The lightest Higgs boson mass in the Minimal Supersymmetric Standard Model

We compute the upper bound on the mass of the lightest Higgs boson in the Minimal Supersymmetric Standard Model in a model-independent way, including leading (one-loop) and next-to-leading order (two-loop) radiative corrections. We find that (contrary to some recent claims) the two-loop corrections are negative with respect to the one-loop result and relatively small ($\simlt 3$\%). After defining physical (pole) top quark mass $M_t$, by including QCD self-energies, and physical Higgs mass $M_H$, by including the electroweak self-energies $\Pi\left(M_H~2\right)-\Pi(0)$, we obtain the upper limit on $M_H$ as a function of supersymmetric parameters. We include as supersymmetric parameters the scale of supersymmetry breaking $M_S$, the value of $\tan \beta$ and the mixing between stops $X_t= A_t + \mu \cot\beta$ (which is responsible for the threshold correction on the Higgs quartic coupling). Our results do not depend on further details of the supersymmetric model. In particular, for $M_S\leq 1$ TeV, maximal threshold effect $X_t~2=6M_S~2$ and any value of $\tan\beta$, we find $M_H\leq 140$ GeV for $M_t\leq 190$ GeV. In the particular scenario where the top is in its infrared fixed point we find $M_H\leq 86$ GeV for $M_t = 170$ GeV.