CO D EX TUTORIAL

Model Examples

A. Examples with single BSM fieldB. Examples with multiple BSM fields

This page acts as a database of results obtained by CoDEx for a portfolio of representative models. The intension is to simultaneously showcase the range of functionality of CoDEx, as well as guide the user to successfully apply CoDEx to their own model.

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A. Examples with single BSM field

1) Electro-weak SU(2)L Real Singlet Scalar

Field Definitions:
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Build the Lagrangian:
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Lagrangian:

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Initialize generators:
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Wilson Coefficients in "Warsaw" basis:
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Wilson Coefficients in "SILH" basis:
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2) Electro-weak SU(2)L Real Triplet Scalar (Y=0)

Field Definitions:
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Build the Lagrangian:
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Lagrangian:

L superset 2 kappa H^|tau^aH Phi^a -eta Phi^a Phi^a TemplateBox[{H}, Abs]^2 -1/4lambda (Phi^a Phi^a)^2

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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

Wilson Coefficients in "Warsaw" basis:
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Wilson Coefficients in "SILH" basis:
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3) Electro-weak SU(2)L Complex Triplet Scalar (Y=1)

AKA Type-II seesaw.

Field Definitions:
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Build the Lagrangian:
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Now, if

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and,

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Then the Lagrangian:

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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

Wilson Coefficients in "Warsaw" basis:
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Wilson Coefficients in "SILH" basis:
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There's one dimension 5 operator as well::
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4) Electro-weak SU(2)L Quartet Scalar (Y=)

Field Definitions:
In[2]:=
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Build the Lagrangian:
In[3]:=
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Out[3]=
In[4]:=
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In[5]:=
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Out[5]=
In[13]:=
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Now, the Lagrangian is:

In[15]:=
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Initialize generators:
In[7]:=
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Check the documentation page CoDExParafernalia for details.

Wilson Coefficients in "Warsaw" basis:
In[12]:=
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Out[14]=
Wilson Coefficients in "SILH" basis:
In[10]:=
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Out[11]=

5) SU(2)L -singlet Heavy Right-handed neutrino

AKA Type-I seesaw.

Field Definitions:
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Build the Lagrangian:
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Thus, the Lagrangian is:

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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

There's one dimension 5 operator:
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The extra prompt in the output above tells you that there's no point searching for Wilson coefficients in any dim. 6 operator basis.

6) SU(2)L Real triplet Heavy fermion (Y = 0)

AKA Type-III seesaw.

Field Definitions:
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Build the Lagrangian:
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In[20]:=
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In[21]:=
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In[22]:=
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Out[22]=
Thus, the Lagrangian is:

In[23]:=
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Initialize generators:
In[24]:=
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Results:
In[13]:=
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Out[13]=
In[14]:=
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Out[14]=

7) 2HDM

Field Definitions:
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Build the Lagrangian:
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Lagrangian:

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Initialize generators:
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Results:
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(Local2) In[15]:=
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(Local2) Out[15]=

8) Exotic SU(2) gauge boson

Field Definitions:
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Build the Lagrangian:
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Lagrangian:

where,

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Initialize generators:
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Results:
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U(1)

Field Definitions:
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Build the Lagrangian:
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Lagrangian:

where,

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Initialize generators:
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Results:
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B. Examples with multiple BSM fields

Field Definitions:
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Build the Lagrangian:
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Here, the Lagrangian is:

where,

,

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,

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and

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Thus,
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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

Results:
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Field Definitions:
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Build the Lagrangian:
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Here, the Lagrangian is:

where,

Singlet part:

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Triplet part:

L_3 superset 2 kappa H^|tau^aH Phi^a -eta Phi^a Phi^a TemplateBox[{H}, Abs]^2 -1/4lambda_Phi (Phi^a Phi^a)^2

(Local2) In[6]:=
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and interaction part:

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Thus,
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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

Results:
(Local2) In[11]:=
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(Local2) In[15]:=
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(Local2) Out[15]=
(Local2) In[12]:=
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(Local2) In[14]:=
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(Local2) Out[14]=

Field Definitions:
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Build the Lagrangian:
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Here, the Lagrangian is:

where,

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Initialize generators:
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Check the documentation page CoDExParafernalia for details.

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Results:
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(Local2) In[14]:=
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