Institut für Theoretische Physik, FB-C, Universität Wuppertal (Germany)
Local Project ID:
HPC Platform used:
JUQUEEN of JSC
Theoretical particle physicists like to compare quantities in different theories. A well-known example is the Witten-Veneziano relation which links the topological susceptibility in SU(3) Yang-Mills gauge theory with the η' - η mass difference in QCD. A subtle issue in this comparison is that it is a priori not clear how the scale in the former theory should be defined. In the latter case - and with each quark flavor taken at its physical mass - the scale is set by reference to experiment. A piece of theory which comes in handy is that the β-function in a class of QCD-like theories is known to depend asymptotically only on Nf, the number of active quark flavors, not on their individual masses. As a practical matter the gluonic scales √t0 and w0 can be calculated on the basis of the gluonic energy density alone, without reference to external sources of color charge and alike. Still, in order to attribute them a physical value, the product of √t0 or w0 times a physical quantity like the omega baryon mass, MΩ, or the pion decay constant, fπ, must be determined as precisely as possible.