NLOModels: sm_reduced.fr

File sm_reduced.fr, 21.2 KB (added by Benjamin Fuks, 3 years ago)
Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
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$ModelName = "SM_red";
16
17M$Information = {
18 Authors -> {"N. Christensen", "C. Duhr", "B. Fuks"},
19 Version -> "1.4.6",
20 Date -> "15. 04. 2014",
21 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)", "IPHC Strasbourg / University of Strasbourg"},
22 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "benjamin.fuks@cnrs.in2p3.fr"},
23 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** NLO Variables ****** *)
30(******************************)
31
32FR$LoopSwitches = {{Gf, MW}};
33FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
34 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
35
36(* ************************** *)
37(* ***** Change log ***** *)
38(* ************************** *)
39
40(* v1.4.6: NLO variable added. *)
41(* v1.4.5: Added widths for ghosts. *)
42(* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
43(* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
44(* v1.4.2: Set FeynmanGauge=True as default again. *)
45(* v1.4: Added SU(2) representation. *)
46(* -> Modification in the field declarations (doublets are added) *)
47(* -> Modification in the Lagrangian (much simpler). *)
48(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
49(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
50(* Updated parameters to PDG 2010. *)
51(* v1.2: Set FeynmanGauge=True as default. *)
52(* Set Gluonic ghosts to be included in both gauges. *)
53(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
54(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
55(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
56
57(* ************************** *)
58(* ***** Gauge groups ***** *)
59(* ************************** *)
60M$GaugeGroups = {
61 U1Y == {
62 Abelian -> True,
63 CouplingConstant -> g1,
64 GaugeBoson -> B,
65 Charge -> Y
66 },
67 SU2L == {
68 Abelian -> False,
69 CouplingConstant -> gw,
70 GaugeBoson -> Wi,
71 StructureConstant -> Eps,
72 Representations -> {Ta,SU2D},
73 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
74 },
75 SU3C == {
76 Abelian -> False,
77 CouplingConstant -> gs,
78 GaugeBoson -> G,
79 StructureConstant -> f,
80 Representations -> {T,Colour},
81 SymmetricTensor -> dSUN
82 }
83};
84
85(* ************************** *)
86(* ***** Indices ***** *)
87(* ************************** *)
88
89IndexRange[Index[SU2W ]] = Unfold[Range[3]];
90IndexRange[Index[SU2D ]] = Unfold[Range[2]];
91IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
92IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
93IndexRange[Index[Generation]] = Range[3];
94
95IndexStyle[SU2W, j];
96IndexStyle[SU2D, k];
97IndexStyle[Gluon, a];
98IndexStyle[Colour, m];
99IndexStyle[Generation, f];
100
101(* ************************** *)
102(* *** Interaction orders *** *)
103(* *** (as used by mg5) *** *)
104(* ************************** *)
105
106M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2}};
107M$InteractionOrderLimit = { {QCD, 99},{QED, 99}};
108
109(* ************************** *)
110(* **** Particle classes **** *)
111(* ************************** *)
112M$ClassesDescription = {
113
114(* Gauge bosons: physical vector fields *)
115 V[1] == {
116 ClassName -> A,
117 SelfConjugate -> True,
118 Mass -> 0,
119 Width -> 0,
120 ParticleName -> "a",
121 PDG -> 22,
122 PropagatorLabel -> "a",
123 PropagatorType -> W,
124 PropagatorArrow -> None,
125 FullName -> "Photon"
126 },
127 V[2] == {
128 ClassName -> Z,
129 SelfConjugate -> True,
130 Mass -> {MZ, 91.1876},
131 Width -> {WZ, 2.4952},
132 ParticleName -> "Z",
133 PDG -> 23,
134 PropagatorLabel -> "Z",
135 PropagatorType -> Sine,
136 PropagatorArrow -> None,
137 FullName -> "Z"
138 },
139 V[3] == {
140 ClassName -> W,
141 SelfConjugate -> False,
142 Mass -> {MW, Internal},
143 Width -> {WW, 2.085},
144 ParticleName -> "W+",
145 AntiParticleName -> "W-",
146 QuantumNumbers -> {Q -> 1},
147 PDG -> 24,
148 PropagatorLabel -> "W",
149 PropagatorType -> Sine,
150 PropagatorArrow -> Forward,
151 FullName -> "W"
152 },
153 V[4] == {
154 ClassName -> G,
155 SelfConjugate -> True,
156 Indices -> {Index[Gluon]},
157 Mass -> 0,
158 Width -> 0,
159 ParticleName -> "g",
160 PDG -> 21,
161 PropagatorLabel -> "G",
162 PropagatorType -> C,
163 PropagatorArrow -> None,
164 FullName -> "G"
165 },
166
167(* Ghosts: related to physical gauge bosons *)
168 U[1] == {
169 ClassName -> ghA,
170 SelfConjugate -> False,
171 Ghost -> A,
172 QuantumNumbers -> {GhostNumber -> 1},
173 Mass -> 0,
174 Width -> 0,
175 PropagatorLabel -> "uA",
176 PropagatorType -> GhostDash,
177 PropagatorArrow -> Forward
178 },
179 U[2] == {
180 ClassName -> ghZ,
181 SelfConjugate -> False,
182 Ghost -> Z,
183 QuantumNumbers -> {GhostNumber -> 1},
184 Mass -> {MZ,91.1876},
185 Width -> {WZ, 2.4952},
186 PropagatorLabel -> "uZ",
187 PropagatorType -> GhostDash,
188 PropagatorArrow -> Forward
189 },
190 U[31] == {
191 ClassName -> ghWp,
192 SelfConjugate -> False,
193 Ghost -> W,
194 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
195 Mass -> {MW,Internal},
196 Width -> {WW, 2.085},
197 PropagatorLabel -> "uWp",
198 PropagatorType -> GhostDash,
199 PropagatorArrow -> Forward
200 },
201 U[32] == {
202 ClassName -> ghWm,
203 SelfConjugate -> False,
204 Ghost -> Wbar,
205 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
206 Mass -> {MW,Internal},
207 Width -> {WW, 2.085},
208 PropagatorLabel -> "uWm",
209 PropagatorType -> GhostDash,
210 PropagatorArrow -> Forward
211 },
212 U[4] == {
213 ClassName -> ghG,
214 SelfConjugate -> False,
215 Indices -> {Index[Gluon]},
216 Ghost -> G,
217 PDG -> 82,
218 QuantumNumbers ->{GhostNumber -> 1},
219 Mass -> 0,
220 Width -> 0,
221 PropagatorLabel -> "uG",
222 PropagatorType -> GhostDash,
223 PropagatorArrow -> Forward
224 },
225
226(* Gauge bosons: unphysical vector fields *)
227 V[11] == {
228 ClassName -> B,
229 Unphysical -> True,
230 SelfConjugate -> True,
231 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
232 },
233 V[12] == {
234 ClassName -> Wi,
235 Unphysical -> True,
236 SelfConjugate -> True,
237 Indices -> {Index[SU2W]},
238 FlavorIndex -> SU2W,
239 Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
240 },
241
242(* Ghosts: related to unphysical gauge bosons *)
243 U[11] == {
244 ClassName -> ghB,
245 Unphysical -> True,
246 SelfConjugate -> False,
247 Ghost -> B,
248 Definitions -> { ghB -> -sw ghZ + cw ghA}
249 },
250 U[12] == {
251 ClassName -> ghWi,
252 Unphysical -> True,
253 SelfConjugate -> False,
254 Ghost -> Wi,
255 Indices -> {Index[SU2W]},
256 FlavorIndex -> SU2W,
257 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
258 } ,
259
260(* Fermions: physical fields *)
261 F[3] == {
262 ClassName -> uq,
263 ClassMembers -> {u, c, t},
264 Indices -> {Index[Generation], Index[Colour]},
265 FlavorIndex -> Generation,
266 SelfConjugate -> False,
267 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
268 Width -> {0, 0, {WT,1.50833649}},
269 QuantumNumbers -> {Q -> 2/3},
270 PropagatorLabel -> {"uq", "u", "c", "t"},
271 PropagatorType -> Straight,
272 PropagatorArrow -> Forward,
273 PDG -> {2, 4, 6},
274 ParticleName -> {"u", "c", "t" },
275 AntiParticleName -> {"u~", "c~", "t~"},
276 FullName -> {"u-quark", "c-quark", "t-quark"}
277 },
278 F[4] == {
279 ClassName -> dq,
280 ClassMembers -> {d, s, b},
281 Indices -> {Index[Generation], Index[Colour]},
282 FlavorIndex -> Generation,
283 SelfConjugate -> False,
284 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
285 Width -> 0,
286 QuantumNumbers -> {Q -> -1/3},
287 PropagatorLabel -> {"dq", "d", "s", "b"},
288 PropagatorType -> Straight,
289 PropagatorArrow -> Forward,
290 PDG -> {1,3,5},
291 ParticleName -> {"d", "s", "b" },
292 AntiParticleName -> {"d~", "s~", "b~"},
293 FullName -> {"d-quark", "s-quark", "b-quark"}
294 },
295
296(* Fermions: unphysical fields *)
297 F[13] == {
298 ClassName -> QL,
299 Unphysical -> True,
300 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
301 FlavorIndex -> SU2D,
302 SelfConjugate -> False,
303 QuantumNumbers -> {Y -> 1/6},
304 Definitions -> {
305 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
306 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
307 },
308 F[14] == {
309 ClassName -> uR,
310 Unphysical -> True,
311 Indices -> {Index[Generation], Index[Colour]},
312 FlavorIndex -> Generation,
313 SelfConjugate -> False,
314 QuantumNumbers -> {Y -> 2/3},
315 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
316 },
317 F[15] == {
318 ClassName -> dR,
319 Unphysical -> True,
320 Indices -> {Index[Generation], Index[Colour]},
321 FlavorIndex -> Generation,
322 SelfConjugate -> False,
323 QuantumNumbers -> {Y -> -1/3},
324 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
325 },
326
327(* Higgs: physical scalars *)
328 S[1] == {
329 ClassName -> H,
330 SelfConjugate -> True,
331 Mass -> {MH,125},
332 Width -> {WH,0.00407},
333 PropagatorLabel -> "H",
334 PropagatorType -> D,
335 PropagatorArrow -> None,
336 PDG -> 25,
337 ParticleName -> "H",
338 FullName -> "H"
339 },
340
341(* Higgs: Goldstones *)
342 S[2] == {
343 ClassName -> G0,
344 SelfConjugate -> True,
345 Goldstone -> Z,
346 Mass -> {MZ, 91.1876},
347 Width -> {WZ, 2.4952},
348 PropagatorLabel -> "Go",
349 PropagatorType -> D,
350 PropagatorArrow -> None,
351 PDG -> 250,
352 ParticleName -> "G0",
353 FullName -> "G0"
354 },
355 S[3] == {
356 ClassName -> GP,
357 SelfConjugate -> False,
358 Goldstone -> W,
359 Mass -> {MW, Internal},
360 QuantumNumbers -> {Q -> 1},
361 Width -> {WW, 2.085},
362 PropagatorLabel -> "GP",
363 PropagatorType -> D,
364 PropagatorArrow -> None,
365 PDG -> 251,
366 ParticleName -> "G+",
367 AntiParticleName -> "G-",
368 FullName -> "GP"
369 },
370
371(* Higgs: unphysical scalars *)
372 S[11] == {
373 ClassName -> Phi,
374 Unphysical -> True,
375 Indices -> {Index[SU2D]},
376 FlavorIndex -> SU2D,
377 SelfConjugate -> False,
378 QuantumNumbers -> {Y -> 1/2},
379 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
380 }
381};
382
383(* ************************** *)
384(* ***** Parameters ***** *)
385(* ************************** *)
386M$Parameters = {
387
388 (* External parameters *)
389 aEWM1 == {
390 ParameterType -> External,
391 BlockName -> SMINPUTS,
392 OrderBlock -> 1,
393 Value -> 127.9,
394 InteractionOrder -> {QED,-2},
395 Description -> "Inverse of the EW coupling constant at the Z pole"
396 },
397 Gf == {
398 ParameterType -> External,
399 BlockName -> SMINPUTS,
400 OrderBlock -> 2,
401 Value -> 1.16637*^-5,
402 InteractionOrder -> {QED,2},
403 TeX -> Subscript[G,f],
404 Description -> "Fermi constant"
405 },
406 aS == {
407 ParameterType -> External,
408 BlockName -> SMINPUTS,
409 OrderBlock -> 3,
410 Value -> 0.1184,
411 InteractionOrder -> {QCD,2},
412 TeX -> Subscript[\[Alpha],s],
413 Description -> "Strong coupling constant at the Z pole"
414 },
415 ymdo == {
416 ParameterType -> External,
417 BlockName -> YUKAWA,
418 OrderBlock -> 1,
419 Value -> 5.04*^-3,
420 Description -> "Down Yukawa mass"
421 },
422 ymup == {
423 ParameterType -> External,
424 BlockName -> YUKAWA,
425 OrderBlock -> 2,
426 Value -> 2.55*^-3,
427 Description -> "Up Yukawa mass"
428 },
429 yms == {
430 ParameterType -> External,
431 BlockName -> YUKAWA,
432 OrderBlock -> 3,
433 Value -> 0.101,
434 Description -> "Strange Yukawa mass"
435 },
436 ymc == {
437 ParameterType -> External,
438 BlockName -> YUKAWA,
439 OrderBlock -> 4,
440 Value -> 1.27,
441 Description -> "Charm Yukawa mass"
442 },
443 ymb == {
444 ParameterType -> External,
445 BlockName -> YUKAWA,
446 OrderBlock -> 5,
447 Value -> 4.7,
448 Description -> "Bottom Yukawa mass"
449 },
450 ymt == {
451 ParameterType -> External,
452 BlockName -> YUKAWA,
453 OrderBlock -> 6,
454 Value -> 172,
455 Description -> "Top Yukawa mass"
456 },
457 yme == {
458 ParameterType -> External,
459 BlockName -> YUKAWA,
460 OrderBlock -> 11,
461 Value -> 5.11*^-4,
462 Description -> "Electron Yukawa mass"
463 },
464 ymm == {
465 ParameterType -> External,
466 BlockName -> YUKAWA,
467 OrderBlock -> 13,
468 Value -> 0.10566,
469 Description -> "Muon Yukawa mass"
470 },
471 ymtau == {
472 ParameterType -> External,
473 BlockName -> YUKAWA,
474 OrderBlock -> 15,
475 Value -> 1.777,
476 Description -> "Tau Yukawa mass"
477 },
478 cabi == {
479 ParameterType -> External,
480 BlockName -> CKMBLOCK,
481 OrderBlock -> 1,
482 Value -> 0.227736,
483 TeX -> Subscript[\[Theta], c],
484 Description -> "Cabibbo angle"
485 },
486
487 (* Internal Parameters *)
488 aEW == {
489 ParameterType -> Internal,
490 Value -> 1/aEWM1,
491 InteractionOrder -> {QED,2},
492 TeX -> Subscript[\[Alpha], EW],
493 Description -> "Electroweak coupling contant"
494 },
495 MW == {
496 ParameterType -> Internal,
497 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
498 TeX -> Subscript[M,W],
499 Description -> "W mass"
500 },
501 sw2 == {
502 ParameterType -> Internal,
503 Value -> 1-(MW/MZ)^2,
504 Description -> "Squared Sin of the Weinberg angle"
505 },
506 ee == {
507 ParameterType -> Internal,
508 Value -> Sqrt[4 Pi aEW],
509 InteractionOrder -> {QED,1},
510 TeX -> e,
511 Description -> "Electric coupling constant"
512 },
513 cw == {
514 ParameterType -> Internal,
515 Value -> Sqrt[1-sw2],
516 TeX -> Subscript[c,w],
517 Description -> "Cosine of the Weinberg angle"
518 },
519 sw == {
520 ParameterType -> Internal,
521 Value -> Sqrt[sw2],
522 TeX -> Subscript[s,w],
523 Description -> "Sine of the Weinberg angle"
524 },
525 gw == {
526 ParameterType -> Internal,
527 Definitions -> {gw->ee/sw},
528 InteractionOrder -> {QED,1},
529 TeX -> Subscript[g,w],
530 Description -> "Weak coupling constant at the Z pole"
531 },
532 g1 == {
533 ParameterType -> Internal,
534 Definitions -> {g1->ee/cw},
535 InteractionOrder -> {QED,1},
536 TeX -> Subscript[g,1],
537 Description -> "U(1)Y coupling constant at the Z pole"
538 },
539 gs == {
540 ParameterType -> Internal,
541 Value -> Sqrt[4 Pi aS],
542 InteractionOrder -> {QCD,1},
543 TeX -> Subscript[g,s],
544 ParameterName -> G,
545 Description -> "Strong coupling constant at the Z pole"
546 },
547 vev == {
548 ParameterType -> Internal,
549 Value -> 2*MW*sw/ee,
550 InteractionOrder -> {QED,-1},
551 TeX -> v,
552 Description -> "Higgs vacuum expectation value"
553 },
554 lam == {
555 ParameterType -> Internal,
556 Value -> MH^2/(2*vev^2),
557 InteractionOrder -> {QED, 2},
558 Description -> "Higgs quartic coupling"
559 },
560 muH == {
561 ParameterType -> Internal,
562 Value -> Sqrt[vev^2 lam],
563 TeX -> \[Mu],
564 Description -> "Coefficient of the quadratic piece of the Higgs potential"
565 }, yl == {
566 ParameterType -> Internal,
567 Indices -> {Index[Generation], Index[Generation]},
568 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
569 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
570 InteractionOrder -> {QED, 1},
571 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
572 TeX -> Superscript[y, l],
573 Description -> "Lepton Yukawa couplings"
574 },
575 yu == {
576 ParameterType -> Internal,
577 Indices -> {Index[Generation], Index[Generation]},
578 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
579 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
580 InteractionOrder -> {QED, 1},
581 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
582 TeX -> Superscript[y, u],
583 Description -> "Up-type Yukawa couplings"
584 },
585 yd == {
586 ParameterType -> Internal,
587 Indices -> {Index[Generation], Index[Generation]},
588 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
589 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
590 InteractionOrder -> {QED, 1},
591 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
592 TeX -> Superscript[y, d],
593 Description -> "Down-type Yukawa couplings"
594 },
595(* N. B. : only Cabibbo mixing! *)
596 CKM == {
597 ParameterType -> Internal,
598 Indices -> {Index[Generation], Index[Generation]},
599 Unitary -> True,
600 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
601 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
602 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
603 TeX -> Superscript[V,CKM],
604 Description -> "CKM-Matrix"}
605};
606
607(* ************************** *)
608(* ***** Lagrangian ***** *)
609(* ************************** *)
610LGauge := -1/4 FS[B,mu,nu] FS[B,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];
611
612LHiggs := Block[{ii,mu}, DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]];
613
614LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, ii,generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
615 (* Pure gauge piece *)
616 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
617 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
618 LGhs = -ghGbar.del[DC[ghG,mu],mu];
619
620 (* Scalar pieces: see Peskin pages 739-742 *)
621 (* phi1 and phi2 are the real degrees of freedom of GP *)
622 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
623 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
624 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
625 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
626 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
627 doublet0 = {0, vev/Sqrt[2]};
628 Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
629 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
630 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
631
632LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0]];
633