The AutoTherm Wolfram package#

Importing the packages#

[1]:

Get["~/Nextcloud/AUTOTHERM/FeynArts-3.12/FeynArts.m"];
Get["~/Nextcloud/AUTOTHERM/FormCalc-9.10/FormCalc.m"];
Get["~/Nextcloud/AUTOTHERM/FormCalc-9.10/tools/VecSet.m"];
Get["~/Nextcloud/AUTOTHERM/autotherm/analytical/autotherm.wl"]


FeynArts 3.12 (24 May 2024)
by Hagen Eck, Sepp Kueblbeck, and Thomas Hahn

FormCalc 9.10 (30 Aug 2022)
by Thomas Hahn

AutoTherm 0.9
by Killian Bouzoud, Jacopo Ghiglieri and Greg Jackson
Please cite XXXXXX

import the MSSM gravitino model#

[5]:

ConfigParse["~/Nextcloud/AUTOTHERM/autotherm/MyModels/mssm_gravitino/mssm_gravitino.m"]

look at the gluon-gluon to gluon, graviton process

[6]:

ggtogG = ComputeMatrixElement[{V[3], V[3]} -> {V[3], T[1]}]

[6]:
Output

we can drop the auxiliary AUTstatpart and AUThast labels

[21]:

ggtogG /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\[Kappa],g3->Subscript[g, 3]}

[21]:
Output

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

[8]:

ggtogg = ComputeMatrixElement[{V[3], V[3]} -> {V[3], V[3]}]

[8]:
Output
[23]:

(Expand[(Simplify[
          ggtogg/g3^4 /. {AUTstatspart[___] -> 1,
             AUThast[___] -> 1,kappa->\[Kappa],g3->Subscript[g, 3]} /. {T  U -> (S^2 - T^2 - U^2)/2}] //
         Expand) /. {x_^4 :> (SolveValues[S + T + U == 0,
             x][[1]])^4}] /. {x_^2/y_^2 :>
       x  SolveValues[S + T + U == 0, x][[1]]/y^2} //
    Expand) Subscript[g, 3]^4 // Simplify

[23]:
Output

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

[10]:

16  8  9

[10]:

1152

and

[24]:

ggtogg/(16 g3^4 8 9 (3- S U/T^2- T U/S^2 -S T/U^2)) /. {AUTstatspart[___] -> 1,
   AUThast[___] -> 1} // Simplify[#, Assumptions -> S + T + U == 0] &

[24]:

1

look at the gluino-gluino to gluino, gravitino process

[13]:

gtgttogtGt = ComputeMatrixElement[{F[8], F[8]} -> {F[8], F[11]}]

[13]:
Output

consider all the crossings

[25]:

gtgttogtGtall =
 ComputeMatrixElement[{F[8], F[8]} -> {F[8], F[11]}] +
    ComputeMatrixElement[{F[8], -F[8]} -> {-F[8], F[11]}] +
    ComputeMatrixElement[{-F[8], F[8]} -> {-F[8],
       F[11]}] /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\[Kappa],g3->Subscript[g, 3]} //
  Simplify

[25]:
Output
[27]:

gtgttogtGtall/ggtogG /. {AUTstatspart[___] -> 1, AUThast[___] -> 1,kappa->\[Kappa],g3->Subscript[g, 3]} //
  Simplify[#, Assumptions -> S + T + U == 0] &

[27]:
Output

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

[28]:

gtgttogtGtbarall =
 ComputeMatrixElement[{-F[8], -F[8]} -> {-F[8], -F[11]}] +
    ComputeMatrixElement[{F[8], -F[8]} -> {F[8], -F[11]}] +
    ComputeMatrixElement[{-F[8],
       F[8]} -> {F[8], -F[11]}] /. {AUTstatspart[___] -> 1,
    AUThast[___] -> 1,kappa->\[Kappa],g3->Subscript[g, 3]} // Simplify

[28]:
Output

Compute the thermal masses#

We can compute all of them

[30]:

AllMasses/.{kappa->\[Kappa],g3->Subscript[g, 3],g2->Subscript[g, 2],g1->Subscript[g, 1],ht->Subscript[h, t]}

Dynamic[Computing the thermal mass for particle <>

      ToString[AutoTherm`Private`part$25871]]

[30]:
Output

Or compute them one by one

[29]:

ThermalMass[F[1]]/.{kappa->\[Kappa],g3->Subscript[g, 3],g2->Subscript[g, 2],g1->Subscript[g, 1],ht->Subscript[h, t]}

[29]:
Output