# Higgs to gluon gluon vertex

Dear Calchep authors,

I'd like to ask about the higgs coupling to gluon gluon at func3.mdl,
LmbdGG : did you use here the Higgs effective field theory (heft) model ?
where the coupling defined by the approximation:

g_hgg = alpha_s/3* pi*vev (1 + 7/30 tau + 2/21 tau^2 + 26/525 tau^3 + ..), tau = m_h^2/4m_t^2,

but I try to understand the syntax of LmbdGG, it's not like this definition ..
Also there are some symbols I can't get like :

cabs (HggF((Mh/2/Mcp)^2)*Cq

What is cabs, HggF and why Mcp is here ?

Thanks,
Safinaz

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Alexander Pukhov
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 Revision history for this message Alexander Pukhov (pukhov) said on 2014-01-09: #1

LmbdGG indeed is an effective coupling of higgs-gluon-gluon interaction.
All details are explained in e-Print: arXiv:1207.6082.
We include contribution of t, b,c loops. Arguments of Passarino-Veltman function HggF is Mh/2/Mqp where Mqp is a pole mass of quark. In particular Mcp - is a pole mass of c-quark.
If 2*Mqp< Mh then loop calculation gives a complex number. We assume that this number will be multiplied on conjugated one. Thus we replace complex coupling on its absolute value. The cabs() function is used for it.

Alexander Pukhov

 Revision history for this message Safinaz (sramadan) said on 2014-01-10: #2

Thanks Alexander Pukhov, that solved my question.

 Revision history for this message Safinaz (sramadan) said on 2014-01-11: #3

Hi sir,

Do you think that one can use the same formulas for another heavier scalar for Sgg effective coupling with MS >> 2Mtop ?

When I returned to the manual and the Refs at it I found the effective coupling of hgg derived at the low energy theorem
where the Higgs scalar is too light or the propagator is too heavy ..

So if this effective coupling is for light scalars , how can heavy scalars couple to gluon gluon effectively ?

Regards,
Safinaz

 Revision history for this message Alexander Pukhov (pukhov) said on 2014-01-12: #4

The leading term of H->gg is presented without approximations. But loop corrections are indeed presented in the limit of large virtual mass in loop diagram. I am not shure that there are other formulas for generic model with needed precision (NNLO). Say, Hdecay uses the same formulas for heavy higgs decay. It is a good question what is precision of this apprach. I don't know. I

From the other side I have a filling that results obtained by simple formulas are reasonable taking into account that H->gg mode is not a very good one for Higgs detection.

 Revision history for this message Safinaz (sramadan) said on 2014-01-12: #5

All right, thanks.
Safinaz