Non-universal critical initial slip of parity conserving branching and annihilating random walkers with long-range diffusion

We consider a parity conserving model of branching and annihilating random walkers with long-range diffusion. We follow the short-time dynamics at the critical region to obtain the set of critical exponents associated to the growth in the number particles and its fluctuations, as well as the critical second-order moment ratio. Diffusion and branching processes are controlled by a diffusion probability p and the flight distance follows a Lévy distribution with exponent α. Three short-time scaling regimes are identified as a function of the Lévy exponent. For α≤5∕2 infinitesimal branching is relevant and leads to a finite density of walkers. An absorbing-state dynamic phase transition takes place at a finite branching probability for α>5∕2. Short-range power-law scaling occurs for α≥7∕2. In the intermediate regime, continuously varying exponents are obtained with the second-order cumulant depicting a non-monotonous behavior. The relative influence of Lévy diffusion and branching on the critical diffusion probability is also discussed.