Estimating the Color Lifetime of Energetic Quarks

Using a simple geometric framework with a realistic nuclear density distribution, we fit published HERMES data to determine fundamental properties of hadronization using the nuclear medium as a spatial analyzer. Our approach uses a fit to the transverse momentum broadening observable and the hadronic multiplicity ratio; the simultaneous fit to two different observables strongly constrains the outcome. Using the known sizes of the target nuclei, we extract the color lifetime, finding a z$\mathrm{_h}$-dependent range of values from 2 to 8 fm/c for these data. We also extract estimates for the $\hat{q}$ transport coefficient characterizing the strength of the interaction between the quark and the cold nuclear medium, finding an average value of 0.035$\pm$0.011 GeV$\mathrm{^2}$/fm. With a three-parameter model we obtain satisfactory fits to the data with a goodness-of-fit parameter $\chi ^2$/dof of 1.1 or less. In a secondary fit of the results from that model we independently find a value for the Lund String Model string tension of 1.00$\pm$0.05 GeV/fm. We evaluated the sensitivity for extracting quark energy loss and effective in-medium hadronic cross sections using four-parameter variants of the model, finding large uncertainties in both cases. Our results suggest that hadronic interaction of forming hadrons in the nuclear medium is the primary dynamical cause of meson attenuation in the HERMES data, with quark energy loss playing a more minor role.