Spectroscopy

This morning at the conference there was a report on the search for resonances in the electron-positron collisions studied by the Belle collaboration. The existence of several new bound states (new particles, that is) was proven, but that is only the beginning of a long study of the properties of these bodies. Two new states, temporarily denominated X(3940) and Y(3940), were discussed among the others. At an early stage, when one reconstructs the invariant mass of the observed particles escaping the interaction point, the "evidence" for a new particle is just a bump in a smooth histogram, such as the big or the small one on the figure (which is a particle decaying to a J/psi meson and two pions, if you cared to ask). What does it mean ? One takes the energy and momentum of each observed particle in a collision, computes the total energy of them, and obtains the "rest mass" or "invariant mass" of the system. By filling a histogram with the invariant mass of each collision, one obtains a plot such as the one shown. The shape of the distribution is generally a smooth one, but if some of the collisions have actually created a massive particle, you will see a bump. That means that in some of the collisions the particles appear to come from the decay of a "resonance", a state of well-defined mass. The mass is the first entry in the ID of a particle: all particles have one. So if you are to prove you discovered a new particle, you've better show a bump in a histogram of reconstructed mass.

For the X(3940) and Y(3940) states mentioned above, the matter is complicated by the fact that these two newfound babies appear to have the same mass: 3940 MeV, in fact. Are they the same particle after all ? Well, besides the mass, other properties are fundamental in a particle. A particle must have a well-defined spin (which is indeed the quantum mechanics analogue of the rotation of a sphere around itself), several other distinctive quantum numbers (such as the Parity, which can be positive or negative), and a carnet of allowed decay modes - different ways of dying, that is: just as we are about as likely to die in a car accident as of heart attack, but much less so in a plane crash, a particle may be likely to disintegrate in two pions or two kaons, but much less so in two muons. So X and Y appear to be different, due to their different decay properties, but we do need much more information to be sure.

By hearing of these two states, I could not help recalling that particle physics has done enormous leaps forwards in the last century, but the name of the game has not changed much. Bump hunting! Fifty years ago, we were at the very beginning of the particle accelerator era, and we were already dealing with the same issues. In particular, there was a time when a puzzle arose, which is similar to what I described above for the X and Y states. Two particles were discovered, who appeared to have the same mass, but different decay modes which appeared incompatible: named Tau and Theta, the former decayed to three pions, the latter to two pions. They could not be the same particle, since the two decay modes betrayed a different quantum number: one of them had positive parity, and the other had negative parity. This "tau-theta puzzle" kept physicists busy in the mid-fifties, until Lee and Yang, in a groundbreaking paper, demonstrated that what everybody assumed as a untouchable truth, the conservation of parity, had not been demonstrated in weak interactions. And in fact, in an experiment at the National Bureau of Standards in Paris (where the technology for keeping small samples at very low temperature had just been developed), the violation of parity conservation was demonstrated shortly thereafter by studying beta decays of supercold Cobalt 60 sample held in a high magnetic field. The Cobalt atoms behave like spinning spheres, with their axes all aligned in the direction of the magnetic field if the temperature is low enough. Every once in a while one Cobalt nucleus undergoes beta decay, whereby one of its neutrons becomes a proton, emitting an electron and a neutrino. If more electrons are emitted in the direction of the magnetic field rather than opposite to it, parity is violated. This is what was indeed observed. Weak interactions, responsible for the disintegration of the Cobalt 60 as well as of many hadrons, do not in fact conserve the parity quantum number: a particle may have positive parity, but its decay products may collectively have negative parity if the decay is mediated by the weak interaction - that is, by the exchange of a weak boson (a W or a Z boson).