Reconstruction of Point Event in Detectors with Total Reflection

The detector response model is vital for vertex and energy reconstruction. In the liquid scintillator detector with water buffer, each PMT is blind to some region due to the total reflection. We use the regression method to parameterize the detector response model, which provides an unbiased vertex reconstruction in the total reflection region. We also analyzed the convexity of the detector response model, giving a constraint for detector design. Finally, we verify the convexity and the bias by different geometries.