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Björn Garbrecht
ccb
Commits
1c7f4658
Commit
1c7f4658
authored
Apr 30, 2014
by
Ben O'Leary
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BOL edits
parent
294da305
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discussion.tex
View file @
1c7f4658
\section
{
Discussion and conclusion
}
\label
{
sec:discussion
}
Blah
method.tex
View file @
1c7f4658
\section
{
Parameter point selection and stability evaluation
}
\label
{
sec:method
}
Blah
We categorize the stability or metastability of a parameter point by a
multi-stage process. First, a consistent set of Lagrangian parameters at a
fixed renormalization scale is generated by
\spheno\ \cite
{
Porod:2003um,Porod:2011nf
}
, such that the MSSM physics at the
DSB vacuum is consistent with the SM inputs (
$
m
_{
Z
}
, G
_{
F
}$
,
\etc
), and these
parameters are stored in a file in the
\slha
format which is passed to
\vcs
.
\vcs
is a publicly-available code
\cite
{
Camargo-Molina:2013qva
}
that then
prepares the minimization conditions for the tree-level potential as input for
the publicly-available binary
\homps\ \cite
{
lee2008hom4ps
}
that finds all
possible solutions to the particular minimization conditions of the parameter
point. These are then used by
\vcs
as starting points for gradient-based
minimization by
\minuit\ \cite
{
James:1975dr
}
through
\pyminuit\ \cite
{
pyminuit
}
to minimize the full one-loop potential with
thermal corrections at a given temperature. If a minimum deeper than the DSB
vacuum is found, the probability of tunneling out of the false DSB vacuum is
then calculated through
\cosmotransitions\ \cite
{
Wainwright:2011kj
}
.
If a parameter point is found to have a deeper CCB minimum, we label it as
metastable, otherwise we label it stable
\footnote
{
It may be that a parameter
point is actually metastable if other scalar fields such as the partners of
bottom quarks were allowed non-zero
\vevs
. However, we restrict ourselves to
a region of parameter space where such concerns are negligible as the
relevant trilinear interaction is small, but note also that this restriction
cannot mistakenly label a stable parameter point as metastable.
}
. We then
divide the metastable points into short-lived points which would tunnel out
of the false DSB vacuum in 3 giga-years or less (corresponding to a
survival probability of lasting 14 Gy of one per-cent or less), and the rest
as long-lived. Finally, we divide the long-lived points into thermally
excluded, by having a probability of the DSB vacuum surviving thermal
fluctuations of one per-cent or less, or allowed, by having a survival
probabiltity of greater than one per-cent.
\subsection
{
Thermal corrections
}
\label
{
sec:thermal
_
corrections
}
\BOL
{
\vcs
1.1: thermal
}
\subsubsection
{
Comparison in methodology to previous works
}
\label
{
sec:comparison
_
to
_
previous
}
\subsection
{
Parameter scan
}
\label
{
sec:parameter
_
scan
}
\BOL
{
Parameters of scan
}
While spontaneous symmetry breaking in the SM is triggered by a negative
mass-squared term in the Lagrangian for the Higgs
field
\footnote
{
The possibility that it is due to a massless Coleman-Weingberg
model has been ruled out by measurements of the top mass, for
example~
\cite
{
Sher:1988mj
}
.
}
, it is neither a necessary nor sufficient
condition for any scalar field in a multi-scalar theory to develop a non-zero
\vev
. In particular, a positive mass-squared for the stop fields does not
preclude a parameter point from having a CCB minimum, especially if the
effective trilinear interaction
$
X
_{
t
}$
between the stops and the Higgs is
large.
We refer the reader to section
$
2
.
1
$
of
\Ref
~
\cite
{
Blinov:2013fta
}
or
section B of
\Ref
~
\cite
{
Chowdhury:2013dka
}
for the explicit form of the
relevant part of the tree-level scalar potential. One may also inspect the
file
\verbatim
{
SARAH-SPhenoMSSM
_
RealHiggsAndStopVevs.vin
}
provided in the
\verbatim
{
MSSM
}
sub-directory of the
\vcs
download, where the tree-level
potential and also the mass-squared matrices required for assembling the
loop corrections, as described in
\cite
{
Camargo-Molina:2013qva
}
, are shown.
results.tex
View file @
1c7f4658
\section
{
Constraining relevant regions of the Natural MSSM parameter space
}
\label
{
sec:
constraining
}
\label
{
sec:
results
}
Blah
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