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[Phys-l] Why CERN May Not Find SUSY




Why CERN May Not Find SUSY


So far the Large Hadron collider has failed to find any sign of SUSY or
any conclusive evidence for the Higgs Boson. It certainly is far too early
to think CERN will fail to find evidence for SUSY, but I will argue here
that there is some theoretical justification to think it won't because we
might better expect that SUSY will break at a much higher energy scale than
Minimal SUSY predicts and that all the super partners have masses beyond the
reach of the LHC.

The Gravitino Problem.


There is a severe problem with low energy SUSY that is too seldom
discussed. Given low energy SUSY the super partner of the Graviton is required to
have mass at the TEV scale. If we assume that the Gravitino is the Dark
matter candidate calculations reveal that the Gravitino density would be much
higher than the observed Dark Energy density. If we assume instead that
the Gravitino is not stable we can expect its mean decay time to be on the
order of 1E5 seconds, far beyond the era of nucleosynthesis. Since one
possible decay channel for the Gravitino must include a photon , a charged meson
or lepton we would expect a disruption of the nucleosynthesis that would
make the baryon density we observe in our Universe impossible.

Split SUSY

A possible solution to the Gravitino problem is a model called Split SUSY,
first proposed by John Wells and later expanded on by Nima Arkani-Hamed
and Savas Dimopoulos. Additional work on this model has been done by Gian
Giudice, Andrea Romanino. and others.

The basic idea of Split SUSY is that although SUSY breaks at an energy
scale just below the GUT scale, there would still be a set of Fermion super
partners which masses at the TEV scale. These particles are ;


Gluino ( 8,1)_0

Wino (1,3)_0

Bino (1,1)_0

Higgsino (up) ( 1,2)_1

Higgsino (dn) ( 1,2)_ - 1


Where the notation means

(color multiplet number, Non Color multiplet number)_ hypercharge.



All the scalars super partners and the Gravitino would have masses on the
order of the SUSY breaking scale. Given a high mass Gravitino there would be
too few to disrupt nucleosynthesis in the early Universe. In this model
there would still be a light Higgs, though its mass would not be constrained
to fall no higher than 130-135 Gev, which may explain why no Higgs has been
observed so far.

The Bad News


While Split SUSY does generate a unification of the running couplings of
the fundamental interactions it provides no help with the Hierarchy problem,
the stabilization of the Higgs mass , needed to make the Higgs mass
generating process work. interestingly Moffat has suggested that scalar field
stabilization can be solved by invoking Ghost Sector quantum fields, the so
called unphysical particle states in a recent paper. Of course this
proposal is speculative.

Also while this model neatly solves the problem of the Gravitino the
specific masses of the low mass Fermion super partners, may be outside the reach
of the LHC. Based on a paper by Fei Wang, Wen yu Wang and Jin Min Yang "
Gravitino Dark Matter From Gluino Decay in Split Super symmetry" the mass
of the lightest Fermion Super Partner may higher then 14 Gev , beyond the
reach of the LHC. Other proponents of Split SUSY have also predicted that the
masses of the lightest Fermion Super partner may be beyond the reach of
the LHC, though their versions of the Split SUSY model do allow the
possibility that there may exist Super Partners with masses low enough to be
detected at CERN.


Where Does SUSY really Break

Split SUSY predicts a breaking of SUSY on the order of

M_susy= M_gut^2/M_planck

Which puts the SUSY breaking scale between 1E13-1E14 Gev.

If we assume a breaking scale of 5.5E13 Gev for the sake of argument we
find that the maximum ZPE energy density equals 1.71E92 J/m^3. This has
interesting implications for the model of Induced Gravity I have posted on
several times. Given that


T_mu,nu= -K*{chi_a*Integral Dw L(+) + chi^a*Integral Dw L(-)}*g_mu,nu

Where we get

rho_vac= - (3/8*pi*G)*g^2

Where g is the gravity field


We get a gravity kernel in the black hole decay process with a mass of
about 1E-15 KG with a circumference of 1E -41 meters. This kernel will
generate a powerful gravity field but will not have gravity diverge at its
boundary, hence it will have no event horizon.

v = sqrt[ 2*R*g]

Here g becomes constant preventing the divergence as R falls below the
Schwarzschild radius.

Again using a SUSY breaking scale of 5.5E13 Gev we can replace the
singularity inside a black hole by a kernel whose radius is given by :

R_ker ( meters)= 2.61E-28*sqrt [M_bh (KG)]



Quantum Einstein Gravity


The above model is operationally identical to a model of gravity proposed
by Weinberg in the 1970's under the name of the "Asymptotic Safe Gravity
Model" It's more recent incarnation has been proposed is a far more rigorous
form by Martin Reuter and others and goes under the name of Quantum
Einstein Gravity. In this model gravity has a cutoff point where the strength of
the gravity field stops increasing.

One reason to think that gravity stops increasing at small scales is that
this is what quantum field theory tells us the other forces do. At very
small scales, even the nuclear force drops to zero. This is called asymptotic
freedom and its discovery earned David Gross, David Politzer and Frank
Wilczek the 2004 Nobel Prize. However the force of gravity wouldn't go to zero
, but rather to some finite strength.


Weinberg and others weren't able to pursue the idea at the time because
the Mathematical tools to calculate the cutoff point for gravity in General
Relativity didn't exist until Reuter developed them in the 1990's.

Quantum Einstein Gravity , like Causal Dynamical Triangulations (CDT) comes
up with a fractal pattern to small scale space time, and the number of
dimensions drops to two. Reuter has noted that this could mean that CDT and
his approach are fundamentally equivalent.


Bob Zannelli