I recently came across this paper about axino (fermion superparter of axion) mass in supergravity:
- T. Goto, M. Yamaguchi, "Is axino dark matter possible in supergravity?", Phys. Lett. B 276 (1992) 103-107.
In this paper, they think of a specific superpotential (they consider two cases. I focus on the first one.) that is separated into visible sector and hidden sector. Also they assume minimal form of the Kahler potential. With the superpotential and Kahler potential defined, we can define a dimensionless Kahler function $G$.
(Here, $z$ is the hidden sector field, and $h(z)$ is the hidden sector superpotential which is not specified. $g$ is the visible sector superpotential. $\phi$ and $\phi^\prime$ are the chiral multiplets with opposite PQ charge, and $X$ is a PQ singlet.)
With this $G$, we can compute the fermion mass matrix.
QCD axion is a pseudo-Nambu-Goldstone boson and it has very small mass (usually $\mu$eV scale) from non-perturbative effects of QCD (I don't want to discuss this point in detail). If we ignore this effect, axion is massless at tree level. If supersymmetry is not broke, axino should be massless at tree level also.
Now here is their argument in the paper: If we calculate the axino mass from the fermion mass matrix using $G$, the axino mass is about gravitino mass.
It seems that from SUGRA mediation effect (at least in the first example they showed), mass of the axino gets huge correction. I am very new to supergravity, and I wonder how all the other fermions in the Standard model are safe from this effect. I also noticed that there has been many efforts to understand axino mass in supergravity. But they don't mention about the mass correction of other fermions other than axino. I guess I am missing a point.
Is there a way to understand how the other fermion masses (such as Standard model fermions) are safe from this kind of effect?