Speaker
Description
The effective radius of the proton varies depending on the force through which it interacts with its surroundings. While the charge radius, relevant to electromagnetic interactions, is known to within a few hundredths of a fermi, the mass radius, relevant to gravitational interactions, is still heavily disputed. Experimental measurements (e.g. from GlueX), lattice QCD calculations and various theoretical models pin the value to between 0.55 and 0.7 fm. We instead calculate the mass radius using a potential model of the strong force interaction between quarks. We adapt the Coulomb-plus-linear, or Cornell, potential for the proton in two ways. In the naive method, chromoelectric flux tubes extend pairwise between each pair of quarks and the potential energy only depends on the relative distances between them. In the second method, we modify the confining part of the potential so that the flux tubes join together at a central junction. Additionally, we consider a quark-diquark configuration. In all cases, we mandate that the proton wave functions reproduce the known charge radius. In addition to calculating its mass radius, this technique allows us to map the spatial energy distribution of the proton and discern which contributions to the total energy are dominant at different mass radii. We find that the charge radius strongly constrains the quarks’ dynamical contributions which would give a mass radius in the relatively high range. We also find that the mass radius is sensitive to how the vacuum contributions such as the constituent quark mass are treated, which could lead to a considerably smaller mass radius.
