SPHALERONS IN THE MSSM

We construct the sphaleron solution, at zero and finite temperature, i n the Minimal Supersymmetric Standard Model as a function of the super symmetric parameters, including the leading one-loop corrections to th e effective potential in the presence of the sphaleron. At zero temper ature we have included the one-loop radiative corrections, dominated b y the top/stop sector. The sphaleron energy E(MSSM) mainly depends on an effective Higgs mass m(h)(eff) = lim(mA much greater than mW) m(h), where m(h) is the lightest CP-even Higgs mass and m(A) the pseudoscal ar mass. We have compared it with the Standard Model result, with m(h) (SM) = m(h)(eff), and found small differences (1-2%) in all cases. At finite temperature we have included the one-loop effective potential i mproved by daisy diagram resummation. The sphaleron energy at the crit ical temperature can be encoded in the temperature dependence of the v acuum expectation value of the Higgs field with an error less than or similar to 10%. The light stop scenario has been re-examined and the e xistence of a window where baryon asymmetry is not erased after the ph ase transition, confirmed. Although large (low) values of m(h) (m(A)) are disfavored by the strength of the phase transition, that window (a long with LEP results) allows for m(h) less than or similar to 80 GeV, m(A) greater than or similar to 110 GeV and A(t) less than or similar to 0.4m(Q).