Gluon Plasma (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.

Topological Defects / Branes in Field Theory and Supersymmetry (Trodden, Wali)  

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.

Although spontaneous symmetry breaking through Higgs scalars has been immensely successful, it is perhaps the most unsatisfactory feature of the standard model because of a multiple of reasons involving the number of parameters, quadratic divergences and the associated problem of fine tuning. Also in the light of the emerging picture of extra spatial dimensions, the 3+1 dimensional universe of ours becomes a brane or a domain wall embedded in a higher dimensional space. If that is the case, then Wali and collaborators have discovered a phenomenon that one may designate as “clash of symmetries” can provide a new method of symmetry breaking of some continuous symmetries. A global G_cts * G_discrete is spontaneously broken to H_cts *H_discrete, where the continuous H_cts can be embedded in several different ways in the parent group G_cts, ¬ and H_discrete< G_discrete. A certain class of topological domain wall solutions connects two vacua that are invariant under differently embedded H_cts. groups. On the domain wall, there is an enhanced symmetry breakdown to the intersection of the two subgroups. In the brane limit, one obtains a configuration with H_cts but the smaller intersection symmetry on the brane itself. A class of models, non-trivial but still in the nature of toy models have been investigated to study this phenomenon and more realistic models are currently being studied. This phenomenon in curved space-time, in a Randall-Sundrum type model, is also being investigated.

Wali is also studying extended objects such as ‘t Hooft-Polykov non-Abelian monopoles and dyons in curved space-time, since these provide a fertile theoretical laboratory to study the interplay between the gravitational and gauge interactions. Although gravitational interaction is weak, the non-linear nature of interactions has profound effects leading to such interesting objects as monopoles within black holes or black holes within monopoles. Static, finite energy solutions displaying such objects have been found in the Higgs vacuum. More general solutions with a dynamic Higgs fields are currently under study.