Asymptotic single-particle states and exact Lorentz-violating all-loop quantum corrections for scalar field theory

We perform the all-loop renormalization of the O($N$) $\lambda\phi^{4}$ scalar field theory with Lorentz violation which is exact in the Lorentz-violating $K_{\mu\nu}$ coefficients. This task is fulfilled analytically firstly explicitly at next-to-leading order and later at all loop levels through an induction process based on a general theorem emerging from the exact approach. We show that the exact results reduce to the approximated ones, previously obtained, in the appropriated limit and comment on their implications. The current exact calculation involving such a symmetry breaking mechanism in the referred theory is the first one in literature for our knowledge. At the end, we analyze the effect of Lorentz violation on the asymptotic single-particle states.