Killing the cMSSM softly
Eur. Phys. J. C
Killing the cMSSM softly
Philip Bechtle 2
José Eliel Camargo-Molina 1
Klaus Desch 2
Herbert K. Dreiner 0 2
Matthias Hamer 6
Michael Krämer 5
Ben O'Leary 4
Werner Porod 4
Björn Sarrazin 2
Tim Stefaniak 3
Mathias Uhlenbrock 2
Peter Wienemann 2
0 Bethe Center for Theoretical Physics, University of Bonn , Bonn , Germany
1 Department of Astronomy and Theoretical Physics, Lund University , 223-62 Lund , Sweden
2 Physikalisches Institut, University of Bonn , Bonn , Germany
3 Santa Cruz Institute for Particle Physics, University of California , Santa Cruz, CA 95064 , USA
4 Institut für Theoretische Physik und Astrophysik, University of Würzburg , Würzburg , Germany
5 Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen , Aachen , Germany
6 Centro Brasileiro de Pesquisas Fisicas , Rio de Janeiro , Brazil
We investigate the constrained Minimal Supersymmetric Standard Model (cMSSM) in the light of constraining experimental and observational data from precision measurements, astrophysics, direct supersymmetry searches at the LHC and measurements of the properties of the Higgs boson, by means of a global fit using the program Fittino. As in previous studies, we find rather poor agreement of the best fit point with the global data. We also investigate the stability of the electro-weak vacuum in the preferred region of parameter space around the best fit point. We find that the vacuum is metastable, with a lifetime significantly longer than the age of the Universe. For the first time in a global fit of supersymmetry, we employ a consistent methodology to evaluate the goodness-of-fit of the cMSSM in a frequentist approach by deriving p values from large sets of toy experiments. We analyse analytically and quantitatively the impact of the choice of the observable set on the p value, and in particular its dilution when confronting the model with a large number of barely constraining measurements. Finally, for the preferred sets of observables, we obtain p values for the cMSSM below 10 %, i.e. we exclude the cMSSM as a model at the 90 % confidence level.
1 Introduction
Supersymmetric theories [
1,2
] offer a unique extension of the
external symmetries of the Standard Model (SM) with
spinorial generators [3]. Due to the experimental constraints on
the supersymmetric masses, supersymmetry must be broken.
Supersymmetry allows for the unification of the
electromagnetic, weak and strong gauge couplings [
4–6
]. Through
radiative symmetry breaking [
7,8
], it allows for a dynamical
connection between supersymmetry breaking and the breaking
of SU(2)×U(1), and thus a connection between the
unification scale and the electroweak scale. Furthermore,
supersymmetry provides a solution to the fine-tuning problem of the
SM [
9,10
], if at least some of the supersymmetric particles
have masses below or near the TeV scale [
11
]. Furthermore,
in supersymmetric models with R-parity conservation [
12,
13
], the lightest supersymmetric particle (LSP) is a
promising candidate for the dark matter in the universe [
14,15
].
Of all the implementations of supersymmetry, there is one
which has stood out throughout, in phenomenological and
experimental studies: the constrained Minimal
Supersymmetric Standard Model (cMSSM) [
16,17
]. As we show in
this paper, eventhough it is a simple model with a great set of
benefits over the SM, it has come under severe experimental
pressure. To explain and – for the first time – to quantify this
pressure is the aim of this paper.
The earliest phenomenological work on supersymmetry
was performed almost 40 years ago [
12,13,18–20
] in the
framework of global supersymmetry. Due to the mass sum
rule [
21
], simple models of breaking global
supersymmetry are not viable. One set of realistic models employs local
supersymmetry, or supergravity [
16,22–24
], on which we
focus here. Another possible solution to the mass sum rule
problem, are the widely studied models on gauge mediated
supersymmetry breaking [
25–27
]. The cMSSM is an
effective parametrisation motivated by realistic supergravity
models. Since we wish to critically investigate the viability of the
cMSSM in detail here, it is maybe in order to briefly recount
some of its history.
The cMSSM as we know it was first employed in [
28
] and
then actually called cMSSM in [
29
]. However, it is based on a
longer development in the construction of realistic
supergravity models. A globally supersymmetric model with explicit
soft supersymmetry breaking [
30
] added by hand was first
introduced in [
31
]. It is formulated as an SU(5) gauge
theory, but is otherwise already very similar to the cMSSM, as
we study it at colliders. It was however not motivated by a
fundamental supergravity theory. A first attempt at a realistic
model of spontaneously breaking local supersymmetry and
communicating it with gravity mediation is given in [
32
]. At
tree-level, it included only the soft breaking g (...truncated)