{
"cells": [
{
"cell_type": "markdown",
"id": "f6c8f14c-ff44-47dd-9543-fe717469a1d5",
"metadata": {},
"source": [
"# The AutoTherm Wolfram package"
]
},
{
"cell_type": "markdown",
"id": "0881d8ad-4749-4ead-b6f6-bfd439ea747f",
"metadata": {},
"source": [
"### Importing the packages"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9f121b2b-d428-4fd6-b656-bbefdca8646a",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"FeynArts 3.12 (24 May 2024)\n",
"by Hagen Eck, Sepp Kueblbeck, and Thomas Hahn\n",
"\n",
"FormCalc 9.10 (30 Aug 2022)\n",
"by Thomas Hahn\n",
"\n",
"AutoTherm 0.9\n",
"by Killian Bouzoud, Jacopo Ghiglieri and Greg Jackson\n",
"Please cite XXXXXX\n",
"\n"
]
}
],
"source": [
"Get[\"~/Nextcloud/AUTOTHERM/FeynArts-3.12/FeynArts.m\"]; \n",
"Get[\"~/Nextcloud/AUTOTHERM/FormCalc-9.10/FormCalc.m\"]; \n",
"Get[\"~/Nextcloud/AUTOTHERM/FormCalc-9.10/tools/VecSet.m\"];\n",
"Get[\"~/Nextcloud/AUTOTHERM/autotherm/analytical/autotherm.wl\"]"
]
},
{
"cell_type": "markdown",
"id": "a6e03a94-46d3-414e-b1ce-8f01ce8fad42",
"metadata": {},
"source": [
"### import the MSSM gravitino model"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0015d3db-1401-4160-8188-fb57826a808e",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [],
"source": [
"ConfigParse[\"~/Nextcloud/AUTOTHERM/autotherm/MyModels/mssm_gravitino/mssm_gravitino.m\"]"
]
},
{
"cell_type": "markdown",
"id": "66d9f988-e87f-4b28-b0c4-62a0c23e073e",
"metadata": {},
"source": [
"look at the gluon-gluon to gluon, graviton process"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8b6b93f3-a4ad-4649-8964-38fe5cd2c851",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 2 2 2 2 2\n",
"48 g3 kappa (T + T U + U ) AUThast[{{T, V[3]}, {U, V[3]}}] AUTstatspart[1, 1, 1]\n",
"------------------------------------------------------------------------------------\n",
" S T U"
]
},
"execution_count": 6,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"ggtogG = ComputeMatrixElement[{V[3], V[3]} -> {V[3], T[1]}]"
]
},
{
"cell_type": "markdown",
"id": "93343995-031a-4df2-809d-0542dd79cbba",
"metadata": {},
"source": [
"we can drop the auxiliary ``AUTstatpart`` and ``AUThast`` labels"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "3ee803e8-7f14-44bb-9742-8556296fae36",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 2 2 2 2 2\n",
"48 (T + T U + U ) \\[Kappa] g\n",
" 3\n",
"---------------------------------\n",
" S T U"
]
},
"execution_count": 21,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"ggtogG /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\\[Kappa],g3->Subscript[g, 3]}"
]
},
{
"cell_type": "markdown",
"id": "acd328bc-2c7d-49eb-bb59-4025169118a1",
"metadata": {},
"source": [
"we can look at any process, not just those with a non-equilibrium particle in the final state. For instance, the well-known gluon gluon to gluon gluon at LO in the SM reads"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "255e6f96-f3dc-455a-85e0-b69b1c281907",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 4 2 2 3\n",
"1152 g3 (T + T U + U ) AUThast[{{T, V[3]}, {U, V[3]}}] AUTstatspart[1, 1, 1]\n",
"-------------------------------------------------------------------------------\n",
" 2 2 2\n",
" S T U"
]
},
"execution_count": 8,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"ggtogg = ComputeMatrixElement[{V[3], V[3]} -> {V[3], V[3]}]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "4045208c-3fb9-48fa-b5fb-2a8ff9d9d56d",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" S T S U T U 4\n",
"1152 (3 - --- - --- - ---) g\n",
" 2 2 2 3\n",
" U T S"
]
},
"execution_count": 23,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"(Expand[(Simplify[\n",
" ggtogg/g3^4 /. {AUTstatspart[___] -> 1, \n",
" AUThast[___] -> 1,kappa->\\[Kappa],g3->Subscript[g, 3]} /. {T U -> (S^2 - T^2 - U^2)/2}] // \n",
" Expand) /. {x_^4 :> (SolveValues[S + T + U == 0, \n",
" x][[1]])^4}] /. {x_^2/y_^2 :> \n",
" x SolveValues[S + T + U == 0, x][[1]]/y^2} // \n",
" Expand) Subscript[g, 3]^4 // Simplify"
]
},
{
"cell_type": "markdown",
"id": "e9fa6c10-d95e-4f6c-993c-51b923da3020",
"metadata": {},
"source": [
"this should read $16 g_3^4 d_A C_A^2(3 - s u/t^2-t u/s^2 -t s/u^2)$. Indeed"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "56933cb3-bccc-4785-adc3-bd6d78e29d4d",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1152"
]
},
"execution_count": 10,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"16 8 9 "
]
},
{
"cell_type": "markdown",
"id": "d98a5a2a-a89b-45bf-b812-164ef7dc173f",
"metadata": {},
"source": [
"and"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "5736bd72-dbc2-4fd7-b488-863d3b247695",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1"
]
},
"execution_count": 24,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"ggtogg/(16 g3^4 8 9 (3- S U/T^2- T U/S^2 -S T/U^2)) /. {AUTstatspart[___] -> 1, \n",
" AUThast[___] -> 1} // Simplify[#, Assumptions -> S + T + U == 0] &"
]
},
{
"cell_type": "markdown",
"id": "166c4ce0-447d-4cd5-bcf5-b92fbcf2ea81",
"metadata": {},
"source": [
"look at the gluino-gluino to gluino, gravitino process"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a2366cca-4d82-4c40-b465-9571da5fe7a1",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 2 2 3\n",
"12 g3 kappa S AUThast[{{T, V[3]}, {U, V[3]}}] AUTstatspart[-1, -1, -1]\n",
"-------------------------------------------------------------------------\n",
" T U"
]
},
"execution_count": 13,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"gtgttogtGt = ComputeMatrixElement[{F[8], F[8]} -> {F[8], F[11]}]"
]
},
{
"cell_type": "markdown",
"id": "a01ec9c9-26af-4ca7-ae22-efe6deb167ac",
"metadata": {},
"source": [
"consider all the crossings"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "9ab8627c-ad63-47ad-a7ee-91de6b1ff9b6",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 4 4 4 2 2\n",
"12 (S + T + U ) \\[Kappa] g\n",
" 3\n",
"-------------------------------\n",
" S T U"
]
},
"execution_count": 25,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"gtgttogtGtall = \n",
" ComputeMatrixElement[{F[8], F[8]} -> {F[8], F[11]}] + \n",
" ComputeMatrixElement[{F[8], -F[8]} -> {-F[8], F[11]}] + \n",
" ComputeMatrixElement[{-F[8], F[8]} -> {-F[8], \n",
" F[11]}] /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\\[Kappa],g3->Subscript[g, 3]} // \n",
" Simplify"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "121ff4e7-14e7-41e3-8c03-a2d499b72435",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1\n",
"-\n",
"2"
]
},
"execution_count": 27,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"gtgttogtGtall/ggtogG /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\\[Kappa],g3->Subscript[g, 3]} //\n",
" Simplify[#, Assumptions -> S + T + U == 0] &"
]
},
{
"cell_type": "markdown",
"id": "da95318f-9b5c-4442-9a44-644e9a138498",
"metadata": {},
"source": [
"the ratio agrees with SUSY expectations. Recall that the graviton production is summed over its two polarisations, whereas the gravitino only considers one helicity state. The equivalent contribution from the \"antiparticle\" helicity state is "
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "3cf621c2-54d8-414b-8c2b-5a5cb9946fc7",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 4 4 4 2 2\n",
"12 (S + T + U ) \\[Kappa] g\n",
" 3\n",
"-------------------------------\n",
" S T U"
]
},
"execution_count": 28,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"gtgttogtGtbarall = \n",
" ComputeMatrixElement[{-F[8], -F[8]} -> {-F[8], -F[11]}] + \n",
" ComputeMatrixElement[{F[8], -F[8]} -> {F[8], -F[11]}] + \n",
" ComputeMatrixElement[{-F[8], \n",
" F[8]} -> {F[8], -F[11]}] /. {AUTstatspart[___] -> 1, \n",
" AUThast[___] -> 1,kappa->\\[Kappa],g3->Subscript[g, 3]} // Simplify"
]
},
{
"cell_type": "markdown",
"id": "e521bd29-bdcf-47ad-943b-fb027925968a",
"metadata": {},
"source": [
"### Compute the thermal masses"
]
},
{
"cell_type": "markdown",
"id": "e73b9d99-a4a2-4839-bc0b-21254c69b8c0",
"metadata": {},
"source": [
"We can compute all of them"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "fcb3f103-254a-4a86-822e-890be9364c0e",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Dynamic[Computing the thermal mass for particle <>\n",
" \n",
" ToString[AutoTherm`Private`part$25871]]\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
" 2 2 2\n",
" g + 3 g g\n",
" 1 2 1\n",
"{{F[1], -----------}, {F[2], ---}, {F[3], \n",
" 8 2\n",
" \n",
" 2 2 2 2 2 2 2 2 2 2\n",
" g + 27 g + 48 g g + 27 g + 48 g g + 27 g + 48 g + 18 h\n",
" 1 2 3 1 2 3 1 2 3 t\n",
" {---------------------, ---------------------, ------------------------------}}, \n",
" 72 72 72\n",
" \n",
" 2 2 2 2 2 2 2\n",
" 2 (g + 3 g ) 2 (g + 3 g ) 2 (g + 3 g ) h\n",
" 1 3 1 3 1 3 t\n",
" {F[4], {---------------, ---------------, --------------- + ---}}, \n",
" 9 9 9 2\n",
" \n",
" 2 2 2 2 2\n",
" g + 12 g 11 g 9 g 9 g\n",
" 1 3 1 2 3\n",
" {F[5], ------------}, {F[6], ------}, {F[7], -----}, {F[8], -----}, \n",
" 18 4 4 4\n",
" \n",
" 2 2 2 2 2 2 2 2\n",
" g + 3 g + 6 h g + 3 g g + 3 g + 6 h\n",
" 1 2 t 1 2 1 2 t\n",
" {F[9], -------------------}, {F[10], -----------}, {S[1], -------------------}, \n",
" 8 8 8\n",
" \n",
" 2 2 2 2 2\n",
" g + 3 g g + 3 g g\n",
" 1 2 1 2 1\n",
" {S[2], -----------}, {S[3], -----------}, {S[4], ---}, \n",
" 8 8 2\n",
" \n",
" 2 2 2 2 2 2\n",
" g + 27 g + 48 g g + 27 g + 48 g\n",
" 1 2 3 1 2 3\n",
" {S[5], {---------------------, ---------------------, \n",
" 72 72\n",
" \n",
" 2 2 2 2\n",
" g + 27 g + 48 g + 18 h\n",
" 1 2 3 t\n",
" ------------------------------}}, \n",
" 72\n",
" \n",
" 2 2 2 2 2 2 2\n",
" 2 (g + 3 g ) 2 (g + 3 g ) 2 (g + 3 g ) h\n",
" 1 3 1 3 1 3 t\n",
" {S[6], {---------------, ---------------, --------------- + ---}}, \n",
" 9 9 9 2\n",
" \n",
" 2 2 2 2 2\n",
" g + 12 g 11 g 9 g 9 g\n",
" 1 3 1 2 3\n",
" {S[7], ------------}, {V[1], ------}, {V[2], -----}, {V[3], -----}}\n",
" 18 2 2 2"
]
},
"execution_count": 30,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
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],
"source": [
"AllMasses/.{kappa->\\[Kappa],g3->Subscript[g, 3],g2->Subscript[g, 2],g1->Subscript[g, 1],ht->Subscript[h, t]}"
]
},
{
"cell_type": "markdown",
"id": "e5c171a9-1656-4293-a9f1-ee6602899004",
"metadata": {},
"source": [
"Or compute them one by one"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "99f10911-64ae-422c-b12b-09e22991e89a",
"metadata": {
"vscode": {
"languageId": "wolfram language"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
" 2 2\n",
"g + 3 g\n",
" 1 2\n",
"-----------\n",
" 8"
]
},
"execution_count": 29,
"metadata": {
"text/html": [],
"text/plain": []
},
"output_type": "execute_result"
}
],
"source": [
"ThermalMass[F[1]]/.{kappa->\\[Kappa],g3->Subscript[g, 3],g2->Subscript[g, 2],g1->Subscript[g, 1],ht->Subscript[h, t]}"
]
}
],
"metadata": {
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"language": "Wolfram Language",
"name": "wolframlanguage14"
},
"language_info": {
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"file_extension": ".m",
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