symbolic calculation in different gauges not agreed for SM

  Send me model files obtained by FeynRules.

First of all I'll try to confirm your message about problem with gauge
invariance.

<email address hidden>

Best

    Alexander Pukhov

On 13.09.2019 22:52, Yong Du wrote:
> New question #683906 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/683906
>
> Hi,
>
> Let me briefly explain what I have done:
> 1. I first used the built-in SM to calculate W+ W+ -> W+ W+ in both the Feynman and the unitary gauges, and output the results in REDUCE code.
> 2. I then called the cmp.red file and found these two results agreed.
> 3. I then used the built-in SM.fr file of FeynRules and generated the CalcHEP model file, and put it in CalcHEP to calculate the same process mentioned above in the two gauges, but they do not agree (I even substituted all independent variables by hand inside the cmp.red file.)
>
> This is very strange... Any suggestions? I could provide some files if needed.
>
> FYI: I'm using CalcHEP3.7.5, FeynRules 2.3.34 and REDUCE with revision number 4956.
>
> Thanks in advance!
> Yong
>

  Terms with ghost fields are absent in your Lagrangian. I mean Z.c,
Z.C, Z.f  plus  the same  for W. Please look how they appear in  default
SM included in the distribution.

Thus  Feynman gauge gives wrong result.  Results obtained in Unitary
gauge look fine. In particular cross section W+,W-->Z,Z is a constant at
large energies.

When you'll improve your Lagrangian, please note, that your need
substitutions like

MW:=MZ*cw;
vev:=2*MW*sw/EE;
x20x0:=1/sw^2;
x17x0:=vev/sw^2;
x19x0:=-cw/sw;
let sw2=sw^2;
let cw^2=1-sw^2;

to see gauge invariance.

Best

     Alexander Pukhov

On 14.09.2019 23:27, Alexander Pukhov wrote:
> Question #683906 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/683906
>
> Status: Open => Answered
>
> Alexander Pukhov proposed the following answer:
>  Send me model files obtained by FeynRules.
>
> First of all I'll try to confirm your message about problem with gauge
> invariance.
>
> <email address hidden>
>
> Best
>
>    Alexander Pukhov
>
>
> On 13.09.2019 22:52, Yong Du wrote:
>> New question #683906 on CalcHEP:
>> https://answers.launchpad.net/calchep/+question/683906
>>
>> Hi,
>>
>> Let me briefly explain what I have done:
>> 1. I first used the built-in SM to calculate W+ W+ -> W+ W+ in both the Feynman and the unitary gauges, and output the results in REDUCE code.
>> 2. I then called the cmp.red file and found these two results agreed.
>> 3. I then used the built-in SM.fr file of FeynRules and generated the CalcHEP model file, and put it in CalcHEP to calculate the same process mentioned above in the two gauges, but they do not agree (I even substituted all independent variables by hand inside the cmp.red file.)
>>
>> This is very strange... Any suggestions? I could provide some files if needed.
>>
>> FYI: I'm using CalcHEP3.7.5, FeynRules 2.3.34 and REDUCE with revision number 4956.
>>
>> Thanks in advance!
>> Yong
>>

Hi Alexander,

Thank you for the checking. You are right, the ghosts are not there in the SM model file I previously generated because I used Feynman gauge while generating the CalcHEP model file using the SM model file of FeynRules. But since we are working at tree level, ghosts shall not matter in any sense, so I suppose the absence of ghosts shall not affect the final result. Do you agree?

Actually I do regenerate the SM model file which has the ghosts, but again I see the disagreement between Feynman gauge and Unitary gauge (I do make the replacements you mentioned in your post). Could you double check? I will send you the new model file via email.

Thanks and best,
Yong

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

I do not know what's wrong with the SM generated by suing the SM.fr from FeynRules, but I'm able to obtain gauge invariant results for my own model in the end. Also checked with hand-calculated results, and everything looks good.

So I will close this post and thank Alexander for all the useful discussion.

Best,
Yong

Dear Yong,
thank you for confirming this.

What do you mean under "your own model"?
Regards,
Alexander Belyaev

Dear Alexander,

By "my own model", I mean the real triplet model that I'm currently working on. I did not start from FeynRules for that, instead, I wrote my own CalcHEP model files. And I checked gauge invariance, also cross checked symbolic calculations between CalcHEP's built-in symbolic calculator and REDUCE's symbolic calculation. Everything looks good on my side for the real triplet model.

Best,
Yong

Sorry to respond late. Have you tried checking gauge invariance of the result numerically in CalcHEP? That is, is the problem only in the reduce output? Or, is the problem also in the numerical results produced by CalcHEP. We checked this very carefully long ago. We did not check the reduce code. We only checked the numerical results in both gauges and got agreement for this process and every other of the SM.

Hi Neil,

Thanks for the comment.

I did check numerically and the results in different gauges disagree. I did try several different ways in the past to cross check, but always got results that did not agree with each other (both symbolically and numerically).

I knew and also appreciated the cross checks you and your collaborators did for SM, that's why I was so surprised at the beginning. Not sure if this issue is only related to the latest version of the program though.

Best,
Yong

Dear Yong,

I see,

if the results in two gauges agree, this is a very good sign.

Not sure what the problem was in FR.

You could cross check your model in LanHEP to identify the problem.

Regards,

Alexander

On 01/10/2019 15:22, Yong Du wrote:
> Question #683906 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/683906
>
> Yong Du posted a new comment:
> Dear Alexander,
>
> By "my own model", I mean the real triplet model that I'm currently
> working on. I did not start from FeynRules for that, instead, I wrote my
> own CalcHEP model files. And I checked gauge invariance, also cross
> checked symbolic calculations between CalcHEP's built-in symbolic
> calculator and REDUCE's symbolic calculation. Everything looks good on
> my side for the real triplet model.
>
> Best,
> Yong
>
--
______________________________________________________________________
Prof. Alexander S Belyaev (<email address hidden>)
https://www.hep.phys.soton.ac.uk/content/alexander-belyaev

School of Physics & Astronomy, University of Southampton
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.....................................................................
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.....................................................................
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______________________________________________________________________

Hi Yong,

Could you send your Mathematica notebook that generates the CH files from the FR files to me (<email address hidden>).

To answer your earlier question, you do need ghosts in CH, even at tree level.

Best!
Neil