Folded

Gustavo Burdman University of São Paulo - IAS Princeton

with Z. Chacko, R. Harnik, H. Goh, L. de Lima, C. Verhaaren Outline

• Can we save naturalness ? • Folded Supersymmetry • Some Phenomenology • Outlook Naturalness and the LHC Is the Electroweak scale natural ? • The LHC found the Higgs • Plus … nothing else.

MPlanck

Ebounds

Little hierarchy vEW } Naturalness and the LHC Is the Electroweak scale natural ? • The LHC found the Higgs • Plus … nothing else.

MPlanck E few TeV bounds ⇠

Ebounds

Tuned SM Little hierarchy vEW } Naturalness and the LHC 2 UV sensitivity of m h dominated by top

+

• Top partners X carry color ) { • Easily produced at the LHC Colorless Top Partners Last refuge of naturalness ?

Top partners need not carry color

2 If symmetry protecting m h does not commute with SU(3)c

Exchanges SU(3) SU(3)0 c !

The X’s are charged under SU(3)0

Bounds on m X not as stringent Colorless X models are more natural Colorless Top Partners General idea To solve the Little Hierarchy problem

MPlanck

Ebounds

Little hierarchy vEW } SM + colorless top partners Colorless Top Partners Ingredients for neutral naturalness

• Symmetry protecting the Higgs: spontaneously broken global symmetry, SUSY, … • Extend the color gauge symmetry to have at least [SU(3)]2

• Either impose a discrete symmetry or orbifold In general, CTP theories can be obtained from orbifolding N.Craig, S.Knapen, P. Longhi, 1410.6806, 1411.7393 Folded Supersymmetry w/ Z.Chacko, H. Goh, R. Harnik , hep-ph/0609152

• Squarks need to be charged under SU(2)L

• Need not be charged under SU(3)c Folded Supersymmetry w/ Z.Chacko, H. Goh, R. Harnik , hep-ph/0609152

• Squarks need to be charged under SU(2)L

• Need not be charged under SU(3)c

u q,˜ u˜

t t Hu Hu

Hu Hu q 2 t

Can we have SUSY with colorless stops ? Folded Supersymmetry Ingredients • Supersymmetry • Extended gauge symmetry:

G SU(3) SU(3) A ⇥ B

• Break SUSY at a high scale to obtain at low energies

qA , q˜B Accidental low energy SUSY cancels quadratic div. at one loop Large N Orbifold Correspondence

S.Kachru, E. Silverstein, hep-th/9802183; M.Bershadsky, A.Johansen, hep-th/9803248; M.Schmaltz, hep-th/9805218

Orbifold Parent theory Daugther theory

1 (C.F.) = (C.F.) + O( ) Parent Daughter N Bifold Protection

Global U(N) SQi Q¯i i =1...,N

2 MS is quadratically divergent

• Supersymmetrize

• Duplicate index running in loop: i =1,....,2N Bifold Protection • Define

+1 1 .. . 0 . 1 . +1 N =B C B 1 C N +1 B C B . C . B .. C . B C . B 1 C B C 2N @ A

• Theory is invariant under

S S odd Z Q ! Q Z2R 2 i ! i even Q ⇤ Q¯ { i ! i { Bifold Protection Orbifold projection: Project out states odd under Z Z 2 ⇥ 2R

Z2

q1 q˜1 . . 1 . . qN q˜N

qN+1 q˜N+1 . . +1 . . q2N q˜2N

1 +1 Z2R Bifold Protection Project out states odd under Z Z 2 ⇥ 2R Z2

q1 q˜1 . . 1 . . qN q˜N

qN+1 q˜N+1 . . +1 . . q2N q˜2N

1 +1 Z2R Bifold Protection Accidental SUSY: spectrum not supersymmetric

q1 q˜N+1 . . . + . qN q˜2N

But still cancels one-loop quadratic divergence

q˜j S qi S S S

j = N +1,...,2N i =1,...,N Folded SUSY Model

Extend color SU(3) SU(3)A SU(3)B Z2 ⇥ ⇥ Orbifold so that:

qA,uA + q˜B, u˜B remain in the spectrum No Yukawas obey

( h q u +h.c.)+2 q˜ h 2 + 2 u˜ 2 h 2 t u A A t | B u| t | B| | u| 2 Accidental SUSY still protects mh Folded SUSY UV Completion

Can be realized in 5D compactified on S1/Z2

SU(3) SU(3) Z A ⇥ B ⇥ 2 SUSY broken by BCs HU ,HD SU(2) U(1) L ⇥ Y (Scherk-Schwarz)

QˆA, QˆB, UˆA, UˆB , Dˆ A, Dˆ B BCs break Z 2 at ⇡R LˆA, LˆB, EˆA, EˆB

0 ⇡R Folded SUSY UV Completion

• =1 in 5D =2 in 4D N N • 5D Hypermultiplet Qˆ (Q, Qc) in terms of 4D superfields ⇠ Q =(˜q, q) Qc =(˜qc,qc) or

c 0c c Q0 =(˜q⇤ ,q) Q =( q˜⇤,q ) Folded SUSY UV Completion

• =1 in 5D =2 in 4D N N • 5D Hypermultiplet Qˆ (Q, Qc) in terms of 4D superfields ⇠ Q =(˜q, q) Qc =(˜qc,qc) at y =0 or =1 N

c 0c c Q0 =(˜q⇤ ,q) Q =( q˜⇤,q ) at y = ⇡R

related by SU (2) R rotation parametrized by ↵ } 1 in this example ↵ = 2 (more in David Pinner’s talk) Folded SUSY Spectrum

c (QA,QA) +,- at y =0

Qˆ zero mode A ⇠

0c (QA0 ,QA) +,- at y = ⇡R

c +,- at y =0 { (QB,QB) Qˆ scalar zero mode B ⇠

0c (QB0 ,QB) -,+ at y = ⇡R {BCs break Z 2 (A B) at y = ⇡R Folded SUSY Spectrum • Fermion zero modes from

QˆA, UˆA, Dˆ A, LˆA, EˆA

• Scalar zero modes from

QˆB, UˆB, Dˆ B, LˆB, EˆB

• Localize Higgses at y =0

(y) Q H U + Q H U t { 3A U 3A 3B U 3B}

generates desired Yukawas at low energies Folded SUSY Spectrum

2/R

3/2R Top contributions cancel in all 1/R KK levels at one loop

1/2R

0 q q˜

But weak gauge loops give (finite) contributions Folded SUSY Spectrum

Zero-mode Folded : A. Delgado, A. Pomarol, M Quiros, hep-ph/9812489

1 4 3 1 1 m2 = K g2 + g2 + g2 Q 4⇡4 3 3 4 2 36 1 R2 ✓ ◆ 1 4 4 1 m2 = K g2 + g2 U 4⇡4 3 3 9 1 R2 ✓ ◆ 1 4 1 1 m2 = K g2 + g2 D 4⇡4 3 3 9 1 R2 ✓ ◆ 1 3 1 1 m2 = K g2 + g2 L 4⇡4 4 2 4 1 R2 ✓ ◆ 1 1 m2 = K g2 E 4⇡4 1 R2 plus Yukawa contributions for 3rd generation

2 1 2 1 m2 = K t m2 = K t Q3 8⇡4 R2 U3 4⇡4 R2 Folded SUSY

⇤ ⇤R<4 ⇠ 5D SUSY 1 1 (5 7) TeV R R ⇠ Accidental SUSY vEW Folded SUSY Model Building Many important issues: • Smallish ⇤ R forced by top Yukawa volume suppression Potentially dangerous brane kinetic terms at y = ⇡R

Requires additional discrete symmetry at y = ⇡R

• Electroweak symmetry breaking ?

2 K 2 2 1 (m )gauge (3g + g ) from gauge loops H ' 16⇡4 2 1 R2 2 1 (m2 ) t M 2 log H top '4⇡2 t˜ RM from top sector 2 loops ✓ t˜◆

Does this work ? Probably not. See David Pinner’s talk. Folded SUSY Model Building

• Just as the MSSM, Folded MSSM needs help for mh = 125 GeV

E.g.: non-decoupling D terms from a U(1)X Folded SUSY Signals Folded SUSY Signals at the LHC Electroweak pair production of F-squarks

But mT ⇤QCD0 few GeV they do not hadronize ' q˜⇤

p p

q˜

“squirks” have to come back for annihilation Squirk Annihilation w/Z.Chacko, H.Goh, R. Harnik, C. Krenke, 0805.4667

q u˜ W ±⇤ W ±

q¯ d˜

• Annihilation is prompt • Onium is in s-wave before annihilation Squirk Annihilation Bounds from the LHC w/ Z.Chacko et al., 1411.3310

Assumes • No smearing • No decay

mT

320 Direct search better m > T 445 GeV than Higgs couplings { 465 } Folded Sleptons (in progress) In the minimal model, hypermultiplets

Lˆ (1, 1, 2, 1/2) Lˆ (1, 1, 2, 1/2) A B EˆA(1, 1, 1, 1) EˆB(1, 1, 1, 1)

Zero modes: F-sleptons

Lightest F-slepton is stable ! Need to add Z 2 preserving HDOs

U U D E U U D E (y) d✓2 A A A B + B B B A E.g. ⇤ ⇤ Z ✓ ◆ Folded Sleptons Decays Leading to, e.g.: e˜ j R j q˜ j,, t h˜

• Long lifetime goes through detector below or close to top threshold

• Bounds from CMS (1305.0491):

Me˜R > 340 GeV Folded Sleptons Decays Leading to, e.g.: e˜ j R j q˜ j,, t h˜

• Long lifetime goes through detector below or close to top threshold

• Bounds from CMS (1305.0491):

Me˜R > 340 GeV

• Could be an important bound on the naturalness of the model Folded SUSY Prospects

• LHC searches for W

• Model the associated radiation ( 0 s and )

• Possible signals for glueball decay to SM fermions with displaced vertices (see David Curtain’s talk)

• Folded sleptons Conclusions/Outlook • Folded SUSY: colorless stops

• Experimental signals: ★ Quirky dynamics: details of highly excited states

★ Glueball decay

★ Folded sleptons

• Model building issues: UV completions, dark , …

• For the future (100 TeV): explore the physics of the cut-off.