Infinities in nature 2: SUSY, Squarks and Sleptons are the answer!

David Bailin, my former tutor at Sussex University, left some detailed comments on my article on the idea that there are infinities in nature. His comments deserve a wider audience, particularly Part 2 on super symmetry and the Higgs. So here they are:

The infinity in QED, and other quantum field theories, derives from a short-distance cut-off which should be zero, IF there is no new physics at all. We know that QED does not include quantum gravitational effects, and the electron surely interacts with gravity. So at the very least there should be a cut-off at the Planck length, corresponding to an energy scale of 10^{19} GeV. The observed (finite) mass is then the sum of the bare mass and the finite quantum radiative correction, so evidently the bare mass is finite too. I share your (and Dirac’s) view that infinity in a phsical theory is a sign that something is wrong, i.e. that there is other relevant, generally new, physics.

Further, the radiative correction to the electron’s mass, and in general any fermion’s, depends only logarithmically on the cut-off. Even if the cut-off is as large as the Planck scale, the radiative correction is of the same order of magnitude as the observed mass, and so, therefore, is the bare mass.

Now suppose that the Higgs boson is indeed discovered at the LHC, with a mass of order 125 Gev/c^2. Unlike a fermion, the radiative correction to the mass(-squared) of a SCALAR particle is proportional to the cut-off (squared). In this case then, if the cut-off is of order the Planck scale, the bare mass(-squared) must also be of this order; in fact the bare mass-squared and the radiative correction have to cancel to one part in 10^{34}! Many people, including me, think that this is implausible, although there is no theoretical reason why it should not be thus. It is an aesthetic objection called the “fine-tuning problem”. The only known way to evade it is SUPERSYMMETRY (SUSY), which requires all of the known particles to have partners with the opposite statistics: fermions have (scalar) boson partners (selectrons, squarks, sleptons), and bosons have fermionic partners (photinos, gluinos, Winos, Zinos, Higgsinos). None have yet been observed, so the symmetry cannot be exact. However, the breaking cannot be at too high a scale. Otherwise it will not solve the fine tuning problem. This is why we expect SUSY to be discovered soon. It is another reason why the discovery of the Higgs would be of such importance. It would be the first known fundamental scalar particle, and would show that there is no obstruction in principle to the existence of the susy scalar particles.

Well, I think those are the best new particle names I have come across in years. I can’t wait until they discover a Wino in the LHC :-).

Happy Christmas


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