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Dec 21st, 2014
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  1. Subscript[m, 1] = 125.6; v = 246; [Lambda]hs = 0.015; Subscript[M,
  2. p] = 32;
  3. (*initial condition for higgs coupling dependent on M and Sin[Theta]
  4. and at t=0*)
  5. [Lambda]h =
  6. Divide[Subscript[m, 1]^2,
  7. 2*v^2] + (Sin[[Theta]])^2 Divide[(M^2 - Subscript[m, 1]^2),
  8. 2*v^2];
  9. (*initial condition for singlet coupling dependent on M and Sin
  10. [Theta] and at t=0*)
  11. [Lambda]s =
  12. Divide[2*[Lambda]hs^2, (Sin[2*[Theta]])^2]*
  13. Divide[v^2, (M^2 - Subscript[m, 1]^2)]*(Divide[
  14. M^2, (M^2 - Subscript[m, 1]^2)] - Sin[[Theta]]^2);
  15. gsu = 0.64;(*initial condition for Su(2) coupling at t=0, where
  16. t=Divide[[Mu],mtop]*)
  17. gy = 0.34;(*initial condition for u(1)
  18. coupling at t=0*)
  19. gs = 1.16;(*initial condition for SU(3) coupling at
  20. t=0*)
  21. yt = 0.93;(*initial condition for top quark coupling at t=0*)
  22.  
  23. ode2[tp_, [Theta]_, M_] :=
  24. Module[{sol},
  25. sol = NDSolve[{16*Pi^2*Dt[g[t], t] == Divide[-19, 6]*g[t]^3,
  26. 16*Pi^2*Dt[Subscript[g, Y][t], t] ==
  27. Divide[41, 6]*Subscript[g, Y][t]^3,
  28. 16*Pi^2*Dt[Subscript[g, s][t], t] ==
  29. Divide[-7, 1]*Subscript[g, s][t]^3,
  30. 16*Pi^2*Dt[Subscript[y, [Tau]][t], t] ==
  31. Divide[9, 2]*Subscript[y, [Tau]][t]^3 -
  32. 8*Subscript[g, s][t]^2*Subscript[y, [Tau]][t] -
  33. Divide[9, 4]*g[t]^2*Subscript[y, [Tau]][t] -
  34. Divide[17, 12]*Subscript[g, Y][t]^2*Subscript[y, [Tau]][t],
  35. 16*Pi^2*Dt[Subscript[[Lambda], h][t], t] ==
  36. 24*Subscript[[Lambda], h][t]^2 - 6*Subscript[y, [Tau]][t]^4 +
  37. Divide[3, 8]*(2*g[t]^4 + (g[t]^2 + Subscript[g, Y][t]^2)^2) +
  38. Subscript[[Lambda], h][
  39. t]*(-9*g[t]^2 - 3*Subscript[g, Y][t]^2 +
  40. 12*Subscript[y, [Tau]][t]^2) +
  41. Divide[1, 2]*Subscript[[Lambda], hs][t]^2,
  42. 16*Pi^2*Dt[Subscript[[Lambda], hs][t], t] ==
  43. 4*Subscript[[Lambda], hs][t]^2 +
  44. 12*Subscript[[Lambda], h][t]*Subscript[[Lambda], hs][t] -
  45. Divide[3, 2]*(3*g[t]^2 + Subscript[g, Y][t]^2)*
  46. Subscript[[Lambda], hs][t] +
  47. 6*Subscript[[Lambda], hs][t]*Subscript[y, [Tau]][t]^2 +
  48. 6*Subscript[[Lambda], s][t]*Subscript[[Lambda], hs][t],
  49. 16*Pi^2*Dt[Subscript[[Lambda], s][t], t] ==
  50. 2*Subscript[[Lambda], hs][t]^2 +
  51. 18*Subscript[[Lambda], s][t]^2, g[0] == gsu,
  52. Subscript[g, Y][0] == gy, Subscript[g, s][0] == gs,
  53. Subscript[y, [Tau]][0] == yt,
  54. Subscript[[Lambda], h][0] == [Lambda]h,
  55. Subscript[[Lambda], hs][0] == [Lambda]hs,
  56. Subscript[[Lambda], s][0] == [Lambda]s}, {g[t],
  57. Subscript[g, Y][t], Subscript[g, s][t], Subscript[y, [Tau]][t],
  58. Subscript[[Lambda], h][t], Subscript[[Lambda], hs][t],
  59. Subscript[[Lambda], s][t]}, {t, 0, 40}]; {Subscript[[Lambda],
  60. h][tp], Subscript[[Lambda], hs][tp],
  61. Subscript[[Lambda], s][tp], g[tp], Subscript[g, Y][tp],
  62. Subscript[g, s][tp], Subscript[y, [Tau]][tp]} /. sol[[1]]]
  63. RegionPlot[
  64. Evaluate[ode2[tp, [Theta], M][[1]], {tp, 0, 40}] >
  65. 0; {Sin[[Theta]], 0, 1}, {M, 0,
  66. 10^5}](*I want to see the RegionPlot only for the Higgs
  67. coupling(Subscript[[Lambda], h]) for {tp,0,40}, when I vary Sin
  68. [Theta] and M.*)
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