by Mike Albrow, January 29, 2007

Pentaquarks

Protons and neutrons stick together in atomic nuclei through the strong force, much stronger than electromagnetism but only transmitted over a very short range. There are very many other strongly interacting particles, with names such as pions ( $\pi$ ) and kaons, all called hadrons. In the early 1960's it was realized that the hadrons are not fundamental, but are composed of much smaller (and perhaps really fundamental, like electrons) particles that were called quarks by Murray Gell-Mann, originator of the idea with George Zweig. All of the 100 or so hadrons known at the time could be ``explained" as being made out of only three different types of quark (

), called up (

), down (

) and strange (

) and their anti-particles ( $\bar{q}$ ) $\bar{u},\bar{d}$ and $\bar{s}$ . Quarks and antiquarks are somewhat like electrons and their antiparticles, positrons, except that they interact with the strong force and their electric charge is not -1 and +1 but $+\frac{2}{3}, -\frac{1}{3}, -\frac{1}{3}$ for quarks, the opposite for antiquarks. Using these quarks and antiquarks, one could build up all known hadrons with a simple rule: put together three quarks [

] (protons and neutrons are like that) or three antiquarks [ $\bar{q}\bar{q}\bar{q}$ ] (making antiprotons and antineutrons and others) or a quark and an antiquark [ $q\bar{q}$ ] (pions and kaons are like that). This scheme was taken very seriously when a particle it predicted, made of three strange quarks, $\Omega^-$ [

], was found at Brookhaven in 1964. But what was the reason for that rule? A result of the rule is that hadrons have only integer electric charges, $Q = 0, \pm 1, \pm 2$ .

As we have seen, electric charges can be positive or negative: the charge on the electron is (the -ve sign is purely conventional) and that on the positron is $Q(\bar{e}) = +1$ . The rule is ``Like charges repel, unlike charges attract", so the proton electrically attracts a negative electron and they thus combine to make a neutral hydrogen atom. Neutral atoms are made out of equal-in-magnitude but opposite-in-sign electric charges. The strong force also has an associated charge, different in interesting ways from the electric charge. This charge can have three distinct values, each with its own ``antivalue". You have to put all three together for them to cancel out and make neutral, or (strong) chargeless. Or you can put one of these charges together with its anticharge and they cancel and make neutral. Now we can state our puzzling rule as: ``All hadrons have no strong charge"; they are neutral as far as the strong force is concerned. Actually although the strong charges of the quarks cancel inside hadrons (protons, neutrons, ...) they can still stick together through a residual weaker remnant of the force, just as electrically neutral atoms stick together to make solids and liquids.

The idea of the three strong charges combining to make neutral reminded physicists of how shining three colored lights, Red, Blue, and Green on a surface makes white light. (The fact that three colors are needed is more biology than physics; it is because we humans have three color receptors in our eyes!) So these strong quark charges were labelled $R,G,B,\bar{R},\bar{G},\bar{B}$ and the new theory of the strong interaction acquired the name Quantum Chromodynamics, QCD, in the tradition of the theory of electromagnetic interactions Quantum Electrodynamics. (Of course this colorful vocabulary has nothing to do with the real colors of light, we just borrowed the names.) Any particular quark is constantly changing its ``color" between and by emitting and receiving force particles (``gluons" which carry a color and an anticolor, such as $R\bar{G}$ . Another contrast between the theories is that the electric force between two charges gets weaker as they separate, while the strong force between two strong quark charges gets stronger as they separate. The 2004 Nobel Physics prize was given to Gross, Politzer and Wilczek for calculating how this happens. One result is that you can never pull a quark out of a proton. If you try, the energy you pump in just ends up making more hadrons! No free quarks! Another result is that the strong quark-quark force at large distances is complicated and very difficult to calculate. Only in some limited cases can we make accurate calculations.

You may have noticed that the rules for combining quarks given above allow other combinations. For example [ $qq\bar{q}\bar{q}$ ] could be [ $R\bar{R}G\bar{G}$ ] and neutral overall. Some hadrons seem to have this composition, although such a tetraquark can sometimes transform itself into (``mix with") a common [ $q\bar{q}$ ] hadron. Another possibility is [ $qqqq\bar{q}$ ] or pentaquark (from the greek for five, pente). This is like a common [] and a [ $q\bar{q}$ ] stuck together, but deeply stuck together so that they do not fall apart for a relatively long time (long for us means about $10^{-22}$ seconds!). It doesn't actually have five quarks, but four quarks and an antiquark. A deeply bound $n[udd]K^+[u\bar{s}]$ would have to have quark content $[uudd\bar{s}]$ and could not be made from the old rule. Physicists looked for such so-called ``exotic" states way back in the 1960's but none was found. On the other hand it was never proven in Quantum Chromodynamics theory that they could not exist; the theory is too difficult in this domain. Still, it caused a stir in 2003 when several experiments claimed to see evidence for a state. If this pentaquark state exists there should be many others. For example, there is a hadron called the Xi-minus, $\Xi^-$ with quark content []. If it could be deeply bound with a $\pi^-[\bar{u}d]$ the combination $[ssdd\bar{u}]$ would have to be a pentaquark. There were claims from some experiments for such a state. Finding pentaquarks would not overthrow QCD but would be a challenge to the theorists to understand them and their properties. If they exist they should sometimes be produced when high energy protons and antiprotons collide in the Fermilab Tevatron, currently the highest energy particle collider on Earth. With the Collider Detector at Fermilab, CDF, we collected about 36,000 $\Xi^-$ events, leaving tracks at least a few cm long. We combined these with pion $\pi^-$ tracks, calculating the combined mass, i.e. the mass a parent particle would have if it decayed to the $\Xi^-$ and the $\pi^-$ . The resulting mass distribution shows no tell-tale peak where the pentaquark would be, and where the claimed observations were made. On the other hand the neutral combination $\Xi^-\pi^+$ showed a very clear peak corresponding to a known hadron, $\Xi(1530)$ . The experimental conditions at CDF and the other experiments are different. It is conceivable, but seems unlikely, that these different conditions could explain how the pentaquarks could exist but not be seen in CDF. Were the experiments that claimed signals mistaken, or perhaps misled by some unlikely statistical fluctuations? It is an interesting situation, and further experiments will surely clear it up. For the present we can only say that we see no evidence for these states at the Tevatron, and we do not know why we would not, if they exist. Whether or not they exist, it is a challenge to QCD theorists to explain the experimental facts.