Can two colliding photons create a Higgs Boson? The LHC discovered the Higgs using the following decay mode:
$$ H^0 \rightarrow \gamma \gamma $$
This got me thinking: if we reverse this mode, will it be valid? In some annihilation/decay pairs, these will stay valid:  
$$e^+e^- \rightarrow \gamma\gamma$$
$$\gamma\gamma \rightarrow e^+e^-$$
So if the Higgs will decay into two high energy photons, will the annihilation of two high energy photons create a Higgs by this mode?:
$$ \gamma \gamma \rightarrow H^0 $$
 A: In principle, yes. You can reverse any decay process and the corresponding synthesis will be valid - in this case, since $H_0\to\gamma\gamma$ happens, then $\gamma\gamma\to H_0$ will also happen, assuming the kinematics work out.
However, the corresponding probability is very small. Out of all the possible things that could happen when two photons cross paths, turning into a Higgs boson is a relatively unlikely one. In fact, by far the most common option is nothing, because photons don't directly interact with each other. In order to get an interaction, you need one of the photons to quantum-fluctuate into a pair of charged particles, so that the other photon can interact with one of them - this makes it a second-order interaction at best. And Higgs production is even more unlikely because photons don't interact with the Higgs either, so you need another fluctuation to go from the charged particles to the Higgs boson. All the Feynman diagrams are third-order or higher, which makes for a very unlikely process indeed.
