There are probably only three generations of matter. Why is this? How do we know? That would happen if there was a fourth generation? The Z boson holds the answers!

Plot taken from http://pdg.lbl.gov/2012/reviews/rpp2012-rev-cross-section-plots.pdf

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Does this mean that other generations of matter can’t have other than nonzero lifetime?

Is there a constraint on energy level (amount of energy) that particle can obtain? (e.g. photon)

And thank you for your short lectures!

Hi Adrii, good questions! If a fourth (and possibly higher generations) exist then all of the particles in those generations would have finite lifetimes. The neutrino mass for a fourth generation would need to be above 45GeV according to the LEP measurements (and above 62GeV now that we have seen what we think is the Higgs boson.) This is more than enough mass to decay to lower generations, resulting in a finite lifetime. Similarly the other particles (charged lepton, quarks) would have enough mass to decay to the lower generations. It’s interesting to note that there is no particular reason to associate the “1st” generation of leptons (electron, electron neutrino) with the 1st genration of quarks (up, down), so perhaps the ordering of the generations is more complicated than we think. Even so, this does not change the limits on the masses of a heavier neutrino and its finite lifetime.

When it comes to energy of a photon (and this is an excellent example to take!) we need to consider the wavelength, since that does have limits. The shortest wavelength a photon can have is roughly equal to the Planck wavelength, and the longest wavelength it can have is roughly the width of the visible universe. We can then get the energies by using the relation E = hbar/lambda, where lambda is the wavelength in natural units. It turns out the limits on the energy are very very low for the low limit, and very very high for the high limit. Practically we can ignore these limits, but in principle they prevent some infra red and ultra violet divergences from creating infinities in some of our equations. There are some consequences for general relativity coming from very high energy densities as well, but I forget the details! I think it’s possible to create a photon of sufficiently high energy that it warps the space time around it to form a mini black hole, but I could be wrong there. The details are very subtle.