7 8 π $_{2}$dm 2 D dt = 2 ξ$_{b}$ − 16 3 g 2 $_{3}$M 2 3 − 4 15 g 2 $_{1}$M 2 1 + 2 5 g 2 $_{1}$ξ$_{1}$ + 4 λ $^{2}$m2 $_{D}$, (A3) 8 π $_{2}$dm 2 L dt = ξ$_{τ}$ − 3 g 2 $_{2}$M 2 2 − 3 5 g 2 $_{1}$M 2 1 − 3 5 g 2 $_{1}$ξ$_{1}$ + 4 λ $^{2}$m2 $_{L}$, (A4) 8 π $_{2}$dm 2 E dt = 2 ξ$_{τ}$ − 12 5 g 2 $_{1}$M 2 1 + 6 5 g 2 $_{1}$ξ$_{1}$ + 4 λ $^{2}$m2 $_{E}$, (A5) where and Here the trace means the sum over the generations. The above equations for the squarks and sleptons apply to the 3rd family; the equations for the 1st and the 2nd families are obtained from above by simply omitting the Yukawa and the A-term contributions (i.e. neglecting the ξ$_{t}$ , ξ$_{b}$ , ξ$_{τ}$ terms). All the other RGE (the gauge couplings, the gaugino masses, the Yukawa couplings and the A-terms) are unaffected and are given e.g. in [17]. 8 π $_{2}$dm 2 H u dt = 3 ξ$_{t}$ − 3 g 2 $_{2}$M 2 2 − 3 5 g 2 $_{1}$M 2 1 + 3 5 g 2 $_{1}$ξ$_{1}$ + 4 λ $^{2}$m2 H $_{u}$, (A6) 2 8 π $_{2}$dm H d dt = 3 ξ$_{b}$ + ξ$_{τ}$ − 3 g 2 $_{2}$M 2 2 − 3 5 g 2 $_{1}$M 2 1 − 3 5 g 2 $_{1}$ξ$_{1}$ + 4 λ $^{2}$m2 H $_{d}$, (A7) ξ$_{t}$ = y 2 $_{t}$( m 2 H u + m 2 Q + m 2 U + A 2 $_{t}$) , (A8) ξ$_{b}$ = y 2 $_{b}$( m 2 H d + m 2 Q + m 2 D + A 2 $_{b}$) , (A9) ξ$_{τ}$ = y 2 $_{τ}$( m 2 H d + m 2 L + m 2 E + A 2 $_{τ}$) , (A10) ξ$_{1}$ = 1 2 { m 2 H u − m 2 H d + Tr( m 2 Q − 2 m 2 U + m 2 D + m 2 E − m 2 $_{L}$) } . (A11) [27] J. Pradler and F. D. Steffen, Phys. Rev. D75 , 023509 (2007), hep-ph/0608344. [11] R. N. Mohapatra, N. Okada, and H.-B. Yu, Phys. Rev. D78 , 075011 (2008), 0807.4524. [26] M. Bolz, A. Brandenburg, and W. Buchmuller, Nucl. Phys. B606 , 518 (2001), hep-ph/0012052. [25] M. Ratz, K. Schmidt-Hoberg, and M. W. Winkler, JCAP 0810 , 026 (2008), 0808.0829. [24] M. Kaplinghat and A. Rajaraman, Phys. Rev. D74 , 103004 (2006), astro-ph/0606209. [23] K. Kohri and F. Takayama, Phys. Rev. D76 , 063507 (2007), hep-ph/0605243. [22] R. H. Cyburt, J. R. Ellis, B. D. Fields, K. A. Olive, and V. C. Spanos, JCAP 0611 , 014 (2006), astro- ph/0608562. [21] M. Pospelov, Phys. Rev. Lett. 98 , 231301 (2007), hep- ph/0605215. [20] E. Cremmer et al., Phys. Lett. B79 , 231 (1978). [19] S. Deser and B. Zumino, Phys. Rev. Lett. 38 , 1433 (1977). [18] G. Abbiendi et al. (OPAL), Phys. Lett. B572 , 8 (2003), hep-ex/0305031. [17] D. J. Castano, E. J. Piard, and P. Ramond, Phys. Rev. D49 , 4882 (1994), hep-ph/9308335. [16] K. A. Intriligator, R. G. Leigh, and N. Seiberg, Phys. Rev. D50 , 1092 (1994), hep-th/9403198. [15] N. Seiberg, Phys. Lett. B318 , 469 (1993), hep- ph/9309335. [14] B. A. Campbell, J. Ellis, and D. W. Maybury (2008), 0810.4877. [13] A. G. Cohen, T. S. Roy, and M. Schmaltz, JHEP 02 , 027 (2007), hep-ph/0612100. [12] M. Dine et al., Phys. Rev. D70 , 045023 (2004), hep- ph/0405159. [10] K. Hamaguchi, M. M. Nojiri, and A. de Roeck, JHEP 03 , 046 (2007), hep-ph/0612060. [9] J. L. Feng and B. T. Smith, Phys. Rev. D71 , 015004 (2005), hep-ph/0409278. [8] K. Hamaguchi, Y. Kuno, T. Nakaya, and M. M. Nojiri, Phys. Rev. D70 , 115007 (2004), hep-ph/0409248. [7] J. L. Feng, A. Rajaraman, and F. Takayama, Int. J. Mod. Phys. D13 , 2355 (2004), hep-th/0405248. [6] W. Buchmuller, K. Hamaguchi, M. Ratz, and T. Yanagida, Phys. Lett. B588 , 90 (2004), hep- ph/0402179. [5] M. Kawasaki, K. Kohri, T. Moroi, and A. Yotsuyanagi, Phys. Rev. D78 , 065011 (2008), 0804.3745. [4] S. Dimopoulos, S. D. Thomas, and J. D. Wells, Nucl. Phys. B488 , 39 (1997), hep-ph/9609434. [3] S. Dimopoulos, M. Dine, S. Raby, and S. D. Thomas, Phys. Rev. Lett. 76 , 3494 (1996), hep-ph/9601367. [2] M. Dine, W. Fischler, and M. Srednicki, Nucl. Phys. B189 , 575 (1981); S. Dimopoulos and S. Raby, Nucl. Phys. B192 , 353 (1981); L. Alvarez-Gaume, M. Claud- son, and M. B. Wise, Nucl. Phys. B207 , 96 (1982); M. Dine and W. Fischler, Nucl. Phys. B204 , 346 (1982); C. R. Nappi and B. A. Ovrut, Phys. Lett. B113 , 175 (1982); M. Dine and A. E. Nelson, Phys. Rev. D48 , 1277 (1993), hep-ph/9303230; M. Dine, A. E. Nelson, and Y. Shirman, Phys. Rev. D51 , 1362 (1995), hep- ph/9408384; M. Dine, A. E. Nelson, Y. Nir, and Y. Shir- man, Phys. Rev. D53 , 2658 (1996), hep-ph/9507378. [1] E. Komatsu et al. (WMAP), Astrophys. J. Suppl. 180 , 330 (2009), 0803.0547.