The log canonical threshold plays a fundamental role in algebraic geometry, especially birational geometry and Mori theory. Recently the problem of classifying foliations on algebraic varieties has been revolutionized by introducing ideas from Mori theory.   We introduce a version of the log canonical threshold in this context. We conjecture that this satisfies the ascending chain condition and we check that this conjecture holds in dimension two. On the way we introduce an interpolated canonical divisor and we show that we can run the MMP for such divisors.