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JHEP04(2019)043

Published for SISSA by Springer

Received: February 5, 2019

Accepted: April 1, 2019

Published: April 4, 2019

LHC SUSY and WIMP dark matter searches confront

the string theory landscape

Howard Baer,

Vernon Barger,

Shadman Salam,

Hasan Serce

and Kuver Sinha

Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma,

440 West Brooks, Norman, OK 73019, U.S.A.

Department of Physics, University of Wisconsin,

1150 University Avenue, Madison, WI 53706 U.S.A.

E-mail: baer@ou.edu, barger@pheno.wisc.edu, shadman.salam@ou.edu,

serce@ou.edu, kuver.sinha@ou.edu

Abstract: The string theory landscape of vacua solutions provides physicists with some

understanding as to the magnitude of the cosmological constant. Similar reasoning can be

applied to the magnitude of the soft SUSY breaking terms in supersymmetric models of

particle physics: there appears to be a statistical draw towards large soft terms which is

tempered by the anthropic requirement of the weak scale lying not too far from ∼ 100 GeV.

For a mild statistical draw of m

soft

with n = 1 (as expected from SUSY breaking due to a

single F term) then the light Higgs mass is preferred at ∼ 125 GeV while sparticles are all

pulled beyond LHC bounds. We confront a variety of LHC and WIMP dark matter search

limits with the statistical expectations from a fertile patch of string theory landscape. The

end result is that LHC and WIMP dark matter detectors see exactly that which is expected

from the landscape: a Standard Model-like Higgs boson of mass 125 GeV but as yet no

sign of sparticles or WIMP dark matter. SUSY from the n = 1 landscape is most likely

to emerge at LHC in the soft opposite-sign dilepton plus jet plus MET channel. Multi-ton

noble liquid WIMP detectors should be able to completely explore the n = 1 landscape

parameter space.

Keywords: Supersymmetry Phenomenology, Strings and branes phenomenology

ArXiv ePrint: 1901.11060

Open Access,

 The Authors.

Article funded by SCOAP

https://doi.org/10.1007/JHEP04(2019)043

JHEP04(2019)043

Contents

1 Intro duction 1

2 Statistics of the SUSY breaking scale 3

2.1 Brief review of some previous work and goals of the present work 6

3 Landscape predictions vs. LHC search limits 8

3.1 Landscape predictions for NUHM2 model 8

3.2 Landscape predictions for NUHM3 model 9

4 Landscape predictions vs. WIMP DM search limits 13

5 Conclusions 16

1 Intro duction

It is sometimes lamented that the emergence of the landscape of string vacua [1–3] has ren-

dered string theory non-predictive since how are we to pick out the (meta-stable) vacuum

corresponding to our universe from (perhaps) of order 10

500

possibilities? Such sentiment

ignores one of the great predictions of the latter 20th century [4, 5]: namely that given a

multiverse which includes a vast assortment of pocket-universes with varying cosmological

constants, then it may not be surprising to ﬁnd Λ ∼ 10

−120

since if it was much bigger,

then galaxy condensation would not occur and we would not even be here to discuss the

issue. The situation is portrayed in ﬁgure 1 which depicts the fact that the cosmological

constant ought to be at its most natural value subject to the constraint that we can exist

to observe it. Such anthropic reasoning relies on the existence of a vast landscape of possi-

bilities that is provided for by the discretuum of ﬂux vacua from string theory [1–3, 6, 7].

Can such reasoning be applied to the origin of other mass scales that appear in

fundamental physics?

An obvious target would be the magnitude of the weak scale

weak

' m

W,Z,h

' 100 GeV) and why it is suppressed by 16 orders of magnitude com-

pared to the (reduced) Planck scale m

' 2.4 × 10

GeV. Anthropically, one expects

a universe with electroweak symmetry properly broken such that weak bosons gain mass

W,Z

∼ 100 GeV while solutions with charge or color breaking minima would be excluded.

In addition, nuclear physics calculations by Agrawal et al. [9, 10] require that the magni-

tude of the weak scale shouldn’t exceed its measured value by a factor of 2–3 in order to

gain a livable universe.

Weinberg states [8]: “The most optimistic hypothesis is that the only constants that scan are the few

whose dimensionality is a positive power of mass: the vacuum energy, and whatever scalar mass or masses

set the scale of electroweak symmetry breaking”.

– 1 –

JHEP04(2019)043

naturalness: vacua with natural observables are expected to be far more common than

vacua with unnatural observables.

Thus, in this paper we will focus on vacua solutions which include the Minimal Super-

symmetric Standard Model (MSSM) as their weak scale eﬀective theory. This restricts our

attention to a fertile patch of landscape solutions which include the SM as the weak scale

eﬀective theory (in accord with experiment) but where the weak scale is stable against

quantum corrections (as in the MSSM). We will further assume that the MSSM arises

from a 4-d supergravity theory (SUGRA) where SUSY breaking occurs via spontaneous

SUGRA breaking in a hidden sector of the theory with a, perhaps, complicated SUSY

breaking sector including possibly numerous SUSY breaking F- and D-term ﬁelds which

gain vevs. The question that can be addressed is then: what does a statistical sampling of

this fertile patch of the landscape say about the scale of SUSY breaking, and hence the like-

lihood of observable signals at the CERN Large Hadron Collider (LHC) or at WIMP dark

matter direct and indirect detection experiments? Indeed, this question has already been

investigated early on by Douglas et al. [13–15], Susskind [12] and by Dine et al. [16, 17].

(For some reviews, see e.g. refs. [18, 19].)

2 Statistics of the SUSY breaking scale

In this section, we assume a vast ensemble of string vacua states which give rise to a D = 4,

N = 1 supergravity eﬀective ﬁeld theory at high energies. Furthermore, the theory consists

of a visible sector containing the MSSM along with a perhaps large assortment of ﬁelds

that comprise the hidden sector. The scalar potential is given by the usual supergravity

form [20]

V = e

K/m



W D

∗

−

|W |



(2.1)

= e

K/m

− 3

|W |

(2.2)

where W is the holomorphic superpotential, K is the real K¨ahler potential and F

= D

W =

DW/Dφ

≡ ∂W/∂φ

+ (1/m

)(∂K/∂φ

)W are the F -terms and D

∼

†

φ are the

D-terms and the φ

are chiral superﬁelds. Supergravity is assumed to be broken sponta-

neously via the super-Higgs mechanism either via F -type breaking or D-type breaking or

in general a combination of both leading to a gravitino mass m

3/2

= e

K/2m

|W |/m

. The

(metastable) minima of the scalar potential can be found by requiring ∂V/∂φ

= 0 with

∂

V/∂φ

∂φ

> 0 to ensure a local minimum. The cosmological constant is given by

= m

hidden

− 3e

K/m

|W |

(2.3)

Since the landscape allows for an apparently unnatural value of Λ

 m

, it is sometimes interpreted

that vacua with other highly unnatural observables should also be entertained. In the case of Λ

, we should

ﬁnd ourselves in a universe where the cosmological constant is as natural as possible such that we gain a

livable universe. Then we would expect Λ

∼ 10

−120

rather than say 10

−200

– 3 –

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