The light CP-even MSSM Higgs mass resummed to fourth logarithmic order.

We present the calculation of the light neutral CP-even Higgs mass in the MSSM for a heavy SUSY spectrum by resumming enhanced terms through fourth logarithmic order (N$^3$LL), keeping terms of leading order in the top Yukawa coupling $\alpha_t$, and NNLO in the strong coupling $\alpha_s$. To this goal, the three-loop matching coefficient for the quartic Higgs coupling of the SM to the MSSM is derived to order $\alpha_t^2\alpha_s^2$ by comparing the perturbative EFT to the fixed-order expression for the Higgs mass. The new matching coefficient is made available through an updated version of the program Himalaya. Numerical effects of the higher-order resummation are studied using specific examples, and sources of theoretical uncertainty on this result are discussed.