Physics News Update no. 574

The American Institute of Physics Bulletin of Physics
Number 574, January 23, 2002

New Limits on the Search for Missing SUSY

High-energy physics is often in search of kinship properties. For example, physicists want to know whether particles and antiparticles act alike. Are physical laws the same if you reflect an interaction between two particles in a hypothetical mirror or run the movie backwards?

Many kinships, or to use the preferred term, "symmetries," have broken down as the universe has expanded and cooled. Thus a left-right asymmetry developed during the early universe, at least for those interactions mediated by the weak nuclear force.

Another symmetry or kinship thought to have broken down over the course of time is the supposed kinship between fermions (particles with a half-integer value of spin -- examples being quarks and electrons) and bosons (particles with integer spin values, such as the force-carrying particles --- the photon, gluon, and Z boson).

This particular kinship, embodied in the theory of "supersymmetry," specifies that all of the known bosons have supersymmetric (SUSY) fermion partners (named by adding an "ino" to the end; e.g., the gluon's partner would be the "gluino") and the known fermions have boson counterparts (named by adding as "s" to the beginning (e.g., the SUSY version of a quark is a squark).

Just as the Neanderthals disappeared while Homo Sapiens survived, so something in the early universe favored some particles (such as the up and down quarks and electrons) while others (such as most of those promulgated in SUSY) became extinct. Except, perhaps, at a place like Fermilab where, amid fiery proton-antiproton collisions, the earlier conditions favoring supersymmetry can be reconstructed.

Looking for events in which three jets of energetic particles stream out of the reaction zone, physicists at the CDF detector have performed the most authoritative search yet for SUSY particles. Finding no positive evidence, the Fermilab scientists have established a new lower limit (195 GeV) on the mass of one prominent SUSY particle, the gluino.

The data base for this painstaking analysis was actually gathered several years ago; with the new, more intense Tevatron beam, five times as much data is expected within a year, and this will aid the search for these very rare events. If and when a gluino were produced it would promptly decay into a hypothetical lightest supersymmetric particle (LSP), a stable but neutrino-like entity which interacts so ineffectually that its presence would be inferred only by its absence; with a mass of at least 40 GeV, it would presumably carry off a large chunk of energy that would be missing from the overall accounting of interaction energy.

This situation is not unlike Lavoisier's early analytic studies of the chemistry of combustion, which helped to establish our modern notions of atoms and energy. The LSP, by the way, belongs not just to particle physics; in some theories it accounts for the bulk of cold dark matter in the universe. (Affolder et al., Physical Review Letters, 28 Jan 2002; contact Maria Spiropulu, University of Chicago, 773-702-7481; smaria@hep.uchicago.edu)

The Science of Roughness

The science of roughness is how Benoit Mandelbrot describes the use of fractal mathematics to understand objects in the real world. Euclid and the ancient Greeks may have assumed that lines are smooth and one dimensional, but many typical curves in nature are tortuously indented; however, their roughness can be expressed as a fractal dimensionality, one that is greater than one but less than two.

In a trailblazing 1967 paper Mandelbrot showed, for instance, that the coastline length of Britain was anything but an "objective" constant. Instead it grew as one shrank the size of the ruler used to lay out the coast. In fact the measured coastline, and many other perimeters, grow as the inverse of the ruler size, raised to a power: perimeter=(1/R)D, where R is the ruler size and D is the fractal "dimensionality."

This power-law relationship can also typify the "time series" behavior of many phenomena, such as volcanos, earthquakes, and hurricanes. What this means is that a plot of the likelihood of an event of a certain magnitude (an earthquake's energy, say) versus the magnitude has a power-law shape. Formulating the chances of large-but-rare floods or earthquakes is obviously not merely of academic interest. Understanding the math behind large systems like a forest or a geologic fault have enormous implications for public safety and insurance underwriting.

These are some of the issues that arose at a series of talks at the recent American Geophysical Union meeting in San Francisco, where the recently formed nonlinear geophysics committee sponsored a variety of sessions on things that are "rough" in the fractal sense.

Here is a sampling of results. Bruce Malamud (King's College, London, bruce@malamud.com) and Donald Turcotte (Cornell University, turcotte@geology.cornell.edu) argued that "fractal" assessments of natural hazards are often more realistic than older statistical models in predicting rare but large disasters. He cited as an example the great Mississippi flood of 1993; a fractal-based calculation for a flood of this magnitude predicts one every 100 years or so, while the more-often-used "log-Pearson" model predicts a period of about 1500 years.

In the realm of earthquakes, John Rundle (who heads the Colorado Center for Chaos and Complexity at the University of Colorado, rundle@cires.colorado.edu, 303-492-1149) described a model in which the customary spring-loaded sliding blocks used to approximate individual faults have a more realistic built-in leeway (or "leaky thresholds," not unlike "integrate-and-fire" provisions used in the study of neural networks) for simulating the way in which faults jerk past each other. Applying these ideas to seismically active southern California, 3000 coarse-grained regions, each 10 km by 10 km (the typical size for a magnitude-6 quake), are defined. Then a coarse-grained wave function, analogous to those used in quantum field theory, is worked out for the region, and probabilities for when and where large quakes would occur are determined. Rundle claims to have good success in predicting, retroactively, the likelihood for southern-California earthquakes over the past decade and makes comparable prognostications for the coming decade. (See also Rundle et al., Physical Review Letters, 1 October 2001; and Rundle et al., PNAS, in press).

Two diffusion-limited aggregation clusters. Top: simulation using 105 particles. Bottom: simulation using 108 particles.

At the AGU meeting Mandelbrot himself delivered the first Lorenz Lecture, named for chaos pioneer Edward Lorenz. Mandelbrot discussed, among other things, how the process of diffusion limited aggregation (DLA) is characterized by not one but two fractal dimensions. DLA plays a key role in many natural phenomena, such as the fingering that occurs when two fluids interpenetrate. In a DLA simulation, one begins with a single seed particle. Then other particles, after undergoing a "random walk," attach themselves to the cluster. This results in a branching dendritic-like structure in which the placement of new particles is subject to the blockage of existing limbs. You can study the dimensionality of this structure by drawing a circle and counting the number of particles lying on the circle at that radius out from the original seed particle, and counting up the angular gaps between branches at that radius.

For many years studies of DLA have been confused by conflicting reports as to the underlying fractal dimensionality. Now Mandelbrot (at both IBM-914-945-1712, fractal@watson.ibm.com and at Yale, mel@math.yale.edu), Boaz Kol, and Amnon Aharony (aharony@post.tau.ac.il, 972-3-640-8558 at the University of Tel Aviv) have shown-by employing a massive simulation involving 1000 clusters, each of 30 million particles (previous efforts had used no more than tens of thousands of particles)-that two different dimensionalities are always present, but this only becomes apparent in huge simulations. Comparing a modest (10⁵ particles) and a large (10⁸ particles) simulation shows that the larger cluster is not merely a scaled up version of the smaller (see figures). These results (Mandelbrot et al., 4 February 2002 issue of Physical Review Letters) are the first quantitative evidence for this type of nonlinear self-similarity.

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