2
$\begingroup$

I read in a paper by Scott Willenbrock that gluinos can have a Majorana mass although they have SU(3) color symmetry. The explanation was that gluinos transform under the adjoint representation which is real.

Here is my understanding: gluinos are fermions in the adjoint representation of SU(3) and we can write a Lorenz invariant mass term for it because in the group notation we have $8 \times 8 = 1 + \cdots$ So, because there is a singlet we can have a Majorana mass term for gluinos.

Is my understanding right?

$\endgroup$
2
$\begingroup$

The gauge bosons in QCD are gluons with the $$ (c_i\bar c_j + c_j\bar c_i)/\sqrt{2},~i(c_j\bar c_i - c_i\bar c_j)/\sqrt{2} $$ $$ (r\bar r - b\bar b)/\sqrt{2},~(r\bar r + b\bar b - 2g\bar g)/\sqrt{6}, $$ for $c_ i = (r, b, g)$. These gluons are 3 plus 3 as the root space vectors plus 1 plus 1 as the weights, or the diagonal Gel-Mann matrices. This defines the 8 of SU(3).

The gluons are combinations of color and anti-color charges. This means the gluon is its own antiparticle. In the supersymmetric setting the fermion similarly has a combination of color and anticolor charges. This requires the gluino be Majorana.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.