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