g g -> e+e-mu+mu-

Antoine Laureys

Centre for Cosmology, Particle Physics and Phenomenology (CP3)
Université Catholique de Louvain
Chemin du Cyclotron 2
1348 Louvain-La-Neuve, Belgium

mail : antoine.laureys@uclouvain.be
Last modification : 2012-10-17

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$\underline{gg~ $\rightarrow h^0 $ \rightarrow (Z^0\slash \gamma^) (Z^0\slash \gamma^) \rightarrow e^+ e^- \mu^+ \mu^-}$

This code¹ is a MadGraph standalone code based on MadLoop5.

Unweighted events can be generated for

$\rm a\)~~\sigma_{\rm B+i+S}^{\rm LO} = |\cal{M}$_{\rm{cont}}|^2 + 2\rm{Re}$\cal{M}_{\rm{cont}}^*\cal{M}_{\rm{S}}$ + |\cal{M}$_{\rm{S}}|^2$}$

as well as for

$\rm b\)~~ \sigma_{\rm B+i}^{\rm LO} = |\cal{M}$_{\rm{cont}}|^2 + 2\rm{Re}$\cal{M}_{\rm{cont}}^*\cal{M}_{\rm{S}}$$$

with the full heavy quark mass dependence at one loop. Results obtained for a) are equivalent to those of MCFM as the calculation contains the same elements.

The code and the events for B+i (case b), on the other hand, can be used to be combined with the full NLO calculation of the signal in the ADDITIVE SCHEME. In other words, let's define

$\sigma^{\rm NLO}_{\rm S},$

the cross section (and the events) at NLO accuracy via the MC@NLO method. They can be generated via the latest MC@NLOv4.09 i.e. with the FULL TOP AND BOTTOM MASS DEPENDENCE UP TO TWO LOOPS (in the virtuals) and ONE LOOP in the real contributions. This is the implementation of references arXiv:hep-ph/0611266 and arXiv:0709.4227 in the MC@NLO framework.

RUNNING THE CODES SEPARATELY for $\rm \sigma_{\rm B+i}^{\rm LO}$ on one hand and $\sigma^{\rm NLO}_{\rm S}$ on the other hand, with the same input parameters and by combining the events afterwards, allows you to generate events for the full gluon induced Z boson pair production process with the Higgs signal at NLO in the additive scheme :

$$\sigma$_{\rm B+i}^{\rm LO}$ + \sigma$_{\rm S}^{\rm NLO}$ = $\vert\cal{M}$_{\rm{cont}}\vert^2 + $2$\rm{Re}$$\cal{M}_{\rm cont}^*\cal{M}_{\rm S }$$ + \sigma^{\rm NLO}_{\rm S}$ .

As an illustration we show, on the figure below, the invariant mass distribution of the four final leptons. We compare the full LO result (blue) from MadGraph for ${\color[rgb]{0.000000,0.000000,1.000000}\sigma_{\rm B+i+S}^{\rm LO}}$ with the analogue distribution where the signal is computed at NLO (red), ${\color[rgb]{1.000000,0.000000,0.000000}\sigma_{\rm B+i}^{\rm LO} + \sigma_{\rm S}^{\rm NLO}~}$ . In addition, the black curve shows the same distribution where the interference is neglected, i.e.

$\sigma_{\rm B}^{\rm LO}+\sigma_{\rm S}^{\rm NLO}},~ \rm where~ \sigma_{\rm B}^{\rm LO} = |\cal{M}$_{\rm{cont}}|^2$ .

¹This code necessitates gfortran v4.6