# Trilinear Higgs self coupling

Hello Sir
i want to work on cross section as a function Trilinear Higgs self coupling (ghhh/ghhh^sm ). unfortunately i did seen this variable in calchep. sir guide me how i work on it in type 1 2hdm for the process of e1,E1->h,h,n1,N1 and e1,E1->Z,h,h at 3TeV of CM energy.

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Alexander Pukhov
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 Revision history for this message Alexander Pukhov (pukhov) said on 2021-06-20: #1

Trilinear Higgs self coupling indeed can be responsible for importing cosmological effects. But in the SM it is not a free parameter. In general measuring this coupling people try to find deviation from the SM. So, the best way is to replace SM on another one where this coupling is a free parameter or just different form SM one.

Also you can find h|h|h vertex

h    |h    |h    | |-3*EE*Mh^2/(2*MW*SW)                              |1

and replace SM coupling -3*EE*Mh^2/(2*MW*SW) on some parameter defined as a new variable of the model. Such trick will lead to breaking of gauge invarience.

Best
Alexander Pukhov

On 6/20/21 8:15 PM, Muhammad Aamir wrote:
> New question #697634 on CalcHEP:
>
> Hello Sir
> i want to work on cross section as a function Trilinear Higgs self coupling (ghhh/ghhh^sm ). unfortunately i did seen this variable in calchep. sir guide me how i work on it in type 1 2hdm for the process of e1,E1->h,h,n1,N1 and e1,E1->Z,h,h at 3TeV of CM energy.
>

 Revision history for this message Muhammad Aamir (muhammad-aamir) said on 2021-06-21: #2

Thanks for your quick response sir.
Sir I tried every possible way to add coupling in constraints and
variables. Can you add this variable for me in type 1 2hdm if i mail you
all files of type1 2hdm.

On Sun, Jun 20, 2021, 11:25 PM Alexander Pukhov <

> Your question #697634 on CalcHEP changed:
>
>
> Alexander Pukhov proposed the following answer:
> Trilinear Higgs self coupling indeed can be responsible for importing
> cosmological effects. But in the SM it is not a free parameter. In
> general measuring this coupling people try to find deviation from the
> SM. So, the best way is to replace SM on another one where this coupling
> is a free parameter or just different form SM one.
>
> Also you can find h|h|h vertex
>
> h |h |h | |-3*EE*Mh^2/(2*MW*SW) |1
>
> and replace SM coupling -3*EE*Mh^2/(2*MW*SW) on some parameter
> defined as a new variable of the model. Such trick will lead to
> breaking of gauge invarience.
>
> Best
> Alexander Pukhov
>
>
>
> On 6/20/21 8:15 PM, Muhammad Aamir wrote:
> > New question #697634 on CalcHEP:
> >
> > Hello Sir
> > i want to work on cross section as a function Trilinear Higgs self
> coupling (ghhh/ghhh^sm ). unfortunately i did seen this variable in
> calchep. sir guide me how i work on it in type 1 2hdm for the process of
> e1,E1->h,h,n1,N1 and e1,E1->Z,h,h at 3TeV of CM energy.
> >
>
> --
> know that it is solved:
>
> If you still need help, you can reply to this email or go to the
> following page to enter your feedback:
>
>

 Revision history for this message Alexander Pukhov (pukhov) said on 2021-06-21: #3

I can improve your model but can not be responsible for model
self-consictensy .

I general I do not expect problems from your side in model modification.
Say, for SM  we have  in  lgrng1.mdl

Z.f  |Z.f  |h    | |-EE*Mh^2/(2*MW*SW)      |1
h    |h    |h    |     |-3*EE*Mh^2/(2*MW*SW)    |1
A    |A    |W+   |W-   |-EE^2 |2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3

You need correction in the second line  should be

Z.f  |Z.f  |h    | |-EE*Mh^2/(2*MW*SW)      |1
h    |h    |h    |     | newh3                  |1
A    |A    |W+   |W-   |-EE^2 |2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3

Also you have to add to  file vars1.mdl  definition of newh3 parameter

Name   | Value       |> Comment                                   <|
newh3 |0.1          | h^3 coupling

But one has to pay attention on the following point, the [Z.f  |Z.f  |h]
vertex has the same source h^3. Indeed Higgs  doublet contains

vev/sqrt(2) +h -i*Z.f  where Z.f is goldstone.

Best

Alexander Pukhov

On 6/21/21 4:41 AM, Muhammad Aamir wrote:
> Question #697634 on CalcHEP changed:
>
>
> Muhammad Aamir is still having a problem:
> Thanks for your quick response sir.
> Sir I tried every possible way to add coupling in constraints and
> variables. Can you add this variable for me in type 1 2hdm if i mail you
> all files of type1 2hdm.
>
> On Sun, Jun 20, 2021, 11:25 PM Alexander Pukhov <
>
>> Your question #697634 on CalcHEP changed:
>>
>>
>> Alexander Pukhov proposed the following answer:
>> Trilinear Higgs self coupling indeed can be responsible for importing
>> cosmological effects. But in the SM it is not a free parameter. In
>> general measuring this coupling people try to find deviation from the
>> SM. So, the best way is to replace SM on another one where this coupling
>> is a free parameter or just different form SM one.
>>
>> Also you can find h|h|h vertex
>>
>> h |h |h | |-3*EE*Mh^2/(2*MW*SW) |1
>>
>> and replace SM coupling -3*EE*Mh^2/(2*MW*SW) on some parameter
>> defined as a new variable of the model. Such trick will lead to
>> breaking of gauge invarience.
>>
>> Best
>> Alexander Pukhov
>>
>>
>>
>> On 6/20/21 8:15 PM, Muhammad Aamir wrote:
>>> New question #697634 on CalcHEP:
>>>
>>> Hello Sir
>>> i want to work on cross section as a function Trilinear Higgs self
>> coupling (ghhh/ghhh^sm ). unfortunately i did seen this variable in
>> calchep. sir guide me how i work on it in type 1 2hdm for the process of
>> e1,E1->h,h,n1,N1 and e1,E1->Z,h,h at 3TeV of CM energy.
>> --
>> know that it is solved:
>>
>> If you still need help, you can reply to this email or go to the
>> following page to enter your feedback: