The mass eigenstates of squarks and sleptons are, in principle,
mixtures of their left- and right-handed components, given by:
In many high-energy models,
the soft SUSY-breaking sfermion mass parameters are
taken to be equal at the high-energy scale, but, in principle,
they can be different for
each generation or even within a generation.
However, the sfermion flavor dependence can have important effects on
low-energy observables, and it is often strongly constrained.
The suppression of flavor changing neutral currents (FCNC's), such as
, requires that either the squark soft
SUSY-breaking mass matrix is diagonal and degenerate,
or the masses of the
first- and second-generation sfermions are very large. Thus we make the
data-motivated simplification of setting
sfermion mixing is determined by the product of
soft SUSY-breaking parameters and the mass of
the corresponding fermion.
Unless the soft SUSY-breaking parameters for the first two
generations are orders of magnitude greater than for
the third generation, the mixing in
the first two generations can be neglected. This simplifying assumption is
also made in PYTHIA: the sfermions
, are the real mass eigenstates with
For the third generation sfermions, due to weaker experimental constraints,
the left-right mixing can be nontrivial.
mass matrix for the top squarks (stops) in the (
basis is given by
Because of the large mixing, the lightest stop can be one of the lightest sparticles. For the sbottom, an analogous formula for the mass matrix holds with , , , , and . For the stau, the substitutions , , , , and 1/ are appropriate. The parameters , , and can be independent, or they might be related by some underlying principle. When or is large ( , left-right mixing can also become relevant for the sbottom and stau.
Most of the SUSY input parameters are needed to specify the properties of the sfermions. As mentioned earlier, the effects of mixing between the interaction and mass eigenstates are assumed negligible for the first two generations. Furthermore, sleptons and squarks are treated slightly differently. The physical slepton masses and are set by RMSS(6) and RMSS(7). By default, the mixing is set by the parameters RMSS(13), RMSS(14) and RMSS(17), which represent , and , respectively, i.e. neither -terms nor is included. However, for IMSS(8) = 1, the masses will follow the same pattern as for the first two generations. Previously, it was assumed that the soft SUSY-breaking parameters associated with the stau included -terms. This is no longer the case, and is more consistent with the treatment of the stop and sbottom. For the first two generations of squarks, the parameters RMSS(8) and RMSS(9) are the mass parameters and , i.e. without -terms included. For more generality, the choice IMSS(9) = 1 means that for is set instead by RMSS(22), while for is RMSS(9). Note that the left-handed squark mass parameters must have the same value since they reside in the same doublet. For the third generation, the parameters RMSS(10), RMSS(11), RMSS(12), RMSS(15) and RMSS(16) represent , , , and , respectively.
There is added flexibility in the treatment of stops, sbottoms and staus. With the flag IMSS(5) = 1, the properties of the third generation sparticles can be specified by their mixing angle and mass eigenvalues (instead of being derived from the soft SUSY-breaking parameters). The parameters RMSS(26) - RMSS(28) specify the mixing angle (in radians) for the sbottom, stop, and stau. The parameters RMSS(10) - RMSS(14) specify the two stop masses, the one sbottom mass (the other being fixed by the other parameters) and the two stau masses. Note that the masses RMSS(10) and RMSS(13) correspond to the left-left entries of the diagonalized matrices, while RMSS(11), RMSS(12) and RMSS(14) correspond to the right-right entries. These entries need not be ordered in mass.