# NLSM: ChiPT.fr

File ChiPT.fr, 4.0 KB (added by claudeduhr, 10 years ago) |
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1 | (**********************************************************) |

2 | (* *) |

3 | (* Model for Chiral perturbation Theory at lowest order *) |

4 | (* *) |

5 | (**********************************************************) |

6 | |

7 | M$ModelName = "ChiPT"; |

8 | |

9 | M$Information = {Authors -> {"C. Degrande"}, |

10 | Date->"12/06/2009" |

11 | Institutions -> {"Universite catholique de Louvain (CP3)"}, |

12 | Emails -> {"celine.degrande@uclouvain.be"}, |

13 | Version -> 1, |

14 | URLs->"http://feynrules.phys.ucl.ac.be/view/Main/NLSM" |

15 | }; |

16 | |

17 | (********** Index definition *********) |

18 | |

19 | |

20 | (***** Parameter list ******) |

21 | |

22 | M$Parameters = { |

23 | f == {ParameterType -> External, |

24 | Value->0.14, |

25 | Description->"decay constant" |

26 | }, |

27 | b == {ParameterType -> External, |

28 | Value->1/6, |

29 | Description->"expansion parameter" |

30 | }, |

31 | c == {ParameterType -> External, |

32 | Value->1/120, |

33 | Description->"expansion parameter" |

34 | }, |

35 | r == {ParameterType -> External, |

36 | Description->"mass term coefficient" |

37 | }, |

38 | m0 == {ParameterType -> External, |

39 | Value->0.8, |

40 | TeX -> Subscript[m, 0], |

41 | Description->"anomalous term coefficient" |

42 | }, |

43 | |

44 | md == {ParameterType -> External, |

45 | Value->0.008, |

46 | TeX -> Subscript[m, d], |

47 | Description->"mass of the down quark" |

48 | }, |

49 | |

50 | (*isospin limit : mup=md*) |

51 | mup == {ParameterType -> Internal, Value->md, |

52 | Value->0.004, |

53 | TeX -> Subscript[m, u], |

54 | Description->"mass of the up quark" |

55 | }, |

56 | ms == {ParameterType -> External, |

57 | Value->0.125, |

58 | TeX -> Subscript[m, s], |

59 | Description->"mass of the strange quark" |

60 | }, |

61 | |

62 | T == {ParameterType -> Internal, |

63 | Value->ArcTan[2 Sqrt[2]*r*(ms-md)/(r*(ms-md)-3m0^2)]/2, |

64 | TeX -> \[Theta], |

65 | Description->"mixing angle" |

66 | } |

67 | } |

68 | |

69 | (***** Gauge group list ******) |

70 | |

71 | M$GaugeGroups = { |

72 | } |

73 | |

74 | (***** Particle classes list ******) |

75 | |

76 | M$ClassesDescription = {S[1] == {ClassName -> pi0, |

77 | SelfConjugate -> True, |

78 | Mass->0.135, |

79 | Width->0 |

80 | }, |

81 | |

82 | S[2] == {ClassName -> pim, |

83 | SelfConjugate -> False, |

84 | Mass->0.14, |

85 | Width->0 |

86 | }, |

87 | |

88 | S[3] == {ClassName -> K0, |

89 | SelfConjugate -> False, |

90 | Mass->0.5, |

91 | Width->0 |

92 | }, |

93 | |

94 | S[4] == {ClassName -> Km, |

95 | SelfConjugate -> False, |

96 | Mass->0.5, |

97 | Width->0 |

98 | }, |

99 | |

100 | S[5] == {ClassName -> eta, |

101 | SelfConjugate -> True, |

102 | Mass->0.55, |

103 | Width->0 |

104 | }, |

105 | |

106 | S[6] == {ClassName -> etap, |

107 | SelfConjugate -> True, |

108 | Mass->0.96, |

109 | Width->0 |

110 | } |

111 | |

112 | } |

113 | |

114 | pip = anti[pim]; |

115 | pipbar=pim; |

116 | |

117 | Kp = anti[Km]; |

118 | Kpbar = Km; |

119 | |

120 | (*matrix of the pseudo goldstone boson*) |

121 | |

122 | Pion = {{pi0 + (Cos[T] eta + Sin[T] etap)/Sqrt[3] + Sqrt[2/3] (-Sin[T] eta + Cos[T] etap), |

123 | Sqrt[2]*pip, |

124 | Sqrt[2]*Kp}, {Sqrt[2]*pim, -pi0 + (Cos[T] eta + Sin[T] etap)/Sqrt[3] + |

125 | Sqrt[2/3] (-Sin[T] eta + Cos[T] etap), Sqrt[2]*K0}, {Sqrt[2]*Km, |

126 | Sqrt[2]*K0bar, -2 (Cos[T] eta + Sin[T] etap)/Sqrt[3] + |

127 | Sqrt[2/3] (-Sin[T] eta + Cos[T] etap)}}; |

128 | |

129 | (*mass matrix of the light quarks*) |

130 | |

131 | M = DiagonalMatrix[{mup, md, ms}]; |

132 | |

133 | (*U developed at the pi^6*) |

134 | |

135 | U = IdentityMatrix[3] + I Sqrt[2] Pion/f - MatrixPower[Pion, 2]/f^2 - |

136 | 2 Sqrt[2] I b MatrixPower[Pion, 3]/f^3 + |

137 | 4 (b - 1/8) MatrixPower[Pion, 4]/f^4 + I 4 Sqrt[2]*c MatrixPower[Pion, 5]/f^5 - 8*(c+b^2/2-b/2+1/16) MatrixPower[Pion, 6]/f^6; |

138 | Ubar = IdentityMatrix[3] - I Sqrt[2] Pion/f - MatrixPower[Pion, 2]/f^2 + |

139 | 2 Sqrt[2] I b MatrixPower[Pion, 3]/f^3 + |

140 | 4 (b - 1/8) MatrixPower[Pion, 4]/f^4 - I 4 Sqrt[2]*c MatrixPower[Pion, 5]/f^5 - 8*(c+b^2/2-b/2+1/16) MatrixPower[Pion, 6]/f^6; |

141 | |

142 | (*U at the order pi^5 to speed up the compution of Lkin*) |

143 | |

144 | Uk = IdentityMatrix[3] + I Sqrt[2] Pion/f - MatrixPower[Pion, 2]/f^2 - |

145 | 2 Sqrt[2] I b MatrixPower[Pion, 3]/f^3 + |

146 | 4 (b - 1/8) MatrixPower[Pion, 4]/f^4 + I 4 Sqrt[2]*c MatrixPower[Pion, 5]/f^5; |

147 | Ukbar = IdentityMatrix[3] - I Sqrt[2] Pion/f - MatrixPower[Pion, 2]/f^2 + |

148 | 2 Sqrt[2] I b MatrixPower[Pion, 3]/f^3 + |

149 | 4 (b - 1/8) MatrixPower[Pion, 4]/f^4 - I 4 Sqrt[2]*c MatrixPower[Pion, 5]/f^5; |

150 | |

151 | (*Lagrangian*) |

152 | |

153 | Lkin := f^2/8 Tr[del[Uk,mu].del[Ukbar,mu]]; |

154 | Lm := r*f^2/8 Tr[M.U+M.Ubar]; |

155 | La := -f^2 m0^2/12 Tr[Pion/f-2 (b-1/6) MatrixPower[Pion, 3]/f^3 + 4 (c-b/2+3/40) MatrixPower[Pion, 5]/f^5]^2; |

156 | |

157 | L := Lkin+Lm+La; |

158 |