331: 331_3.fr

File 331_3.fr, 61.0 KB (added by zhangdongming, 9 years ago)

The 331 model file for beta=+sqrt(3).

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the 331 model where beta equals to Sqrt[3] ******)
3(****** ******)
4(****** Authors: Dongming Zhang ******)
5(****** ******)
6(****** Choose whether Feynman gauge is desired. ******)
7(****** If set to False, unitary gauge is assumed. ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
10(***************************************************************************************************************)
11
12(* ************************** *)
13(* ***** Information ***** *)
14(* ************************** *)
15M$ModelName = "331_3 Model";
16
17M$Information = {
18 Authors -> {"Dongming Zhang"},
19 Version -> "1.0.0",
20 Date -> "22. 01. 2014",
21 Institutions -> {"Peking University"},
22 Emails -> {"zhangdongming@pku.edu.cn"},
23 URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/331"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** Change log ***** *)
30(* ************************** *)
31
32(* ************************** *)
33(* ***** vevs ***** *)
34(* ************************** *)
35M$vevs = { {Rho[2],v}, {Phi[1],v2}, {Chi[3],v3} };
36
37(* ************************** *)
38(* ***** Gauge groups ***** *)
39(* ************************** *)
40M$GaugeGroups = {
41 U1X == {
42 Abelian -> True,
43 CouplingConstant -> gx,
44 GaugeBoson -> K,
45 Charge -> X
46 },
47 SU3L == {
48 Abelian -> False,
49 CouplingConstant -> gw,
50 GaugeBoson -> Wi,
51 StructureConstant -> x,
52 Representations -> {Ta,SU3T},
53 Definitions -> {Ta[a_,b_,c_]->Gellmann[a,b,c]/2,FSU3L[i_,j_,k_]:> I x[i,j,k]},
54 SymmetricTensor -> dSUN
55 },
56 ASU3L == {
57 Abelian -> False,
58 CouplingConstant -> gw,
59 GaugeBoson -> WWi,
60 StructureConstant -> x,
61 Representations -> {Tb,ASU3T},
62 Definitions -> {Tb[a_,b_,c_]->-Gellmann[a,c,b]/2,FSU3L[i_,j_,k_]:> I x[i,j,k]},
63 SymmetricTensor -> dSUN
64 },
65 SU3C == {
66 Abelian -> False,
67 CouplingConstant -> gs,
68 GaugeBoson -> G,
69 StructureConstant -> f,
70 Representations -> {T,Colour},
71 SymmetricTensor -> dSUN
72 }
73};
74
75(* ************************** *)
76(* *** Gellmann matrices *** *)
77(* ************************** *)
78
79Table[Gellmann[i, j, k] = 0, {i, 1, 8}, {j, 1, 3}, {k, 1, 3}] //
80 Flatten;
81
82Gellmann[1] = {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}};
83Gellmann[2] = {{0, -I, 0}, {I, 0, 0}, {0, 0, 0}};
84Gellmann[3] = {{1, 0, 0}, {0, -1, 0}, {0, 0, 0}};
85Gellmann[4] = {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}};
86Gellmann[5] = {{0, 0, -I}, {0, 0, 0}, {I, 0, 0}};
87Gellmann[6] = {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}};
88Gellmann[7] = {{0, 0, 0}, {0, 0, -I}, {0, I, 0}};
89Gellmann[8] = 1/Sqrt[3] {{1, 0, 0}, {0, 1, 0}, {0, 0, -2}};
90
91Gellmann[1, 1, 2] = 1; Gellmann[1, 2, 1] = 1;
92Gellmann[2, 1, 2] = -I; Gellmann[2, 2, 1] = I;
93Gellmann[3, 1, 1] = 1; Gellmann[3, 2, 2] = -1;
94Gellmann[4, 1, 3] = 1; Gellmann[4, 3, 1] = 1;
95Gellmann[5, 1, 3] = -I; Gellmann[5, 3, 1] = I;
96Gellmann[6, 2, 3] = 1; Gellmann[6, 3, 2] = 1;
97Gellmann[7, 2, 3] = -I; Gellmann[7, 3, 2] = I;
98Gellmann[8, 1, 1] = 1/Sqrt[3]; Gellmann[8, 2, 2] = 1/Sqrt[3];
99Gellmann[8, 3, 3] = -2/Sqrt[3];
100
101
102Gellmann[i_Integer, j_Integer, k_Integer] := Gellmann[i][[j, k]];
103Gellmann[xx___, Index[_, i_Integer], yy___] := Gellmann[xx, i, yy];
104
105Gellmann /:
106 Gellmann[i1_, i2_, i3_?(Not[NumericQ[#]] &)] Gellmann[j1_, i3_,
107 j3_] :=
108 Gellmann[i1, i2, 1] Gellmann[j1, 1, j3] +
109 Gellmann[i1, i2, 2] Gellmann[j1, 2, j3] +
110 Gellmann[i1, i2, 3] Gellmann[j1, 3, j3];
111
112Table[x[i, j, k] = 0, {i, 1, 8}, {j, 1, 8}, {k, 1, 8}] // Flatten;
113x[1, 2, 3] = 1; x[2, 3, 1] = 1; x[3, 1, 2] = 1;
114x[2, 1, 3] = -1; x[1, 3, 2] = -1; x[3, 2, 1] = -1;
115x[1, 5, 6] = -1/2; x[3, 6, 7] = -1/2; x[1, 7, 4] = -1/2;
116x[2, 6, 4] = -1/2; x[2, 7, 5] = -1/2; x[3, 5, 4] = -1/2;
117x[6, 1, 5] = -1/2; x[7, 3, 6] = -1/2; x[4, 1, 7] = -1/2;
118x[4, 2, 6] = -1/2; x[5, 2, 7] = -1/2; x[4, 3, 5] = -1/2;
119x[5, 6, 1] = -1/2; x[6, 7, 3] = -1/2; x[7, 4, 1] = -1/2;
120x[6, 4, 2] = -1/2; x[7, 5, 2] = -1/2; x[5, 4, 3] = -1/2;
121x[1, 6, 5] = 1/2; x[3, 7, 6] = 1/2; x[1, 4, 7] = 1/2;
122x[2, 4, 6] = 1/2; x[2, 5, 7] = 1/2; x[3, 4, 5] = 1/2;
123x[5, 1, 6] = 1/2; x[7, 6, 3] = 1/2; x[4, 7, 1] = 1/2;
124x[4, 6, 2] = 1/2; x[5, 7, 2] = 1/2; x[4, 5, 3] = 1/2;
125x[6, 5, 1] = 1/2; x[6, 3, 7] = 1/2; x[7, 1, 4] = 1/2;
126x[6, 2, 4] = 1/2; x[7, 2, 5] = 1/2; x[5, 3, 4] = 1/2;
127x[4, 5, 8] = Sqrt[3]/2; x[6, 7, 8] = Sqrt[3]/2;
128x[8, 4, 5] = Sqrt[3]/2; x[8, 6, 7] = Sqrt[3]/2;
129x[5, 8, 4] = Sqrt[3]/2; x[7, 8, 6] = Sqrt[3]/2;
130x[4, 8, 5] = -Sqrt[3]/2; x[6, 8, 7] = -Sqrt[3]/2;
131x[5, 4, 8] = -Sqrt[3]/2;
132x[7, 6, 8] = -Sqrt[3]/2; x[8, 7, 6] = -Sqrt[3]/2;
133x[8, 5, 4] = -Sqrt[3]/2;
134
135x /: x[ii___, Except[Index[___] | _?NumericQ, jj_], kk___] f_[aa___,
136 Index[name_, jj_], cc___] :=
137 x[ii, Index[name, jj], kk] f[aa, Index[name, jj], cc];
138x /: x[ii___, Except[Index[___] | _?NumericQ, jj_],
139 kk___] f_[aa___, Index[name_, jj_], cc___][ind___] :=
140 x[ii, Index[name, jj], kk] f[aa, Index[name, jj], cc][ind];
141x /: x[ii___, Except[Index[___] | _?NumericQ, jj_], kk___] f_[aa___,
142 g_[xx___, Index[name_, jj_], yy___], cc___] :=
143 x[ii, Index[name, jj], kk] f[aa, g[xx, Index[name, jj], yy], cc];
144x /: x[ii___, Except[Index[___] | _?NumericQ, jj_],
145 kk___] f_[aa___, g_[xx___, Index[name_, jj_], yy___], cc___][
146 ind___] :=
147 x[ii, Index[name, jj], kk] f[aa, g[xx, Index[name, jj], yy], cc][
148 ind];
149
150x[ii___, Except[_Index | _Done[Index] | _FV,
151 jj_?(Not[NumericQ[#]] &)], kk___, Index[name_, ll_], mm___] :=
152 x[ii, Index[name, jj], kk, Index[name, ll], mm];
153x[ii___, Index[name_, ll_], kk___,
154 Except[_Index | _Done[Index] | _FV, jj_?(Not[NumericQ[#]] &)],
155 mm___] := x[ii, Index[name, ll], kk, Index[name, jj], mm];
156
157x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
158 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
159 i_, m_, n_] :=
160 x[1, j, k] x[1, m, n] + x[2, j, k] x[2, m, n] +
161 x[3, j, k] x[3, m, n] + x[4, j, k] x[4, m, n] +
162 x[5, j, k] x[5, m, n] + x[6, j, k] x[6, m, n] +
163 x[7, j, k] x[7, m, n] + x[8, j, k] x[8, m, n];
164
165x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
166 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
167 m_, n_, i_] := x[i, j, k] x[i, m, n];
168x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
169 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
170 m_, i_, n_] := x[i, j, k] x[i, n, m];
171x /: x[j_,
172 i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
173 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), k_] x[m_, i_,
174 n_] := x[i, k, j] x[i, n, m];
175x /: x[j_,
176 i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
177 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), k_] x[m_, n_,
178 i_] := x[i, k, j] x[i, m, n];
179x /: x[j_, k_,
180 i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
181 Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &)] x[m_, n_,
182 i_] := x[i, j, k] x[i, m, n];
183
184x /: x[___, i_, ___, j_, ___] FV[a_, i_] FV[a_, j_] := 0;
185x /: x[___, i_, ___, j_, ___] del[del[_, i_], j_] := 0;
186x /: x[___, i_, ___, j_, ___] del[del[_, j_], i_] := 0;
187
188x[xx___, Index[name_, i_?NumericQ], yy___] := x[xx, i, yy];
189
190(* ************************** *)
191(* ***** Indices ***** *)
192(* ************************** *)
193
194IndexRange[Index[SU3W ]] = Unfold[Range[8]];
195IndexRange[Index[ASU3W ]] = Unfold[Range[8]];
196IndexRange[Index[ASU3T ]] = Unfold[Range[3]];
197IndexRange[Index[SU3T ]] = Unfold[Range[3]];
198IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
199IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
200IndexRange[Index[Generation1]] = Range[3,3];
201IndexRange[Index[Generation2]] = Range[2];
202IndexRange[Index[Generation]] = Range[3];
203
204IndexStyle[SU3W, j];
205IndexStyle[ASU3W, o];
206IndexStyle[ASU3T, p];
207IndexStyle[SU3T, k];
208IndexStyle[Gluon, a];
209IndexStyle[Colour, m];
210IndexStyle[Generation1, r];
211IndexStyle[Generation2, g];
212IndexStyle[Generation, f];
213
214
215(* ************************** *)
216(* *** Interaction orders *** *)
217(* *** (as used by mg5) *** *)
218(* ************************** *)
219
220M$InteractionOrderHierarchy = {
221 {QCD, 1},
222 {QED, 2}
223};
224
225
226(* ************************** *)
227(* **** Particle classes **** *)
228(* ************************** *)
229M$ClassesDescription = {
230
231(* Gauge bosons: physical vector fields *)
232 V[1] == {
233 ClassName -> A,
234 SelfConjugate -> True,
235 Mass -> 0,
236 Width -> 0,
237 ParticleName -> "a",
238 PDG -> 22,
239 PropagatorLabel -> "a",
240 PropagatorType -> W,
241 PropagatorArrow -> None,
242 FullName -> "Photon"
243 },
244 V[2] == {
245 ClassName -> Z,
246 SelfConjugate -> True,
247 Mass -> {MZ, 91.1876},
248 Width -> {WZ, 2.4952},
249 ParticleName -> "Z",
250 PDG -> 23,
251 PropagatorLabel -> "Z",
252 PropagatorType -> Sine,
253 PropagatorArrow -> None,
254 FullName -> "Z"
255 },
256 V[3] == {
257 ClassName -> ZP,
258 SelfConjugate -> True,
259 Mass -> {MZP, Internal},
260 Width -> {WZP, 10},
261 ParticleName -> "ZP",
262 PropagatorLabel -> "ZP",
263 PropagatorType -> Sine,
264 PropagatorArrow -> None,
265 FullName -> "ZP"
266 },
267 V[4] == {
268 ClassName -> W,
269 SelfConjugate -> False,
270 Mass -> {MW, 80.385},
271 Width -> {WW, 2.085},
272 ParticleName -> "W+",
273 AntiParticleName -> "W-",
274 QuantumNumbers -> {Q -> 1},
275 PDG -> 24,
276 PropagatorLabel -> "W",
277 PropagatorType -> Sine,
278 PropagatorArrow -> Forward,
279 FullName -> "W"
280 },
281 V[5] == {
282 ClassName -> YY,
283 SelfConjugate -> False,
284 Mass -> {MY, Internal},
285 Width -> {WY, 10},
286 ParticleName -> "Y--",
287 AntiParticleName -> "Y++",
288 QuantumNumbers -> {Q -> -2},
289 PropagatorLabel -> "YY",
290 PropagatorType -> Sine,
291 PropagatorArrow -> Forward,
292 FullName -> "YY"
293 },
294 V[6] == {
295 ClassName -> V,
296 SelfConjugate -> False,
297 Mass -> {MV, Internal},
298 Width -> {WV, 10},
299 ParticleName -> "V-",
300 AntiParticleName -> "V+",
301 QuantumNumbers -> {Q -> -1},
302 PropagatorLabel -> "V",
303 PropagatorType -> Sine,
304 PropagatorArrow -> Forward,
305 FullName -> "V"
306 },
307 V[7] == {
308 ClassName -> G,
309 SelfConjugate -> True,
310 Indices -> {Index[Gluon]},
311 Mass -> 0,
312 Width -> 0,
313 ParticleName -> "g",
314 PDG -> 21,
315 PropagatorLabel -> "G",
316 PropagatorType -> C,
317 PropagatorArrow -> None,
318 FullName -> "G"
319 },
320
321(* Ghosts: related to physical gauge bosons *)
322 U[1] == {
323 ClassName -> ghA,
324 SelfConjugate -> False,
325 Ghost -> A,
326 QuantumNumbers -> {GhostNumber -> 1},
327 Mass -> 0,
328 Width -> 0,
329 PropagatorLabel -> "uA",
330 PropagatorType -> GhostDash,
331 PropagatorArrow -> Forward
332 },
333 U[2] == {
334 ClassName -> ghZ,
335 SelfConjugate -> False,
336 Ghost -> Z,
337 QuantumNumbers -> {GhostNumber -> 1},
338 Mass -> {MZ,91.1876},
339 Width -> {WZ, 2.4952},
340 PropagatorLabel -> "uZ",
341 PropagatorType -> GhostDash,
342 PropagatorArrow -> Forward
343 },
344 U[3] == {
345 ClassName -> ghZP,
346 SelfConjugate -> False,
347 Ghost -> ZP,
348 QuantumNumbers -> {GhostNumber -> 1},
349 Mass -> {MZP,Internal},
350 Width -> {WZP, 10},
351 PropagatorLabel -> "uZP",
352 PropagatorType -> GhostDash,
353 PropagatorArrow -> Forward
354 },
355 U[41] == {
356 ClassName -> ghWp,
357 SelfConjugate -> False,
358 Ghost -> W,
359 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
360 Mass -> {MW, 80.385},
361 Width -> {WW, 2.085},
362 PropagatorLabel -> "uWp",
363 PropagatorType -> GhostDash,
364 PropagatorArrow -> Forward
365 },
366 U[42] == {
367 ClassName -> ghWm,
368 SelfConjugate -> False,
369 Ghost -> Wbar,
370 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
371 Mass -> {MW, 80.385},
372 Width -> {WW, 2.085},
373 PropagatorLabel -> "uWm",
374 PropagatorType -> GhostDash,
375 PropagatorArrow -> Forward
376 },
377 U[51] == {
378 ClassName -> ghYp,
379 SelfConjugate -> False,
380 Ghost -> YY,
381 QuantumNumbers -> {GhostNumber -> 1, Q -> -2},
382 Mass -> {MY, Internal},
383 Width -> {WY, 10},
384 PropagatorLabel -> "uYp",
385 PropagatorType -> GhostDash,
386 PropagatorArrow -> Forward
387 },
388 U[52] == {
389 ClassName -> ghYm,
390 SelfConjugate -> False,
391 Ghost -> YYbar,
392 QuantumNumbers -> {GhostNumber -> 1, Q -> 2},
393 Mass -> {MY, Internal},
394 Width -> {WY, 10},
395 PropagatorLabel -> "uYm",
396 PropagatorType -> GhostDash,
397 PropagatorArrow -> Forward
398 },
399 U[61] == {
400 ClassName -> ghVp,
401 SelfConjugate -> False,
402 Ghost -> V,
403 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
404 Mass -> {MV,Internal},
405 Width -> {WV, 10},
406 PropagatorLabel -> "uVp",
407 PropagatorType -> GhostDash,
408 PropagatorArrow -> Forward
409 },
410 U[62] == {
411 ClassName -> ghVm,
412 SelfConjugate -> False,
413 Ghost -> Vbar,
414 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
415 Mass -> {MV,Internal},
416 Width -> {WV, 10},
417 PropagatorLabel -> "uVm",
418 PropagatorType -> GhostDash,
419 PropagatorArrow -> Forward
420 },
421 U[7] == {
422 ClassName -> ghG,
423 SelfConjugate -> False,
424 Indices -> {Index[Gluon]},
425 Ghost -> G,
426 QuantumNumbers ->{GhostNumber -> 1},
427 Mass -> 0,
428 Width -> 0,
429 PropagatorLabel -> "uG",
430 PropagatorType -> GhostDash,
431 PropagatorArrow -> Forward
432 },
433
434(* Gauge bosons: unphysical vector fields *)
435 V[12] == {
436 ClassName -> K,
437 Unphysical -> True,
438 SelfConjugate -> True,
439 Definitions -> { K[mu_] -> c3 (cz ZP[mu]-sz Z[mu]) + s3 (-sw (cz Z[mu]+sz ZP[mu]) + cw A[mu])}
440 },
441 V[13] == {
442 ClassName -> Wi,
443 Unphysical -> True,
444 SelfConjugate -> True,
445 Indices -> {Index[SU3W]},
446 FlavorIndex -> SU3W,
447 Definitions -> {
448Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
449Wi[mu_,4] -> (YYbar[mu]+YY[mu])/Sqrt[2], Wi[mu_,5] -> (YY[mu]-YYbar[mu])/(I*Sqrt[2]),
450Wi[mu_,6] -> (Vbar[mu]+V[mu])/Sqrt[2], Wi[mu_,7] -> (V[mu]-Vbar[mu])/(I*Sqrt[2]),
451Wi[mu_,3] -> cw (cz Z[mu]+sz ZP[mu]) + sw A[mu], Wi[mu_,8] -> -s3 (cz ZP[mu]-sz Z[mu]) + c3 (-sw (cz Z[mu]+sz ZP[mu]) +cw A[mu])}
452 },
453 V[14] == {
454 ClassName -> WWi,
455 Unphysical -> True,
456 SelfConjugate -> True,
457 Indices -> {Index[ASU3W]},
458 FlavorIndex -> ASU3W,
459 Definitions -> {
460WWi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], WWi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
461WWi[mu_,4] -> (YYbar[mu]+YY[mu])/Sqrt[2], WWi[mu_,5] -> (YY[mu]-YYbar[mu])/(I*Sqrt[2]),
462WWi[mu_,6] -> (Vbar[mu]+V[mu])/Sqrt[2], WWi[mu_,7] -> (V[mu]-Vbar[mu])/(I*Sqrt[2]),
463WWi[mu_,3] -> cw (cz Z[mu]+sz ZP[mu]) + sw A[mu], WWi[mu_,8] -> -s3 (cz ZP[mu]-sz Z[mu])+c3 (-sw (cz Z[mu]+sz ZP[mu])+cw A[mu])}
464 },
465
466(* Ghosts: related to unphysical gauge bosons *)
467 U[12] == {
468 ClassName -> ghK,
469 Unphysical -> True,
470 SelfConjugate -> False,
471 Ghost -> K,
472 Definitions -> { ghK -> -c3 (cz ghZP-sz ghZ) + s3 (-sw (cz ghZ+sz ghZP) + cw ghA)}
473 },
474 U[13] == {
475 ClassName -> ghWi,
476 Unphysical -> True,
477 SelfConjugate -> False,
478 Ghost -> Wi,
479 Indices -> {Index[SU3W]},
480 FlavorIndex -> SU3W,
481 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[4] -> (ghYp+ghYm)/Sqrt[2], ghWi[5] -> (ghYp-ghYm)/(I*Sqrt[2]),ghWi[6] -> (ghVp+ghVm)/Sqrt[2], ghWi[7] -> (ghVp-ghVm)/(I*Sqrt[2]), ghWi[3] -> cw (cz ghZ+sz ghZP)+sw ghA, ghWi[8] -> -s3 (cz ghZP-sz ghZ)+c3 (-sw (cz ghZ+sz ghZP) + cw ghA)}
482 },
483
484(* Fermions: physical fields *)
485 F[1] == {
486 ClassName -> vl,
487 ClassMembers -> {ve,vm,vt},
488 Indices -> {Index[Generation]},
489 FlavorIndex -> Generation,
490 SelfConjugate -> False,
491 Mass -> 0,
492 Width -> 0,
493 QuantumNumbers -> {LeptonNumber -> 1},
494 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
495 PropagatorType -> S,
496 PropagatorArrow -> Forward,
497 PDG -> {12,14,16},
498 ParticleName -> {"ve","vm","vt"},
499 AntiParticleName -> {"ve~","vm~","vt~"},
500 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
501 },
502 F[2] == {
503 ClassName -> l,
504 ClassMembers -> {e, mu, ta},
505 Indices -> {Index[Generation]},
506 FlavorIndex -> Generation,
507 SelfConjugate -> False,
508 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
509 Width -> 0,
510 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
511 PropagatorLabel -> {"l", "e", "mu", "ta"},
512 PropagatorType -> Straight,
513 PropagatorArrow -> Forward,
514 PDG -> {11, 13, 15},
515 ParticleName -> {"e-", "mu-", "ta-"},
516 AntiParticleName -> {"e+", "mu+", "ta+"},
517 FullName -> {"Electron", "Muon", "Tau"}
518 },
519 F[3] == {
520 ClassName -> EE,
521 ClassMembers -> {Ee, Emu, Eta},
522 Indices -> {Index[Generation]},
523 FlavorIndex -> Generation,
524 SelfConjugate -> False,
525 Mass -> {ME, {MEE,1*^3}, {MEMU,1*^3}, {META,1*^3}},
526 Width -> {WE, {WEE,10},{WEMU,10},{WETA,10}},
527 QuantumNumbers -> {Q -> 1, LeptonNumber -> 1},
528 PropagatorLabel -> {"E", "Ee", "Emu", "Eta"},
529 PropagatorType -> Straight,
530 PropagatorArrow -> Forward,
531 ParticleName -> {"Ee+", "Emu+", "Eta+"},
532 AntiParticleName -> {"Ee-", "Emu-", "Eta-"},
533 FullName -> {"HElectron", "HMuon", "HTau"}
534 },
535 F[4] == {
536 ClassName -> uq,
537 ClassMembers -> {u, c, t},
538 Indices -> {Index[Generation], Index[Colour]},
539 FlavorIndex -> Generation,
540 SelfConjugate -> False,
541 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
542 Width -> {0, 0, {WT,1.50833649}},
543 QuantumNumbers -> {Q -> 2/3},
544 PropagatorLabel -> {"uq", "u", "c", "t"},
545 PropagatorType -> Straight,
546 PropagatorArrow -> Forward,
547 PDG -> {2, 4, 6},
548 ParticleName -> {"u", "c", "t" },
549 AntiParticleName -> {"u~", "c~", "t~"},
550 FullName -> {"u-quark", "c-quark", "t-quark"}
551 },
552 F[5] == {
553 ClassName -> dq,
554 ClassMembers -> {d, s, b},
555 Indices -> {Index[Generation], Index[Colour]},
556 FlavorIndex -> Generation,
557 SelfConjugate -> False,
558 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
559 Width -> 0,
560 QuantumNumbers -> {Q -> -1/3},
561 PropagatorLabel -> {"dq", "d", "s", "b"},
562 PropagatorType -> Straight,
563 PropagatorArrow -> Forward,
564 PDG -> {1,3,5},
565 ParticleName -> {"d", "s", "b" },
566 AntiParticleName -> {"d~", "s~", "b~"},
567 FullName -> {"d-quark", "s-quark", "b-quark"}
568 },
569 F[6] == {
570 ClassName -> Jq12,
571 ClassMembers -> {Jd, Js},
572 Indices -> {Index[Generation2], Index[Colour]},
573 FlavorIndex -> Generation2,
574 SelfConjugate -> False,
575 Mass -> {MJ12, {MJD,1*^3}, {MJS,1*^3}},
576 Width -> {WJQ12,{WJD,10},{WJS,10}},
577 QuantumNumbers -> {Q -> -4/3},
578 PropagatorLabel -> {"Jq12", "Jd", "Js"},
579 PropagatorType -> Straight,
580 PropagatorArrow -> Forward,
581 ParticleName -> {"Jd", "Js"},
582 AntiParticleName -> {"Jd~", "Js~"},
583 FullName -> {"Jd-quark", "Js-quark"}
584 },
585 F[7] == {
586 ClassName -> Jt,
587 Indices -> {Index[Colour]},
588 SelfConjugate -> False,
589 Mass -> {MJT,1*^3},
590 Width -> 10,
591 QuantumNumbers -> {Q -> 5/3},
592 PropagatorLabel -> "Jt",
593 PropagatorType -> Straight,
594 PropagatorArrow -> Forward,
595 ParticleName -> "Jt",
596 AntiParticleName -> "Jt~",
597 FullName -> "Jt-quark"
598 },
599
600
601
602(* Fermions: unphysical fields *)
603 F[11] == {
604 ClassName -> LL,
605 Unphysical -> True,
606 Indices -> {Index[ASU3T], Index[Generation]},
607 FlavorIndex -> ASU3T,
608 SelfConjugate -> False,
609 QuantumNumbers -> {X ->0},
610 Definitions -> {
611 LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]],
612 LL[sp1_,2,ff_] :> -Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]],
613 LL[sp1_,3,ff_] :> Module[{sp2}, ProjM[sp1,sp2] EE[sp2,ff]]}
614 },
615 F[12] == {
616 ClassName -> lR,
617 Unphysical -> True,
618 Indices -> {Index[Generation]},
619 FlavorIndex -> Generation,
620 SelfConjugate -> False,
621 QuantumNumbers -> {X -> -1},
622 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
623 },
624 F[13] == {
625 ClassName -> EER,
626 Unphysical -> True,
627 Indices -> {Index[Generation]},
628 FlavorIndex -> Generation,
629 SelfConjugate -> False,
630 QuantumNumbers -> {X -> 1},
631 Definitions -> { EER[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] EE[sp2,ff]] }
632 },
633 F[14] == {
634 ClassName -> QL12,
635 Unphysical -> True,
636 Indices -> {Index[SU3T], Index[Generation2], Index[Colour]},
637 FlavorIndex -> SU3T,
638 SelfConjugate -> False,
639 QuantumNumbers -> {X -> -1/3},
640 Definitions -> {
641 QL12[sp1_,1,1,cc_] :> Module[{sp2,ff2}, RU[1,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
642 QL12[sp1_,1,2,cc_] :> Module[{sp2,ff2}, RU[2,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
643 QL12[sp1_,2,1,cc_] :> Module[{sp2,ff2}, CKM[1,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
644 QL12[sp1_,2,2,cc_] :> Module[{sp2,ff2}, CKM[2,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
645 QL12[sp1_,3,ff12_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] Jq12[sp2,ff12,cc]]}
646 },
647 F[15] == {
648 ClassName -> QL3,
649 Unphysical -> True,
650 Indices -> {Index[ASU3T], Index[Generation1], Index[Colour]},
651 FlavorIndex -> ASU3T,
652 SelfConjugate -> False,
653 QuantumNumbers -> {X -> 2/3},
654 Definitions -> {
655 QL3[sp1_,1,3,cc_] :> Module[{sp2,ff2}, CKM[3,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
656 QL3[sp1_,2,3,cc_] :>-Module[{sp2,ff2}, RU[3,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
657 QL3[sp1_,3,3,cc_] :> Module[{sp2}, ProjM[sp1,sp2] Jt[sp2,cc]]}
658 },
659 F[16] == {
660 ClassName -> QL,
661 Unphysical -> True,
662 Indices -> {Index[SU3T], Index[Generation], Index[Colour]},
663 FlavorIndex -> SU3T,
664 SelfConjugate -> False,
665 QuantumNumbers -> {X -> -1/3, X -> -1/3, X -> 2/3},
666 Definitions -> {
667 QL[sp1_,1,1,cc_] :> QL12[sp1,1,1,cc],
668 QL[sp1_,1,2,cc_] :> QL12[sp1,1,2,cc],
669 QL[sp1_,1,3,cc_] :> QL3[sp1,1,3,cc],
670 QL[sp1_,2,1,cc_] :> QL12[sp1,2,1,cc],
671 QL[sp1_,2,2,cc_] :> QL12[sp1,2,2,cc],
672 QL[sp1_,2,3,cc_] :> QL3[sp1,2,3,cc],
673 QL[sp1_,3,1,cc_] :> QL12[sp1,3,1,cc],
674 QL[sp1_,3,2,cc_] :> QL12[sp1,3,2,cc],
675 QL[sp1_,3,3,cc_] :> QL3[sp1,3,3,cc]}
676 },
677 F[17] == {
678 ClassName -> uR,
679 Unphysical -> True,
680 Indices -> {Index[Generation], Index[Colour]},
681 FlavorIndex -> Generation,
682 SelfConjugate -> False,
683 QuantumNumbers -> {X -> 2/3},
684 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
685 },
686 F[18] == {
687 ClassName -> dR,
688 Unphysical -> True,
689 Indices -> {Index[Generation], Index[Colour]},
690 FlavorIndex -> Generation,
691 SelfConjugate -> False,
692 QuantumNumbers -> {X -> -1/3},
693 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
694 },
695 F[19] == {
696 ClassName -> JR12,
697 Unphysical -> True,
698 Indices -> {Index[Generation2], Index[Colour]},
699 FlavorIndex -> Generation2,
700 SelfConjugate -> False,
701 QuantumNumbers -> {X -> -4/3},
702 Definitions -> { JR12[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] Jq12[sp2,ff,cc]] }
703 },
704 F[20] == {
705 ClassName -> JR3,
706 Unphysical -> True,
707 Indices -> {Index[Generation1], Index[Colour]},
708 FlavorIndex -> Generation1,
709 SelfConjugate -> False,
710 QuantumNumbers -> {X -> 5/3},
711 Definitions -> { JR3[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] Jt[sp2,cc]] }
712 },
713 F[21] == {
714 ClassName -> JR,
715 Unphysical -> True,
716 Indices -> {Index[Generation], Index[Colour]},
717 FlavorIndex -> Generation,
718 SelfConjugate -> False,
719 QuantumNumbers -> {X -> -4/3, X -> -4/3, X -> 5/3},
720 Definitions -> { JR[sp1_,1,cc_] :> JR12[sp1,1,cc],
721 JR[sp1_,2,cc_] :> JR12[sp1,2,cc],
722 JR[sp1_,3,cc_] :> JR3[sp1,3,cc] }
723 },
724
725(* Higgs: physical scalars *)
726 S[1] == {
727 ClassName -> h,
728 SelfConjugate -> True,
729 Mass -> {Mh,125},
730 Width -> {Wh,0.00407},
731 PropagatorLabel -> "h",
732 PropagatorType -> D,
733 PropagatorArrow -> None,
734 PDG -> 25,
735 ParticleName -> "h",
736 FullName -> "h"
737 },
738 S[2] == {
739 ClassName -> H2,
740 SelfConjugate -> True,
741 Mass -> {MH2,Internal},
742 Width -> {WH2,10},
743 PropagatorLabel -> "H2",
744 PropagatorType -> D,
745 PropagatorArrow -> None,
746 ParticleName -> "H2",
747 FullName -> "H2"
748 },
749 S[3] == {
750 ClassName -> H3,
751 SelfConjugate -> True,
752 Mass -> {MH3,Internal},
753 Width -> {WH3,10},
754 PropagatorLabel -> "H3",
755 PropagatorType -> D,
756 PropagatorArrow -> None,
757 ParticleName -> "H3",
758 FullName -> "H3"
759 },
760 S[4] == {
761 ClassName -> H0,
762 SelfConjugate -> True,
763 Mass -> {MH0,Internal},
764 Width -> {WH0,10},
765 PropagatorLabel -> "H0",
766 PropagatorType -> D,
767 PropagatorArrow -> None,
768 ParticleName -> "H0",
769 FullName -> "H0"
770 },
771 S[5] == {
772 ClassName -> HW,
773 SelfConjugate -> False,
774 Mass -> {MHW,Internal},
775 Width -> {WHW,10},
776 ParticleName -> "HW+",
777 AntiParticleName -> "HW-",
778 QuantumNumbers -> {Q -> 1},
779 PropagatorLabel -> "HW",
780 PropagatorType -> D,
781 PropagatorArrow -> Forward,
782 FullName -> "HW"
783 },
784 S[6] == {
785 ClassName -> HY,
786 SelfConjugate -> False,
787 Mass -> {MHY,Internal},
788 Width -> {WHY,10},
789 ParticleName -> "HY--",
790 AntiParticleName -> "HY++",
791 QuantumNumbers -> {Q -> -2},
792 PropagatorLabel -> "HY",
793 PropagatorType -> D,
794 PropagatorArrow -> Forward,
795 FullName -> "HY"
796 },
797 S[7] == {
798 ClassName -> HV,
799 SelfConjugate -> False,
800 Mass -> {MHV,Internal},
801 Width -> {WHV,10},
802 ParticleName -> "HV-",
803 AntiParticleName -> "HV+",
804 QuantumNumbers -> {Q -> -1},
805 PropagatorLabel -> "HV",
806 PropagatorType -> D,
807 PropagatorArrow -> Forward,
808 FullName -> "HV"
809 },
810
811
812(* Higgs: physical scalars *)
813 S[8] == {
814 ClassName -> GZ,
815 SelfConjugate -> True,
816 Goldstone -> Z,
817 Mass -> {MZ, 91.1876},
818 Width -> {WZ, 2.4952},
819 PropagatorLabel -> "GZ",
820 PropagatorType -> D,
821 PropagatorArrow -> None,
822 PDG -> 250,
823 ParticleName -> "GZ",
824 FullName -> "GZ"
825 },
826 S[9] == {
827 ClassName -> GZP,
828 SelfConjugate -> True,
829 Goldstone -> ZP,
830 Mass -> {MZP, Internal},
831 Width -> {WZP, 10},
832 PropagatorLabel -> "GZP",
833 PropagatorType -> D,
834 PropagatorArrow -> None,
835 ParticleName -> "GZP",
836 FullName -> "GZP"
837 },
838 S[10] == {
839 ClassName -> GW,
840 SelfConjugate -> False,
841 Goldstone -> W,
842 Mass -> {MW, 80.385},
843 QuantumNumbers -> {Q -> 1},
844 Width -> {WW, 2.085},
845 PropagatorLabel -> "GW",
846 PropagatorType -> D,
847 PropagatorArrow -> None,
848 PDG -> 251,
849 ParticleName -> "GW+",
850 AntiParticleName -> "GW-",
851 FullName -> "GW"
852 },
853 S[11] == {
854 ClassName -> GY,
855 SelfConjugate -> False,
856 Goldstone -> YY,
857 Mass -> {MY, Internal},
858 QuantumNumbers -> {Q -> -2},
859 Width -> {WY, 10},
860 PropagatorLabel -> "GY",
861 PropagatorType -> D,
862 PropagatorArrow -> None,
863 ParticleName -> "GY--",
864 AntiParticleName -> "GY++",
865 FullName -> "GY"
866 },
867 S[12] == {
868 ClassName -> GV,
869 SelfConjugate -> False,
870 Goldstone -> V,
871 Mass -> {MV, Internal},
872 QuantumNumbers -> {Q -> -1},
873 Width -> {WV, 10},
874 PropagatorLabel -> "GV",
875 PropagatorType -> D,
876 PropagatorArrow -> None,
877 ParticleName -> "GV-",
878 AntiParticleName -> "GV+",
879 FullName -> "GV"
880 },
881
882
883(* Higgs: unphysical scalars *)
884 S[13] == {
885 ClassName -> Rho,
886 Unphysical -> True,
887 Indices -> {Index[SU3T]},
888 FlavorIndex -> SU3T,
889 SelfConjugate -> False,
890 QuantumNumbers -> {X ->0},
891 Definitions -> { Rho[1] -> -I (HW svv2+GW cvv2), Rho[2] -> (v + UH11 h + UH12 H2 + UH13 H3 + I (Uh11 H0 + Uh12 GZ + Uh13 GZP))/Sqrt[2], Rho[3] -> -I (HV svv3+GV cvv3)}
892 },
893 S[14] == {
894 ClassName -> Phi,
895 Unphysical -> True,
896 Indices -> {Index[SU3T]},
897 FlavorIndex -> SU3T,
898 SelfConjugate -> False,
899 QuantumNumbers -> {X -> -1},
900 Definitions -> { Phi[1] -> (v2 + UH21 h + UH22 H2 + UH23 H3 + I (Uh21 H0 + Uh23 GZP))/Sqrt[2], Phi[2] -> -I(GWbar svv2 -HWbar cvv2), Phi[3] -> -I(HY sv2v3+GY cv2v3) }
901 },
902 S[15] == {
903 ClassName -> Chi,
904 Unphysical -> True,
905 Indices -> {Index[SU3T]},
906 FlavorIndex -> SU3T,
907 SelfConjugate -> False,
908 QuantumNumbers -> {X -> 1},
909 Definitions -> { Chi[1] -> -I (GYbar sv2v3-HYbar cv2v3), Chi[2] -> -I (GVbar svv3-HVbar cvv3), Chi[3] -> (v3 + UH31 h + UH32 H2 + UH33 H3 + I (Uh31 H0 + Uh32 GZ + Uh33 GZP))/Sqrt[2] }
910 },
911 S[16] == {
912 ClassName -> Su,
913 Unphysical -> True,
914 Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
915 FlavorIndex -> SU3T,
916 SelfConjugate -> False,
917 Definitions -> {Su[1,1,kk_] -> Phi[kk], Su[1,2,kk_] -> 0, Su[1,3,kk_] -> 0, Su[2,1,kk_] -> 0, Su[2,2,kk_] -> Phi[kk], Su[2,3,kk_] -> 0, Su[3,1,kk_] -> 0, Su[3,2,kk_] -> 0, Su[3,3,kk_] -> -Rhobar[kk]}
918 },
919 S[17] == {
920 ClassName -> Sd,
921 Unphysical -> True,
922 Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
923 FlavorIndex -> SU3T,
924 SelfConjugate -> False,
925 Definitions -> {Sd[1,1,kk_] -> Rho[kk], Sd[1,2,kk_] -> 0, Sd[1,3,kk_] -> 0, Sd[2,1,kk_] -> 0, Sd[2,2,kk_] -> Rho[kk], Sd[2,3,kk_] -> 0, Sd[3,1,kk_] -> 0, Sd[3,2,kk_] -> 0, Sd[3,3,kk_] -> Phibar[kk]}
926 },
927 S[18] == {
928 ClassName -> SJ,
929 Unphysical -> True,
930 Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
931 FlavorIndex -> SU3T,
932 SelfConjugate -> False,
933 Definitions -> {SJ[1,1,kk_] -> Chi[kk], SJ[1,2,kk_] -> 0, SJ[1,3,kk_] -> 0, SJ[2,1,kk_] -> 0, SJ[2,2,kk_] -> Chi[kk], SJ[2,3,kk_] -> 0, SJ[3,1,kk_] -> 0, SJ[3,2,kk_] -> 0, SJ[3,3,kk_] -> Chibar[kk]}
934 }
935};
936
937
938(* ************************** *)
939(* ***** Gauge ***** *)
940(* ***** Parameters ***** *)
941(* ***** (FeynArts) ***** *)
942(* ************************** *)
943
944GaugeXi[ V[1] ] = GaugeXi[A];
945GaugeXi[ V[2] ] = GaugeXi[Z];
946GaugeXi[ V[3] ] = GaugeXi[ZP];
947GaugeXi[ V[4] ] = GaugeXi[W];
948GaugeXi[ V[5] ] = GaugeXi[YY];
949GaugeXi[ V[6] ] = GaugeXi[V];
950GaugeXi[ V[7] ] = GaugeXi[G];
951GaugeXi[ S[1] ] = 1;
952GaugeXi[ S[2] ] = 1;
953GaugeXi[ S[3] ] = 1;
954GaugeXi[ S[4] ] = 1;
955GaugeXi[ S[5] ] = 1;
956GaugeXi[ S[6] ] = 1;
957GaugeXi[ S[7] ] = 1;
958GaugeXi[ S[8] ] = GaugeXi[Z];
959GaugeXi[ S[9] ] = GaugeXi[ZP];
960GaugeXi[ S[10] ] = GaugeXi[W];
961GaugeXi[ S[11] ] = GaugeXi[YY];
962GaugeXi[ S[12] ] = GaugeXi[V];
963GaugeXi[ U[1] ] = GaugeXi[A];
964GaugeXi[ U[2] ] = GaugeXi[Z];
965GaugeXi[ U[3] ] = GaugeXi[ZP];
966GaugeXi[ U[41] ] = GaugeXi[W];
967GaugeXi[ U[42] ] = GaugeXi[W];
968GaugeXi[ U[51] ] = GaugeXi[YY];
969GaugeXi[ U[52] ] = GaugeXi[YY];
970GaugeXi[ U[61] ] = GaugeXi[V];
971GaugeXi[ U[62] ] = GaugeXi[V];
972GaugeXi[ U[7] ] = GaugeXi[G];
973
974
975(* ************************** *)
976(* ***** Parameters ***** *)
977(* ************************** *)
978M$Parameters = {
979
980 (* External parameters *)
981 aEWM1 == {
982 ParameterType -> External,
983 BlockName -> SMINPUTS,
984 OrderBlock -> 1,
985 Value -> 127.9,
986 InteractionOrder -> {QED,-2},
987 Description -> "Inverse of the EW coupling constant at the Z pole"
988 },
989 Gf == {
990 ParameterType -> External,
991 BlockName -> SMINPUTS,
992 OrderBlock -> 2,
993 Value -> 1.16637*^-5,
994 InteractionOrder -> {QED,2},
995 TeX -> Subscript[G,f],
996 Description -> "Fermi constant"
997 },
998 aS == {
999 ParameterType -> External,
1000 BlockName -> SMINPUTS,
1001 OrderBlock -> 3,
1002 Value -> 0.1184,
1003 InteractionOrder -> {QCD,2},
1004 TeX -> Subscript[\[Alpha],s],
1005 Description -> "Strong coupling constant at the Z pole"
1006 },
1007 ymdo == {
1008 ParameterType -> External,
1009 BlockName -> YUKAWA,
1010 OrderBlock -> 1,
1011 Value -> 5.04*^-3,
1012 Description -> "Down Yukawa mass"
1013 },
1014 ymup == {
1015 ParameterType -> External,
1016 BlockName -> YUKAWA,
1017 OrderBlock -> 2,
1018 Value -> 2.55*^-3,
1019 Description -> "Up Yukawa mass"
1020 },
1021 yms == {
1022 ParameterType -> External,
1023 BlockName -> YUKAWA,
1024 OrderBlock -> 3,
1025 Value -> 0.101,
1026 Description -> "Strange Yukawa mass"
1027 },
1028 ymc == {
1029 ParameterType -> External,
1030 BlockName -> YUKAWA,
1031 OrderBlock -> 4,
1032 Value -> 1.27,
1033 Description -> "Charm Yukawa mass"
1034 },
1035 ymb == {
1036 ParameterType -> External,
1037 BlockName -> YUKAWA,
1038 OrderBlock -> 5,
1039 Value -> 4.7,
1040 Description -> "Bottom Yukawa mass"
1041 },
1042 ymt == {
1043 ParameterType -> External,
1044 BlockName -> YUKAWA,
1045 OrderBlock -> 6,
1046 Value -> 172,
1047 Description -> "Top Yukawa mass"
1048 },
1049 ymD == {
1050 ParameterType -> External,
1051 BlockName -> YUKAWA,
1052 OrderBlock -> 7,
1053 Value -> 1*^3,
1054 Description -> "Heavy Down Yukawa mass"
1055 },
1056 ymS == {
1057 ParameterType -> External,
1058 BlockName -> YUKAWA,
1059 OrderBlock -> 8,
1060 Value -> 1*^3,
1061 Description -> "Heavy Strange Yukawa mass"
1062 },
1063 ymT == {
1064 ParameterType -> External,
1065 BlockName -> YUKAWA,
1066 OrderBlock -> 9,
1067 Value -> 1*^3,
1068 Description -> "Heavy Top Yukawa mass"
1069 },
1070 yme == {
1071 ParameterType -> External,
1072 BlockName -> YUKAWA,
1073 OrderBlock -> 11,
1074 Value -> 5.11*^-4,
1075 Description -> "Electron Yukawa mass"
1076 },
1077 ymm == {
1078 ParameterType -> External,
1079 BlockName -> YUKAWA,
1080 OrderBlock -> 13,
1081 Value -> 0.10566,
1082 Description -> "Muon Yukawa mass"
1083 },
1084 ymtau == {
1085 ParameterType -> External,
1086 BlockName -> YUKAWA,
1087 OrderBlock -> 15,
1088 Value -> 1.777,
1089 Description -> "Tau Yukawa mass"
1090 },
1091 ymEe == {
1092 ParameterType -> External,
1093 BlockName -> YUKAWA,
1094 OrderBlock -> 16,
1095 Value -> 1*^3,
1096 Description -> "Heavy Electron Yukawa mass"
1097 },
1098 ymEm == {
1099 ParameterType -> External,
1100 BlockName -> YUKAWA,
1101 OrderBlock -> 17,
1102 Value -> 1*^3,
1103 Description -> "Heavy Muon Yukawa mass"
1104 },
1105 ymEtau == {
1106 ParameterType -> External,
1107 BlockName -> YUKAWA,
1108 OrderBlock -> 18,
1109 Value -> 1*^3,
1110 Description -> "Heavy Tau Yukawa mass"
1111 },
1112 cabi == {
1113 ParameterType -> External,
1114 BlockName -> CKMBLOCK,
1115 OrderBlock -> 1,
1116 Value -> 0.227736,
1117 TeX -> Subscript[\[Theta], c],
1118 Description -> "Cabibbo angle"
1119 },
1120 v2 == {
1121 ParameterType -> External,
1122 BlockName -> OTHERS,
1123 OrderBlock -> 21,
1124 Value -> 174.105,
1125 InteractionOrder -> {QED,-1},
1126 Description -> "phi vacuum expectation value"
1127 },
1128 v3 == {
1129 ParameterType -> External,
1130 BlockName -> OTHERS,
1131 OrderBlock -> 1,
1132 Value -> 761.11,
1133 InteractionOrder -> {QED,-1},
1134 Description -> "Chi vaccum expectation value"
1135 },
1136 lam2 == {
1137 ParameterType -> External,
1138 BlockName -> OTHERS,
1139 OrderBlock -> 2,
1140 Value -> -1,
1141 InteractionOrder -> {QED, 2},
1142 TeX -> Subscript[\[Lambda], 2],
1143 Description -> "phi quartic coupling"
1144 },
1145 lam3 == {
1146 ParameterType -> External,
1147 BlockName -> OTHERS,
1148 OrderBlock -> 3,
1149 Value -> -1,
1150 InteractionOrder -> {QED, 2},
1151 TeX -> Subscript[\[Lambda], 3],
1152 Description -> "Chi quartic coupling"
1153 },
1154 lam12 == {
1155 ParameterType -> External,
1156 BlockName -> OTHERS,
1157 OrderBlock -> 4,
1158 Value -> -1,
1159 InteractionOrder -> {QED, 2},
1160 TeX -> Subscript[\[Lambda], 12],
1161 Description -> "Rho Rho and phi phi quartic coupling"
1162 },
1163 lam13 == {
1164 ParameterType -> External,
1165 BlockName -> OTHERS,
1166 OrderBlock -> 5,
1167 Value -> -1,
1168 InteractionOrder -> {QED, 2},
1169 TeX -> Subscript[\[Lambda], 13],
1170 Description -> "Rho Rho and Chi Chi quartic coupling"
1171 },
1172 lam23 == {
1173 ParameterType -> External,
1174 BlockName -> OTHERS,
1175 OrderBlock -> 6,
1176 Value -> -1,
1177 InteractionOrder -> {QED, 2},
1178 TeX -> Subscript[\[Lambda], 23],
1179 Description -> "Chi Chi and phi phi quartic coupling"
1180 },
1181 lam12P == {
1182 ParameterType -> External,
1183 BlockName -> OTHERS,
1184 OrderBlock -> 7,
1185 Value -> -1,
1186 InteractionOrder -> {QED, 2},
1187 TeX -> Subscript[\[Lambda]', 12],
1188 Description -> "Rho phi and phi Rho quartic coupling"
1189 },
1190 lam13P == {
1191 ParameterType -> External,
1192 BlockName -> OTHERS,
1193 OrderBlock -> 8,
1194 Value -> -1,
1195 InteractionOrder -> {QED, 2},
1196 TeX -> Subscript[\[Lambda]', 13],
1197 Description -> "Rho Chi and Chi Rho quartic coupling"
1198 },
1199 lam23P == {
1200 ParameterType -> External,
1201 BlockName -> OTHERS,
1202 OrderBlock -> 9,
1203 Value -> -1,
1204 InteractionOrder -> {QED, 2},
1205 TeX -> Subscript[\[Lambda]', 23],
1206 Description -> "phi Chi and Chi phi quartic coupling"
1207 },
1208 UH11 == {
1209 ParameterType -> External,
1210 BlockName -> OTHERS,
1211 OrderBlock -> 10,
1212 Value -> -0.798432,
1213 TeX -> Subsuperscript[U,11,H],
1214 Description -> "11 rotation-matrix element of Realscalar"
1215 },
1216 UH12 == {
1217 ParameterType -> External,
1218 BlockName -> OTHERS,
1219 OrderBlock -> 11,
1220 Value -> 0.598063,
1221 TeX -> Subsuperscript[U,12,H],
1222 Description -> "12 rotation-matrix element of Realscalar"
1223 },
1224 UH13 == {
1225 ParameterType -> External,
1226 BlockName -> OTHERS,
1227 OrderBlock -> 12,
1228 Value -> 0.0694831,
1229 TeX -> Subsuperscript[U,13,H],
1230 Description -> "13 rotation-matrix element of Realscalar"
1231 },
1232 UH21 == {
1233 ParameterType -> External,
1234 BlockName -> OTHERS,
1235 OrderBlock -> 13,
1236 Value -> -0.593153,
1237 TeX -> Subsuperscript[U,21,H],
1238 Description -> "21 rotation-matrix element of Realscalar"
1239 },
1240 UH22 == {
1241 ParameterType -> External,
1242 BlockName -> OTHERS,
1243 OrderBlock -> 14,
1244 Value -> -0.801136,
1245 TeX -> Subsuperscript[U,22,H],
1246 Description -> "22 rotation-matrix element of Realscalar"
1247 },
1248 UH23 == {
1249 ParameterType -> External,
1250 BlockName -> OTHERS,
1251 OrderBlock -> 15,
1252 Value -> 0.0796957,
1253 TeX -> Subsuperscript[U,23,H],
1254 Description -> "23 rotation-matrix element of Realscalar"
1255 },
1256 UH31 == {
1257 ParameterType -> External,
1258 BlockName -> OTHERS,
1259 OrderBlock -> 16,
1260 Value -> 0.103328,
1261 TeX -> Subsuperscript[U,31,H],
1262 Description -> "31 rotation-matrix element of Realscalar"
1263 },
1264 UH32 == {
1265 ParameterType -> External,
1266 BlockName -> OTHERS,
1267 OrderBlock -> 17,
1268 Value -> 0.0224175,
1269 TeX -> Subsuperscript[U,32,H],
1270 Description -> "32 rotation-matrix element of Realscalar"
1271 },
1272 UH33 == {
1273 ParameterType -> External,
1274 BlockName -> OTHERS,
1275 OrderBlock -> 18,
1276 Value -> 0.994395,
1277 TeX -> Subsuperscript[U,33,H],
1278 Description -> "33 rotation-matrix element of Realscalar"
1279 },
1280 tz == {
1281 ParameterType -> External,
1282 BlockName -> OTHERS,
1283 OrderBlock -> 19,
1284 Definitions -> {tz->0},
1285 Description -> "Tan of z zp mixing angle"
1286 },
1287 lam1 == {
1288 ParameterType -> External,
1289 BlockName -> OTHERS,
1290 OrderBlock -> 20,
1291 Value -> 0.799425,
1292 InteractionOrder -> {QED, 2},
1293 TeX -> Subscript[\[Lambda], 1],
1294 Description -> "Rho quartic coupling"
1295 },
1296 lamWS == {
1297 ParameterType -> External,
1298 BlockName -> WOLFENSTEIN,
1299 OrderBlock -> 1,
1300 Value -> 0.2253,
1301 TeX -> \[Lambda],
1302 Description -> "Wolfenstein variable lam"
1303 },
1304 AWS == {
1305 ParameterType -> External,
1306 BlockName -> WOLFENSTEIN,
1307 OrderBlock -> 2,
1308 Value -> 0.808,
1309 TeX -> A,
1310 Description -> "Wolfenstein variable A"
1311 },
1312 rhoWS == {
1313 ParameterType -> External,
1314 BlockName -> WOLFENSTEIN,
1315 OrderBlock -> 3,
1316 Value -> 0.132,
1317 TeX -> \[Rho],
1318 Description -> "Wolfenstein variable rho"
1319 },
1320 etaWS == {
1321 ParameterType -> External,
1322 BlockName -> WOLFENSTEIN,
1323 OrderBlock -> 4,
1324 Value -> 0.341,
1325 TeX -> \[Eta],
1326 Description -> "Wolfenstein variable eta"
1327 },
1328
1329
1330 (* Internal Parameters *)
1331 beta == {
1332 ParameterType -> Internal,
1333 Definitions -> {beta -> Sqrt[3]},
1334 TeX -> \[Beta],
1335 Description -> "beta"
1336 },
1337 aEW == {
1338 ParameterType -> Internal,
1339 Value -> 1/aEWM1,
1340 InteractionOrder -> {QED,2},
1341 TeX -> Subscript[\[Alpha], EW],
1342 Description -> "Electroweak coupling contant"
1343 },
1344 sw2 == {
1345 ParameterType -> Internal,
1346 Value -> 1-(MW/MZ)^2,
1347 Description -> "Squared Sin of the Weinberg angle"
1348 },
1349 ee == {
1350 ParameterType -> Internal,
1351 Value -> Sqrt[4 Pi aEW],
1352 InteractionOrder -> {QED,1},
1353 TeX -> e,
1354 Description -> "Electric coupling constant"
1355 },
1356 cw == {
1357 ParameterType -> Internal,
1358 Value -> Sqrt[1-sw2],
1359 TeX -> Subscript[c,w],
1360 Description -> "Cosine of the Weinberg angle"
1361 },
1362 sw == {
1363 ParameterType -> Internal,
1364 Value -> Sqrt[sw2],
1365 TeX -> Subscript[s,w],
1366 Description -> "Sine of the Weinberg angle"
1367 },
1368 c3 == {
1369 ParameterType -> Internal,
1370 Definitions -> {c3->beta sw/cw},
1371 TeX -> Subscript[c,3],
1372 Description -> "Cosine of the 331 angle"
1373 },
1374 s3 == {
1375 ParameterType -> Internal,
1376 Definitions -> {s3->Sqrt[1-(1+beta^2)*sw^2]/cw},
1377 TeX -> Subscript[s,3],
1378 Description -> "Sine of the 331 angle"
1379 },
1380 gw == {
1381 ParameterType -> Internal,
1382 Definitions -> {gw->ee/sw},
1383 InteractionOrder -> {QED,1},
1384 TeX -> Subscript[g,w],
1385 Description -> "Weak coupling constant at the Z pole"
1386 },
1387 gx == {
1388 ParameterType -> Internal,
1389 Definitions -> {gx->gw sw/Sqrt[1-(1+beta^2)*sw^2]},
1390 InteractionOrder -> {QED,1},
1391 TeX -> Subscript[g,x],
1392 Description -> "U(1)X coupling constant at the Z pole"
1393 },
1394 gs == {
1395 ParameterType -> Internal,
1396 Value -> Sqrt[4 Pi aS],
1397 InteractionOrder -> {QCD,1},
1398 TeX -> Subscript[g,s],
1399 ParameterName -> G,
1400 Description -> "Strong coupling constant at the Z pole"
1401 },
1402 v == {
1403 ParameterType -> Internal,
1404 Value -> Sqrt[4*MW^2*sw2/(ee^2)-v2^2],
1405 InteractionOrder -> {QED,-1},
1406 Description -> "Rho vaccum expectation value"
1407 },
1408 v3 == {
1409 ParameterType -> Internal,
1410 Value -> MZP Sqrt[3*(1-4*sw^2)]/(gw*cw),
1411 InteractionOrder -> {QED,-1},
1412 Description -> "Chi vaccum expectation value"
1413 },
1414 cz == {
1415 ParameterType -> Internal,
1416 Definitions -> {cz->1/Sqrt[1+tz^2]},
1417 Description -> "Cosin of z zp mixing angle"
1418 },
1419 sz == {
1420 ParameterType -> Internal,
1421 Definitions -> {sz->-tz/Sqrt[1+tz^2]},
1422 Description -> "Sin of z zp mixing angle"
1423 },
1424 svv2 == {
1425 ParameterType -> Internal,
1426 Value -> 1/Sqrt[1+(v/v2)^2],
1427 TeX -> Subscript[s,vv2],
1428 Description -> "Sine of the vv2 angle"
1429 },
1430 cvv2 == {
1431 ParameterType -> Internal,
1432 Value -> Sqrt[1-svv2^2],
1433 TeX -> Subscript[c,vv2],
1434 Description -> "Cosine of the vv2 angle"
1435 },
1436 svv3 == {
1437 ParameterType -> Internal,
1438 Value -> 1/Sqrt[1+(v/v3)^2],
1439 TeX -> Subscript[s,vv3],
1440 Description -> "Sine of the vv3 angle"
1441 },
1442 cvv3 == {
1443 ParameterType -> Internal,
1444 Value -> Sqrt[1-svv3^2],
1445 TeX -> Subscript[c,vv3],
1446 Description -> "Cosine of the vv3 angle"
1447 },
1448 sv2v3 == {
1449 ParameterType -> Internal,
1450 Value -> 1/Sqrt[1+(v2/v3)^2],
1451 TeX -> Subscript[s,v2v3],
1452 Description -> "Sine of the v2v3 angle"
1453 },
1454 cv2v3 == {
1455 ParameterType -> Internal,
1456 Value -> Sqrt[1-sv2v3^2],
1457 TeX -> Subscript[c,v2v3],
1458 Description -> "Cosine of the v2v3 angle"
1459 },
1460 ff == {
1461 ParameterType -> Internal,
1462 Value -> -v3/(2Sqrt[2]),
1463 InteractionOrder -> {QED,1},
1464 TeX -> f,
1465 Description -> "Coefficient of the cubic piece of the Higgs potential"
1466 },
1467 mu1 == {
1468 ParameterType -> Internal,
1469 Definitions -> {mu1->Sqrt[-lam1*v^2-lam12*v2^2/2-lam13*v3^2/2+ff*v3*v2/v]},
1470 Description -> "Coefficient of the quadratic piece of the Rho potential"
1471 },
1472 mu2 == {
1473 ParameterType -> Internal,
1474 Definitions -> {mu2->Sqrt[-lam2*v2^2-lam12*v^2/2-lam23*v3^2/2+ff*v3*v/v2]},
1475 Description -> "Coefficient of the quadratic piece of the phi potential"
1476 },
1477 mu3 == {
1478 ParameterType -> Internal,
1479 Definitions -> {mu3->Sqrt[-lam3*v3^2-lam13*v^2/2-lam23*v2^2/2+ff*v*v2/v3]},
1480 Description -> "Coefficient of the quadratic piece of the Chi potential"
1481 },
1482 yl == {
1483 ParameterType -> Internal,
1484 Indices -> {Index[Generation], Index[Generation]},
1485 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1486 Value -> {yl[1,1] -> Sqrt[2] yme / v2, yl[2,2] -> Sqrt[2] ymm / v2, yl[3,3] -> Sqrt[2] ymtau / v2},
1487 InteractionOrder -> {QED, 1},
1488 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
1489 TeX -> Superscript[y, l],
1490 Description -> "Lepton Yukawa couplings"
1491 },
1492 yE == {
1493 ParameterType -> Internal,
1494 Indices -> {Index[Generation], Index[Generation]},
1495 Definitions -> {yE[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1496 Value -> {yE[1,1] -> Sqrt[2] ymEe / v3, yE[2,2] -> Sqrt[2] ymEm / v3, yE[3,3] -> Sqrt[2] ymEtau / v3},
1497 InteractionOrder -> {QED, 1},
1498 ParameterName -> {yE[1,1] -> yEe, yl[2,2] -> yEm, yl[3,3] -> yEtau},
1499 TeX -> Superscript[y, E],
1500 Description -> "Heavy Lepton Yukawa couplings"
1501 },
1502 yu == {
1503 ParameterType -> Internal,
1504 Indices -> {Index[Generation], Index[Generation]},
1505 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1506 Value -> {yu[1,1] -> Sqrt[2] ymup/v2, yu[2,2] -> Sqrt[2] ymc/v2, yu[3,3] -> Sqrt[2] ymt/v2},
1507 InteractionOrder -> {QED, 1},
1508 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
1509 TeX -> Superscript[y, u],
1510 Description -> "Up-type Yukawa couplings"
1511 },
1512 yd == {
1513 ParameterType -> Internal,
1514 Indices -> {Index[Generation], Index[Generation]},
1515 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1516 Value -> {yd[1,1] -> Sqrt[2] ymdo/v, yd[2,2] -> Sqrt[2] yms/v, yd[3,3] -> Sqrt[2] ymb/v},
1517 InteractionOrder -> {QED, 1},
1518 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
1519 TeX -> Superscript[y, d],
1520 Description -> "Down-type Yukawa couplings"
1521 },
1522 yJ == {
1523 ParameterType -> Internal,
1524 Indices -> {Index[Generation], Index[Generation]},
1525 Definitions -> {yJ[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1526 Value -> {yJ[1,1] -> Sqrt[2] ymD/v3, yJ[2,2] -> Sqrt[2] ymS/v3, yJ[3,3] -> Sqrt[2] ymT/v3},
1527 InteractionOrder -> {QED, 1},
1528 ParameterName -> {yJ[1,1] -> yD, yJ[2,2] -> yS, yJ[3,3] -> yT},
1529 TeX -> Superscript[y, J],
1530 Description -> "Heavy-type Yukawa couplings"
1531 },
1532 MY == {
1533 ParameterType -> Internal,
1534 Value -> 1/2 gw Sqrt[v3^2+v2^2],
1535 TeX -> Subscript[M,Y],
1536 Description -> "YY mass"
1537 },
1538 MV == {
1539 ParameterType -> Internal,
1540 Value -> 1/2 gw Sqrt[v3^2+v^2],
1541 TeX -> Subscript[M,V],
1542 Description -> "V mass"
1543 },
1544 MH2 == {
1545 ParameterType -> Internal,
1546 Value -> Sqrt[2] Sqrt[ff UH22 UH32 v-lam1 UH12^2 v^2+ff UH12 UH32 v2-lam12 UH12 UH22 v v2-lam2 UH22^2 v2^2-(ff UH32^2 v v2)/(2 v3)+ff UH12 UH22 v3-lam13 UH12 UH32 v v3-(ff UH22^2 v v3)/(2 v2)-lam23 UH22 UH32 v2 v3-(ff UH12^2 v2 v3)/(2 v)-lam3 UH32^2 v3^2],
1547 TeX -> Subscript[M,H2],
1548 Description -> "H2 mass"
1549 },
1550 MH3 == {
1551 ParameterType -> Internal,
1552 Value -> Sqrt[2] Sqrt[ff UH23 UH33 v-lam1 UH13^2 v^2+ff UH13 UH33 v2-lam12 UH13 UH23 v v2-lam2 UH23^2 v2^2-(ff UH33^2 v v2)/(2 v3)+ff UH13 UH23 v3-lam13 UH13 UH33 v v3-(ff UH23^2 v v3)/(2 v2)-lam23 UH23 UH33 v2 v3-(ff UH13^2 v2 v3)/(2 v)-lam3 UH33^2 v3^2],
1553 TeX -> Subscript[M,H3],
1554 Description -> "H3 mass"
1555 },
1556 Uh11 == {
1557 ParameterType -> Internal,
1558 Value -> v3/(v Sqrt[1 + (1/v^2 + 1/v2^2) v3^2]),
1559 TeX -> Subsuperscript[U, 11, h],
1560 Description -> "11 rotation-matrix element of Pseudoscalar"
1561 },
1562 Uh12 == {
1563 ParameterType -> Internal,
1564 Value -> -v/(Sqrt[1 + v^2/v3^2] v3),
1565 TeX -> Subsuperscript[U, 12, h],
1566 Description -> "12 rotation-matrix element of Pseudoscalar"
1567 },
1568 Uh13 == {
1569 ParameterType -> Internal,
1570 Value -> -(v v2 v3^2 (v^2 + v3^2))/(Sqrt[
1571 v2^2 (v^2 + v3^2)^2] Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
1572 v^2 (v2^2 + v3^2))]),
1573 TeX -> Subsuperscript[U, 13, h],
1574 Description -> "13 rotation-matrix element of Pseudoscalar"
1575 },
1576 Uh21 == {
1577 ParameterType -> Internal,
1578 Value -> v3/(v2 Sqrt[1 + (1/v^2 + 1/v2^2) v3^2]),
1579 TeX -> Subsuperscript[U, 21, h],
1580 Description -> "21 rotation-matrix element of Pseudoscalar"
1581 },
1582 Uh23 == {
1583 ParameterType -> Internal,
1584 Value -> Sqrt[
1585 v2^2 (v^2 + v3^2)^2]/Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
1586 v^2 (v2^2 + v3^2))],
1587 TeX -> Subsuperscript[U, 23, h],
1588 Description -> "23 rotation-matrix element of Pseudoscalar"
1589 },
1590 Uh31 == {
1591 ParameterType -> Internal,
1592 Value -> 1/Sqrt[1 + (1/v^2 + 1/v2^2) v3^2],
1593 TeX -> Subsuperscript[U, 31, h],
1594 Description -> "31 rotation-matrix element of Pseudoscalar"
1595 },
1596 Uh32 == {
1597 ParameterType -> Internal,
1598 Value -> 1/Sqrt[1 + v^2/v3^2],
1599 TeX -> Subsuperscript[U, 32, h],
1600 Description -> "32 rotation-matrix element of Pseudoscalar"
1601 },
1602 Uh33 == {
1603 ParameterType -> Internal,
1604 Value -> -(v^2 v2 v3 (v^2 + v3^2))/(Sqrt[
1605 v2^2 (v^2 + v3^2)^2] Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
1606 v^2 (v2^2 + v3^2))]),
1607 TeX -> Subsuperscript[U, 33, h],
1608 Description -> "33 rotation-matrix element of Pseudoscalar"
1609 },
1610 MH0 == {
1611 ParameterType -> Internal,
1612 Value -> Sqrt[2] Sqrt[-ff Uh21 Uh31 v-ff Uh11 Uh31 v2-(ff Uh31^2 v v2)/(2 v3)-ff Uh11 Uh21 v3-(ff Uh21^2 v v3)/(2 v2)-(ff Uh11^2 v2 v3)/(2 v)],
1613 TeX -> Subscript[M,H0],
1614 Description -> "H0 mass"
1615 },
1616 MHW == {
1617 ParameterType -> Internal,
1618 Value -> Sqrt[ (v^2+v2^2) ((-ff v3)/(v v2)-lam12P/2)],
1619 TeX -> Subscript[M,HW],
1620 Description -> "HW mass"
1621 },
1622 MHY == {
1623 ParameterType -> Internal,
1624 Value -> Sqrt[ (v2^2+v3^2) ((-ff v)/(v2 v3)-lam23P/2)],
1625 TeX -> Subscript[M,HY],
1626 Description -> "HY mass"
1627 },
1628 MHV == {
1629 ParameterType -> Internal,
1630 Value -> Sqrt[ (v^2+v3^2) ((-ff v2)/(v v3)-lam13P/2)],
1631 TeX -> Subscript[M,HV],
1632 Description -> "HV mass"
1633 },
1634
1635
1636
1637
1638(* N. B. : only Cabibbo mixing! *)
1639 CKM == {
1640 ParameterType -> Internal,
1641 Indices -> {Index[Generation], Index[Generation]},
1642 Unitary -> True,
1643 Value -> {CKM[1,1] -> 1-lamWS^2/2, CKM[1,2] -> lamWS, CKM[1,3] -> AWS*lamWS^3*(rhoWS-I*etaWS), CKM[2,1] -> -lamWS, CKM[2,2] -> 1-lamWS^2/2, CKM[2,3] -> AWS*lamWS^2, CKM[3,1] -> AWS*lamWS^3*(1-rhoWS-I*etaWS), CKM[3,2] -> -AWS*lamWS^2, CKM[3,3] -> 1},
1644 TeX -> Superscript[V,CKM],
1645 Description -> "CKM-Matrix"
1646 },
1647 RU == {
1648 ParameterType -> Internal,
1649 Indices -> {Index[Generation], Index[Generation]},
1650 Unitary -> True,
1651 Definitions -> {RU[1,1] -> 1, RU[1,2] -> 0, RU[1,3] -> 0, RU[2,1] -> 0, RU[2,2] -> 1, RU[2,3] -> 0, RU[3,1] -> 0, RU[3,2] -> 0, RU[3,3] -> 1},
1652 TeX -> Superscript[R,u],
1653 Description -> "RU-Matrix"
1654 }
1655
1656};
1657
1658(* ************************** *)
1659(* ***** Lagrangian ***** *)
1660(* ************************** *)
1661
1662LGauge := Block[{mu,nu,ii,aa},
1663
1664 ExpandIndices[-1/4 FS[K,mu,nu] FS[K,mu,nu] - 1/4 FS[Wi,mu,nu,ii]FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU3W]];
1665
1666
1667LFermions := Block[{mu,fermi},
1668
1669 fermi=ExpandIndices[I*(
1670QL12bar.Ga[mu].DC[QL12, mu] + QL3bar.Ga[mu].DC[QL3, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + JR12bar.Ga[mu].DC[JR12,mu] + JR3bar.Ga[mu].DC[JR3,mu] + lRbar.Ga[mu].DC[lR, mu] + EERbar.Ga[mu].DC[EER, mu]),
1671 FlavorExpand->{SU3W,SU3T,ASU3W,ASU3T}];
1672 fermi = ExpandIndices[fermi]];
1673
1674LHiggs := Block[{ii,mu, feynmangaugerules},
1675 feynmangaugerules = If[Not[FeynmanGauge], {GZ|GZP|GW|GWbar|GY|GYbar|GV|GVbar ->0}, {}];
1676
1677 ExpandIndices[DC[Rhobar[ii],mu] DC[Rho[ii],mu] + DC[Phibar[ii],mu] DC[Phi[ii],mu] + DC[Chibar[ii],mu] DC[Chi[ii],mu] + mu1^2 Rhobar[ii] Rho[ii] + lam1 Rhobar[ii] Rho[ii] Rhobar[jj] Rho[jj] + mu2^2 Phibar[ii] Phi[ii] + lam2 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] + mu3^2 Chibar[ii] Chi[ii] + lam3 Chibar[ii] Chi[ii] Chibar[jj] Chi[jj] + lam12 Rhobar[ii] Rho[ii] Phibar[jj] Phi[jj] + lam13 Rhobar[ii] Rho[ii] Chibar[jj] Chi[jj] + lam23 Phibar[ii] Phi[ii] Chibar[jj] Chi[jj] + lam12P Rhobar[ii] Phi[ii] Phibar[jj] Rho[jj] + lam13P Rhobar[ii] Chi[ii] Chibar[jj] Rho[jj] + lam23P Phibar[ii] Chi[ii] Chibar[jj] Phi[jj] + Sqrt[2] ff Eps[ii,jj,kk] Rho[ii] Phi[jj] Chi[kk] + Sqrt[2] ff HC[Eps[ii,jj,kk] Rho[ii] Phi[jj] Chi[kk]], FlavorExpand->{SU3T,SU3W}]/.feynmangaugerules
1678 ];
1679
1680LYukawa := Block[{sp,ii,cc,ff1,ff3,ff4,yuk,feynmangaugerules},
1681 feynmangaugerules = If[Not[FeynmanGauge], {GZ|GZP|GW|GWbar|GY|GYbar|GV|GVbar ->0}, {}];
1682
1683 yuk = ExpandIndices[
1684 -yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phibar[ii]
1685 -yE[ff1, ff3] LLbar[sp, ii, ff1].EER [sp, ff3] Chibar[ii]
1686 -yu[ff1, ff3] RU[ff2, ff1] QLbar[sp, ii, ff4, cc].uR [sp, ff3, cc] Su[ff4, ff1, ii]
1687 -yd[ff1, ff3] CKM[ff2, ff1] QLbar[sp, ii, ff4, cc].dR [sp, ff3, cc] Sd[ff4, ff2, ii]
1688 -yJ[ff1, ff3] QLbar[sp, ii, ff2, cc].JR[sp, ff3, cc] SJ[ff2, ff1, ii],
1689FlavorExpand -> {SU3T}];
1690 yuk = ExpandIndices[yuk] /.{CKM[a_, b_] Conjugate[CKM[a_, c_]] -> 1/3 IndexDelta[b, c],CKM[b_, a_] Conjugate[CKM[c_, a_]] -> 1/3 IndexDelta[b, c]};
1691 yuk+HC[yuk]/.feynmangaugerules
1692 ];
1693
1694LGhost := Block[{LGh1,LGhw,LGhs,LGhhiggs,LGhrho,LGhphi,LGhchi,mu, generators,gh,ghbar,Vectorize,rho1,rho2,rho3,rho4,phi1,phi2,phi3,phi4,chi1,chi2,chi3,chi4,togoldstones,rho,rho0,phi,phi0,chi,chi0},
1695 (* Pure gauge piece *)
1696 LGh1 = -ghKbar.del[DC[ghK,mu],mu];
1697 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
1698 LGhs = -ghGbar.del[DC[ghG,mu],mu];
1699
1700 (* Scalar pieces: see Peskin pages 739-742 *)
1701 (* rho1, rho2, rho3 and rho4 are the real degrees of freedom of HW and GW *)
1702 (* Vectorize transforms a triplet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
1703 gh = {ghK, ghWi[1], ghWi[2], ghWi[3], ghWi[4], ghWi[5], ghWi[6], ghWi[7], ghWi[8]};
1704 ghbar = {ghKbar, ghWibar[1], ghWibar[2], ghWibar[3], ghWibar[4], ghWibar[5], ghWibar[6], ghWibar[7], ghWibar[8]};
1705 generators = {-I/2 gx IdentityMatrix[3], -I/2 gw Gellmann[1], -I/2 gw Gellmann[2], -I/2 gw Gellmann[3], -I/2 gw Gellmann[4], -I/2 gw Gellmann[5], -I/2 gw Gellmann[6], -I/2 gw Gellmann[7], -I/2 gw Gellmann[8]};
1706 rho = Expand[{(-I rho1 - rho2)/Sqrt[2], (UH11 h + UH12 H2 + UH13 H3 + I (Uh11 H0 + Uh12 GZ + Uh13 GZP))/Sqrt[2], (-I rho3 - rho4)/Sqrt[2] } ];
1707 rho0 = {0, v/Sqrt[2], 0};
1708 phi = Expand[{(UH21 h + UH22 H2 + UH23 H3 + I (Uh21 H0 + Uh23 GZP))/Sqrt[2], (-I phi1 - phi2)/Sqrt[2], (-I phi3 - phi4)/Sqrt[2] } ];
1709 phi0 = {v2/Sqrt[2], 0, 0};
1710 chi = Expand[{(-I chi1 - chi2)/Sqrt[2], (-I chi3 - chi4)/Sqrt[2], (UH31 h + UH32 H2 + UH33 H3 + I (Uh31 H0 + Uh32 GZ + Uh33 GZP))/Sqrt[2] } ];
1711 chi0 = {0, 0, v3/Sqrt[2]};
1712 Vectorize[{a_, b_, c_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]], Sqrt[2] Re[Expand[c]], Sqrt[2] Im[Expand[c]]}/.{Im[_]->0, Re[num_]->num}];
1713 togoldstones := {
1714rho1 -> (HW svv2 + GW cvv2 + HWbar svv2 + GWbar cvv2)/Sqrt[2],
1715rho2 -> (- HW svv2 - GW cvv2 + HWbar svv2 + GWbar cvv2)/(I Sqrt[2]),
1716rho3 -> (GV cvv3 + HV svv3 + GVbar cvv3 + HVbar svv3)/Sqrt[2],
1717rho4 -> (- GV cvv3 - HV svv3 + GVbar cvv3 + HVbar svv3)/(I Sqrt[2]),
1718phi1 -> (- HW cvv2 + GW svv2 - HWbar cvv2 + GWbar svv2)/Sqrt[2],
1719phi2 -> (HWbar cvv2 - GWbar svv2 - HW cvv2 + GW svv2)/(I Sqrt[2]),
1720phi3 -> (GY cv2v3 + HY sv2v3 + GYbar cv2v3 + HYbar sv2v3)/Sqrt[2],
1721phi4 -> (- GY cv2v3 - HY sv2v3 + GYbar cv2v3 + HYbar sv2v3)/(I Sqrt[2]),
1722chi1 -> (- HY cv2v3 + GY sv2v3 - HYbar cv2v3 + GYbar sv2v3)/Sqrt[2],
1723chi2 -> (HYbar cv2v3 - GYbar sv2v3 - HY cv2v3 + GY sv2v3)/(I Sqrt[2]),
1724chi3 -> (- HV cvv3 + GV svv3 - HVbar cvv3 + GVbar svv3)/Sqrt[2],
1725chi4 -> (HVbar cvv3 - GVbar svv3 - HV cvv3 + GV svv3)/(I Sqrt[2])};
1726 LGhrho=
1727Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].(rho0)].Vectorize[generators[[lll]].(rho + rho0)],{kkk,9},{lll,9}]];
1728 LGhphi=
1729Plus@@Flatten[Table[-ghbar[[kkkk]].gh[[llll]] Vectorize[generators[[kkkk]].(phi0)].Vectorize[generators[[llll]].(phi + phi0)],{kkkk,9},{llll,9}]];
1730 LGhchi=
1731Plus@@Flatten[Table[-ghbar[[kkkkk]].gh[[lllll]] Vectorize[generators[[kkkkk]].(chi0)].Vectorize[generators[[lllll]].(chi + chi0)],{kkkkk,9},{lllll,9}]];
1732
1733 LGhhiggs=LGhrho+ LGhphi+ LGhchi /.togoldstones;
1734
1735ExpandIndices[ LGhs + If[FeynmanGauge, LGhw +LGh1 + LGhhiggs ,0], FlavorExpand->SU3W]];
1736
1737LThree:= LHiggs+LFermions+LYukawa+LGhost+LGauge;