Incorrect kinetic term for a guage boson particle

Propagator is inverted quadratic term of Lagrangian.  But
F_{munu}F^{munu} can not be inverted because it has a zero mode caused
by gauge invariance.

As usual one has to add gauge fixing terms. Look how it is done in SM

%=== for SU(3)
*lterm  -1/2*(deriv*G)**2.*
lterm -i*GG*f_SU3*ccghost(G)*G^mu*deriv^mu*ghost(G).

%=== for SU(2)*U(1)

do_if gauge_fixing==Feynman.

*lterm  -1/2*(deriv*A)**2
-1/2*(2*(deriv*'W+'+vevh*g2/2*'W+.f')*(deriv*'W-'+vevh*g2/2*'W-.f')
+(deriv*Z+ vevh*g2/2/CW*'Z.f')**2).**
*
lterm -g2*eps*deriv*Gh*gh*W.

lterm vevh*g2**2/4*(-h*('W-.C'*'W+.c' + 'W+.C'*'W-.c' +
'Z.C'*'Z.c'/CW**2)  +i*'Z.f'*('W-.C'*'W+.c' - 'W+.C'*'W-.c') ).

lterm -i*g2**2*vevh/4/CW*(
         'W+.f'*('W-.C'*'Z.c'*(1-2*SW**2)+'W-.c'*'Z.C' +
2*CW*SW*'W-.C'*'A.c')
       - 'W-.f'*('W+.C'*'Z.c'*(1-2*SW**2)+'W+.c'*'Z.C' +
2*CW*SW*'W+.C'*'A.c')
                     ).
end_if.

It seems, in the unitary gauge you'll not meet this problem.

Best

    Alexander Pukhov

On 8/13/21 1:25 AM, Vishnu Padmanabhan Kovilakam wrote:
> New question #698355 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/698355
>
> Hello!
>
> I am implementing a model (which contains an additional gauge boson) in lanhep. I got an error in Masses.chk file as follows:
>
> !-----------------------------------------------------------------
> Incorrect kinetic term for particle Zd/Zd :
> (-1)*p1**2+(+1)*p1^mu*p1^nu
> !-----------------------------------------------------------------
>
> the corresponding "lterm" is given below
>
> !-----------------------------------------------------------------
> lterm -F**2/4 where
> F=deriv^mu*Zd^nu-deriv^nu*Zd^mu.
> !-----------------------------------------------------------------
>
> here Zd is the additional gauge boson.
>
> Could you please tell me what is the problem here? I am also encountering the same error for the photon field also.
>
> Thanks in advance,
> Regards,
>
> Vishnu
>
>
>

Dear Dr. Pukhov,

Thanks for your prompt reply and clarification. I forget to mention that I was actually working in the unitary gauge (by choosing " keys gauge_fixing = unitary."), and still, lanhep was showing this warning.

Thanks once again,

Regards,

Vishnu

Dear Dr. Pukhov,

Thanks for your clarification. That's indeed the case.

Thanks once again,

Regards,

Vishnu

Thanks Alexander Pukhov, that solved my question.