Supersymmetry Breaking

Supersymmetry in the equation for the MSSM Lagrangian is an exact symmetry. This implies the mass degeneration for the components of each supermultiplet. Anyway, if the superparticles had the same masses of the respective particles, they would have already been observed and the Supersymmetry should therefore be broken.

Although it is widely believed that a mechanism of spontaneous breaking (similar to the Higgs’ one) is at the basis of Supersymmetry breaking too. For simplicity, we are lead to consider an explicit breaking mechanism introducing in the MSSM Lagrangian a term of soft breaking \mathcal{L}_{soft}, which explicitly violate the Supersymmetry. The subscript “soft” indicates the requirement that the new term must not affect the solution of the hierarchy problem.

The introduction of \mathcal{L}_{soft} in the MSSM Lagrangian, which de facto completes the MSSM theory, makes rise the total number of free parameters to 124, more than a hundred of them coming right from \mathcal{L}_{soft}. However, it is thought that once understood the mechanism of Supersymmetry breaking, it is possible to drastically reduce the number of the parameters of the theory.

Furthermore, the spontaneous breaking of the electroweak symmetry produces the mixing of states characterized by the same charge, spin and colour, in the MSSM; the eigenstates of mass, then, are combination of the gauge ones like to what happens in the SM between the W^0 and B states and the coefficients of these combinations are uniquely determined by the Higgs mechanism.

The mixing between neutral higgsino (\tilde{h}^0_u , \tilde{h}_d^0) and gaugino (\tilde{B}, \tilde{W}^0) states leads to the definition of four states of mass said neutralinos and according to the increasing order of their masses indicated by

\tilde\chi_1^0,\ \tilde\chi_2^0,\ \tilde\chi_3^0,\ \tilde\chi_4^0,

while charginos (\tilde{\chi}_1^\pm, \tilde{\chi}_2^\pm) come from mixing of charged higgsinos (\tilde{h}^0_u ,\tilde{h}_d^0) and gauginos (\tilde{W}^+,\tilde{W}^-).

Since the SU(3)_C symmetry stays unbroken, gluinos cannot mix with
other particles and they constitute mass eigenstates.
For s-fermions, instead, the mixing can occur both within the same generation
among left-handed and right-handed particles and between particles of different generations involving the flavor changing neutral current processes. In the case of the s-fermions mixing between the same generation there may be remarkable left-right mixings of the s-tops (\tilde{t}), s-bottoms (\tilde{b}) and s-taus (\tilde{\tau}) because of the high masses of their partners.

References and further readings:
S. Baer and X. Tata, Weak Scale Supersymmetry, (Cambridge University Press), 2006
R.H. Mohapatra, Unification and Supersymmetry: the Frontiers of Quark-Lepton Physics – Third Edition, (Springer-Verlag), 2002.
Aitchison I.J.R., Supersymmetry in Particle Physics, (Cambridge University Press).