Abstract
The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (non-vanishing) lower bound μ₀ of the mass spectrum. The survival probability P_p(t), the instantaneous mass M_p(t) and the instantaneous decay rate Γ_p(t) of the moving unstable particle are evaluated over short and long times for an arbitrary value p of the (constant) linear momentum. The ultrarelativistic and non-relativistic limits are studied. Over long times, the survival probability P_p(t) is approximately related to the survival probability at rest P₀(t) by a scaling law. The scaling law can be interpreted as the effect of the relativistic time dilation if the asymptotic value M_p(∞) of the instantaneous mass is considered as the effective mass of the unstable particle over long times. The effective mass has magnitude μ₀ at rest and moves with linear momentum p or, equivalently, with constant velocity 1/√1+μ₀²/p². The instantaneous decay rate Γ_p(t) is approximately independent of the linear momentum p, over long times, and, consequently, is approximately invariant by changing reference frame.