INTER ACTIONS 2001

On Mendeleev's Path guidance from the lattice

by Colin Morningstar

Colin Morningstar received his Ph.D. in physics from the University of Toronto in 1991. He was a postdoctoral research associate at the Stanford Linear Accelerator Center, the University of Edinburgh in Scotland, and the University of California at San Diego before becoming an assistant professor at Florida International University in Miami. He joined the faculty of Carnegie Mellon as an assistant professor in the fall of 2000.

Dimitri Mendeleev’s periodic table of the elements (1869) was a great breakthrough toward answering the age-old question: Of what is the world made? The regularities in his table, along with results from the µ particle scattering experiments of Rutherford, Geiger and Marsden (1906-1913), helped fashion the theory of the atom as a heavy nucleus containing protons and neutrons, surrounded by a cloud of light electrons. By this time, the interactions between electrically charged particles were reasonably well understood, but what held the nucleus together? Protons had positive electric charge, whereas neutrons were neutral. Since like charges repelled, clearly the nucleus was not held together by electromagnetic forces.

In 1935, Hideki Yukawa put forward his now-famous theory of the nuclear force mediated by a spinless exchange particle with a mass approximately 250 times that of the electron. When such a particle (called the p meson) was discovered in 1947 (two years after the incredible power of this new force had been demonstrated to the world), it was clear that great progress toward understanding the fundamental constituents of the universe and their interactions had been made.

Experiments quickly revealed that the proton and the neutron were not alone, but rather, the lightest particles in a large spectrum of strongly interacting fermions, called baryons. The p mesons were also found to be the lightest members of an equally numerous sequence of strongly interacting bosons, called mesons. Analogous to Mendeleev’s periodic table, this proliferation of particles suggested a deeper substructure.

Further peeling of the cosmic onion led in the early 1960s to the quark model, which proposed that all baryons and mesons (collectively called hadrons) were constructed from elementary particles whimsically named quarks by Murray Gell-Mann. Quarks came in three so-called flavors, up, down and strange (three more flavors have since been discovered), and possessed fractional electric charge. When a watershed experiment in 1968 at the Stanford Linear Accelerator Center scattered electrons off protons and showed that the proton had substructure consistent with the proposed quark model, the existence of the quark was established.

A satisfactory theory describing the interactions between quarks emerged by the early 1970s. In this theory, named quantum chromodynamics (QCD), quarks possessed a new kind of charge called color which came in three varieties. The theory resembled quantum electrodynamics (QED); the massless carrier of the force was called the gluon, the analogue of the photon in QED. However, unlike photons, gluons not only mediated the force, but also were a source of the force since they possessed color charge. This seemingly simple difference leads to the physical content of QCD being completely unlike that of QED. Note that the interaction of quarks and gluons is the true strong force; the binding of protons and neutrons in the nucleus and current weapons of mass destruction use only a feeble, van der Waals-like remnant of the strong force!

The calculational tools (small-coupling expansions) that work so well for high precision studies of electromagnetic phenomena utterly fail when applied to hadron formation in QCD. In 1974, Ken Wilson suggested a novel approach for studying hadrons in which QCD could be formulated using a discrete space-time lattice and sophisticated renormalization group methods. An important advantage of his approach was that it facilitated computer simulations of quarks and gluons using Monte Carlo methods, at last freeing theorists from the shackles of small-coupling expansions and controversial approximations.

Wilson’s paper marks the beginning of a new branch of particle physics known as lattice gauge theory or lattice QCD. The field has grown considerably during the past 25 years. Large grand-challenge collaborations with dedicated supercomputer resources have emerged not only in the USA, but in several other countries, including Japan, Germany, Italy, the United Kingdom and Australia. I am currently a member of a collaboration centered at both Jefferson Lab and MIT and dedicated to the study of hadronic physics relevant to the experimental program at Jefferson Lab.

Lattice simulations have told us much about QCD, but there is still very much more to learn. During the 1990s, significant advances in our simulation techniques allowed accurate calculations of many quantities for the first time. However, the full incorporation of virtual quarks still remains problematical and a very active subject of research.

Figure 1. A few of the lowest-lying energies of the stationary states of the gluon field in the presence of a static quark-antiquark pair versus the quark-antiquark separation r. In collaboration with J. Juge and J. Kuti.

A key feature of QCD is the fact that its fundamental degrees of freedom, quarks and gluons, cannot be observed in isolation; they are confined inside the hadrons which we observe. Lattice simulations tell us that the magnitude of the attractive force between a quark and an antiquark from gluon exchange remains constant as the quark-antiquark separation becomes large, unlike the inverse-square law of the Coulomb force in electrostatics. In other words, the static quark-antiquark potential rises linearly with the separation (see Fig. 1). This suggests that the gluon field forms a string-like object connecting the quark and antiquark, making it impossible to isolate an individual quark. The gluon field can be excited, and our lattice simulations have determined some of its excitation energies (Fig. 1). These excitations are relevant for understanding new exotic hadrons known as hybrid mesons that may have recently been seen at Brookhaven and CERN and will soon be studied in greater detail at Jefferson Lab.

Another difference from electromagnetism is the fact that gluons can bind together into new forms of matter called glueballs; the (nonexistent) electromagnetic analogue would be a massive globule of pure light. After more than a decade of unsuccessful attempts, our simulation techniques have advanced sufficiently to allow an accurate glimpse of the glueball spectrum, neglecting quarks (see Fig. 2). These calculations are a first step toward unearthing the mysteries of these bizarre hypothetical clumps of matter. The existence of such states is suggested by tantalizing results from Crystal Barrel at CERN. New glueball searches will soon be undertaken by the CLEO collaboration at Cornell University (hopefully) and at other accelerator centers.

Figure 2. The predicted mass spectrum of glueballs (neglecting quarks). Uncertainties are indicated by the vertical extents of the boxes. In collaboration with M. Peardon. 

Understanding exactly how quarks and gluons are confined inside hadrons is a primary goal of hadronic physics. In fact, quark confinement has been highlighted as one of the main science issues in the recent Department of Energy Strategic Plan, and the Clay Mathematics Institute of Cambridge, Mass. (http://www.claymath.org) has chosen the origin of the glueball mass in Yang-Mills theory (QCD without quarks) as one of its seven Millennium Prize Problems whose solution will be awarded $1 million. Also, studies of the finite-temperature deconfinement phase transition into the quark-gluon plasma are important for understaning the early universe. Lattice simulations are an important tool for addressing such problems and guiding us along the path of Mendeleev.