Uniaxial Lifshitz Point at $O({ϵ}_L^2)$

The critical exponents ${\nu }_{L2},{\eta }_{L2}$ and ${\gamma }_{L2}$ of a uniaxial Lifshitz point are calculated at two-loop level using renormalization group and ${ϵ}_L$-expansion techniques. We found a new constraint involving the loop momenta along the competition axis, which allows to solve the two-loop integrals. The exponent ${\gamma }_{L2}$ obtained using our method is in good agreement with numerical estimates based on Monte Carlo simulations.