What is a Resonance Particle?

Chris Dudley

The most straightforward explanation of resonance particles, or resonances, is that they are extremely short lived particles. The lifetime of these particles is on the order of 10-23 seconds. Traveling at the speed of light, these particles could only travel about 10-15 meters, or about the diameter of a proton, before decaying. Distances of this magnitude cannot be measured in bubble chambers or any other device for detecting subatomic particles.

How can we know anything about particles we cannot detect? To understand how we deduce properties of resonance particles, it is first necessary to examine another, more complicated, explanation of their existence. This explanation involves the scattering cross-section of a particle. When two particles move towards each other and collide, it is possible to say that the collision was caused by the cross-section of the particles. The greater the cross-section of the particles is, the more likely it is that there will be a collision. So, if we have two beams of particles, the amount of scattering that occurs is related to the cross-section of the particles that make up the beams (this is a simplification, but it helps to understand resonances). We can measure the cross-section of a particle by knowing how much scattering occurs when two beams of particles collide.

If we graph the results of our observations for the cross-section of the particles versus the total energy of the particles (see Ohanian pg. 468 for an example of such graphs), we can see that the graphs have peaks and valleys. This means that the cross-section of the colliding particles changes as a function of the total energy in the collision. Most collisions have several possible outcomes, and each possibility has peak cross-sections at certain energies. When graphs of the different possible results of the same collision are compared, we find that the peak cross-sections occur at the same energies for each possibility. There must be some reason why all the peaks occur at the same energy.

There are two explanations for the peaks, both involving resonances. In one view, the peaks themselves are resonant states or resonances. The resonance is the peak itself, not a particle. Resonances are simply energies at which the cross section of a particle reaches a maximum. In this view, resonances are similar to atomic energy levels, the only difference being that energy levels can be explained by quantum electro-magnetic theory and the need for discussing peak electron levels at certain energies is gone. Elementary particles are not as well understood, so most of the information we have comes from the resonances.

The second explanation says that the peaks are evidence for actual particles that form as intermediate steps in the collision. In this view, the presence of resonance particles adds to the cross-section of the particles in the collision, making the collision more likely. The peaks are interpreted as evidence for the presence of resonance particles, and the different peaks are caused by a large number of distinct particles, which are just as real as other particles, the only difference being a difference in lifetime.

Both explanations, resonant states and resonance particles, have their advantages, and either can be used to find resonance properties. The energy of resonaces is easy to find; it is just the energy at which the cross-section reaches a peak. In the particle theory, the energy is the mass of an intermediate particle through which the reaction takes place. The particle is formed by the collision but almost instantly decays into more stable particles. According to the resonance explanation, the energy is a resonant state of the reaction between the colliding particles, an energy at which the collision is more probable.

Finding the lifetime of a resonance is also fairly uncomplicated. According to the uncertainty principle, dE*dt is greater than or equal to h/2. The mean lifetime is given by t=h/dE. This is the same formula used to find lifetimes of excited nuclear states. dE is the width of the peak at the half maximum. If resonances are particles, then this formula gives their lifetimes. If they are resonant states, then the lifetime is the duration of the resonance, which is harder to understand. Again, the comparison to atomic energy states is useful. The time of the resonance is analogous to the time an electron stays in an excited state.

The debate over the nature of resonances will probably last until we have equipment sensitive enough to measure the extremely short distances which resonances would travel if they were particles. Whether particle or resonant state is of little practical importance, since we can measure the properties of resonances whichever explanation we accept.

Sources

Beiser, Arthur. Concepts of Modern Physics. McGraw-Hill Book Co. New York, 1987.

Ohanian, Hans C. Modern Physics. Pretence Hall. Englewood Cliffs, NJ, 1987.

Polkinghorne, J.C. The Particle Play. WH Freeman and Co. Oxford, 1979.

Thomas, Edward. From Quarks to Quasars. The Athlone Press. London, 1977.

Tipler, Paul A. Modern Physics. Worth Publishers. Rochester, MI, 1978.