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The Dielectron Mass Spectrum and the Search for the Smallest Constituents of Matter

March 23, 1999

What are Quarks and how do you look at them?

Physicists have a long history of uncovering layers of matter-- understanding how things are made of smaller things which in turn are made of yet smaller things. First, it was understood that everyday objects are made of molecules, then that these molecules are composed of atoms. The atoms were later discovered to consist of a nucleus orbited by electrons, and by the 1930's it was found that the nucleus is made up of particles called protons and neutrons. In the 1960's a series of experiments at the Stanford Linear Accelerator Center in California demonstrated that these protons and neutrons are themselves made out of smaller objects, which were named "quarks" (a quirky name perhaps in tune with the spirit of the sixties).

Over the last three decades physicists developed a theory which describes all matter and forces in the universe (except gravity) called the standard model. This theory describes all known particles and interactions with just a few input numbers; it says that all matter is composed of leptons (electrons are a type of lepton) and quarks. In this theory, the quarks and leptons are assumed to be fundamental objects: that is, there are no smaller objects inside of them.

Physicists working at the world's highest energy particle accelerator, the Tevatron collider at Fermilab (near Chicago), have investigated the collisions of protons with their antimatter counterparts anti-protons, at a combined energy of almost two trillion electron volts (2 TeV). (The electron volt is a measure of energy; an electrically charged particle like a proton can be given more energy, or accelerated, using an electric voltage. The energy of the Tevatron accelerator is the same as if six hundred million regular 1.5 volt batteries had been hooked together to provide this voltage --- though of course it is not really done this way). In these high energy collisions, one of the quarks inside the proton collides with one of the quarks inside the anti-proton; the two may annihilate to produce a pair of electrons of opposite charge.

Physicists use large and complex arrays of instrumentation called "detectors" to measure these electrons. Production of these high-energy electrons is one of the signs that the quarks inside the proton and anti-proton are hitting each other hard.

What is the Dielectron Mass?

By measuring the energy and direction of each of the electrons, physicists can calculate the mass of the intermediate object that decayed into the electrons (using Einstein's E=mc2), this is called the dielectron mass. The Tevatron accelerator is capable of producing electrons with a dielectron mass of up to 400 GeV (400 billion electron volts), which is two times heavier than a gold atom!

The standard model predicts the number of times we expect to see a proton anti-proton collision produce two electrons with a given dielectron mass. If more events than predicted are found with a very large dielectron mass, this could be interpreted as evidence that quarks and electrons are not the smallest objects possible and that they may be made up of something even smaller. This is because at high mass one is probing the quarks and electrons at small distances, mass (or energy) being inversely related to distance through Heisenberg's Uncertainty Principle of quantum mechanics. If at these small distances the quarks and electrons have constituents, the interaction between these constituents creates more ways for the quark-electron scattering to occur, and the dielectron production rate increases.

New Results from DØ

A new measurement of these dielectron events has been made by the ("D-zero") detector group. is an international collaboration of about four hundred physicists who designed and constructed a detector to study these high energy proton-anti-proton collisions. In a paper recently submitted to Physical Review Letters, the physicists describe how they selected collisions where the highest energy electrons were produced. The masses of the electrons from each collision were found to have a distribution that is similar to that predicted by the standard model.

A plot of the measured distribution (solid circles) of the dielectron masses compared with
the standard model prediction. Also shown is the prediction of a hypothetical model of quark and
electron substructure, with a compositeness scale of 3000 GeV.

Hence, the quarks and electrons are behaving exactly like a mathematical point - something with no size at all, and not composed of any smaller building blocks. Given the precision of the measurement, this means we can be sure that quarks and electrons are smaller than one twenty thousandth of a trillionth of a centimeter, or 5 x 10-17 cm. This is about ten thousand times smaller than the size of a proton! These new results are the world's best test of the point-like nature of quarks and electrons and are in fact the best measurement of these smallest known objects.

For further information contact Prof. Ashutosh Kotwal, Columbia University (now at Duke University),

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