How come two protons create top-antitop quark pair? (A question regarding CERN courier May 2016)

Question

I am not very well versed in particle physics lingo but as much as I know $p$ stands for proton and $t$ stands for top-quark. Then, how could this be possible?

I hope I am wrong about what is written since that would mean,

$$\text{proton} + \text{proton}\quad\rightarrow\quad \text{top-quark} + \text{anti-top-quark}$$

because this is certainly wrong since it violates baryon number conservation (and so many other rules I studied in particle physics course). In fact I can not see any sanity in any of the equations proposed. So definitely I am wrong. But then what these mean. I believe someone here can enlighten me.

PS: I found this in CERN courier magazine, issue May, 2016. The article was appropriately titled "At the heart of every LHC collision".

Answer 1

The notation $pp \rightarrow t\bar{t}$ doesn't literally mean the two protons disappear leaving just a top and antitop. It means a top and antitop are created as well as a shower of other debris.

Because protons are composite objects a 13TeV proton-proton collision is an exceedingly messy business. At that energy the quarks are resolved so it's really a quark-quark collision with the other contents of the proton more or less involved. As the reaction products leave the site of the collision the QCD binding energy produces a whole mess of particles. The dominant process for top-antitop production of the LHC is from two gluons i.e. $gg \rightarrow t\bar{t}$.

The calculation of the $pp \rightarrow t\bar{t}$ probability is the probability that the debris includes a top-antitop pair. Likewise for the other reactions listed on that page.