| 1 | (* Automatically generated from HDecay output *
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| 2 | * (c.f. "HDECAY: A Program for Higgs boson decays in the standard model and *
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| 3 | * its supersymmetric extension.", A. Djouadi, J. Kalinowski, M. Spira, *
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| 4 | * Comput.Phys.Commun.108:56-74,1998) *)
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| 5 |
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| 6 | BeginPackage ["Hdecay`"];
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| 7 | Begin ["Hdecay`p`"];
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| 8 |
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| 9 | data = {{0, 0}, {1., 2.251*^-7}, {6.0201, 0.00002011}, {11.0402, 0.0001738}, {16.0603, 0.0004549},
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| 10 | {21.0804, 0.0006405}, {26.1005, 0.0007918}, {31.1206, 0.0009277}, {36.1407, 0.001055},
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| 11 | {41.1608, 0.001178}, {46.1809, 0.001298}, {51.201, 0.001416}, {56.2211, 0.001533},
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| 12 | {61.2412, 0.001649}, {66.2613, 0.001766}, {71.2814, 0.001883}, {76.3015, 0.002},
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| 13 | {81.3216, 0.002119}, {86.3417, 0.00224}, {91.3618, 0.002364}, {96.3819, 0.002495},
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| 14 | {101.402, 0.002642}, {106.422, 0.002816}, {111.442, 0.003041}, {116.462, 0.003347},
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| 15 | {121.482, 0.003782}, {126.503, 0.00442}, {131.523, 0.005373}, {136.543, 0.00683},
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| 16 | {141.563, 0.009133}, {146.583, 0.013}, {151.603, 0.02027}, {156.623, 0.03847},
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| 17 | {161.643, 0.1316}, {166.663, 0.2903}, {171.683, 0.4168}, {176.704, 0.5386},
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| 18 | {181.724, 0.6883}, {186.744, 0.9035}, {191.764, 1.105}, {196.784, 1.3}, {201.804, 1.499},
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| 19 | {206.824, 1.705}, {211.844, 1.922}, {216.864, 2.151}, {221.884, 2.394}, {226.905, 2.651},
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| 20 | {231.925, 2.924}, {236.945, 3.213}, {241.965, 3.519}, {246.985, 3.843}, {252.005, 4.184},
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| 21 | {257.025, 4.545}, {262.045, 4.925}, {267.065, 5.324}, {272.085, 5.742}, {277.106, 6.182},
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| 22 | {282.126, 6.642}, {287.146, 7.123}, {292.166, 7.625}, {297.186, 8.15}, {302.206, 8.696},
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| 23 | {307.226, 9.265}, {312.246, 9.856}, {317.266, 10.47}, {322.286, 11.1}, {327.307, 11.76},
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| 24 | {332.327, 12.44}, {337.347, 13.13}, {342.367, 13.83}, {347.387, 14.61}, {352.407, 15.7},
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| 25 | {357.427, 16.91}, {362.447, 18.18}, {367.467, 19.51}, {372.487, 20.89}, {377.508, 22.31},
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| 26 | {382.528, 23.77}, {387.548, 25.27}, {392.568, 26.81}, {397.588, 28.38}, {402.608, 29.99},
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| 27 | {407.628, 31.63}, {412.648, 33.3}, {417.668, 35.01}, {422.688, 36.76}, {427.709, 38.53},
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| 28 | {432.729, 40.34}, {437.749, 42.19}, {442.769, 44.06}, {447.789, 45.97}, {452.809, 47.92},
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| 29 | {457.829, 49.9}, {462.849, 51.91}, {467.869, 53.96}, {472.889, 56.05}, {477.91, 58.17},
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| 30 | {482.93, 60.33}, {487.95, 62.52}, {492.97, 64.76},
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| 31 | {497.99, 67.03}};
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| 32 |
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| 33 | interpolation[x_, l_] := Plus @@ ((#[[1]] * x^#[[2]])& /@ l);
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| 34 |
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| 35 | params = {{-0.26293901351164234, 1}, {0.001368182199849752, 2}, {-2.3048363155706936*^-6, 3},
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| 36 | {3.1498414039397794*^-9, 4}, {-1.977234012939224*^-12, 5},
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| 37 | {6.665973758092558*^-16, 6}};
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| 38 |
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| 39 | Hdecay`Hdecay[mh_] := If[mh < 500, Max[Interpolation[data, InterpolationOrder->1][mh], 0], interpolation[mh, params]]/;(mh >= 0);
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| 40 | Hdecay`Hdecay::usage = "usage: Hdecay [mh]";
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| 41 |
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| 42 | End[];
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| 43 | Protect[Hdecay];
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| 44 | EndPackage[];
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| 45 | (* Spectrum calculator for compact HEIDI. For more information, please take *
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| 46 | * a look at *
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| 47 | * *
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| 48 | * "Exploring the golden channel for HEIDI models using an interface between *
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| 49 | * WHIZARD and FeynRules", N. D. Christensen, C. Duhr, B. Fuks, J. Reuter,*
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| 50 | * C. Speckner, arXiv:1010.3251 *
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| 51 | * *
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| 52 | * Please cite above reference if you use this program. *)
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| 53 |
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| 54 | BeginPackage["Heidi`"];
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| 55 | Begin["Heidi`p`"];
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| 56 | Needs["Hdecay`"];
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| 57 |
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| 58 | (* Initialize the package and clear all caches. *)
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| 59 | Heidi`InitHeidi[mv_, mmh_, mcs_, mmb_, mg2_, mprec_] := Block[{},
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| 60 | v = mv;
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| 61 | mh = mmh;
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| 62 | cs = mcs;
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| 63 | mb = mmb;
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| 64 | g2 = mg2;
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| 65 | g = N[Sqrt[g2]];
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| 66 | alpha = N[g2 / mb * Coth[mb * Pi / cs]];
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| 67 | lambda = N[mh^2 / v^2 / 2];
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| 68 | prec = mprec;
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| 69 | Clear[MassCache, WFCache, WidthCache];
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| 70 | If[lambda <= alpha,
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| 71 | mh = 1.1 * Sqrt[2*alpha] * v;
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| 72 | Print["WARNING: choosen Higgs mass is to small; using mh "
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| 73 | <> ToString [mh] <> "GeV instead!"];
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| 74 | InitHeidi[v, mh, cs, mb, g2, prec];
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| 75 | ];
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| 76 | ];
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| 77 |
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| 78 | Heidi`InitHeidi[v_, mh_, cs_, mb_, g2_] := InitHeidi[v, mh, cs, mb, g2, 0.000001];
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| 79 |
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| 80 | Heidi`InitHeidi::usage = "usage: InitHeidi [v, mh, cs, mb, g2, prec]
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| 81 | v : higgs VeV
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| 82 | mh : higgs mass
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| 83 | cs : compactification scale
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| 84 | mb : bulk mass
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| 85 | g2 : 5D mixing squared
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| 86 | prec : precision for the numeric determination of the masses
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| 87 | (optional; default: 0.000001)";
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| 88 |
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| 89 |
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| 90 | (* Calculate the nth mass eigenvalue *)
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| 91 | Heidi`HeidiMass[n_] := Block[{fun, l, r, x, oldx},
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| 92 | If[NumericQ[MassCache[n]],
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| 93 | MassCache[n]
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| 94 | ,
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| 95 | If[n > 0,
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| 96 | fun = (mh^2 - mb^2 + 2*g2*v^2/# * Cot[Pi/cs*#] - #^2)&;
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| 97 | l = (n - 1) * cs; r = n * cs;
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| 98 | ,
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| 99 | fun = (mb^2 - mh^2 + 2*g2*v^2/# * Coth[Pi/cs*#] - #^2)&;
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| 100 | l = 0; r = mb;
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| 101 | ];
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| 102 | oldx = l;
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| 103 | x = (l + r) / 2;
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| 104 | While[Abs[(x - oldx) / x] > prec,
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| 105 | oldx = x;
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| 106 | If[fun[x] > 0, l = x, r = x];
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| 107 | x = (l + r) / 2;
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| 108 | ];
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| 109 | MassCache[n] = If[n == 0, Sqrt[mb^2 - N[x]^2], Sqrt[N[x]^2 + mb^2]]
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| 110 | ]
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| 111 | ]/;(n >= 0);
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| 112 |
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| 113 | Heidi`HeidiMass::usage = "usage: HeidiMass [n]
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| 114 | n : mode index";
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| 115 |
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| 116 |
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| 117 | (* Calculate the mth component of the nth wavefunction *)
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| 118 | Heidi`HeidiWavefunction[n_, m_] := Block[{},
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| 119 | If[NumericQ[WFCache[n, m]],
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| 120 | WFCache[n, m]
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| 121 | ,
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| 122 | If[m == 0,
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| 123 | WFCache[n, m] = N[1/Sqrt[
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| 124 | 1 + g2*v^2*Pi/cs/(HeidiMass[n]^2 - mb^2) +
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| 125 | (HeidiMass[n]^2 - mh^2)/2/(HeidiMass[n]^2 - mb^2) +
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| 126 | (HeidiMass[n]^2 - mh^2)^2 * Pi/4/g2/v^2/cs
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| 127 | ]]
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| 128 | ,
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| 129 | WFCache[n, m] = N[HeidiWavefunction[n, 0] *
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| 130 | 2*g*v*Sqrt[cs/Pi/If[m == 1, 2, 1]] /
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| 131 | (HeidiMass[n]^2 - mb^2 - (m - 1)^2*cs^2)]
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| 132 | ]
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| 133 | ]
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| 134 | ]/;((n >= 0) && (m >= 0));
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| 135 |
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| 136 | Heidi`HeidiWavefunction::usage = "usage: HeidiWavefunction [n, m]
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| 137 | n : mode index
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| 138 | m : wavefunction component index (0 = pre-mixing higgs)";
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| 139 |
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| 140 |
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| 141 | Heidi`HeidiScalarCoupling[i__] := Block[{},
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| 142 | -I*6 * (Times @@ (Heidi`HeidiWavefunction[#, 0]& /@ {i}))
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| 143 | ]/;((Length[{i}] == 4) && (And @@ ((# >= 0)& /@ {i})));
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| 144 |
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| 145 | Heidi`HeidiScalarCoupling[i__] := Block [{thing},
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| 146 | -2*I*v * (Times @@ (Heidi`HeidiWavefunction[#, 0]& /@ {i})) *
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| 147 | (3*lambda - ((Plus @@ ((HeidiMass[#]^2)& /@ {i})) - 3 * mh^2)/2/v^2)
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| 148 | ]/;((Length[{i}] == 3) && (And @@ ((# >= 0)& /@ {i})));
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| 149 |
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| 150 | Heidi`HeidiScalarCoupling::usage = "usage: HeidiScalarCoupling [i1, ..., in]
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| 151 | i1, ..., in : modes meeting at the vertex (n = 3 or n = 4)";
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| 152 |
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| 153 |
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| 154 | Heidi`HeidiScalarWidth[i_] := Block[{calc},
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| 155 | calc[{x_, j_, k_}] := Which[
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| 156 | j == i, {x, j, k},
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| 157 | (HeidiMass[i] < HeidiMass[j] + HeidiMass[k]) || (k > j), {x, j+1, 0},
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| 158 | True, {
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| 159 | Sqrt[
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| 160 | (HeidiMass[i]^2 - (HeidiMass[j] + HeidiMass[k])^2) *
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| 161 | (HeidiMass[i]^2 - (HeidiMass[j] - HeidiMass[k])^2)]
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| 162 | /16/Pi/HeidiMass[i]^3 * Abs[HeidiScalarCoupling[i, j, k]]^2
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| 163 | /If[j == k, 2, 1] + x, j, k+1}
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| 164 | ];
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| 165 | If[NumericQ[WidthCache[i]], WidthCache[i], WidthCache[i] = FixedPoint[calc, {0, 0, 0}][[1]]]
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| 166 | ]/;(i >= 0);
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| 167 |
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| 168 | Heidi`HeidiScalarWidth::usage = "usage: HeidiScalarWidth [n]
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| 169 | n : mode index";
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| 170 |
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| 171 |
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| 172 | Heidi`HeidiSMWidth[i_] := Block[{},
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| 173 | Hdecay[HeidiMass[i]] * HeidiWavefunction[i, 0]^2
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| 174 | ]/;(i >= 0);
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| 175 |
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| 176 | Heidi`HeidiSMWidth::usage = "usage: HeidiSMWidth [n]
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| 177 | n : mode index";
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| 178 |
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| 179 |
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| 180 | Heidi`HeidiWidth[i_] := HeidiSMWidth[i] + HeidiScalarWidth[i];
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| 181 |
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| 182 | Heidi`HeidiWidth::usage = "usage: HeidiWidth [n]
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| 183 | n : mode index";
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| 184 |
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| 185 | End[];
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| 186 | Protect[InitHeidi, HeidiMass, HeidiWavefunction, HeidiScalarCoupling, HeidiScalarWidth,
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| 187 | HeidiSMWidth, HeidiWidth];
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| 188 | EndPackage[];
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| 189 | (* *************************************************************************************
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| 190 | HEIDI Higgs with a compact extra dimension.
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| 191 |
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| 192 | The model is intended for use on top of the Standard Model where it replaces the
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| 193 | Higgs sector. As the theory contains a variable number of modes below the cutoff
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| 194 | (the masses of which cannot be expressed analytically), the HEIDI parameters have to
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| 195 | be set before creating the Feynman rules and model files. Those parameters are:
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| 196 |
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| 197 | Heidi$v : higgs VeV. Optional, default is the value.
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| 198 | Heidi$mh : higgs Mass. Optional, default is the SM value
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| 199 | Heidi$cs : compactification scale
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| 200 | Heidi$mb : bulk mass
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| 201 | Heidi$g2 : 5D trilinear coupling squared
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| 202 | Heidi$cutoff : cutoff scale
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| 203 | Heidi$nmodes : if Heidi$cutoff is undefined, Heidi$nmodes determines the number of
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| 204 | modes in the spectrum (starting from index 0)
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| 205 |
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| 206 | Masses, widths and couplings are calculated statically. DO NOT CHANGE THOSE OR THE
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| 207 | ELECTROWEAK PARAMETERS AFTER CREATING THE MODEL.
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| 208 |
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| 209 | This model file is a descendant of Claude Duhr's SMScalars model.
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| 210 |
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| 211 | *)
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| 212 |
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| 213 |
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| 214 | (* Make sure everything we need is at our disposal *)
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| 215 | Needs["Heidi`"];
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| 216 | Block[{error},
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| 217 | error[s_] := (Print["HEIDI error: please set " <> s]; Throw[Null]);
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| 218 | If[!NumericQ[Heidi$v], error["Heidi$v"]];
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| 219 | If[!NumericQ[Heidi$mh], error["Heidi$mh"]];
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| 220 | If[!NumericQ[Heidi$cs], error["Heidi$cs"]];
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| 221 | If[!NumericQ[Heidi$mb], error["Heidi$mb"]];
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| 222 | If[!NumericQ[Heidi$g2], error["Heidi$g2"]];
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| 223 | If[FeynmanGauge,
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| 224 | Print["HEIDI error: the model currently only supports unitarity gauge"
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| 225 | <> "; please set FeynmanGauge = False."];
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| 226 | Throw[Null];
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| 227 | ];
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| 228 | ];
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| 229 |
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| 230 | (* Init HEIDI *)
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| 231 | InitHeidi[Heidi$v, Heidi$mh, Heidi$cs, Heidi$mb, Heidi$g2];
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| 232 |
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| 233 | (* Determine the number of modes we have been requested to include *)
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| 234 | If[NumericQ[Heidi$cutoff],
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| 235 | Heidi$nmodes = FixedPoint[If[HeidiMass[#] < Heidi$cutoff, # + 1, #]&, 0];
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| 236 | ];
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| 237 | If[!NumericQ[Heidi$nmodes],
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| 238 | Print["HEIDI error: please set either Heidi$cutoff or Heidi$nmodes"];
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| 239 | Throw[Null];
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| 240 | ];
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| 241 |
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| 242 | (* Model metadata *)
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| 243 | M$ModelName = "HEIDI";
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| 244 | M$Information = {Authors -> "C. Speckner",
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| 245 | Institutions -> "Universitaet Freiburg",
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| 246 | Emails -> "Christian.Speckner@physik.uni-freiburg.de",
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| 247 | Date -> "30.07.2010",
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| 248 | Version -> "0.1",
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| 249 | URLs -> "None",
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| 250 | References -> (
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| 251 | ""
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| 252 | <> "\"Exploring the golden channel for HEIDI models using an "
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| 253 | <> "interface between WHIZARD and FeynRules\", "
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| 254 | <> "N. D. Christensen, C. Duhr, B. Fuks, J. Reuter, C. Speckner, "
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| 255 | <> "arXiv:1010.3251")
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| 256 | };
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| 257 |
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| 258 | (* The flavor index for the HEIDI modes *)
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| 259 | IndexRange[Index[Heidi]] = Range[Heidi$nmodes];
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| 260 | IndexStyle[Heidi, k];
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| 261 |
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| 262 | M$Parameters = {
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| 263 | (* The Higgs wavefunction is a tensor parameter, the entries of which are *
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| 264 | * stored numerically as external parameters. *)
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| 265 | xi == {
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| 266 | Indices -> {Index[Heidi]},
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| 267 | ComplexParameter -> False,
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| 268 | Value -> Table[Rule[xi[n], HeidiWavefunction[n - 1, 0]],
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| 269 | {n, 1, Heidi$nmodes}],
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| 270 | Description -> "Higgs wave function",
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| 271 | ParameterType -> External,
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| 272 | AllowSummation -> True
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| 273 | },
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| 274 | (* K factor for the effective ggh coupling *)
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| 275 | kggh == {
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| 276 | Value -> 1,
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| 277 | ParamterType -> External,
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| 278 | Description -> "ggh K factor"
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| 279 | }
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| 280 | };
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| 281 |
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| 282 |
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| 283 | (* Enter the HEIDI scalars *)
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| 284 | M$ClassesDescription = {
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| 285 | S[4] == {
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| 286 | ClassName -> Hh,
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| 287 | ClassMembers -> Table[Symbol["Hh" <> ToString[n]], {n, 1, Heidi$nmodes}],
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| 288 | SelfConjugate -> True,
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| 289 | Indices -> {Index[Heidi]},
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| 290 | FlavorIndex -> Heidi,
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| 291 | Mass -> Table[{Symbol["mhh" <> ToString[n]], HeidiMass[n - 1]}, {n, 1, Heidi$nmodes}],
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| 292 | Width -> Table[{Symbol["whh" <> ToString[n]], HeidiWidth[n - 1]}, {n, 1, Heidi$nmodes}],
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| 293 | PDG -> Table[990000 + n, {n, 1, Heidi$nmodes}]
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| 294 | }
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| 295 | }
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| 296 |
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| 297 | (* Construct HEIDI Lagrangian *)
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| 298 | LHEIDI := (LSM /. {muH -> 0, \[Lambda] -> 0}) /. H -> (Hh[n]*xi[n]);
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| 299 | LHEIDI::usage = "LHEIDI: HEIDI lagrangian";
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| 300 |
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| 301 | (* Optional: the effective ggh_i lagrangian *)
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| 302 | LHEIDIgg[mode_] := Block[{fun, piece, tt, mm, hh},
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| 303 | Print["adding effective scalar-gluon-gluon vertices " <> If[mode == "heavytop",
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| 304 | "in heavy top limit", "with dynamical loop factor"]];
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| 305 | tt[m_] := 4*MT^2 / m^2;
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| 306 | fun[tau_] := If[mode == "heavytop", 2/3,
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| 307 | tau * (1 + (1 - tau)* If[NumericalValue[tau] > 1,
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| 308 | ArcSin[Sqrt[1 / tau]]^2
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| 309 | ,
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| 310 | -1/4 * (Log[(1 + Sqrt[1 + tau])/(1 - Sqrt[1 - tau])]
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| 311 | - I*Pi)^2
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| 312 | ])
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| 313 | ];
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| 314 | mm[n_] := Symbol["mhh" <> ToString[n]];
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| 315 | hh[n_] := Symbol["Hh" <> ToString[n]];
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| 316 | piece[n_] :=
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| 317 | Sqrt[kggh] * gs^2/32/Pi^2/v * fun[tt[mm[n]]] * xi[n] *
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| 318 | hh[n] * (del[G[mu, a], nu] - del[G[nu, a], mu])^2;
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| 319 | Plus @@ (piece /@ Range[Heidi$nmodes])
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| 320 | ];
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| 321 | LHEIDIgg[] := LHEIDIgg[""];
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| 322 | LHEIDIgg::usage = "LHEIDIgg [mode]: HEIDI effective scalar-gluon-gluon couplings
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| 323 | mode : optional, set to \"heavytop\" to use heavy top limit";
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| 324 |
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| 325 | (* Protect our symbols. *)
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| 326 | Protect[LHEIDI, LHEIDIgg];
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| 327 |
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| 328 | (* Spit out final warnings. *)
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| 329 | Print["HEIDI initialized. Please doublecheck that the runtime parametrization of "
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| 330 | <> "the electroweak sector is consistent with the parameters you used for HEIDI "
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| 331 | <> "before running any code."];
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