# Why can gluino (superpartner of gluon) have a Majorana mass?

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?

## 1 Answer

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.