The SUSY Twin Higgs Diego Redigolo Higgs Hunting, Paris August - - PowerPoint PPT Presentation

The SUSY Twin Higgs

Diego Redigolo

Higgs Hunting, Paris August 31st

based on to appear with

• A. Katz, A. Mariotti, S. Pokorski

and R. Ziegler

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

EXACT SYMMETRIES

General Lesson:

COLORED TOP-PARTNERS

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Twin Higgs is the easier implementation

0506256 Chacko, Goh and Harnik

4d description

easier=

/accidental symmetry enforced by a Z2 (less easy ways have been explored

0609152 Burdman, Chacko, Goh and Harnik 1411.7393 Craig, Knapen, Longhi 1601.07181 Craig, Knapen, Longhi,Strassler 1601.07181 Cohen, Craig, Lou, Pinner

exchanging two copies of the SM

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES

2 challenges (in the original Twin already)

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES

2 challenges (in the original Twin already)

EXPLORING THE PARAMETER SPACE of the Twin Higgs

Z2

Breaking introduces some degree of model dependence:

Neutral Naturalness

is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 %

General Lesson:

COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES

2 challenges (in the original Twin already)

EXPLORING THE PARAMETER SPACE of the Twin Higgs

Z2

Breaking introduces some degree of model dependence: UV COMPLETIONS of Twin Higgs constructions:

FINE TUNING vs LHC searches: How long to exclude 10% FT @ LHC?

A fresh look to the Twin Higgs

Twin Higgs: Setup

Natural Z2 exchange symmetry: HA HB ← → . . . H, Q3, U3 → HA, Q3A, U3A HB, Q3B, U3B +

visible sector

} }

“dark” sector: neutral under SM!

GSM GA

SM

GB

SM

×

→

Double SM gauge fields, Higgs and tops

Affect a lot of phenomenology both cosmological and at collider but we leave it unspecified in our discussion…

Minimal (“fraternal”) Twin Higgs 1501.05310 Craig, Katz, Strassler & Sundrum

Z2 involves the full SM

0509242 Barbieri, Hall & Gregoire

the rest of the spectrum

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

κ > 0 Z2 unbroken

(see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken)

7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

SM Higgs is a PGB

mh ⌧ mH as long as κ ⌧ λ

κ > 0 Z2 unbroken

(see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken)

7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

SM Higgs is a PGB

mh ⌧ mH as long as κ ⌧ λ

κ > 0 Z2 unbroken

(see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken)

7 GB - 6 eaten = SM Higgs is a GB

Z2 preserved

maximal mixing

sθ = 1/ √ 2 > 0.45

excluded!

h = hAcθ + hBsθ

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

SM Higgs is a PGB

mh ⌧ mH as long as κ ⌧ λ

κ > 0 Z2 unbroken

(see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken)

7 GB - 6 eaten = SM Higgs is a GB

Z2 preserved

maximal mixing

sθ = 1/ √ 2 > 0.45

excluded!

h = hAcθ + hBsθ

˜ µ2 ρ

soft breaking hard breaking

Linear sigma model

{

even under HA ↔ HB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 V U4

{

V /

U 4,Z2

{

V /

U 4,/ Z2 respects U(4)

λ > 0

f 2 > 0

U(4)

spontaneously broken

SM Higgs is a PGB

mh ⌧ mH as long as κ ⌧ λ

κ > 0 Z2 unbroken

(see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken)

7 GB - 6 eaten = SM Higgs is a GB

Z2 preserved

maximal mixing

sθ = 1/ √ 2 > 0.45

excluded!

h = hAcθ + hBsθ

sθ ≈ v/f > 0.45

f > 2.3v ≈ 400 GeV

viable! ˜ µ2 ρ

soft breaking hard breaking

• 0.10-0.05 0.00 0.05 0.10 0.15 0.20
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 m é2ê f 2 r

0.25 0.2 0.15 0.1 0.05

fêv > 2.3

mh=130 GeV mh=125 GeV mh=120 GeV

k<0

soft Z2-breaking

k

{

4 parameters:

˜ µ2 κ ρ f

{ ,

, ,

• 2 constraints:

EWSB+ HIGGS 2 dimensional par. space

f/v > 2.3

with the constraint

THE TWIN HIGGS on a plane…

• 0.10-0.05 0.00 0.05 0.10 0.15 0.20
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 m é2ê f 2 r

0.25 0.2 0.15 0.1 0.05

fêv > 2.3

mh=130 GeV mh=125 GeV mh=120 GeV

k<0

soft Z2-breaking

k

{

4 parameters:

˜ µ2 κ ρ f

{ ,

, ,

• 2 constraints:

EWSB+ HIGGS 2 dimensional par. space

f/v > 2.3

with the constraint

Hard breaking offer new possibilities:

THE TWIN HIGGS on a plane…

• 0.10-0.05 0.00 0.05 0.10 0.15 0.20
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 m é2ê f 2 r

0.25 0.2 0.15 0.1 0.05

fêv > 2.3

mh=130 GeV mh=125 GeV mh=120 GeV

k<0

soft Z2-breaking

k

{

4 parameters:

˜ µ2 κ ρ f

{ ,

, ,

• 2 constraints:

EWSB+ HIGGS 2 dimensional par. space

f/v > 2.3

with the constraint

Hard breaking offer new possibilities: soft-breaking: tuning

˜ µ2 ≈ 2κf 2

ρ ⌧ ˜ µ2/f 2

to get

f/v > 2.3

THE TWIN HIGGS on a plane…

• 0.10-0.05 0.00 0.05 0.10 0.15 0.20
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 m é2ê f 2 r

0.25 0.2 0.15 0.1 0.05

fêv > 2.3

mh=130 GeV mh=125 GeV mh=120 GeV

k<0

soft Z2-breaking

k

{

4 parameters:

˜ µ2 κ ρ f

{ ,

, ,

• 2 constraints:

EWSB+ HIGGS 2 dimensional par. space

f/v > 2.3

with the constraint

Hard breaking offer new possibilities: hard-breaking:

˜ µ2/f 2 ⌧ ρ

tuning

κ ⌧ ρ

to get mh soft-breaking: tuning

˜ µ2 ≈ 2κf 2

ρ ⌧ ˜ µ2/f 2

to get

f/v > 2.3

THE TWIN HIGGS on a plane…

soft

m2

h ≈ 8κv2

low fine-tuning favours small f

Extra positive κ0 to get mh = 125 GeV

∆soft

v/f ≈ 1 − f 2

2v2

soft

m2

h ≈ 8κv2

low fine-tuning favours small f

Extra positive κ0 to get mh = 125 GeV

∆soft

v/f ≈ 1 − f 2

2v2

hard

m2

h|hard ≈

8v2κ F(Λρ, f)

the gain in fine-tuning correspond to an enhancement of the Higgs mass the gain in fine-tuning is larger at large f

∆|hard

v/f ≈

✓ 1 − f 2 2v2 ◆ F(Λρ, f)

soft

m2

h ≈ 8κv2

low fine-tuning favours small f

Extra positive κ0 to get mh = 125 GeV

∆soft

v/f ≈ 1 − f 2

2v2

hard

m2

h|hard ≈

8v2κ F(Λρ, f)

the gain in fine-tuning correspond to an enhancement of the Higgs mass the gain in fine-tuning is larger at large f

∆|hard

v/f ≈

✓ 1 − f 2 2v2 ◆ F(Λρ, f)

F(Λρ, f)

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

• 2
• 1

1 2 3 4 5 fêv e Lr @TeVD

0.1 0.2 0.3 0.4 0.5 0.6 0.7

FHLr , fL

e=+1 e=-1

soft

m2

h ≈ 8κv2

low fine-tuning favours small f

Extra positive κ0 to get mh = 125 GeV

∆soft

v/f ≈ 1 − f 2

2v2

hard

m2

h|hard ≈

8v2κ F(Λρ, f)

the gain in fine-tuning correspond to an enhancement of the Higgs mass the gain in fine-tuning is larger at large f

∆|hard

v/f ≈

✓ 1 − f 2 2v2 ◆ F(Λρ, f)

F(Λρ, f)

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

• 2
• 1

1 2 3 4 5 fêv e Lr @TeVD

0.1 0.2 0.3 0.4 0.5 0.6 0.7

FHLr , fL

e=+1 e=-1

Λρ

parametrize the cut-off of the

Z2- breaking Higgs loops

the sign of the threshold

✏ = ±1

• 0.02
• 0.01

0.01

• 0.02
• 0.01

0.01 0.1 0.25 0.5

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 fêv Lt @TeVD

Lr

2=1 TeV2, m

é

0=0

k0

Dhard Dsoft

k0 < 0 k0 > 0

Extra negative κ0

2 ways of making hard-breaking viable:

i.e getting mh = 125 GeV

Λt is the cut-off of top loops

• 0.02
• 0.01

0.01

• 0.02
• 0.01

0.01 0.1 0.25 0.5

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 fêv Lt @TeVD

Lr

2=1 TeV2, m

é

0=0

k0

Dhard Dsoft

k0 < 0 k0 > 0

Extra negative κ0

2 ways of making hard-breaking viable:

i.e getting mh = 125 GeV What is the UV threshold parametrized by Λρ?

• 2

2 4 6

• 2

2 4 6 0.05 0.05 0.1 0.1 0.2 0.3 0.4

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 fêv Lt @TeVD

Lr

Dhard Dsoft

O(1) differences with Λt can accommodate the Higgs

WARNING: the sign is crucial!

Λt is the cut-off of top loops

Twin Supersymmetry

Exploring UV complete versions of Neutral naturalness

SUSY needs some help:

Ms controls the scale of colored states

WHERE IS EVERYBODY? LITTLE FINE-TUNING PROBLEM

∆SUSY = 3y2

t M 2 s

2π2m2

h

log Λ Ms ∼ 100

Twin Higgs needs a UV completion

ΛTwin

f

v

(Especially true if hard-breaking is present)

Exploring UV complete versions of Neutral naturalness

SUSY needs some help:

Ms controls the scale of colored states

WHERE IS EVERYBODY? LITTLE FINE-TUNING PROBLEM

∆SUSY = 3y2

t M 2 s

2π2m2

h

log Λ Ms ∼ 100

Twin Higgs needs a UV completion

ΛTwin

f

v

ΛTwin = Ms

what happens if

?

(Especially true if hard-breaking is present)

Exploring UV complete versions of Neutral naturalness

SUSY needs some help:

Ms controls the scale of colored states

WHERE IS EVERYBODY? LITTLE FINE-TUNING PROBLEM

∆SUSY = 3y2

t M 2 s

2π2m2

h

log Λ Ms ∼ 100

Twin Higgs needs a UV completion

ΛTwin = Ms

what happens if

?

Λ

Ms

f

v

(Especially true if hard-breaking is present)

“ Twin Higgs ”

Higgs is PGB of accidental global symmetry

top partners uncolored

Supersymmetry

provides calculable UVC ameliorates fine-tuning decouples colored states

“ Twin Higgs ”

Higgs is PGB of accidental global symmetry

top partners uncolored

Supersymmetry

provides calculable UVC ameliorates fine-tuning decouples colored states

Only few existing models (tuning 1-2 %) Explore general structure and identify new promising directions

0604076 Chang, Hall & Weiner 0604066 Falkowski, Pokorski & Schmaltz 1312.1341 Craig & Howe

(tuning 5-10 % !)

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4

quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4

quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

f fixed by Higgses soft masses f tuning calculable..

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4

quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

f fixed by Higgses soft masses f tuning calculable..

{

V /

U 4,Z2

top-stop contributions tree-level D-terms extra contributions from

tA 6= tB

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 κ large & positive

strong constraints from the Higgs mass quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

f fixed by Higgses soft masses f tuning calculable..

{

V /

U 4,Z2

top-stop contributions tree-level D-terms extra contributions from

tA 6= tB

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 κ large & positive

strong constraints from the Higgs mass quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

f fixed by Higgses soft masses f tuning calculable..

{

V /

U 4,Z2

top-stop contributions tree-level D-terms extra contributions from

tA 6= tB

large from non dec. (extra singlet sector)

ρ

{

V /

U 4,/ Z2

matching the SUSY potential to the Twin Higgs linear sigma model: hA

u = HAsA

hB

u = HBsB

hA

d = H† AcA

hB

d = H† BcB

λ(|HA|2 + |HB|2 − f 2)2 + κ(|HA|4 + |HB|4) + ˜ µ2|HA|2 + ρ|HA|4 κ large & positive

strong constraints from the Higgs mass the nature

• f the singlet

sector determines the nature of the cut-off Λρ quartic from non-dec. F-terms

{

V U4

mS MS

W = λSSHuHd

λ ≈ λ2

S

4 s2

2β

f fixed by Higgses soft masses f tuning calculable..

{

V /

U 4,Z2

top-stop contributions tree-level D-terms extra contributions from

tA 6= tB

large from non dec. (extra singlet sector)

ρ

{

V /

U 4,/ Z2

Spectrum controlled by 2 parameters:

mA f 4 Higgs doublet model

2 CP-odd higgses 4 CP-even neutral higgses 2 charged higgses

CAN WE OBSERVE THESE EXTRA HIGGSES @ LHC?

{

h0

2 ∼

√ λf

1505.05488 Buttazzo, Sala & Tesi

∼ q m2

A − λf 2

1504.04630 Craig, D’Eramo, Draper, Thomas, Zhang

The radial mode (Twin Higgs) decays mostly into gauge bosons

{ASM , HSM , H±

SM}

1605.08744 Craig, Hajer, Li, Liu, Zhang

Neutral Naturalness Colored states decoupled BUT

Twin SUSY

Extended Higg Sector

“large f” region the radial mode is light “low f” region MSSM-like Higgses light

diboson searches vs Neutral naturalness MSSM Higgs searches vs (neutral) naturalness

REMARK: Soft Twin SUSY prefers low f Hard Twin SUSY gets lower fine tuning with higher f

500 700 900 1100 400 500 600 700 800

3 4 5 6 7 0.4 0.6 0.8 1.0 1.2 1.4 f @TeVD mA

SM @TeVD

HV33L2 + HV34L2

0.2 0.4 0.6 0.8

• 6
• 4
• 2

2 4 6

measures how much the state is Twin

pp Æ hT Æ SM-SM

8 TeV 13 TeV H100 fb-1L 14 TeV H300 fb-1L TeV 14 TeV H3000 fb-1L b Æ sg H+HtbL 14 TeV H3000 fb-1L b Æ sg Fut.

3 4 5 6 7 0.4 0.6 0.8 1.0 1.2 1.4 fêv mA

SM@TeVD

l=0.9

to close f/v>4 we need more time

PROSPECTS for TWIN SUSY

END of 2018: f/v>4

pp Æ hT Æ SM-SM

8 TeV 13 TeV H100 fb-1L 14 TeV H300 fb-1L TeV 14 TeV H3000 fb-1L b Æ sg H+HtbL 14 TeV H3000 fb-1L b Æ sg Fut.

3 4 5 6 7 0.4 0.6 0.8 1.0 1.2 1.4 fêv mA

SM@TeVD

l=0.9

to close f/v>4 we need more time

PROSPECTS for TWIN SUSY

END of 2018: f/v>4

Twin Higgs searches in SUSY:

for a perturbative quartic the decay of the radial mode to dark gauge bosons are kinematically closed The width is fully dominated by decay into gauge bosons and SM higgs

t¯ t is subleading but

non-negligible

ZZ

searches have the best reach/constraint

1504.00936 CMS collaboration

pp Æ hT Æ SM-SM

8 TeV 13 TeV H100 fb-1L 14 TeV H300 fb-1L TeV 14 TeV H3000 fb-1L b Æ sg H+HtbL 14 TeV H3000 fb-1L b Æ sg Fut.

3 4 5 6 7 0.4 0.6 0.8 1.0 1.2 1.4 fêv mA

SM@TeVD

l=0.9

to close f/v>4 we need more time

PROSPECTS for TWIN SUSY

END of 2018: f/v>4

b → sγ

H+ → tb

t¯ tH , A

associated production can be better but at least 300fb−1 improvement in theory uncertainty up to 700 GeV but at HL

Twin Higgs searches in SUSY:

for a perturbative quartic the decay of the radial mode to dark gauge bosons are kinematically closed The width is fully dominated by decay into gauge bosons and SM higgs

t¯ t is subleading but

non-negligible

ZZ

searches have the best reach/constraint

1504.00936 CMS collaboration

Summary

• Hard breaking has a different parametric of fine-tuning because

it allows for large f/v but overshoots the Higgs mass

• Explicit breaking with marginal (hard) operators enlarge the

parameter space of the Twin

Z2

• SUSY UV completions can be constructed for both soft and hard

breaking.

• Neutral Naturalness can be explored within LHC lifetime via

extra Higgs searches.