The big paper on the mesons is coming along. Yesterday I was checking the mass formulas for heavy quarkonium, a subject which was discussed here a few months ago. While checking numbers for the paper, I found that the Particle Data Group has changed the values for psi(3770) in our favor! For us it was exciting so Kea says I have to blog it. And in fact I feel that I did an inadquate job the last posting on this.
So first, a little background. Mesons are made of a quark and an anti-quark, plus the color and electric force that binds them together. The usual method of modeling them is to simplify the color force and treat it as if it were just a scalar force like the electric force, and then calculate the binding energies (and therefore the masses of the mesons) by using the methods used to calculate atomic energies.
What I’ve been doing instead is looking at the problem from the point of view of quantum information theory. With this one ignores the spatial and momentum information and looks only at the information content of the particle states. When one does this to a spin-1/2 particle like the electron, one uses qubits. Since I want to model the color force but don’t care about spin, I use qutrits instead with the three states being red, green, and blue.
The usual method of modeling the mesons works best for lowest energy states of the heaviest quarkonium. This is because these states are the least relativistic (because the quarks are so heavy) and the color force isn’t as strong (since these quarks are so heavy, their deepest bound states are smaller than other mesons, and since the quarks are close to each other, the color force is reduced by asymptotic freedom). With my method, the reverse should be true; I should be more accurate at bigger states where color is more important. These states are either higher excitations or have lighter quarks. This is because I treat the color states correctly but don’t work on getting momentum modeled correctly.