Some speculation here:
http://www.youtube.com/watch?v=_NMqPT6oKJ8
Is there a possibility it would pass 'undetected' through your hand, or is it certain death?
Can you conclude it to be vital, or only loose your hand?
Would it simply make a small cylindrical hole through your hand, or is there some sort of explosion-effect?
Assume your hand has a cross section of 50cm², and a thickness of 2cm, how much of the beam's energy would be transferred to your hand?
Answer
A mis-steered beam at CEBAF simply cut a hole thought the niobium wall of the cavity and flooded half the accelerator with helium (super-conducting cavities need a liquid helium jacket to work...).
We were down for more than a week.
That is an electron beam machine, and very high current (up to $400\,\mathrm{\mu A}$!), so the details would be rather different than the LHC beam.
Likewise, about $60\,\mathrm{\mu A}$ of $5.5 \,\mathrm{GeV}$ beams from that machine partially melted one of my iron targets (thick enough that about 6% of the beam interacted with the target) despite a raster spreading the beam over roughly $2\,\mathrm{mm}^2$, because we didn't have good enough thermal contact with the water-cooled frame of the target ladder.
High energy, high current beams can carry a lot of power.
Back to the question as asked:
Treat your hand as water. The particle data booklet puts the energy loss per proton at around $2.5\,\mathrm{MeV/g/cm}^2$ or something like $4$–$8\,\mathrm{MeV}$ though your hand, depending on how chubby you are. (We're only a few orders of magnitude above the minimum ionization energy, so this is not very sensitive to the actual beam energy.)
Phillip says $1.2 \times 10^{11}$ protons per beam in the ring, about 11,000 passes per second ($3.0 \times 10^8\,\mathrm{m/s} / 27\,\mathrm{km}$), so $1.3 \times 10^{15}$ protons per second is $8 \times 10^{15}\,\mathrm{MeV/s} = 1300\,\mathrm{J/s}$ is a fair bit of heat, and results in heating of about $300\,\text{K/s/(cubic cm exposed)}$. To finish up here we will have to know something about the beam diameter.
Your reflex time to move your hand is on order of $0.1$–$0.2$ seconds.
It's going to hurt: you will get badly burned, and the damage will extend though the whole depth of the exposed flesh, rather than being limited to the surface as with the contact burns we are all familiar with.
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