Simple and direct communication of dynamical supersymmetry breaking
Andrea RomaninoSISSA
with Francesco Caracciolo arXiv:1207.5376also based on earler work with Nardecchia, Ziegler, Monaco, Spinrath, Pierini
Leads to
Gauge coupling unification
Plausible dark matter candidate (with RP, independently motivated)
Calculable theory, can be extrapolated up to MPl
Needs to be broken, hopefully spontaneously
Effective description in terms of O(100) parameters
Most of the parameter space not viable
FCNC and CPV: useful constraint on supersymmetry breaking
LHC, unavoidable FT (depending on messenger scale)
M3 > 1.2 TeV
LHC, avoidable FT
msq > 1.4 TeV (but m1,2 ≠ m3)
mH ≈ 125 GeV? (but NMSSM, λSUSY)
Supersymmetry
W = �Uij u
ci qj hu + �D
ij dci qj hd + �E
ij eci lj hd + µ huhd
�Lsoft = AUij u
ci qjhu + AD
ij dci qjhd + AE
ij eci ljhd + m2
udhuhd + h.c.
+ (m2q)ij q
†i qj + (m2
uc)ij(uci )
†ucj + (m2
dc)ij(dci )
†dcj + (m2
l )ij l†i lj
+ (m2ec)ij(ec
i )†ec
j + m2hu
h†uhu + m2
hdh†
dhd
+M3
2gAgA +
M2
2WaWa +
M1
2BB + h.c.
Origin of supersymmetry breaking
A wide class of models of supersymmetry breaking
Hidden sector
Observable sector
SUSY breaking MSSM?
Z chiral superfield<Z> = Fθ2
F » (MZ)2SM singlet
Q chiral superfield
�d4�
Z†Z Q†Q
M2
M
[Polchinski Susskind, Dine Fischler,
Dimopoulos Raby, Barbieri Ferrara Nanopoulos]
� m2Q†Q, m =F
M
?
A wide class of models of supersymmetry breaking
Hidden sector
Observable sector
SUSY breaking MSSM?
A useful guideline: the supertrace constraint
Str M2 ≡ ∑bosons m2 - ∑fermions m2 (weighted by # of dofs)
Ren. Kähler + tree level + Tr(Ta) = 0:
Holds separately for each set of conserved quantum numbers
MSSM: incompatible with (Str M2)f,MSSM = ∑sfermions m2 - ∑fermions m2 > 0
G = GSM: incompatible with
m2lightest d-sfermion ⇥ m2
d �13g�DY
StrM2 = 0
(if DY < 0, consider up sfermions)
Addressing the supertrace constraint
Ren. Kähler + tree level + Tr(Ta) = 0 → Str M2 = 0
Supergravity: non-renormalizable Kähler: Str ≠ 0
“Loop” gauge-mediation: loop-induced: Str ≠ 0$$ $
Anomalous U(1)’s: Tr(Ta) ≠ 0: Str ≠ 0$ $ $ $ $ $
Tree-level gauge mediation: Str = 0 $ $ $ $ $ $
FCNC OK
FCNC OK
FCNC OK
FCNC ?
massive vector of aspontaneously broken U(1)
G ⊃ GSM x U(1)
↑
Tree-level gauge mediation
Z†
Z
Q†
QV
�d4�
Z†Z Q†Q
M2
⇒ Z, Q charged under U(1)
M ≈ MV scale of U(1) breaking m2
Q = qQqZF 2
M2V /g
2
SU(5)xU(1) ⊆ G, flavour universal charges, qZ > 0 for definitess
(l, dc) = 5: $$ $ q5 > 0 $ (m25 > 0, tree level)(q, uc, ec) = 10: $ q10 > 0$$ (m210 > 0, tree level)
SU(5)2xU(1) anomaly cancellation: $$ $ $ 0 = 3(q5 + 3q10)
(guaranteed if SU(5)xU(1) is embedded in SO(10))
Masses2 (before EWSB)
$ $ $ $ $ 5 + 10$$ $ $ $ extra = Φ+Φ
$ fermions$ $ 0$ $ $ $ $ $ M2
$ scalars$ $ 0 + m2 $ $ $ $ M2 - m2
Need of extra heavy (through U(1) breaking) fields
-
> 0 < 0+ extra
STr = 0
_-
⇒
M from U(1) breaking
U(1) breaking:$ $ $ <Y> = M
SUSY breaking:$ $ <Z> = Fθ2$
In concrete models: qZ = qY
h Y Φ Φ $ → MΦ = hM $
k Z Φ Φ$ →$$ $ $ $
The extra heavy fields as chiral messengers
_
�
X
Z
�
� �
k
hM
Vlight Vlight
Mg ⇠ �
4⇥
k
h
F
M
_
A wide class of models of supersymmetry breaking
Hidden sector
Observable sector
SUSY breaking MSSM
?
Phenomenologically viable supersymmetric models not always are theoretically complete
Theoretically complete models of susy breaking not always are phenomenologically viable
Phenomenologically viable and theoretically complete models not always are extremely simple
Reminder
Non-renormalization: $ Wcl = Wall orders in PT $$ $
W = Wcl + WNP
“Classical”breaking
“Dynamical”breaking
MSUSY ≈ M0 e-(2π/α b)
The (problematic) role of the R-symmetry
An exact R-symmetry prevents (Majorana) gaugino masses
Nelson-Seiberg: R-symmetry needed in a susy-breaking model where
i) the susy-breaking minimum is stable and
ii) the superpotential is generic
Non vanishing gaugino masses then require
non generic superpotential (R-breaking) $or
metastable susy-breaking minima$ $ $ or
spontaneous R-breaking$ $ $ $ $ $ or
Dirac gaugino masses
as if it that were not enough..
Spontaneous R-breaking in generalized O’R models needs R ≠ 0,2 (e.g. ISS flows to R = 0,2)
Even if R ≠ 0,2: the stability (everywhere) of the pseudoflat direction along which the R-symmetry is spontaneously broken forces Mg = 0 at 1-loop
More gaugino screening takes place (semi-direct)
Shih, hep-th/0703196Curtin Komargodski Shih Tsai, 1202.5331
Komargodski Shih, 0902.0030
Arkani-Hamed Giudice Luty Rattazzi, hep-ph/9803290Argurio Bertolini Ferretti Mariotti, 0912.0743
A simple, viable, dynamical model:3-2 + messenger/observable fields
[N=1 global, canonical K, no FI]
Reminder: 3-2 modelSU(3) strong at Λ3 where SU(2) weak
h « 1: calculability
SU(3) x SU(2) broken at M = Λ3/h1/7 » Λ3
SUSY broken at F = h M2 « M2
<L2> = 0.3 M + 1.3 Fθ2 $$ <L1> = 0
SU(3) SU(2) G ◆ GSM
Q 3 2 1U c 3 1 1Dc 3 1 1L 1 2 1
Wcl = hQDcL WNP =⇤73
detQQ
VNP
Vcl
Q =
✓Dc
U c
◆
[Affleck Dine Seiberg]
FL =�0 a2
�F
L =�0
pa2 � b2
�M
Details
FQ = FQ =
0
@ap
a2 � b2 � 1/(a3b2) 00 �1/(a2b3)0 0
1
AF
a ≈ 1.164b ≈ 1.131
Q = Q =
0
@a 00 b0 0
1
AM
non trivial, Mg = 0
Messengers+MSSM
Coupling to observable fields: semi-direct GM[Seiberg, Volansky, Wecht]
SU(2)
SU(3)
SUSY
Messengers GSM MSSM
� m2
2M2
�±= M2 ± F 2
�i =
✓�i
fi
◆, �i
SU(3) SU(2) G ◆ GSM
Q 3 2 1U c 3 1 1Dc 3 1 1L 1 2 1�i 1 2 RSM
�i 1 1 RSM
Our model[Caracciolo, R]
[no explicit mass term]
f = MSSM fields
W = L�i �i ! M�i�i + F✓2�i�i
�i,�i = messengers of MGM
gaugino masses
L†, Q†
L, Q
Φ†
ΦV3
m2�= 0m2
� = �g2 T3F 2
M2V
= ⌥m2
Mf = 0 M2f= +m2
M�,� = M
�
�
�
�
L
More details
c =2a8b8 + 2a2 + 4a4b4
pa2 � b2 � 2b2
3a8b6 � a6b8⇡ 1.48m2 = c
F 2
M2
Mi = 12a2p
a2 � b2↵i
4⇡
F
MM3(TeV) ⇡ 0.35 m
M > 1011 GeV
L†, Q†
L, Q
f†
f
X
k
Vi Vi
Yukawa interactions and Higgs
Yukawa interactions
SM fermions have T3 = -1/2 → Higgs doublets have T3 = 1 (triplets)
WY = λuij Φi Φj Hu + λdij Φi Φj Hd
The Higgs sector
Is model dependent
Two additional Higgs pairs not coupled to the SM fermions
The Higgs pair interacting with fermions has negative soft masses
Do arise from δK =
Because of the embedding of the messenger U(1) in a larger group (SU(2), SO(10))
Numerically:
A-terms
f†
X
f
�
L1
�
�
hL2i
At ⇡ � ↵y
6↵3M3
W = y L�� = yL2��+ yL1f�
(no A-m2 problem)
In order to get a 125 GeV Higgs
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.05.0
5.5
6.0
6.5
7.0
7.5
8.0
mé t1 HGeVL
y t
tanb = 10
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.05.0
5.5
6.0
6.5
7.0
7.5
8.0
mé t1 HGeVLy t
tanb = 50
2-loop corrections to sfermion masses
“Minimal” gauge mediation:$ $ O(1%)$$ flavour-blind
Matter-messenger couplings:$ O(3%)$$ flavour-safe
More details
mediation ones can be hardly larger than O (1%) and are flavour blind. The ones dueto the couplings in eq. (24) are also small enough to be ignored in the computation ofsfermion masses (for y↵ ⇠ 1, they give a O (3%) correction), but they can be relevantfor flavour processes. More precisely, the second and third couplings in eq. (24) areproportional to the MSSM Yukawas and therefore only give rise to harmless minimalflavour violating [21] (MFV) contributions. The first coupling, on the other hand, isproportional to unknown Yukawas y↵, which can in principle be largely off-diagonal in thebasis in which the MSSM Yukawas are diagonal, thus providing non-MFV contributionsto the soft masses. To show that the latter are also under control, let us write them, inmatrix form, as follows:
�m2f = 2
y⇤fyTf
(4⇡)2
T
2(4⇡)2� 2crf
g2r(4⇡)2
+
y⇤fyTf
(4⇡)2
!✓FL
ML
◆2
, (29)
where f = q, uc, dc, l, nc, ec,
T = Tr
�6yqy
†q + 3yucy
†uc + 3ydcy
†dc + 2yl y
†l + yncy
†nc + yecy
†ec�, (30)
and crf is the quadratic Casimir of the representation f with respect to the SM gaugefactor r.
We are now in the position of studying the bounds on the off-diagonal elements of�m2 from flavour physics. The off-diagonal elements have to be computed of course inthe basis in which the mass matrix of the fermions involved in the process is diagonal.By using the bounds in [22] we find, in the squark sector⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D12,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
12< 1.5–23
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D13,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
13< (0.5–1.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D23,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
23< (1.5–4.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤U12,⇥y⇤ucyTuc
�T/2� 2crug
2r + y⇤ucyTuc
�⇤U12
< 6–75,
where D and U denote the bases in which the up quark and down quark mass matricesare diagonal respectively. The weaker bounds assume that only one insertion at a timeis considered, with the others set to zero. The stronger ones assume that the left- andright-handed insertions are both non-vanishing and equal in size. Analogous limits canbe obtained in the slepton sector. In the limit in which all yukawa are equal, yq = yu =
yd = yl = yn = ye ⌘ y, and neglecting the negligible (for the purpose setting the limitsbelow) gauge contribution, we get
⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D12
< 1.5⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D13
< 0.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D23
< 1.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤U12
< 6.
12
mediation ones can be hardly larger than O (1%) and are flavour blind. The ones dueto the couplings in eq. (24) are also small enough to be ignored in the computation ofsfermion masses (for y↵ ⇠ 1, they give a O (3%) correction), but they can be relevantfor flavour processes. More precisely, the second and third couplings in eq. (24) areproportional to the MSSM Yukawas and therefore only give rise to harmless minimalflavour violating [21] (MFV) contributions. The first coupling, on the other hand, isproportional to unknown Yukawas y↵, which can in principle be largely off-diagonal in thebasis in which the MSSM Yukawas are diagonal, thus providing non-MFV contributionsto the soft masses. To show that the latter are also under control, let us write them, inmatrix form, as follows:
�m2f = 2
y⇤fyTf
(4⇡)2
T
2(4⇡)2� 2crf
g2r(4⇡)2
+
y⇤fyTf
(4⇡)2
!✓FL
ML
◆2
, (29)
where f = q, uc, dc, l, nc, ec,
T = Tr
�6yqy
†q + 3yucy
†uc + 3ydcy
†dc + 2yl y
†l + yncy
†nc + yecy
†ec�, (30)
and crf is the quadratic Casimir of the representation f with respect to the SM gaugefactor r.
We are now in the position of studying the bounds on the off-diagonal elements of�m2 from flavour physics. The off-diagonal elements have to be computed of course inthe basis in which the mass matrix of the fermions involved in the process is diagonal.By using the bounds in [22] we find, in the squark sector⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D12,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
12< 1.5–23
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D13,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
13< (0.5–1.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D23,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
23< (1.5–4.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤U12,⇥y⇤ucyTuc
�T/2� 2crug
2r + y⇤ucyTuc
�⇤U12
< 6–75,
where D and U denote the bases in which the up quark and down quark mass matricesare diagonal respectively. The weaker bounds assume that only one insertion at a timeis considered, with the others set to zero. The stronger ones assume that the left- andright-handed insertions are both non-vanishing and equal in size. Analogous limits canbe obtained in the slepton sector. In the limit in which all yukawa are equal, yq = yu =
yd = yl = yn = ye ⌘ y, and neglecting the negligible (for the purpose setting the limitsbelow) gauge contribution, we get
⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D12
< 1.5⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D13
< 0.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D23
< 1.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤U12
< 6.
12
mediation ones can be hardly larger than O (1%) and are flavour blind. The ones dueto the couplings in eq. (24) are also small enough to be ignored in the computation ofsfermion masses (for y↵ ⇠ 1, they give a O (3%) correction), but they can be relevantfor flavour processes. More precisely, the second and third couplings in eq. (24) areproportional to the MSSM Yukawas and therefore only give rise to harmless minimalflavour violating [21] (MFV) contributions. The first coupling, on the other hand, isproportional to unknown Yukawas y↵, which can in principle be largely off-diagonal in thebasis in which the MSSM Yukawas are diagonal, thus providing non-MFV contributionsto the soft masses. To show that the latter are also under control, let us write them, inmatrix form, as follows:
�m2f = 2
y⇤fyTf
(4⇡)2
T
2(4⇡)2� 2crf
g2r(4⇡)2
+
y⇤fyTf
(4⇡)2
!✓FL
ML
◆2
, (29)
where f = q, uc, dc, l, nc, ec,
T = Tr
�6yqy
†q + 3yucy
†uc + 3ydcy
†dc + 2yl y
†l + yncy
†nc + yecy
†ec�, (30)
and crf is the quadratic Casimir of the representation f with respect to the SM gaugefactor r.
We are now in the position of studying the bounds on the off-diagonal elements of�m2 from flavour physics. The off-diagonal elements have to be computed of course inthe basis in which the mass matrix of the fermions involved in the process is diagonal.By using the bounds in [22] we find, in the squark sector⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D12,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
12< 1.5–23
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D13,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
13< (0.5–1.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤D23,⇥y⇤dcy
Tdc�T/2� 2crdg
2r + y⇤dcy
Tdc�⇤D
23< (1.5–4.5) · 102
⇥y⇤qy
Tq
�T/2� 2crqg
2r + y⇤qy
Tq
�⇤U12,⇥y⇤ucyTuc
�T/2� 2crug
2r + y⇤ucyTuc
�⇤U12
< 6–75,
where D and U denote the bases in which the up quark and down quark mass matricesare diagonal respectively. The weaker bounds assume that only one insertion at a timeis considered, with the others set to zero. The stronger ones assume that the left- andright-handed insertions are both non-vanishing and equal in size. Analogous limits canbe obtained in the slepton sector. In the limit in which all yukawa are equal, yq = yu =
yd = yl = yn = ye ⌘ y, and neglecting the negligible (for the purpose setting the limitsbelow) gauge contribution, we get
⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D12
< 1.5⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D13
< 0.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤D23
< 1.5 · 102⇥y⇤yT
�8Tr(y⇤yT ) + y⇤yT
�⇤U12
< 6.
12
SummarySupersymmetry breaking remains the key of phenomenologically and theoretically successful supersymmetry models
Phenomenological issues/guidelines: FCNC, fine-tuning
Theoretical issues/guidelines: Str, R-symmetry
A simple, theoretically complete, and phenomenologically viable option
Susy breaking is communicated by extra, SB gauge interactions
Messenger and observable fields are charged under the hidden sector gauge group
Positive sfermion masses arise at the tree level, in a dynamical realization of TGM, but are not hierarchically larger than gaugino’s
A-terms are generated, and are possibly sizeable