LArQL: A phenomenological model for treating light and charge generation in liquid argon

Experimental data shows that both ionization charge and scintillation light in LAr depend on the deposited energy density ($dE/dx$) and electric field ($\mathcal{E}$). Moreover, free ionization charge and scintillation light are anticorrelated, complementary at a given ($dE/dx$, $\mathcal{E}$) pair. We present LArQL, a phenomenological model that provides the anticorrelation between light and charge and its dependence on the deposited energy as well as on the electric field applied. It modifies the Birks' charge model considering the contribution from the escape electrons at null and low electric fields, and reconciles with Birks' model prediction at higher fields. Deviations from current Birks' model are observed for LArTPCs operating at low $\mathcal{E}$ and for heavily ionizing particles. The LArQL model presents a satisfactory description at $dE/dx$ and field ranges for interacting particles in LArTPCs and fits well the available data. Improvements via data sets compilation and global fits are also interesting features of the model.