Z'-mediated supersymmetry breaking.

Abstract

We consider a class of models in which supersymmetry breaking is communicated dominantly via a U1' gauge interaction, which also helps solve the mu problem. Such models can emerge naturally in top-down constructions and are a version of split supersymmetry. The spectrum contains heavy sfermions, Higgsinos, exotics, and Z' approximately 10-100 TeV, light gauginos approximately 100-1000 GeV, a light Higgs boson approximately 140 GeV, and a light singlino. A specific set of U1' charges and exotics is analyzed, and we present five benchmark models. The implications for the gluino lifetime, cold dark matter, and the gravitino and neutrino masses are discussed.

Full text

Page 1

arXiv:0710.1632v2 [hep-ph] 5 Feb 2008
Z′-mediated Supersymmetry Breaking
Paul Langacker∗, Gil Paz∗, Lian-Tao Wang†, Itay Yavin†
∗School of Natural Sciences, Institute for Advanced Study, Einstein Drive Princeton, NJ 08540
†Physics Department, Princeton University, Princeton NJ 08544
(Dated: February 5, 2008)
We consider a class of models in which supersymmetry breaking is communicated dominantly via
a U(1)′gauge interaction, which also helps solve the µ problem. Such models can emerge naturally
in top-down constructions and are a version of split supersymmetry. The spectrum contains heavy
sfermions, Higgsinos, exotics, and Z′∼ 10 − 100 TeV; light gauginos ∼ 100 − 1000 GeV; a light
Higgs ∼ 140 GeV; and a light singlino. A specific set of U(1)′charges and exotics is analyzed, and
we present five benchmark models. Implications for the gluino lifetime, cold dark matter, and the
gravitino and neutrino masses are discussed.
PACS numbers: 12.60.Jv, 12.60.Cn, 12.60.Fr
I.INTRODUCTION AND MOTIVATION
To a large extent, the mediation mechanism of super-
symmetry (SUSY) breaking determines the low energy
phenomenology. A well-studied scenario is gravity me-
diation [1]. During the last couple of decades, in order
to satisfy the increasingly stringent constraints from fla-
vor changing neutral current measurements, many other
mediation mechanisms, such as anomaly mediation [2],
gauge mediation [3], and gaugino mediation [4], have
been proposed (for a review, see [5]). In this letter, we
present a alternative mechanism in which SUSY break-
ing is mediated by exotic gauge interactions, such as an
additional U(1)′. Concrete superstring constructions fre-
quently lead to additional, non-anomalous, U(1)′factors
in the low-energy theory (see, e.g., [6]) with properties al-
lowing a U(1)′-mediated SUSY breaking. Scenarios with
an extra U(1)′involved in supersymmetry breaking me-
diation have been studied in various contexts [7]. Here,
we study a new scenario where Z′-mediation is the dom-
inant source for both scalar and gaugino masses.
Another ingredient we would like to consider is the µ-
problem of the Minimal Supersymmetric Standard Model
(MSSM). One class of solutions invokes a spontaneously
broken Peccei-Quinn symmetry (see, e.g.,
the point of view of top-down constructions it is com-
mon that such a symmetry is promoted to a U(1)′gauge
symmetry [9]. Identifying this U(1)′with the mediator
of SUSY breaking sets µ (as well as µB) to the scale of
the other soft SUSY breaking parameters, which are of
the right size whether or not the electroweak symmetry
breaking is finely tuned.
[8]). From
In the setup we propose, schematically shown in Fig. 1,
visible and hidden sector fields do not have direct renor-
malizable coupling with each other. At the same time,
they are both charged under U(1)′.
try breaking Z′-ino mass term, M˜ Z′, is generated due
to the U(1)′coupling to the hidden sector.
servable sector fields feel the supersymmetry breaking
through their couplings to U(1)′. The sfermion masses
are of order m2
A supersymme-
The ob-
˜ f∼ M2
˜ Z′/16π2. The SU(3)C× SU(2)L×
MSSM + S
+ Exotics
DSB
Z’
Hidden SectorVisible Sector
FIG. 1: Z′-mediated supersymmetry breaking.
U(1)Y gaugino masses are generated at higher loop order,
M1,2,3∼ M˜ Z′/(16π2)2, which is 2-3 order of magnitudes
lighter than the sfermions. LEP direct searches suggest
electroweak-ino masses > 100 GeV. We therefore expect
that the sfermions are heavy, typically about 100 TeV. In
this sense, this scenario can be viewed as a mini-version of
split-supersymmetry [10]. In particular, one fine-tuning
is needed to maintain a low electroweak scale. This sce-
nario does not have flavor or CP violation problems due
to the decoupling of the sfermions. One important differ-
ence from split-supersymmetry is the µ-parameter, which
is set by the scale of U(1)′breaking.
II.GENERIC FEATURES OF Z′-MEDIATED
SUPERSYMMETRY BREAKING
The visible sector contains an extension of the MSSM.
First, we introduce an extra U(1)′gauge symmetry. Sec-
ond, the µ parameter is promoted into a dynamical field,
µHuHd → λSHuHd.
which is charged under the U(1)′.
exotic matter multiplets with Yukawa couplings to S,
?
anomalies associated with the U(1)′. Such exotics and
couplings generically exist in string theory constructions.
S is a Standard Model singlet
Third, we include
i∈{exotics}YiSXiXc
i. They are included to cancel the

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2
A.Features of the Spectrum
We parameterize the hidden sector supersymmetry
breaking by a spurion field X = M + θ2F. At the scale
ΛS, supersymmetry breaking is assumed to generate a
mass M˜ Z′ ∼ g2
nent of the˜Z′vector superfield.
We assume that all the chiral superfields in the visible
sector are charged under U(1)′, so all the corresponding
scalars receive soft mass terms at 1-loop,
z′(F/M)/16π2for the fermionic compo-
m2
˜ fi∼
g2
16π2M2
z′Q2
fi
˜ Z′log
?ΛS
M˜ Z′
?
∼ (100 TeV)2
(1)
where gz′ is the U(1)′gauge coupling and Qfiis the U(1)′
charge of fi, which we take to be of order unity.
The SU(3)C× SU(2)L× U(1)Y gaugino masses can
only be generated at 2-loop level since they do not di-
rectly couple to the U(1)′gaugino,
Ma
∼
(2)
∼
g2
z′g2
a
(16π2)2M˜ Z′log
?ΛS
M˜ Z′
?
∼ 102− 103GeV
where gais the gauge coupling for the gaugino˜λa. It is
straightforward to verify that this is indeed the leading
U(1)′contribution to the gaugino mass. In particular, ki-
netic mixing induced by loops of visible sector fields does
not contribute significantly due to chiral symmetries.
The gravitino mass m3/2∼ F/MPdepends strongly on
the scale of supersymmetry breaking. Requiring MSSM
gaugino masses ≥ 100 GeV and assuming√F, M and ΛS
to be of the same order of magnitude, we find√F ∼ 107−
1011GeV. This is very different from gauge mediated
supersymmetry breaking, where the lower scale (∼ 10 −
1000 TeV ) typically implies a gravitino much lighter than
the other superpartners. Here, the scale is constrained
logarithmically by the requirement of radiative symmetry
breaking. Therefore, the gravitino mass is exponentially
sensitive to the choice of model parameters.
We also expect contributions to gaugino masses
through gravity mediation of the order F/MP, which
could be of the same order as Eq. 2. However, its contri-
bution to scalar masses ∼ F2/M2
with the Z′-mediation. Therefore, we expect the hierar-
chy between scalar and gaugino masses to be generic.
Pis negligible compared
B.Symmetry breaking and fine-tuning
The U(1)′gauge symmetry must be broken by the sin-
glet’s VEV ?S?. We assume this is triggered by radia-
tive corrections to the soft mass m2
Yukawa couplings to exotics. Therefore, successful ra-
diative breaking of U(1)′usually requires that those cou-
plings are not small. ?S? is parametrically only an order
S, especially through
of magnitude smaller than M˜ Z′. It is therefore reason-
able to first determine ?S? ignoring the Higgs doublets,
and then to consider the Higgs potential for the doublets
regarding ?S? as fixed.
To generate the electroweak scale ΛEWwe must fine-
tune one linear combination of the two Higgs doublets
to be much lighter than its natural scale. The full mass
matrix for the two Higgs doublets is,
M2
H=


m2
2
−AH?S?
m2
−AH?S?
Hu+ g2
Hd+ g2
1


m2
m2
2= m2
1= m2
z′QSQ2?S?2+ λ2?S?2
z′QSQ1?S?2+ λ2?S?2.(3)
Generically, one can tune various elements in M2
tain one small eigenvalue ∼ Λ2
mass term can be driven small or negative due to the
large top Yukawa coupling.
tions by tuning |m2
linear term is smaller, AH ∼ λg2
TeV, so integrating out Hd will not shift the smaller
eigenvalue significantly. tanβ is well approximated by
tanβ = m2
1/AH?S? ∼ 10 − 100. There is a single Stan-
dard Model-like Higgs scalar, with mass in the range
140 GeV. The remaining Higgs particles are at a scale
of order ∼ 100 TeV. The Higgs mass is somewhat heav-
ier than the typical prediction of the MSSM, due to the
U(1)′D term and the running of the effective quartic
coupling from M˜ Z′ down to the electroweak scale.
It is possible to tune with all the parameters, such
as gz′ and λ, of the same order.
is an interesting limit when gz′ ≪ λ.
we expect ?S? ∼ M˜ Z′/4π.
g2
since |m2
we expect the parameters to be chosen so that the sin-
glet’s VEV is even smaller ?S? ∼ (gz′/λ)M˜ Z′/4π. There-
fore, it is possible to have the singlino be very light
m˜S∼?10−3− 10−5?M˜ Z′. In certain cases, the Z′gauge-
boson, MZ′ ∼ gz′QS?S?, could even be light enough to
be produced at the LHC.
Hto ob-
EW. The up-type Higgs
One typically finds solu-
1∼ g2
z′M˜ Z′/16π2∼ λ × 10
2| ≪ m2
z′M2
˜ Z′/16π2. The tri-
In addition, there
Generically,
The singlino mass is ∼
z′M˜ Z′/16π2≪ M˜ Z′.
z′M2
z′Q2
S?S?2/M˜ Z′ ∼ g2
Hu| ∝ g2
Moreover,
2∼ Λ2
˜ Z′/16π2, to fine-tune m2
EW
III.MODEL PARAMETERS AND
LOW-ENERGY SPECTRUM
The free parameters are gz′, λ, the exotic Yukawa cou-
plings, the U(1)′charges, M˜ Z′, and the supersymmetry
breaking scale ΛS. The charges are chosen to cancel all
the anomalies. A minimal choice, which also leads to a
light wino (M2 < M1,3), involves the introduction of 3
families of colored exotics (D) and two uncolored SU(2)-
singlet families (E). Normalizing the down-type Higgs
charge to unity, Q1= 1, we are left with two independent
parameters, which we choose to be the up-type Higgs and
the left-handed quark charges, Q2and QQrespectively.
Several additional constraints need to be satisfied by the

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3
12345
Q2
QQ
gz′
λ
YD
YE
?S? 2 × 105
tanβ
M1
M2
M3
mH
m˜
Q3
m˜L33 × 105
m3/2
m˜ S
mZ′ 7 × 1041.5 × 1041.3 × 104
−1
−1
0.45
0.5
0.6
0.6
4
−1
−1
0.23
0.8
0.7
0.6
7 × 104
29
735
195
1200
140
5 × 104
105
3600
230
4
−1
−1
0.23
0.8
0.8
0.6
6 × 104
33
650
180
1100
140
4 × 104
105
810
160
4
−1
−2
0.06
0.3
0.4
0.1
2 × 1058 × 104
45
760
340
540
140
8 × 1044 × 104
2 × 104
3
31
5600
2
−1
−2
0.04
0.3
0.6
0.1
2
333
20
2700
710
4300
140
105
60
270
123
200
140
105
0.1
4
2100
890
4300
TABLE I: Model inputs and superpartner spectrum of five
representative models. Masses are in GeV. We fix M˜ Z′ = 106
GeV. The masses of the first two generations of squarks and
sfermions are typically larger than that of the third. The in-
put parameters λ, gz′ and YD,E are defined at ΛS. The spec-
tra are calculated using exact Renormalization Group Equa-
tions (RGE) (see, e.g., [12]). There is a theoretical uncer-
tainty due to multiple RGE thresholds. This mainly affects
mH, leading to a several GeV uncertainty. The gravitino mass
is calculated by m3/2= Λ2
could be deviations from this relation in some SUSY breaking
models which could lead to a gravitino mass that is different
by up to a couple orders of magnitude (typically lower). For
details, see [11].
S/MP assuming ΛS ∼
√F. There
choices of charges and other parameters. U(1)′has to be
spontaneously broken by radiative corrections. It must
allow appropriate fine-tuning to break the electroweak
symmetry.Moreover, since U(1)′D-terms could con-
tribute to scalar masses with either sign, one must check
for the existence of charge or color breaking minima.
We have found several regions in the (QQ,Q2) space
where a solution satisfies all the constraints. A detailed
scan will be presented in a forthcoming publication [11].
The results exhibit a variety of patterns for the low en-
ergy spectrum. In Table I, we display five representa-
tive models. Different ordering of the MSSM gaugino
and singlino masses could give rise to very different phe-
nomenology. The singlino mass typically has more vari-
ation since it is determined by fine-tuning. The appear-
ance of a light Z′in the spectrum, shown in model 5
(with σ×BR(Z′→ ℓ¯ℓ) ? 10 fb), could result in a spec-
tacular signal and help untangle the underlying model.
This generically happens in the case where the singlino
is very light.
A wino as the lightest supersymmetric particle (LSP)
and its nearly degenerate charged partner (the degener-
acy is lifted at one-loop by about 160 MeV [13] and al-
lows the decay˜ W+→˜ W0+π+, which results in a 4 cm
displaced vertex) have been studied extensively [14], es-
pecially in connection with anomaly mediated models [2].
It can annihilate efficiently into gauge bosons. For pure
thermal production the dark matter density is too low for
the several hundred GeV mass range we have assumed.
However, it can be considerably larger for non-standard
cosmological scenarios.
Due to small mixings, at most of the order λv/µtanβ,
the decay chain involving the singlino and wino will have
a long life-time which could result in a displaced vertex.
For example, depending on whether the decay is two or
three-body, the life-time for˜S → h(∗)+˜ W or ˜ W →
h(∗)+˜S is in the range of 10−11− 10−19s. This could
give an interesting signature in case of M2 > M˜S, or
M˜S> M2if the Z′is light enough and has an appreciable
branching ratio for decay into the singlino.
There is a wide range of possible gravitino masses,
m3/2∼ 10−3−104GeV. With typical assumptions about
cosmology, m3/2is strongly constrained by Big Bang Nu-
cleosynthesis (BBN). If the gravitino is not the LSP, we
typically require either it to be heavy (> 10 TeV) so it
decays before BBN, or that the reheating temperature
is less than about 105− 107GeV [15]. In the case that
the gravitino is the LSP and the next to lightest super-
symmetric particle (NLSP) is the wino, we require the
gravitino to be lighter than about 100 MeV [16]. It is
particularly problematic when the singlino is the NLSP
since its decay to the gravitino is further suppressed, un-
less the singlino density is strongly diluted by some late
time entropy generation. We also note that decaying into
a light gravitino, m3/2∼ MeV, is not observable on col-
lider time scales since the NLSP is neutral.
Since the squarks are heavy the gluino decays off-shell
[10]. Its life-time is very sensitive to gz′ and is given by,
τ˜ g= 4×10−16sec
?
m˜ Q
102TeV
?4?1 TeV
M3
?5
∝
1
z′. (4)
g6
Even though the life-time is long enough for the gluino to
hadronize it is too short to result in a displaced vertex.
Since the scalars are heavy, one-loop contributions to
most flavor observables (such as b → sγ ) are highly sup-
pressed. There are also two loop contributions to EDM
and muon g − 2. However, those are suppressed as com-
pared with the Split SUSY scenario [10] since the Hig-
gsinos are heavy and the singlino-wino mixing is small.
The exotic matter in this model is very heavy and does
not enter any collider phenomenology.
IV.DISCUSSION
In this letter, we discussed the generic feature of su-
persymmetry breaking dominantly mediated by an extra
U(1)′. We have used a U(1)′which forbids a µ term.
Such a requirement gives additional constraints and pre-
dicts interesting low energy phenomenology, such as the
existence of a light singlino and Z′in various regions of
the parameter space. However, Z′-mediation is possible
in a wider range of U(1)′models, such as U(1)B−L. We

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4
expect the hierarchy between the soft scalar masses and
the gaugino masses to be generic, although the detailed
pattern of soft terms could be quite different. Consider-
ing Z′-mediation in a broader range of models is certainly
worth pursuing.
The model presented here does not provide a seesaw
mechanism for neutrino mass. However, in a simple vari-
ant the U(1)′symmetry forbids Dirac Yukawa couplings
YνHuLνcat the renormalizable level, but allows them to
be generated by a higher-dimensional operator [17],
Wν= cν
S
MPHuLνc.(5)
This naturally yields small Dirac neutrino masses of order
(0.01cν) eV for ?S? = 100 TeV.
There are several scenarios for the decays and lifetimes
of the heavy exotic particles [18] and for gauge unifica-
tion. These depend on the details of the U(1)′charge
assignments, and will be discussed in [11].
Acknowledgments
We would like to thank Michael Dine, Nathan Seiberg,
and Herman Verlinde for useful discussions. The work of
L.W. and I.Y. is supported by the National Science Foun-
dation under Grant No. 0243680 and the Department of
Energy under grant # DE-FG02-90ER40542. P.L is sup-
ported by the Friends of the IAS and by the NSF grant
PHY-0503584. The work of G.P. was supported in part
by the Department of Energy # DE-FG02-90ER40542
and by the United States-Israel Bi-national Science Foun-
dation grant # 2002272.
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