No-scale SU(5) super-GUTs
Eur. Phys. J. C
John Ellis 1 2
Jason L. Evans 0
Natsumi Nagata 6
Dimitri V. Nanopoulos 3 4 5
Keith A. Olive 7
0 School of Physics , KIAS, Seoul 130-722 , Korea
1 Theoretical Physics Department , CERN, 1211 Geneva 23 , Switzerland
2 Theoretical Physics and Cosmology Group, Department of Physics, King's College London , Strand, London WC2R 2LS , UK
3 Division of Natural Sciences, Academy of Athens , Athens 10679 , Greece
4 Astroparticle Physics Group, Houston Advanced Research Center (HARC) , Mitchell Campus, Woodlands, TX 77381 , USA
5 George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station , TX 77843 , USA
6 Department of Physics, University of Tokyo , Tokyo, Bunkyo-ku 113-0033 , Japan
7 School of Physics and Astronomy, William I. Fine Theoretical Physics Institute, University of Minnesota , Minneapolis, MN 55455 , USA
We reconsider the minimal SU(5) grand unified theory (GUT) in the context of no-scale supergravity inspired by string compactification scenarios, assuming that the soft supersymmetry-breaking parameters satisfy universality conditions at some input scale Min above the GUT scale MGUT. When setting up such a no-scale super-GUT model, special attention must be paid to avoiding the Scylla of rapid proton decay and the Charybdis of an excessive density of cold dark matter, while also having an acceptable mass for the Higgs boson. We do not find consistent solutions if none of the matter and Higgs fields are assigned to twisted chiral supermultiplets, even in the presence of Giudice-Masiero terms. However, consistent solutions may be found if at least one fiveplet of GUT Higgs fields is assigned to a twisted chiral supermultiplet, with a suitable choice of modular weights. Spin-independent dark matter scattering may be detectable in some of these consistent solutions. Globally supersymmetric grand unification has long been an attractive framework for unifying the non-gravitational interactions, with the minimal option using the gauge group SU(5) [1-3]. When incorporating gravity, one must embed such a supersymmetric grand unified theory (GUT) within some supergravity theory, and an attractive option is no-scale supergravity [4-7]. This has the advantages that it leads to an effective potential without holes of depth O(1) in natural units, and emerges in generic string compactifications [8]. No-scale supergravity also allows naturally for the possibility of Planck-compatible cosmological inflation [9, 10]. In
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general, a no-scale K?hler potential contains several
moduli Ti , but here we consider scenarios in which the relevant
dynamics is dominated by a single volume modulus field T .
The construction of no-scale supergravity GUTs
encounters significant hurdles, such as fixing the
compactification moduli. Moreover, pure no-scale boundary conditions
require that all the quadratic, bilinear and trilinear scalar
couplings m0, B0 and A0 vanish, leading to phenomenology
that is in contradiction with experimental constraints.
However, this issue may be avoided in models with (untwisted or
twisted) matter fields with non-vanishing modular weights
as we show below.
The simplest possibility for soft supersymmetry
breaking is to postulate universal values of m0, B0 and A0, as
in the constrained minimal supersymmetric Standard Model
(CMSSM) [11?38]. With the inclusion of a universal
gaugino mass, m1/2, the CMSSM is a four-parameter theory.1
Minimal supergravity places an additional boundary
condition, relating B0 and A0 ( B0 = A0 ? m0) making it a
three-parameter theory [39?41]. No-scale supergravity,
however, is effectively a one-parameter theory since we require
m0 = A0 = B0 = 0. Another one-parameter theory in this
context is pure gravity mediation [42?47], in which the
gaugino masses, A and B terms2 are determined by anomaly
mediation [49?53] leaving only the gravitino mass, m3/2 = m0 as
a free parameter.
These boundary conditions may be too restrictive if they
are imposed at the GUT scale, MGUT, defined as the
renormalization scale where the two electroweak gauge couplings
1 In addition, one must choose the sign of ?, which we take here to
positive.
2 In order to get electroweak symmetry breaking to work, the B terms in
these models also get a contribution from a Giudice?Masiero term [48].
are unified. There is, however, no intrinsic reason that the
boundary conditions for supersymmetry breaking coincide
with gauge coupling unification. Separating these two scales
opens the door for so-called sub-GUT models [37,38,54?56]
where the input universality scale differs from the GUT scale
with Min < MGUT or the possibility that the boundary
conditions are imposed at some higher input scale Min > MGUT,
a scenario we term super-GUT [57,58].
However, the regions of parameter space with acceptable
relic density and Higgs mass typically require quite
special values of the GUT superpotential couplings and rather
large values of tan ? [59], (...truncated)