We study the total particle-current fluctuations in a one-dimensional stochastic system of classical particles consisting of branching and death processes which is a variant of asymmetric zero-temperature Glauber dynamics. The full spectrum of a modified Hamiltonian, whose minimum eigenvalue generates the large deviation function for the total particle-current fluctuations through a Legendre-Fenchel transformation, is obtained analytically. Three examples are presented and numerically exact results are compared to our analytical calculations.
