ArticlePDF Available

Gaugino Mediated Supersymmetry Breaking

Authors:

Abstract and Figures

We consider supersymmetric theories where the standard-model quark and lepton fields are localized on a "3-brane" in extra dimensions, while the gauge and Higgs fields propagate in the bulk. If supersymmetry is broken on another 3-brane, supersymmetry breaking is communicated to gauge and Higgs fields by direct higher-dimension interactions, and to quark and lepton fields via standard-model loops. We show that this gives rise to a realistic and predictive model for supersymmetry breaking. The size of the extra dimensions is required to be of order 10-100 times larger than fundamental scale (e.g. the string scale). The spectrum is similar to (but distinguishable from) the predictions of "no-scale" models. Flavor-changing neutral currents are naturally suppressed. The \mu term can be generated by the Giudice-Masiero mechanism. The supersymmetric CP problem is naturally solved if CP violation occurs only on the observable sector 3-brane. These are the simplest models in the literature that solve all supersymmetric naturalness problems. Comment: Refs. added. 12 pages, 1 figure
Content may be subject to copyright.
arXiv:hep-ph/9911323v3 30 Nov 1999
UMD-PP-00-040, UW-PT/99-26
Gaugino Mediated Supersymmetry Breaking
Z. Chacko,
Markus A. Luty,
Ann E. Nelson,
Eduardo Ponon
Department of Physics, Box 351560
University of Washington
Seattle, Washington, 98195, USA
Department of Physics
University of Maryland
College Park, Maryland 20742, USA
Abstract
We consider supersymmetric theories where the standard-model quark and
lepton fields are localized on a ‘3-brane’ in extra dimensions, while the
gauge and Higgs fields propagate in the bulk. If supersymmetry is broken
on another 3-brane, supersymmetry breaking is communicated to gauge
and Higgs fields by direct higher-dimension interactions, and to quark and
lepton elds via standard-model loo ps. We show that this gives rise to
a realistic and predictive model for supersymmetry breaking. The size of
the extra dimensions is required to be of order 10–100 times larger than
fundamental scale (e.g. the string scale). The spectrum is similar to (but
distinguishable from) the predictions of ‘no-scale’ models. Flavor-changing
neutral currents a re naturally suppressed. The µ term can be generated
by the Giudice-Masiero mechanism. The supersymmetric CP problem is
naturally solved if CP violation occurs only on the observable sector 3-brane.
These are t he simplest models in the literature that solve all supersymmetric
naturalness problems.
November 12, 1999
1 Introduction
Supersymmetry (SUSY) provides an attractive framework for solving the hierarchy
problem, but it introduces naturalness puzzles of its own. Perhaps the most serious
is the ‘SUSY flavor problem:’ why do the squark masses conserve flavor? A natural
solution is given by models of gauge-mediated SUSY breaking [1] or by ‘anomalous
U(1)’ models [2]. In Ref. [3], Randall and Sundrum suggested another solution in
theories where the visible sector fields are localized on a ‘3-brane’ in extra dimensions
and the hidden sector fields are localized on a spatially separated ‘3-brane’. (Models
of this type were introduced in the context of string theory by Hoˇrava and Witten
[4].) Ref. [3] pointed out that in such theories contact terms between the visible and
hidden fields are suppressed if the separation r between the visible and hidden branes
is sufficiently large. The reason is simply that contact terms arising from int egra t ing
out states with mass M are suppressed by a Yukawa factor e
Mr
if M
>
r. Because
the suppression is exponentia l, the separation need only be an order of magnitude
larger than the fundamental scale (e.g. the string scale) to strongly suppress contact
int eractions.
If contact interactions between the hidden and visible sector fields can be ne-
glected, other effects become important for communicating SUSY breaking. One
possibility is the recently-discovered mechanism of anomaly-mediation [3, 5], a model-
independent supergravity effect that is always present. (For a careful discussion
of anomaly mediation in a specific higher-dimensional model, see Ref. [6].) Unfor-
tunately, if anomaly-mediation dominates, and if the visible sector is the minimal
sup ersymmetric standard model (MSSM), then slepton mass-squared terms are neg-
ative. This problem can be avoided in extensions of the MSSM [7]. In this paper,
we will explore the a lternate po ssibility that standard-model gauge and Higg s fields
propagate in the bulk and communicate SUSY breaking between the hidden sector
and visible-sector matter fields. Models with the all the MSSM superfields except
the gauge and Higgs fields localized on a 3 -brane were also considered in R ef. [8]. In
those models supersymmetry was directly broken by the compactification b oundary
conditions, requiring a rather large extra dimension (radius of order TeV
1
) in or -
der to explain the gauge hierarchy. Models similar to the one considered here , i.e.
with a hidden supersymmetry breaking sector sequestered on a different 3-brane and
standard-model gauge and Higg s fields in the bulk, were considered in Ref. [9]. These
models contained an additional U(1) gauge multiplet; the present paper shows that
this is not required to obta in a realistic theory of SUSY breaking.
In the higher-dimensional theory, the standard-model gauge and Higgs fields can
1
int eract only through non-renormalizable interactions. We therefore treat the higher-
dimensional theory as an effective theory with a cutoff M, which may be viewed as
the fundamental scale of the theory. Below the compactification scale µ
c
1/r, the
theory matches onto a 4-dimensional effective theory. In this theory, the couplings
of the gauge and Higgs fields are suppressed by 1/(Mr)
D 4
, where D is the number
of ‘large’ spacetime dimensions. Therefore, the size of the extra dimensions cannot
be too large in units of the fundamental scale. However, because the suppression of
cont act terms is exponential, there is a range of radii with sufficient suppression of
cont act terms to avoid flavor-changing neutral currents without exceeding the strong-
coupling bounds on the couplings in the higher-dimension t heory [9].
In this scenario, SUSY breaking masses for gauginos and Higgs fields are gener-
ated by higher-dimension contact terms between the bulk fields a nd the hidden sector
fields, assumed to arise from a more fundamental theory such as string theory. In par-
ticular, the µ t erm can be generated by the Giudice-Masiero mechanism [10]. Other
direct contact interactions between the hidden and visible sectors are suppressed be-
cause o f their spatial separation. The leading contribution to SUSY breaking for
visible sector fields arises from loops of bulk gauge and Higgs fields, as illustrated in
Fig. 1. These diagrams are ultraviolet convergent (and hence calculable) because the
spatial separation of the hidden and visible branes acts as a physical point-splitting
regulator. In effective field theory language, the contribution from loop momenta
above the compactification scale is a (finite) matching contribution, while the con-
tribution from loop momenta below the compactification scale can be obtained from
the 4 -dimensional effective theory. The higher-dimensional theory therefore gives ini-
tial conditions for the 4-dimensional renormalization group at t he compactification
scale µ
c
: nonzero gaugino masses and Higgs mass parameters, and loop-suppressed
soft SUSY breaking parameters for the squarks and sleptons. This is similar to the
boundary conditions of ‘no-scale’ supergravity models [11], but in the present case
the boundary conditions are justified by the geometry of the higher-dimensional the-
ory. Since the SUSY breaking masses for a ll chiral matter fields other than the third
generation squarks are dominated by the gaugino loop, we call this scenario ‘ga ugino
mediated SUSY breaking’ (˜gMSB).
The renormalization group has a strong effect on the SUSY breaking parameters,
and the soft masses at the weak scale are all of the same order. In fact, the Bino can
be the lightest superpartner (LSP) in this scenario. The spectrum is similar to that
of ‘no-scale’ supergravity models [11], with the important difference that the present
scenario allows a Fayet-Iliopoulos term for hypercharge that can have an important
effect on the slepton spectrum. We obtain realistic spectra without excessive fine-
2
Fig. 1. The leading diagram t hat contributes to SUSY-breaking scalar
masses in the models considered in this paper. The bulk line is a
gaugino propagator with two mass insertions on the hidden brane.
tuning for neutralino and slepton masses below approximately 200 GeV, suggesting
that these superpartners are relatively light in this scenario.
This paper is organized as follows. In Section 2, we discuss the higher-dimensional
theory. We show that the size of the extra dimensions can be large enough to suppress
FCNC’s while still having gauge and Higgs couplings of order 1 at low energies. We
also show how the SUSY CP problem can be naturally solved in this class of models.
In Section 3, we discuss the phenomenology of this class of models. Section 4 contains
our conclusions.
2 Bulk Gauge and Higgs Fields
In this Section, we discuss some general features of higher-dimensional theories with
gauge and Higgs fields in the bulk and other fields localized on ‘3-branes.’ We use
the term ‘3 -branes’ to mean either dynamical surfaces (e.g. topological defects or
string-theory D-branes) or non-dynamical features of t he higher-dimensional space-
time (e.g. o r bifo ld fixed point s). All of these ingredients occur in string theory, but we
will not concern ourselves with the derivation of the model from a more fundamental
theory. We simply write an effective field theory valid below some scale M, which
may be the string scale, the compactification scale a ssociated with additional small
3
dimensions, or some other new physics.
We t herefore consider an effective theory with D spacetime dimensions, with 3 +1
non-compact spacetime dimensions and D 4 compact spatial dimensions with linear
size of order r. The D-dimensional effective lagrangian takes the form
L
D
= L
bulk
(Φ(x, y)) +
X
j
δ
D 4
(y y
j
)L
j
(Φ(x, y
j
), φ
j
(x)), (2.1)
where j runs over the various branes, x are coordinates for the 4 non-compact space-
time dimensions, y are coordinates for the D 4 compact spatial dimensions, Φ is
a bulk field, and φ
j
is a field localized on the j
th
brane. This effective theory can
be treated using the usual techniques of effective field theory, and parameterizes the
most general interactions of the assumed degrees o f freedom below the scale M.
1
We assume that the D 4 extra spatial dimensions are compactified on a distance
of order r 1/M. We also assume that the distance between different branes is also
of order r. This ensures that contact interactions between fields on different branes
arising from states above the cutoff are suppressed by the Yukawa factor e
Mr
.
We assume that the standard-model gauge and Higgs fields propagate in the bulk.
Bulk gauge fields have a gauge coupling with mass dimension 4 D, which is an
irrelevant interaction fo r all D > 4. When we match onto the 4-dimensional theory
at the compactification scale, the effective 4-dimensional gauge coupling is
2
g
2
4
=
g
2
D
V
D 4
, (2.2)
where g
D
is the gauge coupling in the D-dimensional theory a nd V
D 4
r
D 4
is the
vo lume of the compact dimensions. If g
D
1/M
D 4
, we have g
4
1/(Mr)
D 4
1,
which is unacceptable. In order to have g
4
1 (a s observed), we require the gauge
coupling to be larger than unity in units of M. However, it presumably does not make
sense to take g
D
larger than its strong-coupling value, defined to be the value where
loop corrections are order 1 at the scale M. This follows from ‘na¨ıve dimensional
analysis’ (NDA) [14, 15], which is known to work extremely well in supersymmetric
theories [16]. If we assume that the loop corrections are suppressed by ǫ at the scale
M, the lagrangian is [9]
L
D
M
D
ǫℓ
D
L
bulk
(
ˆ
Φ/M, /M) +
X
j
δ
D 4
(y y
j
)
M
4
ǫℓ
4
L
j
(
ˆ
Φ/M,
ˆ
φ
j
/M, /M). (2.3)
1
For a n explicit supersymmetric example and calculations, see Ref. [12].
2
We neglect the effects of gravitational curvature.
4
Torus: Sphere:
D
ML
max
e
ML
max
/2
Mr
max
e
Mr
max
5 740 3 × 10
162
118 4 × 10
52
6
63 2 × 10
14
18 2 × 10
8
7
29 6 × 10
7
11 3 × 10
5
8
20 5 × 10
5
8.7 2 × 10
4
9
16 3 × 10
4
8.0 3 × 10
4
10
14 9 × 10
4
7.8 4 × 10
4
11
13 1 × 10
3
7.8 4 × 10
4
Table 1. Estimates of the maximum size and exponential suppression
factor for propagation between two branes of maximal separation. L
max
is the maximum length of a cycle of a symmetric torus, and r
max
is the
maximum radius of the sphere.
where
D
= 2
D
π
D /2
Γ(D/2) is the geometrical loop factor for D dimensions, and all
couplings in L
bulk
and L
j
are order 1. Note that the fields
ˆ
Φ and
ˆ
φ in Eq. (2.3) do not
have canonical kinetic terms. The idea behind Eq. (2.3) is that the fa ctors multiplying
L
bulk
and L
j
act as loop-counting parameters (like ¯h in the semiclassical expansion)
that cancel the loo p factors and ensure that loop corrections are suppressed by ǫ.
Strong coupling corresponds to ǫ 1.
We can use Eq. (2.3) to read off the value of the D-dimensional gauge coupling
g
2
D
ǫℓ
D
M
D 4
. (2.4)
We can obtain the maximum value for the size of the extra dimension consistent with
the fact that g
4
1 by setting ǫ 1 and using Eq. (2.2) . The results are shown
in Table 1. We see that the exponential suppression factor due to the large size of
the extra dimensions can be substantial even for many extra dimensions [9]. Similar
conclusions hold for the Higgs interactions.
To see how much suppression is required, note that the dangerous contact terms
have the form (using Eq. (2.3))
L
brane
e
Mr
M
2
Z
d
4
θ (
ˆ
φ
hid
ˆ
φ
hid
)(φ
obs
φ
obs
), (2.5)
where the observable fields (but not the hidden fields) have been canonically normal-
ized. This must be compared with the operators that give rise to the gaugino and
5
Higgs SUSY breaking par ameters. From Eq. (2.3) we obtain
L
brane
D
4
Z
d
2
θ
1
M
D 3
ˆ
φ
hid
W
α
W
α
+ h.c.
+
D
4
Z
d
4
θ
(
1
M
D 3
ˆ
φ
hid
H
u
H
d
+ h.c.
+
1
M
D 4
ˆ
φ
hid
ˆ
φ
hid
h
H
u
H
u
+ H
d
H
d
+ (H
u
H
d
+ h.c.)
i
)
,
(2.6)
where W
α
is the gauge field strength and H
u,d
are the Higgs fields, normalized to
have canonical kinetic terms in D dimensions. (More precisely, these are N = 1
sup erfields obtained by projecting the bulk supermultiplets onto the branes. For a
specific example, see Ref. [12].) Matching to the D-dimensional theory, we find
m
1/2
, µ
ˆ
F
hid
M
D
/ℓ
4
M
D 4
V
D 4
, Bµ, m
2
H
u
, m
2
H
d
ˆ
F
2
hid
M
2
D
/ℓ
4
M
D 4
V
D 4
. (2.7)
Note that the Bµ term and the Higg s mass-squared terms are enhanced by a volume
factor.
3
For example,
Bµ
m
2
1/2
4
D
M
D 4
V
D 4
ǫℓ
4
, (2.8)
where we have imposed g
4
1 to obtain the last estimate. We see that if the theory is
strongly coupled at the fundamental scale, we require a fine tuning of order 1/ℓ
4
1%
to obtain all SUSY breaking para meters of the same size [9]. However, for a small
number of extra dimensions, the fundamental theory need not be strongly coupled at
the fundamental scale, and we can naturally obtain all SUSY breaking terms close
to the same size. For example for D = 5 compactified on a circle with circumference
L 20/M, the exponential suppression is e
10
5 × 10
5
and Bµ/m
2
1/2
4. As
the number of extra dimensions increases, the strong coupling estimate is approached
rapidly. See Table 2.
The contribution to visible sector scalar masses from contact terms is
m
2
vis
e
Mr
ˆ
F
hid
M
!
2
. (2.9)
3
This point was missed in an earlier version of this paper . It was pointed out in Ref. [13], which
appeared while this paper was being completed. See also Ref. [9].
6
Torus: Sphere:
D
Bµ/m
2
1/2
Bµ/m
2
1/2
5 3.4 3.4
6
10 16
7
28 43
8
69 85
9
160 130
Table 2. Estimates of Bµ/m
2
1/2
for the symmetric torus and the sphere.
The size of the extra dimension is chosen so that the exponential sup-
pression factor is of order e
8
3 × 10
4
(approximately the maximum
suppression for large D) . This means that the tor us has cycle length
L = 16/M, and the sphere has radius r = 8/M.
The values Eq. (2.7) are the values renormalized at the compactification scale; we will
later see that we require
ˆ
F
vis
/M 200 GeV. Using the experimental constraints
4
m
2
˜
d˜s
m
2
˜s
<
(6 × 10
3
)
m
˜s
1 TeV
, Im
m
2
˜
d˜s
m
2
˜s
!
<
(4 × 10
4
)
m
˜s
1 TeV
, (2.10)
so e
Mr
10
3
to 10
4
is plausibly sufficient to suppress FCNC’s.
We now discuss the loop effects that communicate SUSY breaking to the visible
sector fields, such as those illustrated in Fig. 1. These are ultraviolet convergent be-
cause the separation of the hidden and visible branes acts as a physical point-splitting
regulator for these diagrams. Another way to see this is that there is no local coun-
terterm in the D-dimensional theory that can cancel a possible overall divergence.
5
Given a specific D-dimensional theory, this diagram is therefore calculable. From
the point of view of 4-dimensional effective field theory, the extra dimensions act as a
cutoff of order µ
c
1/r. The effects of this cutoff can be absorbed into a counterterm
for the visible sector scalar masses and A terms of order
m
2
vis
g
2
4
16π
2
m
2
1/2
, A
vis
g
2
4
16π
2
m
1/2
, (2.11)
where m
1/2
is the gaugino mass. The precise value of the counterterms is calculable if
we fully specify the D-dimensional theory. However, we will see that the RG running
of the soft masses f r om µ
c
to the weak scale gives large additive contributions to the
4
For a complete discussion, s ee e.g. Ref. [17].
5
Multiloop diagrams may have subdivergences, but these can always be cancelled by counterterms
localized on one of the branes.
7
visible soft masses, and the final results are rather insensitive to the precise value of
the counterterm. We will therefore be content with the simple estimate above.
Note that the soft terms arising from cont act terms are larger than the anomaly-
mediated contributions, which give
m
λ
g
2
4
16π
2
F
hid
M
4
, m
2
H
u
, m
2
H
d
g
2
4
16π
2
F
hid
M
4
!
2
, (2.12)
where M
4
>
M is the 4-dimensional Planck scale [3, 5]. The other soft terms also get
cont ributions larger than their anomaly-mediated values from the RG, as discussed
above. Therefore, we can neglect the a no maly-mediated contribution in this class of
models.
The higher-dimensional origin of these theories can a lso solve the ‘SUSY CP prob-
lem’ [18]. This problem arises from the fact that the phases in the SUSY breaking
terms must be much less than 1, otherwise t hey give rise t o electron and neutron
electric dipole moments in conflict with experimental bounds. This is a natural-
ness problem because CP is (apparently) maximally violated in the CKM matrix,
and it must be explained why it is not violated in all terms. In the present model,
CP-violating phases can appear in µ, B, and m
1/2
, generated from higher-dimension
operators in Eq. (2.6). The phases in µ a nd B can be rota t ed away using a combi-
nation of U(1)
PQ
and U(1)
R
transformations, leaving a single phase in m
1/2
. This
phase can vanish naturally in the present model if CP is violated only by terms in the
lagrangian localized on the visible brane. This is a natural assumption because loop
effects do not g enerate local CP-violating terms in the bulk or the hidden brane. This
situation can arise (for example) if CP is broken spontaneously by fields localized on
the visible brane. (In order to avoid a lar ge neutron electric dip ole moment, we must
also assume that the effects o f the QCD vacuum angle are suppressed [19].)
There are many ot her aspects of the higher-dimensional theory that we could
discuss, but the basic features of the scenario depend only on the qualitative feature
that the visible and hidden sectors are spatially separated. A complete specification
of the higher-dimensional model would have to take into a ccount the fact that there
are more supersymmetries in higher dimensions. This may be broken spontaneously
or explicitly (e.g. by an orbifold), and couplings between bulk and boundary fields
must be consistent with SUSY. An explicit example with 5 dimensions compactified
on a S
1
/Z
2
orbifold is easily constructed [12, 9]. Another important feature o f the
higher-dimensional theory is the stabilization of the extra dimensions. Stabilization
mechanisms that are appropriate for the scenario we are considering ar e discussed in
Refs. [20, 6]. We conclude that there is no obstacle to constructing realistic effective
field theory models of the type outlined here. The question of whether a model of
8
this type can be derived from a more fundamental theory such as string theory is left
for future work.
3 Phenomenology
We now turn to the phenomenology of these models. We have seen that the SUSY
breaking parameters in the effective 4-dimensional theory are determined at the com-
pactification scale µ
c
1/r. We have also seen that µ
c
is one to two orders of
magnitude below the fundamental scale M, which is most natura lly taken to be
close to the string scale. Therefore, we expect µ
c
to be close to the unification scale
M
GUT
2 × 10
16
GeV. We therefore identif y µ
c
and M
GUT
in making our estimates.
We will further assume that the theory is embedded in a grand-unified theory
(GUT) at the scale M
GUT
, as suggested by the success of gauge coupling unifica-
tion in the MSSM. We therefore consider the following SUSY breaking parameters
renormalized at M
GUT
:
Gaugino masses: M
1
= M
2
= M
3
= m
1/2
,
Higgs masses: m
2
H
u
, m
2
H
d
m
2
1/2
, µ, B m
1/2
,
Squark and slepton masses: m
2
m
2
1/2
16π
2
,
A terms: A
m
1/2
16π
2
.
(3.1)
We have arg ued above that these conditions can emerge naturally in this scenario for
D = 5 or 6. If we neglect the small loop-suppressed parameters, the model is defined
by the 6 para meters m
1/2
, m
2
H
u
, m
2
H
d
, µ, B, and y
t
renormalized at M
GUT
. (We do
not consider large tan β solutions, so we neglect all other Yukawa couplings.) The
value of y
t
at the weak scale fixes tan β fro m the observed value of the top quark.
The requirement that electroweak symmetry breaks with the correct value of M
Z
and
tan β then fixes two more parameters. We see that we are left with essentia lly 4
parameters.
An important issue when analyzing the spectrum at the weak scale is the radiative
corrections t o the lightest neutral Higgs mass [21]. The largest effect can be viewed
as a top loop contribution to a n effective quartic term in the effective potential below
the stop mass [22]. We include an estimate of this effect by adding the term
V
H
=
3y
4
t
8π
2
ln
m
˜
t
m
t
!
(H
u
H
u
)
2
(3.2)
9
to the Higgs p otentia l.
We evolve the 1-loop RG equations from the scale M
GUT
= 2 × 10
16
GeV down
to the weak scale µ
W
= 5 00 GeV, using α
GUT
= 1/(24.3). We use input values of
m
1/2
, m
2
H
u
, m
2
H
d
, and y
t
at M
GUT
and determine µ and B by imp osing electroweak
symmetry breaking. The value of the top quark mass is used to fix tan β; we use
m
t
(µ
W
) = 1 65 GeV, which includes 1-loop QCD corrections. We minimize the Higgs
potential including the term Eq. (3.2) with m
˜
t
taken to be the heaviest of the stop
mass eigenstates, and y
t
renormalized at µ
W
. These approximations could be refined,
but they will suffice to illustrate the main features of the spectrum of this class of
models.
Some parameter choices that give rise to realistic spectra are given in Table 3.
We find that the dependence on the overall scale of the initial SUSY breaking masses
is what would be expected: the superpartners become heavier, a nd the amount of
fine-tuning required to achieve electroweak symmetry breaking increases (see below).
The right-handed sleptons get an important positive contribution from a hypercharge
Fayet-Iliopoulos term if m
2
H
d
> m
2
H
u
at the GUT scale. This distinguishes this model
from ‘no-scale’ models. This is illustrated in the second and third parameter points
in Table 3. For m
2
H
d
> m
2
H
u
, we easily obtain spectra where the LSP is a neutralino.
The value of y
t
mainly influences the value of tan β, which is important because the
lightest Higgs boson is light for small tan β. We also find that tan β
>
2.5 is preferred
in order to have a sufficiently large mass for the lightest neutral Higgs.
An important feature of these results is the amount of fine-tuning required to
achieve electroweak symmetry breaking. We define the fractional sensitivity to a
parameter c (a coupling renormalized a t M
GUT
) to be [23]
sensitivity =
c
v
v
c
, (3.3)
where v is the Higgs VEV and the derivative is ta ken with all other couplings at the
GUT scale held fixed. The largest sensitivity is to m
1/2
and µ, and the values of
the sensitivity parameter are given in Table 3. We see that the sensitivity increases
strongly as the superpartner masses are increased. Note that even for parameters
where the superpartner masses are close to the experimental limits, the sensitivity
parameter is large (
>
20). However, it is argued by Anderson and Casta˜no in Ref. [24]
that sensitivity does not capture the idea of fine-tuning: the theory is fine-tuned only
if the physical quantities significantly more sensitive than a priori allowed choices of
parameters. From this point of view, the fine-tuning of points with low superpartner
masses is much less severe, and naturalness clearly favors regions of parameters with
light superpartner masses [2 4]. In particular, requiring that the naturalness parameter
10
Point 1 Point 2 Point 3
inputs: m
1/2
200 400 400
m
2
H
u
(200)
2
(400)
2
(400)
2
m
2
H
d
(300)
2
(600)
2
(400)
2
µ 370 755 725
B 315 635 510
y
t
0.8 0.8 0.8
neutralinos: m
χ
0
1
78 165 165
m
χ
0
2
140 315 315
m
χ
0
3
320 650 630
m
χ
0
4
360 670 650
char ginos: m
χ
±
1
140 315 315
m
χ
±
2
350 670 645
Higgs: tan β 2.5 2.5 2.5
m
h
0
90 100 100
m
H
0
490 995 860
m
A
490 1000 860
m
H
±
495 1000 860
sleptons: m
˜e
R
105 200 160
m
˜e
L
140 275 285
m
˜ν
L
125 265 280
stops: m
˜
t
1
350 685 690
m
˜
t
2
470 875 875
other squarks: m
˜u
L
470 945 945
m
˜u
R
450 905 910
m
˜
d
L
475 950 945
m
˜
d
R
455 910 905
gluino: M
3
520 1000 1050
sensitivity: m
1/2
16 50 50
µ 19 78 78
Table 3. Sample points in parameter space. All masses are in GeV. In
the first two points, the LSP is mostly Bino, while in the third it is a
right-handed slepton. The sensitivity parameter is defined in the main
text.
11
defined in Ref. [24] be less than 10 implies that the parameter m
1/2
should b e less
than 400 GeV.
4 Conclusions
This model is the simplest supersymmetric theory in the literature that generates
an acceptable spectrum for the sup erpartners while explaining the absence of non-
standard flavor-changing processes a nd electric dipole moments. It is highly pre-
dictive, with squark and slepton masses qualitatively similar to those of ‘no-scale’
sup ergravity models. The nonuniversality o f the up- and down-type Higg s masses at
the GUT scale can distinguish this theory from ‘no-scale’ supergravity—the expected
difference between the up and down type Higgs masses generates a hypercharge Fayet-
Iliopoulos term which affects the slepton mass spectrum. The right-handed sleptons
and the lightest neutralino are significantly lighter than the other superpartners, and
obtaining natural electroweak symmetry breaking requires that these be lighter than
roughly 200 GeV.
While this work was being completed, we received Ref. [13 ], which considers very
similar ideas.
Acknowledgments
M.A.L. and E.P. are supported by the NSF under grant PHY-98-02551. Z.C. and
A.E.N. are supported by the DOE under contra ct DE-FGO3-96-ER40956
References
[1] M. Dine, W. Fischler, M. Srednicki, Nucl. Phys. B189, 575 (1981); S. Dimopou-
los, S. Raby, Nucl. Phys. B192, 353 (1981); L. Alvarez–Gaum´e, M. Claud-
son, M.B. Wise, Nucl. Phys. B207, 96 (1982 ) ; M. Dine, A.E. Nelson, hep-
ph/9303230, Phys. Rev. D48, 1277 (1993); M. Dine, A.E. Nelson, Y. Shirman,
hep-ph/9408384, Phys. Rev. D51, 1362 ( 1995); M. Dine, A.E. Nelson, Y. Nir,
Y. Shirman, hep-ph/9507378, Phys. Rev. D53, 2658 (1996); H. Murayama, hep-
ph/9705271, Phys. Rev. Lett. 79, 18 (1997); S. Dimopoulos, G. Dvali, R. Rat-
tazzi, G .F. Giudice, hep-ph/970530 7, Nucl. Phys. B510, 1 2 (1998 ); M.A. Luty,
hep-ph/9706554, Phys. Lett. 414B, 71 (1997); For a review, see G.F. Giudice,
R. Rattazzi, hep-ph/9801271.
12
[2] G. Dvali, A. Pomarol, hep-ph/9607383, Phys. Rev. Lett. 77, 37 28 (1996); P.
Binetruy, E. Dudas, hep-th/9607172 , Phys. Lett. 389B, 503 (1996); R.N. Moha-
patra and A. Riotto, Phys. Rev. D55, 1138 (1997); A.E. Nelson and D. Wright,
Phys. Rev. D56, 159 8 (1997); N. Arkani-Hamed, M. Dine, S.P. Martin, hep-
ph/9803432, Phys. Lett. 431B, 329 (19 98).
[3] L. Randall, R. Sundrum, hep-th/9810155.
[4] P. Hoˇrava, E. Witten, hep-th/9510209, Nucl. Phys. B460, 506 (1996); E. Wit-
ten, hep-th/960 2070, Nucl. Phys. B471, 135 (1996); P. Hoˇrava, E. Witten, hep-
th/9603142, Nucl. Phys. B475, 94 (1996).
[5] G.F. Giudice, M.A. Luty, H. Murayama, R. Rattazzi, hep-ph/9810442, JHEP
9812, 02 7 (1998).
[6] M.A. Luty, R . Sundrum, hep-th/99102 02.
[7] A. Pomarol, R. Rattazzi, hep-ph/9903448, JHEP 9905, 013 (1999); Z. Chacko,
M.A. Luty, I. Maksymyk, E. Pont´on, hep-ph/9905390; E. Katz, Y. Shadmi, Y.
Shirman, hep-ph/9906296, JHEP 9908, 015 (1999).
[8] I. Antoniadis, Phys. Lett. 246B, 31 7 (1990); I. Antoniadis, K. Benakli, Phys. Lett.
326B, 69 (1994); I. Antoniadis, S. Dimopoulos, G. Dvali, Nucl. Phys. B516, 70
(1998); I. Antoniadis, S. Dimopoulos, A. Pomarol, M. Quiros, Nucl. Phys. B544,
503 (1999); A. Delgado, A. Po marol, M. Quiros, Phys. Rev. D60, 095008 (1999).
[9] Z. Chacko, M.A. Luty, E. Po nt´o n, hep-ph/9909248.
[10] G.F. Giudice, A. Masiero, Phys. Lett. 206B, 480 (1988).
[11] J. Ellis, K. Enqvist, D.V. Nanopoulos, Phys. Lett. 147B, 99 (1984); J. Ellis, C.
Kounnas, D.V. Nanopoulos, Nucl. Phys. B247, 373 (1984); For a review, see
A.B. Lahana s, D.V. Nanopoulos, Phys. Rep. 145, 1 (1 987).
[12] E.A. Mirabelli, M.E. Peskin, hep-th/9712214, Phys. Rev. D58, 065002 (1998).
[13] D.E. Ka plan, G. Kribs, M. Schmaltz, hep-ph/991 1293.
[14] A. Manohar, H. Georgi, Nucl. Phys. B234, 189 (1984); H. Georgi, Weak Inter-
actions and Modern Particle Theory, Benjamin/Cummings, (Menlo Park, 1 984);
H. Georgi, L. Randall, Nucl. Phys. B276, 241 (1986).
13
[15] M.A. Luty, hep-ph/9706235, Phys. Rev. D57, 1531 (1998); A.G. Cohen, D.B.
Kaplan, A.E. Nelson, hep-ph/9706275, Phys. Lett. 412B, 301 (1997).
[16] L. Randall, R. Rattazzi, E. Shuryak, hep-ph/9803 258, Phys. Rev. D59, 035005
(1999); M.A. Luty, R. Rattazzi, hep-th/9908085.
[17] F . Gabbiani, E. Gabrielli, A. Masiero, L. Silvestrini, hep-ph/9604387, Nucl. Phys.
B477, 321 ( 1996).
[18] M. D ugan, B. Grinstein, L. Hall, Nucl. Phys. B255, 413 (1985).
[19] R.D. Peccei, H.R. Quinn, Phys. Rev. Lett. 38, 1440 (1977); Phys. Rev. D16,
1791 (1977 ) ; S. Weinberg, Phys. Rev. Lett. 40, 223 (1978 ); F. Wilczek, Phys.
Rev. Lett. 40, 279 (1978); A.E. Nelson, Phys. Lett. 136BB, 387 (1984); S.M.
Barr, Phys. Rev. Lett. 53, 329 (1 984); D.B. Kaplan, A.V. Manohar Phys. Rev.
Lett. 56, 2004 (1986).
[20] W.D. Goldberger, M.B. Wise, hep-ph/9907447.
[21] Y. Okada, M. Yamaguchi, T. Yanagida, Prog. Theor. Phys. 85, 1 (1991); H.E.
Haber, R. Hempfling, Phys. Rev. Lett. 66, 1 815 (1991); J. Ellis, G. Ridolfi, F.
Zwirner, Phys. Lett. 257B, 83 (1991); Phys. Lett. 262B, 477 (1991 ); R. Ba rbieri,
M. Fr ig eni, F. Caravaglios, Phys. Lett. 258B, 167 (1991); J.R. Espinosa, M.
Quiros, Phys. Lett. 267B, 27 (1991).
[22] H.E. Haber, R. Hempfling, hep-ph/9307201, Phys. Rev. D48, 4 280 (1993).
[23] R. Barbieri, G.F. Giudice, Nucl. Phys. B306, 63 (1988).
[24] G.W. Anderson, D.J. Casta˜no, hep-ph/9409419, Phys. Lett. 347B, 300 (1995);
hep-ph/9412322, Phys. Rev. D52, 1693 (1693).
14
... It is capable of beautifully addressing the electroweak (EW) hierarchy problem, improving the fit to Grand Unification, and offering WIMP dark matter (DM) candidates, if SUSY breaking occurs close to the weak scale. In general, as in any rich weak-scale BSM scenario, it faces the challenge of understanding how excessive flavor-changing neutral currents (FCNCs) and CP violation are suppressed as well as internal challenges such as the µ problem, but there are now robust field theory mechanisms known, such as gauge-mediated SUSY breaking (GMSB) (for a review, see, for example, [2]) and the higher-dimensional sequestered structures of anomaly-mediated SUSY breaking AMSB [3] and gaugino-mediated SUSY breaking (gMSB) [4,5]. ...
... Along these lines, we consider ref. [55], building on ref. [50], to be the most attractive model in the literature so far. It is based ongMSB [4,5], which provides a flexible departure point for flavor-safe model-building to realize the Sleptonic SUSY hierarchy, rooted in a hierarchical UV gaugino mass parameters. The Sleptonic SUSY spectrum provides intriguing physics discovery opportunities at the LHC and future colliders. ...
... The central UV structure is depicted in figure 1. Gaugino-mediation requires an extradimensional interval [4,5], in which the SM fermions and sfermions ("matter" superfields) are localized on one (3 + 1-dimensional) boundary, while the hidden sector responsible for spontaneous SUSY-breaking is localized on the other boundary. The gauge and Higgs superfields propagate in the 5-dimensional bulk. ...
Article
Full-text available
A bstract We study an attractive scenario, “Sleptonic SUSY”, which reconciles the 125 GeV Higgs scalar and the non-observation of superpartners thus far with potentially pivotal roles for slepton phenomenology: providing viable ongoing targets for LHC discovery, incorporating a co-annihilation partner for detectable thermal relic dark matter, and capable of mediating the potential muon g − 2 anomaly. This is accomplished by a modestly hierarchical spectrum, with sub-TeV sleptons and electroweakinos and with multi-TeV masses for the other new states. We study new elements in the UV MSSM realization of Sleptonic SUSY based on higher-dimensional sequestering and the synergy between the resulting gaugino-mediation, hypercharge D -term mediation and Higgs-mediation of SUSY-breaking, so as to more fully capture the range of possibilities. This framework stands out by harmoniously solving the flavor, CP and μ − Bμ problems of the supersymmetric paradigm. We discuss its extension to orbifold GUTs, including gauge-coupling and b -tau unification. We also develop a non-minimal model with extra Higgs fields, in which the electroweak vacuum is more readily cosmologically stable against decay to a charge-breaking vacuum, allowing a broader range of sleptonic spectra than in the MSSM alone. We survey the rich set of signals possible at the LHC and future colliders, covering both R -parity conservation and violation, as well as for dark matter detection. While the multi-TeV squarks imply a Little Hierarchy Problem, intriguingly, small changes in parameter space to improve naturalness result in dramatic phase transitions to either electroweak-preservation or charge-breaking. In a Multiverse setting, the modest unnaturalness may then be explained by the “principle of living dangerously”.
... A detail collider simulation is important but beyond the scope of the present paper. A smaller M inp would effectively lead to larger |µ|-term and thus larger muon g−2 (see (18)). To see this, let us fix the gravitino mass. ...
... One can also consider other flavor-safe mediation mechanisms e.g. Refs.[14][15][16][17][18].2 This kind of cosmological safety with alleviation of the gravitino problem with m 3/2 O(10) TeV can be found in the pure-gravity mediation scenario[19,20], minimal-split SUSY[21] or the split-SUSY[22,23].3 ...
Preprint
A simple model for the explanation of the muon anomalous magnetic moment was proposed by the present authors within the context of the minimal supersymmetric standard model [1607.05705, 1608.06618]: "Higgs-anomaly mediation". In the setup, squarks, sleptons, and gauginos are massless at tree-level, but the Higgs doublets get large negative soft supersymmetry (SUSY) breaking masses squared $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at a certain energy scale, $M_{\rm inp}$. The sfermion masses are radiatively generated by anomaly mediation and Higgs-loop effects, and gaugino masses are solely determined by anomaly mediation. Consequently, the smuons and bino are light enough to explain the muon $g-2$ anomaly while the third generation sfermions are heavy enough to explain the observed Higgs boson mass. The scenario avoids the SUSY flavor problem as well as various cosmological problems, and is consistent with the radiative electroweak symmetry breaking. In this paper, we show that, although the muon $g-2$ explanation in originally proposed Higgs-anomaly mediation with $M_{\rm inp}\sim 10^{16}\,$GeV is slightly disfavored by the latest LHC data, the muon $g-2$ can still be explained at $1\sigma$ level when Higgs mediation becomes important at the intermediate scale, $M_{\rm inp} \sim 10^{12}\,$GeV. The scenario predicts light SUSY particles that can be fully covered by the LHC and future collider experiments. We also provide a simple realization of $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at the intermediate scale.
... There is another breaking mechanism in literature such as the Anomaly mediated SUSY breaking [167,168], Gaugino mediated SUSY breaking [169,170], Gravity-Gauge mediated SUSY breaking [171] and SUSY-breaking using extra dimensions. These both have a fine-tuning problem. ...
Preprint
Full-text available
The discovery of the Higgs boson raises the question of its "lightness" in mass when the Standard Model is considered as an effective quantum field theory. Supersymmetry is the only currently known symmetry which can protect the Higgs mass while still treating the Higgs as an elementary quantum field. However in the view of null experimental confirmation from both direct (LHC) and indirect searches (flavour, dark matter) of the supersymmetric particles and the constraints from the Higgs mass, several possible heavy spectra for supersymmetric partners have been proposed. In the present thesis, we study the possible origins of these heavy spectra by considering a considering many sequestered spurion fields as carriers of supersymmetry breaking. We show that "natural" supersymmetric spectrum is possible in these models and in particular a "coherent" scenario leads to low fine tuning, light Higgsino mixed dark matter ( a la focus point region) even with heavy supersymmetric spectrum. We then consider this model within the context of string landscape, where we use the Bousso-Polchinski framework of four form fluxes to model the spurions. We show that the flavour violating parameters of supersymmetric spectrum can be "diluted" away in the presence of large number of fluxes. One of the possible supersymmetric spectra which emerges by considering all the data is the generation split (Gensplit) spectrum which allows for flavour violation to be present for the first two generations, which are heavy. We study this spectrum within the context of supersymmetric SU(5) and proton decay. The results are quite interesting and dependent on the proton decay mode considered. The strongest bound p to k \nu is now modified depending on the flavour of the neutrino and brings the parameter space within the realms of upcoming experiments of JUNO, DUNE and Hyper K. These results will be discussed.
... Elaborate mechanisms of SUSY breaking such as gauge mediation (see refs. [27, 28] for reviews) and gaugino mediation [29,30] are able to address the issue. ...
Article
Full-text available
A bstract Hierarchical masses of quarks and leptons are addressed by imposing horizontal symmetries. In supersymmetric Standard Models, the same symmetries play a role in suppressing flavor violating processes induced by supersymmetric particles. Combining the idea of spontaneous CP violation to control contributions to electric dipole moments (EDMs), the mass scale of supersymmetric particles can be lowered. We present supersymmetric models with U(1) horizontal symmetries and discuss CP and flavor constraints. Models with two U(1) symmetries are found to give a viable solution to the muon g − 2 anomaly. Interestingly, the parameter space to explain the anomaly will be probed by future electron EDM experiments.
... • Gaugino mediation: In an extra-dimensional setup, Supersymmetry may be broken in a hidden sector on a brane that is separated spatially from the visible sector brane along the extra dimension(s). Here, the gauge supermultiplets propagate in the bulk (i.e. between the branes), and therefore feel the Supersymmetry breaking directly, although the effects are suppressed by the size/length of the extra dimension(s) [44,32,45,46]: ...
Thesis
In this dissertation, we will cover aspects of the phenomenology of supersymmetric models, with an emphasis on models with heavier scalar partners of Standard Model fermions. We first introduce the Standard Model, providing explanations for why it should be extended by Supersymmetry. We also provide an introduction to general aspects of supersymmetric models, making use not only of bottom-up phenomenological constraints, but also top-down theoretical insight from String/M-Theory compactifications. In the body of this dissertation, we study in detail the phenomenology of supersymmetric models with heavier scalars at current and future colliders, as well as in low-energy flavor experiments in both the absence and the presence of CP violation. Finally, we discuss general implications of String theory for dark matter in supersymmetric models, as well as the dynamics of Grand Unified Theories in a broad class of models.
... These flavor violating processes originate from soft SUSY breaking mass parameters which mixes different generations of sfermions. The dangerous flavor violating sfermion masses are avoided when the SUSY breaking masses are generated through gauge interactions and SM Yukawa interactions, leading us to gaugino mediation [10][11][12] or Higgs mediation [13,14]. 1 In these mediation mechanisms, the slepton and squark masses vanish at the tree-level and they are generated radiatively via gaugino loops or Higgs loops. Therefore, the flavor problem is absent within MSSM even if some SUSY particles are as light as O(0.1-1 TeV) [17]. ...
Article
Full-text available
A bstract We consider supersymmetric (SUSY) models for the muon g − 2 anomaly without flavor violating masses at the tree-level. The models can avoid LHC constraints and the vacuum stability constraint in the stau-Higgs potential. Although large flavor violating processes are not induced within the framework of minimal SUSY standard model, once we adopt a seesaw model, sizable lepton flavor violating (LFV) processes such as μ → eγ and μ → e conversion are induced. These LFV processes will be observed at future experiments such as MEG-II, COMET and Mu2e if right-handed neutrinos are heavier than 10 ⁹ GeV motivated by the successful leptogenesis. This conclusion is somewhat model independent since Higgs doublets are required to have large soft SUSY breaking masses, leading to flavor violations in a slepton sector via neutrino Yukawa interactions.
... The origins of supersymmetry-breaking being a separate sector does force us to expand our model of particle physics, but on the upshot this sequestering means we can explore interesting phenomenology in sectors which are unconstrained. One can write down models where supersymmetry breaking is mediated by supergravity effects [123,124,125,126,127,128,129], communicated to the SM fields by our gauge bosons from a sector with new, massive SM-charged particles [130,131,132,133,134,135], or takes place at a physically separate location in an extra dimension [136,137,138,139,140,141,142,143,144,145], for a few examples. A full discussion of the mechanisms and strategies for models of supersymmetry-breaking is beyond our scope, but we highly recommend ...
Preprint
Full-text available
We begin this thesis with an extensive pedagogical introduction aimed at clarifying the foundations of the hierarchy problem. After introducing effective field theory, we discuss renormalization at length from a variety of perspectives. We focus on conceptual understanding and connections between approaches, while providing a plethora of examples for clarity. With that background we can then clearly understand the hierarchy problem, which is reviewed primarily by introducing and refuting common misconceptions thereof. We next discuss some of the beautiful classic frameworks to approach the issue. However, we argue that the LHC data have qualitatively modified the issue into `The Loerarchy Problem'---how to generate an IR scale without accompanying visible structure---and we discuss recent work on this approach. In the second half, we present some of our own work in these directions, beginning with explorations of how the Neutral Naturalness approach motivates novel signatures of electroweak naturalness at a variety of physics frontiers. Finally, we propose a New Trail for Naturalness and suggest that the physical breakdown of EFT, which gravity demands, may be responsible for the violation of our EFT expectations at the LHC.
... These flavor violating processes originate from soft SUSY breaking mass parameters which mixes different generations of sfermions. The dangerous flavor violating sfermion masses are avoided when the SUSY breaking masses are generated through gauge interactions and SM Yukawa interactions, leading us to gaugino mediation [9][10][11] or Higgs mediation [12,13]. 1 In these mediation mechanisms, the slepton and squark masses vanish at the tree-level and they are generated radiatively via gaugino loops or Higgs loops. Therefore, the flavor problem is absent within MSSM even if some SUSY particles are as light as O(0.1-1 TeV) [16]. ...
Preprint
We consider supersymmetric (SUSY) models for the muon $g-2$ anomaly without flavor violating masses at the tree-level. The models can avoid LHC constraints and the vacuum stability constraint in the stau-Higgs potential. Although large flavor violating processes are not induced within the framework of minimal SUSY standard model, once we adopt a seesaw model, sizable lepton flavor violating (LFV) processes such as $\mu \to e \gamma$ and $\mu \to e$ conversion are induced. These LFV processes will be observed at future experiments such as MEG-II, COMET and Mu2e if right-handed neutrinos are heavier than $10^9$ GeV motivated by the successful leptogenesis. This conclusion is somewhat model independent since Higgs doublets are required to have large soft SUSY breaking masses, leading to flavor violations in a slepton sector via neutrino Yukawa interactions.
... One can also consider other flavor-safe mediation mechanisms e.g. refs.[14][15][16][17][18]. ...
Article
Full-text available
A simple model for the explanation of the muon anomalous magnetic moment was proposed by the present authors within the context of the minimal supersymmetric standard model [1, 2]: Higgs-anomaly mediation. In the setup, squarks, sleptons, and gauginos are massless at tree-level, but the Higgs doublets get large negative soft supersymmetry (SUSY) breaking masses squared mHu2≃mHd2<0 at a certain energy scale, Minp. The sfermion masses are radiatively generated by anomaly mediation and Higgs-loop effects, and gaugino masses are solely determined by anomaly mediation. Consequently, the smuons and bino are light enough to explain the muon g − 2 anomaly while the third generation sfermions are heavy enough to explain the observed Higgs boson mass. The scenario avoids the SUSY flavor problem as well as various cosmological problems, and is consistent with the radiative electroweak symmetry breaking. In this paper, we show that, although the muon g − 2 explanation in originally proposed Higgs-anomaly mediation with Minp∼ 1016 GeV is slightly disfavored by the latest LHC data, the muon g − 2 can still be explained at 1σ level when Higgs mediation becomes important at the intermediate scale, Minp∼ 1012 GeV. The scenario predicts light SUSY particles that can be fully covered by the LHC and future collider experiments. We also provide a simple realization of mHu2≃mHd2<0 at the intermediate scale.
Article
Full-text available
We demonstrate that the recent measurement of the anomalous magnetic moment of the muon and dark matter can be simultaneously explained within the minimal supersymmetric standard model. Dark matter is a mostly bino state, with the relic abundance obtained via coannihilations with either the sleptons or wino. The most interesting regions of parameter space will be tested by the next generation of dark matter direct detection experiments.
Article
Full-text available
We give an explanation of the CP conservation of strong interactions which includes the effects of pseudoparticles. We find it is a natural result for any theory where at least one flavor of fermion acquires its mass through a Yukawa coupling to a scalar field which has nonvanishing vacuum expectation value.
Article
We construct a class of simple and calculable theories for the supersymmetry breaking soft terms. They are based on quantum modified moduli spaces. These theories do not break supersymmetry in their ground state; instead we postulate that we live in a supersymmetry breaking plateau of false vacua. We demonstrate that tunneling from the plateau to the supersymmetric ground state is highly supressed. At one loop, the plateau develops a local minimum which can be anywhere between 10 8 GeV and the grand unification scale. The value of this minimum is the mass of the messengers of supersymmetry breaking. Primordial element abundances indicate that the messengers’ mass is smaller than 10 12 GeV.
Article
In the minimal supersymmetric standard model, it is shown that a radiative correction of the top and stop loops gives a finite, but non-negligible contribution to Higgs scalar masses if m_{t} =~ 150-250 GeV. The upper limit to the lightest-scalar mass becomes 70-190 GeV in the range of heavy top quark.
Article
We construct realistic supergravity models where supersymmetry breaking arises from the D terms of an anomalous U(1) gauge symmetry broken at the Planck scale. The model has the attractive feature that the gaugino masses, the A terms, and the mass splittings between the like-charged squarks of the first two generations compared to their average masses (i.e., Δmq̃2/mq̃2) are all suppressed. As a result, the electric dipole moment of the neutron as well as the flavor-changing neutral current effects are predicted to be naturally small. We show how some versions of these models can lead to the expected value of the μ and Bμ terms and qualitatively explain the observed mass hierarchy among quarks and leptons.
Article
It is pointed out that a global U(1) symmetry, that has been introduced in order to preserve the parity and time-reversal invariance of strong interactions despite the effects of instantons, would lead to a neutral pseudoscalar boson, the ''axion,'' with mass roughly of order 100 keV to 1 MeV. Experimental implications are discussed.
Article
In the strong-coupling limit of the heterotic string theory constructed by Horava and Witten, an 11-dimensional supergravity theory is coupled to matter multiplets confined to 10-dimensional mirror planes. This structure suggests that realistic unification models are obtained, after compactification of 6 dimensions, as theories of 5-dimensional supergravity in an interval, coupling to matter fields on 4-dimensional walls. Supersymmetry breaking may be communicated from one boundary to another by the 5-dimensional fields. In this paper, we study a toy model of this communication in which 5-dimensional super-Yang-Mills theory in the bulk couples to chiral multiplets on the walls. Using the auxiliary fields of the Yang-Mills multiplet, we find a simple algorithm for coupling the bulk and boundary fields. We demonstrate two different mechanisms for generating soft supersymmetry breaking terms in the boundary theory. We also compute the Casimir energy generated by supersymmetry breaking.
Article
The requirement that P and T be approximately conserved in the color gauge theory of strong interactions without arbitrary adjustment of parameters is analyzed. Several possibilities are identified, including one which would give a remarkable new kind of very light, long-lived pseudoscalar boson.
Article
We present the first phenomenologically viable model of gauge meditation of supersymmetry breaking without a messenger sector or gauge singlet fields. The standard model gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, it can preserve perturbative gauge unification thanks to the inverted hierarchy mechanism. There is no dangerous negative contribution to m2q~, m2l~ due to two-loop renormalization group equation. The potentially nonuniversal supergravity contribution to m2q~ and m2l~ can be suppressed enough. The model is completely chiral, and one does not need to forbid mass terms for the messenger fields by hand. Cosmology of the model is briefly discussed.
Article
We prove a simple theorem about the anti theta parameter in grand unified models with spontaneous CP breaking. This theorem states two conditions on such models which, if fulfilled, imply that anti theta is zero at tree level. Models which fulfill these conditions are generalizations of a recent model of A. Nelson and are easy to construct. 8 references.