where a$_{ig}$ and b$_{ij}$ are constants, m$_{g}$ is the gaugino mass, h$_{a}$ the Yukawa coupling, A is the A -term, and t = ln M$_{X}$/q . The full RG equations have been listed in [31, 32, 34]. However, let us consider some of the salient features of the MSSM one-loop RG equations. The one-loop RG equations for the three gaugino mass parameters are determined by: where i = 1 , 2 , 3 correspond to U (1) , SU (2) , SU (3). An interesting property is that the three ratios m$_{i}$/g 2 i are RG scale independent. Therefore at the GUT scale, where the gauge couplings unify at M$_{GUT}$ ∼ 2 × 10 16 GeV, it is assumed that gauginos masses also unify with a value m$_{1}$$_{/}$$_{2}$ . Then at any scale: where g$_{GUT}$ is the unified gauge coupling at the GUT scale. The RG evolution due to Yukawa interactions are small except for top. The ones relevant to flat directions, involving the Higgs doublet H$_{u}$ which couples to the top quark, the right-handed stop ˜ u$_{3}$ , the left- handed doublet of third generation squarks ˜ Q$_{3}$ and the A − parameter A$_{t}$ associated with the top Yukawa interaction. The RG equations read [31, 32, 34] Here q denotes the logarithmic scale; this could be an external energy or momentum scale, but in the case at hand the relevant scale is set by the VEV(s) of the fields themselves. h$_{t}$ is the top Yukawa coupling, while g$_{i}$ and m$_{i}$ are respectively the gauge couplings and soft breaking gaugino masses of U (1)$_{Y}$ × SU (2) × SU (3) . If h$_{t}$ is the only large Yukawa coupling (i.e. as long as tan β is not very large), the beta functions for (mass) 2 of squarks of the first and second generations and sleptons only receive significant contributions from gauge/gaugino loops. A review of these effects can be found in [34, 403]. d dt m$_{i}$ = 1 8 π $_{2}$b$_{i}$ g 2 $_{i}$m$_{i}$ , ( b$_{i}$ = 33 / 5 , 1 , − 3) (117) m$_{i}$ g 2 i = m$_{1}$$_{/}$$_{2}$ g 2 GUT , (118) d dq m 2 H$_{u}$ = 3 h 2 t 8 π 2 ( m 2 H$_{u}$ + m 2 Q 3 + m 2 u 3 + | A$_{t}$ | 2 ) − 1 2 π 2 ( 1 4 g 2 1 | m$_{1}$ | 2 + 3 4 g 2 | m$_{2}$ | 2 ) , d dq m 2 u 3 = 2 h 2 t 8 π 2 m 2 H$_{u}$ + m 2 Q 3 + m 2 u 3 + | A$_{t}$ | 2 − 1 2 π 2 4 9 g 2 1 | m$_{1}$ | 2 + 4 3 g 2 3 | m$_{3}$ | 2 , d dq m 2 Q 3 = h 2 t 8 π 2 ( m 2 H$_{u}$ + m 2 Q 3 + m 2 u 3 + | A$_{t}$ | 2 ) − 1 2 π 2 ( 1 36 g 2 1 | m$_{1}$ | 2 + 3 4 g 2 | m$_{2}$ | 2 + 4 3 g 2 3 | m$_{3}$ | 2 ) , d dq A$_{t}$ = 3 h 2 t 8 π $_{2}$A$_{t}$ − 1 2 π 2 ( 13 36 g 2 $_{1}$m$_{1}$ + 3 4 g 2 $_{2}$m$_{2}$ + 4 3 g 2 $_{3}$m$_{3}$ ) . (119) 55