On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

6 Chapter 1. Introduction: Problems beyond the Standard Model
Quadratic divergences cancel and, as expected for a chirally protected mass, all remaining
divergences are logarithmic and vanish in the limit where the Higgs vev goes
to zero. In the limit of exact supersymmetry, mt = M˜t , all corrections vanish. Moreover,
since SUSY is a symmetry of the quantum theory, no divergences will occur at
any loop order, in fact, the masses are not renormalized at all, see [14, Sec. 4].
However, the MSSM does not only –in conflict with experiment– predict degenerate
masses of superpartners, but it necessarily gives the Higgs boson a positive mass
squared. 7 As a consequence, in order to have nondegenerate masses in the MSSM (or
massive particles at all), supersymmetry needs to be broken. There is no phenomenologically
viable way to incoporate SUSY breaking with only the MSSM field content
and a breaking communicated at tree level (a direct couplings to the SUSY-breaking
field) will also lead to inconsistencies8 , see e.g. [5, Sec. 7].
One therefore assumes a hidden sector, in which SUSY is broken and some kind of
messenger fields communicate the breaking to the MSSM. In the spirit of effective field
theory one writes down the relevant terms of the most general Lagrangian parametrizing
the breaking. This introduces 124 new parameters to the MSSM, which are in
general unrelated, and will lead to a breaking of the chiral protection of the scalar
masses, because M˜t = mt + m✘ ✘
SUSY in (1.5) is now sensitive to the size of the breaking
terms. They are usually given by
m✘ ✘ SUSY ∼ 〈F〉
, (1.6)
Λ
where 〈F〉 denotes the vev of the SUSY breaking field and Λ is the SUSY breaking
scale (the mass of the messenger field). These masses should clearly not exceed the
TeV scale by much m✘ ✘ SUSY � TeV in a natural model. However, since the SUSY breaking
sfermion masses induce radiative corrections relative to their Yukawa couplings,
one can relax this bound depending on flavor. For example a 200 GeV stop contributes
roughly as much to ∆m2 H as a sbottom at 3.5 TeV. Natural supersymmetric models
may therefore allow for a large splitting in the superpartner mass spectrum [7]. It
should be noted, that such an ansatz requires the SUSY breaking sector to generate
this hierarchy in superpartner masses.
The modeling of the SUSY breaking sector may accomodate further attractive features.
For a large enough SUSY breaking scale, renormalization group running may
eventually turn one of the scalar mass parameters negative, triggering condensation
of the corresponding field. It would be a disaster, if this would be any sfermion
mass, because it would induce a color- or electromagnetic breaking vacuum. However,
the Higgs boson mass parameter will get the largest negative corrections by the top
Yukawa and thus generically turns negative first, ultimatively triggering EWSB. This
is known as radiative symmetry breaking [6] and although it depends on the values
m✘ ✘ SUSY at the SUSY breaking scale, it is a step beyond the ignorace of the EWSB
7 In order to achieve EWSB in a (unbroken) supersymmetric extension of the SM, one therefore
has to include additional fields, which do not have superpartners in the SM, see for example the
dicsussion in [15, Sec.5.4].
8 There is for example no scalar-gaugino-gaugino term allowed by SUSY, therefore the gauginos
remain massless in such a scenario.