Re: What is the spin of the higgsino? And what is it's ang. momentum?

Hello William,

Good question! However, we can answer it without knowing much about the Higgs particle: As it turns out, it doesn't make sense to give a particle a negative spin. Spin is a vector quantity; this means that (in classical physics, and somewhat in quantum physics too) that you can treat it like a little arrow or pointer, with a magnitude and a direction. An example: there's a one-way sign on the street in front of my house, with an arrow on it. I would say "it's about forty cm long [magnitude!] and it points east [direction!]". If I were to spin it around, I might get it pointing up or west or southeast, but it'll always be positive 40 cm long and pointing in some direction. Spin, angular momentum, velocity, etc., are all vectors and all are defined the same way; the "spin" of a particle is the magnitude of its spin quantum number and is inherently positive. It can point in positive or negative directions, and the "direction" (or "spin projection") can behave counterintuitively sometimes.

Of course, this is just our definition! It would be perfectly valid to come up with a different set of habits and conventions for handling vectors, you could even allow them to be negative if you wanted. But the magnitude-and-direction convention is a very useful one, very convenient, and it somehow "captures the essence" of how the Universe treats vectors much of the time. And, of course, all of these equations dealing with fermions and angular momenta are based on this convention ... so if you wanted to use a different one you'd have to start from the beginning, derive new laws of vector calculus, rederive quantum mechanics, etc..

Anyway, getting back to supersymmetry and Higgs particles: supersymmetry invents an integer-spin particle (or boson) to accompany every 1/2-integer spin particle (fermion). But the spin of the superpartner is required to differ by 1/2 ... it doesn't have to be 1/2-unit less. The reasoning behind this is over my head right now, but I do know that the higgsino, undiscovered superpartner to the still undiscovered spin-0 Higgs boson, should have spin 1/2. But I'm just taking the theorists' word on that. :)

Oh, yes, and I should add that angular momentum is just spin expressed in different units: L = hbar * s. (hbar, an h with a line through it, is common notation for Planck's constant divided by 2 Pi). You're probably thinking of rotational energy, where quantum mechanics sees an L(L+1) where classical mechanics sees L^2.

Historically, though, thinking about wierd negative quantities has been a useful thing to do; Paul Dirac mentally toyed with the idea of negative-energy electrons back in the 1920s; and I'm sure people told him that "no, energy doesn't make sense unless it's positive". However, the idea led him to predict the existence of antimatter. Richard Feynman had similar success imagining particles going backwards in time ("That's ridiculous!"), and Steven Hawking talks about imaginary time ("Poppycock!") ... so maybe negative spins will turn out to be important too!

You can read more about vectors at mathworld.wolfram.com. Check out the the Particle Adventure or the technical Particle Data Group for info on the Higgs and higgsino. Also - breaking news! - the ALEPH experiment at CERN has some data that may be our first glimpse of the Higgs particle. Check out CERN's web page over the next month - they gave the 11-year-old project a stay of execution so they can keep searching.

Thanks for the question,

-Ben Monreal