About the Casimir scaling hypothesis

A lattice calculation shows that the Casimir scaling hypothesis is well verifed in QCD, that is to say that the potential between two opposite colour charges in a colour singlet is proportional to the value of the quadratic Casimir operator. On the other hand, in a bag model calculation for the same system, a scaling of the string tension with the square root of the quadratic Casimir operator is obtained. It is shown that, within the same formalism but with the assumption that the width of the string is independent of the colour charges, the string tension is proportional to value of the quadratic Casimir operator. Some considerations about the colour behaviour of the total interaction are given.