NLSM: ChiPT.fr

File ChiPT.fr, 4.0 KB (added by claudeduhr, 7 years ago)

The model file

Line 
1(**********************************************************)
2(*                                                        *)
3(*  Model for Chiral perturbation Theory at lowest order  *)
4(*                                                        *)
5(**********************************************************)
6
7M$ModelName = "ChiPT";
8
9M$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
22M$Parameters = {
23f == {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
71M$GaugeGroups = {
72  }
73
74(***** Particle classes list ******)
75
76M$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
114pip = anti[pim];
115pipbar=pim;
116
117Kp = anti[Km];
118Kpbar = Km;
119
120(*matrix of the pseudo goldstone boson*)
121
122Pion = {{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
131M = DiagonalMatrix[{mup, md, ms}];
132
133(*U developed at the pi^6*)
134
135U = 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;
138Ubar = 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
144Uk = 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;
147Ukbar = 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
153Lkin := f^2/8 Tr[del[Uk,mu].del[Ukbar,mu]];
154Lm := r*f^2/8 Tr[M.U+M.Ubar];
155La := -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
157L := Lkin+Lm+La;
158