phase minimum nθ$_{min}$ = π is then given by [89]: where m$_{0}$ , A$_{0}$ , and λ$_{n,}$$_{0}$ are the values of m$_{φ}$ , A and λ$_{n}$ given at a scale µ$_{0}$ . Here A$_{0}$ is chosen to be real and positive (this can always be done by re-parameterizing the phase of the complex scalar field φ ), and | K$_{i}$ | < 1 are coefficients determined by the one-loop renormalization group equations. In the limit when | K$_{i}$ | ≪ 1, one finds a simple relationship [89] For n = 6, the coefficient is A ∼ 40 m $_{φ}$, where φ$_{0}$ denotes the point of inflection. The coefficients K$_{i}$ need to be solved from the renormalization group equations at the inflationary scale µ = φ$_{0}$ . Since K$_{i}$ are already one loop corrections, taking the tree-level value as the renormalization scale is sufficient $^{75}$. The radiative corrections do not remove the inflection point nor shift it to unreasonable values. The existence of an inflection point is thus insensitive to radiative corrections. One can analytically obtain the values of K$_{i}$ for the LLe flat direction. For LLe the one-loop RG equations governing the running of m 2 $_{φ}$, A , and λ with the scale µ are given by [31, 32, 89] 75 In general there is no prospect of measuring the non-renormalizable A$_{6}$ term, because interactions are sup- pressed by M$_{P}$ . However, a knowledge of SUSY breaking sector and its communication with the observable sector may help to link the non-renormalizable A -term under consideration to the renormalizable ones. In the case of a Polonyi model where a general A -term at a tree level is given by: m$_{3}$$_{/}$$_{2}$ [( a − 3) W + φ ( dW/dφ )] , with a = 3 − √$_{3 [31, 32]. One then finds a relationship between}$ A -terms corresponding to n = 6 and n = 3 superpotential terms, denoted by A$_{6}$ and A$_{3}$ respectively, at high scales [89]: A$_{6}$ = 3 − √$_{3}$ 6 A$_{3}$ . 155 µ dm 2 φ dµ = − 1 6 π 2 ( 3 2 ˜ m 2 $_{2}$g 2 + 3 2 ˜ m 2 $_{1}$g 2 1 ) , µ dA dµ = − 1 2 π 2 3 2 ˜ m$_{2}$g 2 + 3 2 ˜ m$_{1}$g 2 1 , µ dλ dµ = − 1 4 π $_{2}$λ ( 3 2 g 2 + 3 2 g 2 1 ) . (345) V$_{eff}$ ( φ, θ$_{min}$ ) = 1 2 m 2 $_{0}$φ 2 [ 1 + K$_{1}$ log ( φ 2 µ 2 0 )] − λ$_{n,}$$_{0}$A$_{0}$ nM n − $_{3}$φ n [ 1 + K$_{2}$ log ( φ 2 µ 2 0 )] + λ 2 n, 0 M 2( n − $_{3)}$φ 2( n − 1) [ 1 + K$_{3}$ log ( φ 2 µ 2 0 )] . (342) A 2 = 8( n − 1) m 2 $_{φ}$( φ$_{0}$ ) ( 1 + K$_{1}$ − 4 n K$_{2}$ + 1 n − 1 K$_{3}$ ) , (343) n φ n − 2 0 = M n − $^{3}$m$_{φ}$ ( φ$_{0}$ ) λ$_{n}$ √ 2( n − 1) ( 1 + 1 2 K$_{1}$ − 1 2( n − 1) K$_{3}$ . (344) 2 2