Description
While we enter the precision era of neutrino mixing parameters, there is still one long-standing tension: the solar mass square difference measured by different experiments. The reactor antineutrino experiment KamLAND finds a best fit larger than the one obtained with solar neutrino data. The current tension ($\sim 1.5 \sigma$) is not large enough to consider the measurements incompatible, but future data may help either to close or to stand out this issue. Here, we discuss how a future supernova burst in our galaxy could be used to determine the solar neutrino mass splitting at the Hyper-Kamiokande detector, and discuss how this could contribute to the current situation. We study Earth matter effects for different sets of neutrino spectra and study the impact of the supernova position. Although the final capabilities depend on the details of the supernova neutrino spectra arriving at Earth and the final trajectory through the Earth, for some models and directions, error bands comparable to those obtained with KamLAND data could be attained. If supernova neutrino data prefers the solar data best fit, the tension with KamLAND data could grow up to $\gtrsim 5 \sigma$ level.
