CalcHEP

Discrepancy in evaluating fermion annihilation to Z pair via Higgs

Asked by N_

In order to compute some annihilation processes for some generic fermions, I wanted to compare my analytical derivation of the squared matrix element for a fermion annihilation into two Z bosons, mediated by a Higgs, with the result from CalcHEP. To keep things concise, I referred to the fermion-fermion-Higgs coupling as Bffh and the Higgs-ZZ as Ghzz in the input Lagrangian. The expression are very similar:

(CalcHEP) = Bffh^2 Ghzz^2 (s-4 m_f ^2) (Mh^4 + 12 MZ^4 -4 Mz^2 s) / [ 16 MZ^4 (s-Mh^2)^2 ]

(Analytical) = Bffh^2 Ghzz^2 (s-4 m_f ^2) (s^2 + 12 MZ^4 -4 Mz^2 s) / [ 16 MZ^4 (s-Mh^2)^2 ]

with the only difference of the Mandelstam s^2 in my derivation turning into a Mh^4.
With analogy to the HZZ decay derived in this (http://www.hep.lu.se/atlas/thesis/egede/thesis-node15.html), I suspected that something went wrong with substituting in the 4-momentum squared of the propagator after reducing the sum over polarization states (in the decay example, the propagator has total momentum squared q^2=mH ^2, which transposed to my situation would become an off-shell propagator momentum squared, which is just s).

What can I do to reconcile the two approaches? Thank you in advance.

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Alexander Pukhov
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Best Alexander Pukhov (pukhov) said : 		#1

I guess using unitary gauge in CalcHEP ("Force Unitary Gauge ON" in
menu) you will get agreement with your "Analitical" expression.

Really your "Analitical" breaks unitarity because Higgs resonance
produces only s-wave amplitude. But ZZ production via t-channel
diagram in Unitary gauge also breaks unitarity. Unitarity should
be restored after sum over all diagrams.

By default CalcHEP uses t'Hooft-Feynman gauge where each squared diagram
have unitarity behavior. But in this case squared diagram can give
negative contribution because Feynman gauge means summation other
states with negative norm.

Best
    Alexander Pukhov

On 08/24/2017 05:23 PM, N_ wrote:
> New question #656858 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/656858
>
> In order to compute some annihilation processes for some generic fermions, I wanted to compare my analytical derivation of the squared matrix element for a fermion annihilation into two Z bosons, mediated by a Higgs, with the result from CalcHEP. To keep things concise, I referred to the fermion-fermion-Higgs coupling as Bffh and the Higgs-ZZ as Ghzz in the input Lagrangian. The expression are very similar:
>
> (CalcHEP) = Bffh^2 Ghzz^2 (s-4 m_f ^2) (Mh^4 + 12 MZ^4 -4 Mz^2 s) / [ 16 MZ^4 (s-Mh^2)^2 ]
>
> (Analytical) = Bffh^2 Ghzz^2 (s-4 m_f ^2) (s^2 + 12 MZ^4 -4 Mz^2 s) / [ 16 MZ^4 (s-Mh^2)^2 ]
>
> with the only difference of the Mandelstam s^2 in my derivation turning into a Mh^4.
> With analogy to the HZZ decay derived in this (http://www.hep.lu.se/atlas/thesis/egede/thesis-node15.html), I suspected that something went wrong with substituting in the 4-momentum squared of the propagator after reducing the sum over polarization states (in the decay example, the propagator has total momentum squared q^2=mH ^2, which transposed to my situation would become an off-shell propagator momentum squared, which is just s^2).
>
> What can I do to reconcile the two approaches? Thank you in advance.
>

Revision history for this message
N_ (eigen) said : 		#2

Thanks Alexander Pukhov, that solved my question.