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Particle Physics

Calculating the Mass of a Proton

Scientists have known how much a proton weighs for the better part of a century. But it took a pan-European team of theoretical physicists, building upon decades of research by scientists from around the world, to work out precisely how its mass comes about.1 Led by Zoltan Fodor from the University of Wuppertal and Laurent Lellouch from the CPT in Marseille,2 the team's results confirm that Quantum Chromodynamics (QCD), the fundamental theory of quarks and gluons, correctly describes the interactions which bind these elementary particles together to form hadrons. As Lellouch explains, a proton's main components are two “up” quarks and one “down” quark, which are held together through the exchange of gluons. Yet the masses of the individual constituents do not add up to the mass of a proton, a disparity which had been known for a long time. A full quantitative understanding of this disparity had to wait until last year. “We realized that the different techniques needed were coming together, and that the necessary computing power was now available,” explains Lellouch. The researchers used IBM Blue Gene supercomputers from the Forschungszentrum Jülich in Germany and CNRS' IDRIS,3 applying their ability to perform over 100 trillion calculations/sec.
Though the only parameters of the calculation are the quark masses and the overall strength of the interaction, describing quark and gluon behavior in four-dimensional space-time requires an infinite number of variables. This is where a technique known as lattice QCD comes in. It allows a numerical simulation in which continuous space-time is viewed as a succession of increasingly finer four-dimensional lattices, each composed of sites spaced along rows and columns. After roughly 1020 computer operations, the theorists determined the mass of the proton and of other light hadrons with a precision of a few percent, finding excellent agreement with laboratory measurements and thus confirming that most of it comes not from the masses of the hadron's quark and gluon constituents, but rather from the energy generated by the interactions between them.
These results also helped establish techniques that can be used in other important endeavors, such as the search for new fundamental phenomena surrounding the weak interactions of quarks.

Mark Reynolds

Notes :

1. S. Dürr et al., “Ab-initio determination of light hadron masses,” Science, 2008. 322: 1224-7.
2. Centre de physique théorique (CNRS / Universités d'Aix-Marseille-I and -II / Université du Sud Toulon-Var).
3. Institut du Développement et des Ressources en Informatique Scientifique.

Contacts :

Laurent Lellouch
CPT, Marseille.


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