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The geometrical representation of two-flavor neutrino oscillation representsthe neutrino's flavor eigenstate as a magnetic moment-like vector that evolvesaround a magnetic field-like vector that depicts the Hamiltonian of the system.In the present work, we demonstrate the geometrical interpretation of neutrinoin a vacuum in the presence of decay, which transforms this circular trajectoryof neutrino into a helical track that effectively makes the neutrino systemmimic a classical damped driven oscillator. We show that in the absence of thephase factor $\xi$ in the decay Hamiltonian, the neutrino exactly behaves likethe system of nuclear magnetic resonance(NMR); however, the inclusion of thephase part introduces a $CP$ violation, which makes the system deviate fromNMR. Finally, we make a qualitative discussion on under-damped,critically-damped, and over-damped scenarios geometrically by three differentdiagrams. In the end, we make a comparative study of geometrical picturizationin vacuum, matter, and decay, which extrapolates the understanding of thegeometrical representation of neutrino oscillation in a more straightforwardway.

Geometrical Interpretation of Neutrino Oscillation with decay