Can You Explain The Interactions Of SUSY?

[chadsocky]

Im having a little bit of trouble with SuperSymmerty. I understand all the basics with the sparticles and gauginos being -1/2 less and how their properties change to boson-like and fermion-like respectively. What i don't understand is how do the interact exactly. i know none have been found in particle colliders, but are located they located around us(around normal matter) but just hidden from veiw in some kind of "superspace" or are they completely non existent at our "normal" energies. If they are around us, does an individial particle(an electron here or an electron over there) have its on individial SUSY particles, and how do these SUSY particles come into real space or interact with normal particles(fermions and bosons)? Is there some kinda of transition from SUSY particles to normal ones, or have they even got this far with the theory.
Any help would be greatly appreciated, Thank You

 

[mitchell porter]

You can write an equation for a theory in which the superparticles have the same mass as their partners, and in a world like that, they would be everywhere. But that's a world with "unbroken supersymmetry". The standard view about the real world is that supersymmetry is "broken" by some effect which acts unequally on particles and their superpartners, making the superpartners more massive. Because of E=mc^2, in general, a particle doesn't get created unless there are, say, collisions occurring with an energy greater than its mass. This is why people look to high-energy particle colliders like the LHC in Europe to produce evidence of superparticles. The other place they might be found is in cosmology - the dark matter may be massive superparticles left over from the early universe, when there was plenty of energy around. The other feature of massive particles is that if they can, they tend to decay into less massive particles, so these remnant superparticles would need to have small or zero possibility of decay to still be around.

Particle physics is all about making a hypothesis and then testing it. You say, let's suppose there are particles with certain properties, such as symmetries, and that these are the further details - now let's see what the equations predict. Over the years, many, many, many theories which contain supersymmetry have been proposed. There are many different ways in which supersymmetry can be broken, too - e.g. if you want to see some technical talk, look up "gauge mediation" and "gravity mediation". So supersymmetry is just a feature of the world that you can include in your theory, or not, just like you can include gravity, electromagnetism, or three different types of neutrino in your theory. The only difference is that if your model doesn't contain any of those, we already know it's wrong, but we don't yet know if supersymmetry is real or not.

I may as well add that in another thread in this forum, we have been discussing that supersymmetry is real and already visible, and that the superpartners of the known particles are actually *composite* particles already known from nuclear physics. But this is a weird new idea and it doesn't quite have a proper mathematical expression yet.

 

[chadsocky]

thank you that is very insiteful, i understand now that the SUSY particles arnt normal at our energies (if they are there at all), two more questions though if they are real let's say I am looking at (hypothetically) s'electon or a squark which is a Boson, does it work as a messeger for any force or do they even know yet. My second is i see the term "superspace" that pops up a lot in supersymmetry papers, and they also say that a particles and its superparter are tangled up in superspace together, what exactly are they referring too
thank you
and does anyone know any good resources or books pertaining to this subjuct

 

[mitchell porter]

Yes, they do produce forces, but they're complicated because they can involve transmutation of the matter particles involved. E.g. an electron turning into a photino as it emits a selectron, or a quark turning into a photino as it absorbs a squark. The "MSSM" (minimal supersymmetric standard model) contains numerous complications like that. There would be some big-picture perspective that sums them all up, but unfortunately I'm still lost in the details. http://www.sciencedirect.com/science/article/pii/0370157385900511" is still the best review of the MSSM that I've found, but it's huge, written for professional physicists, and behind a paywall.

In superspace, along with the usual space-time directions which use real numbers as coordinates, you have some extra "directions" which have "Grassmann numbers" as coordinates. The square of the unit real number is one (I'm just saying that 1 squared is 1), but the square of the unit Grassmann number is zero. An example of a mathematical quantity with this property is the matrix (0 1|0 0) - if you square it according to the rules of matrix multiplication, you get back a matrix of zeroes (0 0|0 0). So it's as if each super-direction is defined by a "line" of matrices of the form (0 x|0 0), with x running from -infinity to +infinity.

The usefulness of superspace is that it let's you combine a particle and its superpartner into a single "superfield" in a unified way. The fermionic part of the superfield (the "half-integer spin" or "matter" part) corresponds to how the superfield extends along the Grassmann-number super-directions. The peculiar "squares to zero" property of Grassmann numbers allows you to derive the peculiar "avoids itself" property of fermions just from the existence of the extra superspace dimensions, just as Kaluza-Klein theory derives forces from the existence of extra dimensions of the normal kind (dimensions where distance is measured in real numbers). Usually people tend to treat the usual space-time directions as the only real ones, and the super-directions as just a notation, but I've heard both Witten and Arkani-Hamed talk as if the super-directions are something real.