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Andrew Adare | USLHC | USA

View Blog | Read Bio

Before QCD, there were fireballs

How many different particles can you make from quarks? A lot. Every two years or so, the particle data group puts out a catalog of the ones we know about. I always love getting mine in the mail. It’s as big as a phone book, with thin paper like a Bible. The compilation of all the particles and their properties represents a truly massive intellectual effort. Most of the hadrons are just labeled with Greek letters, but they’re festooned with all kinds of superscripts and asterisks, and their properties have names as colorful and idiosyncratic as their discoverers. For example, the neutral Ξ or “cascade” hyperon is a doubly-strange baryon with negative half-integer isospin. To my ear, most science fiction falls flat compared to real conversations between particle physicists.

By adding energy to hadrons, they can change their nature and go into excited states called resonances. The idea is loosely analogous to exciting atoms in a laser or fluorescent lamp, except more relativistic. Their mass can change. The humble proton, for example, can be excited into something called a Δ resonance, which is around 30% more massive, because some of the absorbed energy converts to mass. They don’t hang around very long, but as you look at higher and higher masses, you see more and more of them. By the 1960’s, the number of newly discovered particles and resonances had grown rapidly in step with the energy of the accelerators that produced them. This proliferation led to questions about how to explain such large variety, and what, if any, the limitations are in the number of states. When the quantum-mechanical rules governing properties like spin, charge, angular momentum, etc. were taken into account, the number of hadronic states was found to rise exponentially with mass. This plot is a fairly recent example:


Up to a certain mass, the number of hadrons rises exponentially. The red curve includes particles that weren't plotted in earlier references, represented by the green curve.

When you see a straight line on a semi-log plot, it’s a dead giveaway for an exponential form. Why is that pattern followed? What’s even more interesting is that the number of particles rises with mass at the same rate as it falls with increasing (transverse) momentum, at least below a few GeV. Several creative ideas emerged as attempts to explain the hadron spectra, but a physicist named Rolf Hagedorn gets the credit for developing a theory using statistical mechanics. This is before the era of quarks, remember: he referred to hadrons as “fireballs”, and considered that the heavy resonances were compositions of lighter ones, which were in turn composed of still lighter ones. In one of his lively papers, he said:

His mathematical line of reasoning implied that if you were to collect a bunch of hadrons together and treat them as a gas of particles, their energy would become infinite as the temperature approached a limiting value. He seems to have been quite a character. In the same paper, he concluded:

It follows that T is the highest possible temperature—a kind of ‘boiling point of hadronic matter’ in whose vicinity particle creation becomes so vehement that the temperature cannot increase anymore, no matter how much energy is fed in.

And now we come to the point. Hagedorn’s argument implies a change in the number of fundamental degrees of freedom of the system. In other words, it has to break down to more fundamental building blocks. Instead of remaining as a gas of hadrons, a superheated system would melt into a phase with simpler constituents at a temperature near what is now known as the Hagedorn temperature. Using the best data available, he extrapolated from the known spectra to obtain a value of the critical temperature near 160 MeV, or in more familiar units, a trillion degrees Celsius.

With a more sophisticated understanding thanks to Quantum Chromodynamics (QCD), more tools have become available to check this number. It’s a tough job, because this physics lies in the so-called “non-perturbative” regime,  where pencil-and-paper solutions to the QCD equations don’t work well. But that’s what supercomputers are for. The founders of QCD devised a way to crunch out the answers by dividing space-time itself into a grid of points called the lattice, “playing” the equations forward numerically in steps. It takes a lot of CPU cycles, but the answer seems to corroborate Hagedorn’s estimate.

So nuclear matter melts if you get it hot enough. It was suggested over 40 years ago, and theoretical innovations only seem to confirm it. So what happens then? And is this temperature achievable in the lab? I’ll post again soon to follow up on these questions.



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