# How to estimate this cross section

• I
Hi all,

Do any has an idea how to give a rough estimation for this process's cross section:

g g -> H -> h h, (h -> b b~), ( h -> b b~) ?

where h is SM Higgs and H is a heavy Higgs boson with BR (H > hh) ~ Gamma (H > hh) ~ 10^-3 GeV and sigma (g g > H ) ~ 10 pb ..

When I calculated it by cross section calculator like MadGraph (https://launchpad.net/mg5amcnlo) it gives sigma ~ 0.2 pb, also sigma (g g -> H -> h h) ~ 10^-1 pb, but I don't understand how these values calculated ..

Note that MG doesn't use Narrow width approximation , i.e., sigma (g g -> H -> h h, (h -> b b~), ( h -> b b~)) not equivalent to sigma (g g -> H -> h h) BR (h -> b b~) BR ( h -> b b~)

## Answers and Replies

ChrisVer
Gold Member
Note that MG doesn't use Narrow width approximation , i.e., sigma (g g -> H -> h h, (h -> b b~), ( h -> b b~)) not equivalent to sigma (g g -> H -> h h) BR (h -> b b~) BR ( h -> b b~)

how so?
I mean the above decomposition seems natural as long as the production of the h's does not somehow affect their decay...
however I can't answer your main question; i mean I don't quiet know how MadGraph works (on which theoretical basis)...

mfb
Mentor
Note that MG doesn't use Narrow width approximation , i.e., sigma (g g -> H -> h h, (h -> b b~), ( h -> b b~)) not equivalent to sigma (g g -> H -> h h) BR (h -> b b~) BR ( h -> b b~)
That would surprise me. The SM Higgs has a decay width of just a few MeV. The off-shell contribution is not completely negligible, but experimentally if you look for the decay to two b-jets you cut away this contribution anyway. The H can have a much larger width but the 125 GeV Higgs decays should be independent of its production.
When I calculated it by cross section calculator like MadGraph (https://launchpad.net/mg5amcnlo) it gives sigma ~ 0.2 pb, also sigma (g g -> H -> h h) ~ 10^-1 pb
The first is a subset of the second, it cannot have a cross section twice as large.