An Attractor for Natural Supersymmetry...Equal mass squarks and gluinos are excluded below 1400 GeV in both scenarios. References [1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008)

Timothy Cohen (SLAC)

Timothy Cohen(SLAC)

with Anson Hook and Gonzalo TorrobaarXiv:1204.1337

Santa Fe “LHC Now” Summer WorkshopJuly 13, 2012

An Attractor for Natural Supersymmetry

1/22Timothy Cohen (SLAC)


The Status of Weak Scale SUSY2Timothy Cohen (SLAC)

ATLAS-CONF-2012-033

/22

gluino mass [GeV]600 800 1000 1200 1400 1600 1800 2000

squark

mass

[G

eV

]

600

800

1000

1200

1400

1600

1800

2000

= 100 fbSUSY

σ

= 10 fbSUSY

σ

= 1 fbSUSY

σ

) = 0 GeV1

0χ∼Squark-gluino-neutralino model, m(

=7 TeVs, -1 L dt = 4.71 fb∫

Combined

PreliminaryATLAS

observed 95% C.L. limitsCL

median expected limitsCL

σ1 ±Expected limit

ATLAS EPS 2011

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[G

eV

]1/2

m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)

q~

(1000)

q ~

(1400)

q ~

(1800)

q ~

>0µ= 0, 0

= 10, AβMSUGRA/CMSSM: tan

=7 TeVs, -1 L dt = 4.71 fb∫Combined

PreliminaryATLAS

Combined



ATLAS EPS 2011

LSPτ∼

LEP Chargino

No EWSB

Figure 7: 95% CLs exclusion limits obtained by using the signal region with the best expected sensitiv-ity at each point in a simplified MSSM scenario with only strong production of gluinos and first- andsecond-generation squarks, and direct decays to jets and neutralinos (left); and in the (m0 ; m1/2) plane ofMSUGRA/CMSSM for tan � = 10, A0 = 0 and µ > 0 (right). The red lines show the observed limits, thedashed-blue lines the median expected limits, and the dotted blue lines the ±1� variation on the expectedlimits. ATLAS EPS 2011 limits are from [17] and LEP results from [59].

7 Summary

This note reports a search for new physics in final states containing high-pT jets, missing transversemomentum and no electrons or muons, based on the full dataset (4.7 fb�1) recorded by the ATLASexperiment at the LHC in 2011. Good agreement is seen between the numbers of events observed in thedata and the numbers of events expected from SM processes.

The results are interpreted in both a simplified model containing only squarks of the first two genera-tions, a gluino octet and a massless neutralino, as well as in MSUGRA/CMSSM models with tan � = 10,A0 = 0 and µ > 0. In the simplified model, gluino masses below 940 GeV and squark masses be-low 1380 GeV are excluded at the 95% confidence level. In the MSUGRA/CMSSM models, values ofm1/2 < 300 GeV are excluded for all values of m0, and m1/2 < 680 GeV for low m0. Equal mass squarksand gluinos are excluded below 1400 GeV in both scenarios.

References

[1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.

[2] H. Miyazawa, Baryon Number Changing Currents, Prog. Theor. Phys. 36 (6) (1966) 1266–1276.

[3] P. Ramond, Dual Theory for Free Fermions, Phys. Rev. D3 (1971) 2415–2418.

[4] Y. A. Golfand and E. P. Likhtman, Extension of the Algebra of Poincare Group Generators andViolation of p Invariance, JETP Lett. 13 (1971) 323–326. [PismaZh.Eksp.Teor.Fiz.13:452-455,1971].

[5] A. Neveu and J. H. Schwarz, Factorizable dual model of pions, Nucl. Phys. B31 (1971) 86–112.

14



ATLAS-CONF-2012-033

/22

gluino mass [GeV]600 800 1000 1200 1400 1600 1800 2000

squark

mass

[G

eV

]

600

800

1000

1200

1400

1600

1800

2000

= 100 fbSUSY

σ

= 10 fbSUSY

σ

= 1 fbSUSY

σ

) = 0 GeV1


=7 TeVs, -1 L dt = 4.71 fb∫

Combined

PreliminaryATLAS




ATLAS EPS 2011

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[G

eV

]1/2

m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)

q~

(1000)

q ~

(1400)

q ~

(1800)

q ~

>0µ= 0, 0



PreliminaryATLAS

Combined



ATLAS EPS 2011

LSPτ∼

LEP Chargino

No EWSB


7 Summary



References






14

mg̃ & 1 TeV

mq̃ & 1.5 TeV



ATLAS-CONF-2012-033

/22

gluino mass [GeV]600 800 1000 1200 1400 1600 1800 2000

squark

mass

[G

eV

]

600

800

1000

1200

1400

1600

1800

2000

= 100 fbSUSY

σ

= 10 fbSUSY

σ

= 1 fbSUSY

σ

) = 0 GeV1


=7 TeVs, -1 L dt = 4.71 fb∫

Combined

PreliminaryATLAS




ATLAS EPS 2011

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[G

eV

]1/2

m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)

q~

(1000)

q ~

(1400)

q ~

(1800)

q ~

>0µ= 0, 0



PreliminaryATLAS

Combined



ATLAS EPS 2011

LSPτ∼

LEP Chargino

No EWSB


7 Summary



References






14

mg̃ & 1 TeV

mq̃ & 1.5 TeV

Does this tell us that the MSSM is unnatural?!?


“Natural Supersymmetry”• Fine tuning in the MSSM:

• Dominant contributions:

3

�m2Z ' 2�|µ|2 + em2Hu

�

� em2Hu ' �y2t

16⇡2

✓12 em2t log⇤+

32

⇡↵s|M3|2 log2 ⇤

◆+ . . .

/22


“Natural Supersymmetry”• A “natural” spectrum only requires that the 3rd generation

squarks and gauginos are light.• Also referred to as a “split-family” or “more-minimal SUSY”

spectrum.• LHC bounds on these particles are weaker then on the 1st

and 2nd generation squarks.• Helps alleviate flavor problems.

• These models can not solve the flavor problem due to tachyonic constraints from 2-loop contributions.

• Known ways of mediating SUSY are flavor blind (e.g. gauge mediation)

• A “natural” spectrum requires novel model building.

4

Papucci, Ruderman, Weiler [arXiv:1110:6926]

Dimopoulos, Giudice [1995];Cohen, Kaplan Nelson [1996]

/22


When is “Natural SUSY” dead?

5

Martin White 11 University of Melbourne

All exclusion limits on one plot

Talk by Martin White [ICHEP 2012]

/22


When is “Natural SUSY” dead?• The discovery of an SM-like Higgs at 125 GeV impacts the

way we think about naturalness and low energy SUSY.• I would like to advocate for the following classification

(naively ordered in decreased tuning)

•(Mini)-Split-SUSY• Stops at O(10-100 TeV) and a tuned/anthropic weak scale.

•The large A-term MSSM• Stop soft masses and A-term at O(TeV). This gives one light stop and

one heavier stop. Maybe both are observable at the LHC?

•The Natural MSSM• Both stop soft masses and A-term are below O(TeV). The stop

parameters do not imply a Higgs mass of 125 GeV.

6

The large A-term MSSM

(Mini)-Split-SUSY

The Natural(er) MSSM

/22


THE MODEL

7/22


The Model

8

SU(3)X SU(3)CFT⌃, ⌃

Q1, u1, d1 Q2, u2, d2 Q3, u3, d3

M (the messenger scale)

⇤CFT (cross-over to the conformal regime)

v (exit the conformal regime)

mW (the weak scale)

A quiver description:

Relevant mass scales:

/22

Timothy Cohen (SLAC) 9

SU(3)CFT SU(3)X SU(2)W U(1)Y

Q3 1 1/6d3 1 1 1/3u3 1 1 �2/3Hu 1 1 1/2Hd 1 1 �1/2⌃ 1 0⌃ 1 0A 1 1 + adj 1 0Q2,1 1 1/6d2,1 1 1 1/3u2,1 1 1 �2/3

Table 1: The particle content and charge assignments for the MSSM quark and CFT sectors. Thesubscripts denote generation assignments and the leptons are charged as in the MSSM. The visiblecolor gauge group is a diagonal subgroup of SU(3)CFT ⇥ SU(3)X .

an escape from the conformal regime while also giving masses to the bi-fundamentals. Thesuperpotential contains the following relevant terms:

W � Q3 Hu u3 +Q3 Hd d3 + ⌃A⌃+W��U(1) . (1)Contractions over gauge indices are implicit. W��U(1) will be instrumental in breaking someof the abelian symmetries which can spoil the desired low energy spectrum. We will discussthis term in detail below.

With this matter content, SU(3)CFT has five flavors and flows to a strongly interactingsuperconformal fixed point in the IR. The dynamical scale below which this group becomesstrong is denoted by ⇤CFT. The remaining gauge groups are IR free and act as spectators tothis strong dynamics. A crucial property of the model is that the third generation Yukawacouplings appear as relevant interactions in the CFT. The Higgs fields will then also bepart of the CFT — they will receive a positive anomalous dimension. These couplings (aswell as the rest of the interactions in Eq. (1)) become marginal below ⇤CFT, so their value isnaturally order one. In contrast, the remaining Yukawas will arise as irrelevant deformations,resulting in a flavor hierarchy between the third and first two generations.

If we do not add extra fields, this matter content spoils gauge coupling unification.However, there are no issues with Landau poles up to the GUT scale and one could imagineUV completing the model using full SU(5) representations. We will come back to this pointbriefly in §4, while here we continue to focus on this minimal realization.

The energy scales in our model are as follows, see Fig. 2. At the messenger scale M , softsupersymmetry breaking operators are generated. The supersymmetry breaking mechanismand mediation can be arbitrary, up to certain assumptions on global symmetries that wedescribe below. The scale M could be above or below ⇤CFT, but the physical soft massesshould be smaller than ⇤CFT so that the superconformal dynamics dominate. At a scale

4

W � Q3 Hu u3 +Q3 Hd d3 + ⌃A⌃+W��U(1)

The matter content:

Marginal superpotential:

Relevant deformation:

The number of flavors associated with is . This gauge group flows to a strongly interacting conformal fixed point in the IR.

SU(3)CFTNf = 5

W � �v2 TrAThis relevant deformation forces which breaks .

⌦⌃⌃

↵= v2

SU(3)CFT ⇥ SU(3)X ! SU(3)C

/22

Timothy Cohen (SLAC) 9

SU(3)CFT SU(3)X SU(2)W U(1)Y

Q3 1 1/6d3 1 1 1/3u3 1 1 �2/3Hu 1 1 1/2Hd 1 1 �1/2⌃ 1 0⌃ 1 0A 1 1 + adj 1 0Q2,1 1 1/6d2,1 1 1 1/3u2,1 1 1 �2/3

Table 1: The particle content and charge assignments for the MSSM quark and CFT sectors. Thesubscripts denote generation assignments and the leptons are charged as in the MSSM. The visiblecolor gauge group is a diagonal subgroup of SU(3)CFT ⇥ SU(3)X .

an escape from the conformal regime while also giving masses to the bi-fundamentals. Thesuperpotential contains the following relevant terms:

W � Q3 Hu u3 +Q3 Hd d3 + ⌃A⌃+W��U(1) . (1)Contractions over gauge indices are implicit. W��U(1) will be instrumental in breaking someof the abelian symmetries which can spoil the desired low energy spectrum. We will discussthis term in detail below.

With this matter content, SU(3)CFT has five flavors and flows to a strongly interactingsuperconformal fixed point in the IR. The dynamical scale below which this group becomesstrong is denoted by ⇤CFT. The remaining gauge groups are IR free and act as spectators tothis strong dynamics. A crucial property of the model is that the third generation Yukawacouplings appear as relevant interactions in the CFT. The Higgs fields will then also bepart of the CFT — they will receive a positive anomalous dimension. These couplings (aswell as the rest of the interactions in Eq. (1)) become marginal below ⇤CFT, so their value isnaturally order one. In contrast, the remaining Yukawas will arise as irrelevant deformations,resulting in a flavor hierarchy between the third and first two generations.

If we do not add extra fields, this matter content spoils gauge coupling unification.However, there are no issues with Landau poles up to the GUT scale and one could imagineUV completing the model using full SU(5) representations. We will come back to this pointbriefly in §4, while here we continue to focus on this minimal realization.

The energy scales in our model are as follows, see Fig. 2. At the messenger scale M , softsupersymmetry breaking operators are generated. The supersymmetry breaking mechanismand mediation can be arbitrary, up to certain assumptions on global symmetries that wedescribe below. The scale M could be above or below ⇤CFT, but the physical soft massesshould be smaller than ⇤CFT so that the superconformal dynamics dominate. At a scale

4

W � Q3 Hu u3 +Q3 Hd d3 + ⌃A⌃+W��U(1)

The matter content:

Marginal superpotential:

Relevant deformation:

The number of flavors associated with is . This gauge group flows to a strongly interacting conformal fixed point in the IR.

SU(3)CFTNf = 5

W � �v2 TrAThis relevant deformation forces which breaks .

⌦⌃⌃

↵= v2

SU(3)CFT ⇥ SU(3)X ! SU(3)C

/22

O(1) Top Yukawa


CFTs and Soft masses

• At the conformal fixed point, all physical couplings flow to their fixed point values.

• Promote couplings to superfields:• The higher theta components have mass dimension and thus flow to

zero. • Since soft parameters are encoded as higher theta components of

these superfields, certain combinations of soft parameters will flow to zero.

10

Nelson, Strassler [hep-ph/0104051]

/22


CFTs and Soft masses• For generic superpotential couplings:

• Promoting the gauge coupling to a superfield implies:

• Since conserved currents are not renormalized, does not flow to zero. • is the charge under a non-anomalous global symmetry.

11

Nelson, Strassler [hep-ph/0104051]

W � �Y

i

�nii =)X

i

ni em2i ! 0

(em�)CFT ! 0 and

qi U(1)

Xdim(i) qi em2i

Xdim(r)Tr em2r ! 0

/22


Soft Masses• Specify .• The remaining unbroken global

symmetries are given by:

12

W��U(1) = (Q3 u3)(Q3 d3)

U(1)

• This implies that the following combinations of soft masses are unchanged by the CFT dynamics:

U(1)1 U(1)2 U(1)3 U(1)R

Q3 1 0 0 1/2u3 �1 �1 0 1/2d3 �1 1 0 1/2Hu 0 1 0 1Hd 0 �1 0 1⌃ 0 0 1 1/3⌃ 0 0 �1 1/3A 0 0 0 4/3

Table 2: The global anomaly free U(1) symmetries for the model given by Eq. (1) with theU(1) breaking superpotential in Eq. (9). The charge assignments for the gauged symmetriesare given in Table 1.

The R-charges in the last column of Table 2 fix the superconformal dimensions � = 32R.One can verify self-consistently that the superpotential in Eq. (1) becomes marginal at thefixed point. The remaining first and second generation fields decouple from the strongdynamics; they are neutral under the non-R symmetries and are (approximately) free fields.

The only combinations of soft masses that are not suppressed as the fixed point isapproached are

em2⌃ � em2⌃2 em2Q3 � em2u3 � em2d3em2Hu � em2Hd + em2d3 � m̃2u3 . (10)

This implies that for arbitrary UV boundary conditions the model does not fully sequestersoft masses. However, if the supersymmetry breaking mechanism preserves approximatecharge conjugation and custodial symmetries, then the contributions from Eq. (10) arenegligible at the messenger scale and are not generated by the strong dynamics. This isthe case in minimal gauge mediation [19], where at the messenger scale the first di↵erencein Eq. (10) vanishes identically, while the linear combinations in the second and third linesare much smaller than each of their respective terms. These combinations can also besuppressed by going beyond minimal gauge mediation or in gravity mediation by imposingdiscrete symmetries.

As we noted before, this analysis neglects e↵ects from the weakly interacting sector ofthe theory. The first two generations and the SM gauginos continuously feed supersymmetrybreaking contributions to the CFT fields, giving rise to “driving terms” in the beta functionsfor the CFT superfield couplings. However, these supersymmetry breaking e↵ects are muchsmaller than the soft masses of the first two generation sfermions and gauginos, since the CFTcouples to such fields only through irrelevant interactions. Specifically, they are suppressedby loop factors and by SM gauge couplings or Yukawa interactions. These corrections willbe taken into account in §3.

Hence, under the assumption that the supersymmetry breaking mechanism (approxi-

7

em2⌃ � em2⌃2 em2Q3 � em

2u3 � em

2d3

em2Hu � em2Hd + em

2d3

� em2u3• In order to fully sequester the soft masses, the SUSY breaking

mechanism must preserve approximate charge conjugation and custodial symmetries (e.g. minimal gauge mediation).

/22


Soft Masses• Specify .• The remaining unbroken global

symmetries are given by:

12

W��U(1) = (Q3 u3)(Q3 d3)

U(1)

• This implies that the following combinations of soft masses are unchanged by the CFT dynamics:

U(1)1 U(1)2 U(1)3 U(1)R

Q3 1 0 0 1/2u3 �1 �1 0 1/2d3 �1 1 0 1/2Hu 0 1 0 1Hd 0 �1 0 1⌃ 0 0 1 1/3⌃ 0 0 �1 1/3A 0 0 0 4/3

Table 2: The global anomaly free U(1) symmetries for the model given by Eq. (1) with theU(1) breaking superpotential in Eq. (9). The charge assignments for the gauged symmetriesare given in Table 1.

The R-charges in the last column of Table 2 fix the superconformal dimensions � = 32R.One can verify self-consistently that the superpotential in Eq. (1) becomes marginal at thefixed point. The remaining first and second generation fields decouple from the strongdynamics; they are neutral under the non-R symmetries and are (approximately) free fields.

The only combinations of soft masses that are not suppressed as the fixed point isapproached are

em2⌃ � em2⌃2 em2Q3 � em2u3 � em2d3em2Hu � em2Hd + em2d3 � m̃2u3 . (10)

This implies that for arbitrary UV boundary conditions the model does not fully sequestersoft masses. However, if the supersymmetry breaking mechanism preserves approximatecharge conjugation and custodial symmetries, then the contributions from Eq. (10) arenegligible at the messenger scale and are not generated by the strong dynamics. This isthe case in minimal gauge mediation [19], where at the messenger scale the first di↵erencein Eq. (10) vanishes identically, while the linear combinations in the second and third linesare much smaller than each of their respective terms. These combinations can also besuppressed by going beyond minimal gauge mediation or in gravity mediation by imposingdiscrete symmetries.

As we noted before, this analysis neglects e↵ects from the weakly interacting sector ofthe theory. The first two generations and the SM gauginos continuously feed supersymmetrybreaking contributions to the CFT fields, giving rise to “driving terms” in the beta functionsfor the CFT superfield couplings. However, these supersymmetry breaking e↵ects are muchsmaller than the soft masses of the first two generation sfermions and gauginos, since the CFTcouples to such fields only through irrelevant interactions. Specifically, they are suppressedby loop factors and by SM gauge couplings or Yukawa interactions. These corrections willbe taken into account in §3.

Hence, under the assumption that the supersymmetry breaking mechanism (approxi-

7

em2⌃ � em2⌃2 em2Q3 � em

2u3 � em

2d3

em2Hu � em2Hd + em

2d3

� em2u3• In order to fully sequester the soft masses, the SUSY breaking

mechanism must preserve approximate charge conjugation and custodial symmetries (e.g. minimal gauge mediation).

Note the R charges, which can be computed simply from considering the superpotential and the mixed anomalies.

/22


Yukawa Hierarchies• Assume all Yukawa couplings are O(1) in the UV:

• Recall that for a SCFT the anomalous dimension of fields is related to the R charge: .

• Then we can compute the RG evolution of the Yukawa couplings:

• Below the exit scale, the Yukawa coupling is given by

with .

13

Nelson, Strassler [hep-ph/0006251, hep-ph/0104051]

W � Y uij Qi Hu uj + Y dij Qi Hd dj + Y u33 Q3 Hu u3 + Y d33 Q3 Hd d3

Y uij (E) =

✓E

⇤CFT

◆ �Qi+�uj +�Hu2

Y uij (⇤CFT)

✏ ⌘ v⇤CFT

Yij(v) = ✏�H2 Yij(⇤CFT) ⌧ Y33(v)

� = 3R� 2

/22


Yukawa Hierarchies• Since the 3rd generation and 1st/2nd generation fields are

charged under different gauge groups, there is no way to write down a renormalizable off-diagonal Yukawa coupling.

• However, the following higher dimensional operators are allowed by the symmetries:

• Below the exit scale these couplings flow to

with .

14

W � 1⇤⇤

⌃Q3 Hu u1,2 +1

⇤⇤Q1,2 Hu ⌃u3 + . . .

Y ui3(v) =v

⇤⇤✏

�Hu+�Q3

+�⌃

2 , Y u3i(v) =v

⇤⇤✏

�Hu+�u3+�⌃

2

✏ ⌘ v⇤CFT

/22


Flavor• The resultant IR Yukawa matrix is given by

with and .

• This structure can reproduce the mass hierarchy and CKM matrix to a good approximation by varying the O(1) starting value for the Yukawa couplings in the UV and taking

15

Y u ⇠

0

B@✏

�Hu2 ✏

�Hu2 ⇠Q ✏

�Hu2

✏�Hu

2 ✏�Hu

2 ⇠Q ✏�Hu

2

⇠u ✏�Hu

2 ⇠u ✏�Hu

2 1

1

CA

⇠Q ⌘v

⇤⇤✏

�⌃

+�Q32 , ⇠u ⌘

v

⇤⇤✏

�⌃+�ū32

v

⇤CFT⇠ 10�4 , ⇤⇤

⇤CFT⇠ 10�1 � 10�2

✏ ⌘ v⇤CFT

/22


EXAMPLE SPECTRA

16/22


Example Spectra• At the exit scale , the soft masses for the 3rd generation

squarks and the Higgs scalars are zero (up to a small correction proportional to the gluino mass).

• The soft masses for the gauginos and 1st/2nd generations are unchanged by the CFT dynamics.

• Choose a value of (assuming gaugino mass unification).• We then RG evolve the masses from the exit scale to the weak scale

including the dominant 2-loop contributions.• The stop masses are generated via gaugino mediation.

• This drives the up-type Higgs soft mass negative resulting in electroweak symmetry breaking.

• Choose a value of .• The weak scale value of is determined from . • This fixes the weak scale value of using the electroweak symmetry

breaking conditions (at tree level).

17

v

tan�µ �m2Z ' 2

�|µ|2 + em2Hu

�

bµ

Kaplan, Kribs, Schmaltz [arXiv:hep-ph/9911293];Chacko, Luty, Nelson, Ponton [arXiv:hep-ph/9911323]

/22

M3

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.5

1.0

1.5

2.0

2.5

3.0

M3 @TeVD

TeV

v = 103 TeV

TeV

M3 [TeV]

v = 103 TeV


• Plots of the spectrum

18

No electroweak symmetry breaking

Tachyonic stops

LEP bounds on the pseudoscalar Higgs

emQ3 ' emu3 ' emd3

mA (with tan� = 2) mA (with tan� = 10)

Assuming unified gauginos and 1st/2nd generation squarks masses of 5 TeV.

/22

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.5

1.0

1.5

2.0

2.5

3.0

M3 @TeVD

TeV

v = 106 TeV

TeV

M3 [TeV]


• Plots of the spectrum

19

No electroweak symmetry breaking

Tachyonic stops

LEP bounds on the pseudoscalar Higgs

emQ3 ' emu3 ' emd3

mA (with tan� = 2) mA (with tan� = 10)

v = 106 TeV

Assuming unified gauginos and 1st/2nd generation squarks masses of 5 TeV.

/22


The Higgs Mass• Our model does not explain a 125 GeV Higgs boson mass.• Since the superpotential term is irrelevant while

the CFT is strongly coupled, our model is incompatible with the NMSSM.

• To increase the Higgs mass, one can add a sector which results in non decoupling D-terms.

• The results is to take all MSSM Higgs sector relationships and make the substitution:

• In the spectrum plots we have assumed there is an additional D-term contribution to the Higgs quartic .

20

SHuHd

m2Z =g2Z2

�⌦Hu

2↵+⌦Hd

2↵�

�! ⌅2 ⌘ g2Z + g

2new

2

�⌦Hu

2↵+

⌦Hd

2↵�

.

⌅ = 150 GeV

Batra, Delgado, Kaplan, Tait [arXiv:hep-ph/0309149]Maloney, Pierce, Wacker [arXiv:hep-ph/049127]

/22


CONCLUSIONS

21/22


Conclusions• Given LHC bounds on superpartners and the discovery of a

Higgs at 125 GeV, we are being pushed to rethink the relationship between SUSY and naturalness.• Maybe SUSY is hidden

• Compressed spectra• R-parity violation• Decays to hidden sectors• Something else?

• Maybe there is a large hierarchy between the 3rd and 1st/2nd generations

• We have presented a model whose dynamics result in:• A split-family superpartner spectrum;• The hierarchical flavor structure of the quark Yukawa matrices.

• A given gluino mass implies the 3rd generation squark and Higgs sector masses.

• Currently, the strongest bounds on the spectrum are due to the non-observation of pseudo-scalar Higgs.

22/22


BACKUP SLIDES

23


Fine-tuning

• To get a sense of fine-tuning in this model we adopt a naive low-scale measure.

• Plotted are contours of with .• We see large regions with O(10%) fine-tuning are allowed.

24

0.4 0.3 0.2

0.1

0.05

0.02

0.01

102102 103103 104104 105105 106106 1071070.5

1.0

1.5

2.0

2.5

3.0

3.5

v @TeVD

M3TeV

��1 ⌘ �2�m2H

m2h= �2

em2Hum2h

,

Kitano, Nomura [arXiv:hep-ph/0509039];Papucci, Ruderman, Weiler [arXiv:1110:6926]

tan� = 2

Exclusion contours are as in the spectrum plots.

Documents

An Attractor for Natural Supersymmetry...Equal mass squarks and gluinos are excluded below 1400 GeV in both scenarios. References [1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008)