What Effect Does Quarks Have on the Lifetimes of Hadrons?
By: Nicholas Stoute
In particle physics, one of the most important aspects of a particle is its lifetime. By knowing a particles lifetime, we can tell if we are able to collect and conduct experiments with them or if we are even able to detect them directly. For instance, we would consider a 10-10 s lifetime, or even as low as a 10-13 s lifetime stable because they live long enough to be collected and shot in a beam at a target. However a 10-23 s lifetime for a particle would be considered unstable because even if the particle were moving at the speed of light it would only move about the distance of a proton's diameter, which is much too small for direct detection. So naturally we would be worried if there were great discrepancies between a theoretical calculation of lifetime and the actual experimental evidence of it. We see two examples of this type of discrepancy in history when a certain unstable meson ([pi]o mesons or neutral pions) decayed and when the J/[Psi] particle was discovered to live a thousand times longer than it was theoretically supposed to. All of these discrepancies in the hadron's lifetimes were cleared up when certain aspects of a fundamental particle came to light. This particle is the quark.
Hadrons are particles that occupy space (unlike leptons which are considered point particles) and interact by both the strong and weak forces. They can be described as collections of quarks and antiquarks. This description was just fine in the physics community until it was discovered that if this model were true, then many baryons (a type of hadron) would have quarks of the same type in their internal structure. Since a quark is a fermion with spin 1/2, it should not violate the exclusion principle ("the property that there can only be at most one fermion in each possible state of motion." (Polkinghorne 129)) The quark model at that time showed that they did violate the exclusion principle. Something had to be done to rectify this problem. So, to fix this problem a new concept of quantum number was introduced, colour. Colour "serves to differentiate three varieties of each type of quark.... Colour in not manifested by observed particles with are all white." (Polkinghorne 129). The colour of the quarks are red, green, and blue. Each quark can have one of these three colours or one of their counterparts: antired, antiblue, or antigreen. By differentiating the quarks as such, two or three of the same type of quark could be in the structure of a particle at the same time but not violate the exclusion principle by all having different colours.
The ideas of such an abstract term as colour is very hard to swallow, however it is instrumental in describing the decay of a pion into two photons (Polkinghorne 103). This decay has a quark-antiquark intermediate reaction which is fundamental in describing it. The quark-antiquark pair is like a catalyst; the more of these pairs there are, the faster the decay occurs. This discrepancy of a factor of 9 between the theoretical calculation of lifetime and the experimental lifetime is resolved completely with the application of the "color tripling (by three new aspects of each quark)" aspect of this new color force of the quark.
The second instance where the expected lifetime is different than the experimental is with the discovery of the J/[Psi] particle. The amazing thing about this particle is that its lifetime is a thousand time longer than the typical lifetime of 10-23 s. Like many other times in physics history, if you can not figure it out, create something new. This is just what happened. In response to the discrepancy came the quantum number of charm. The J/[Psi] is described as a particle with a charm-anticharm pair. These cancel each other out, causing the particle to appear to have no charm. In this case, it is said that the particle has hidden charm. This configuration of a charm-anticharm pair has less phase space ("the set of final state configurations which are possible in an interaction. The larger this set, the more frequently that interaction will occur" (Polkinghorne 132)) than the non charmed quarks in most other Hadrons. This lack of phase spacing causes a longer lifetime.
In particle physics, we see new particles springing up every year, and with them come new ways to describe their structures and interactions with other particles. We saw that two independent aspects of quarks, the colour force, and the quantum number of charm are directly related to the lifetimes of certain hadrons. When we ask if quarks have an effect on the lifetimes of hadrons, we can conclude from the specific examples that they do. Also, from the very fact that the strong force is "nothing but a side effect of the colour force, in much the same way as the Waals force between molecules is a side effect of the electromagnetic force..." (Ohanian 492) we can say that all hadrons' lifetimes (decay rates) are affected by quarks as they are at least affected by the strong force.
Here are some interesting LINKS to particle accelerators around the world:
FermiLab Homepage
CERN - European lab for Particle Physics
SLAC - Stanford Linear Accelerator Center
LINK: http://www.slac.stanford.edu/
DESY - Deutsches Elektronen Synchrotron
Bibliography
Beiser, A., Concepts of Modern Physics (McGraw-Hill, New York, 1987)
Polkinghorne, J. C., The Particle Play (Freeman, Oxford, 1979)
Ohanian, H. C., Modern Physics (Prentice-Hall, New Jersey,1987)
Kane, G., Modern Elementary Particle Physics (Addison-Wesley, Redwood City, 1987)