Partially Composite Supersymmetry

Tony Gherghetta

Theory Institute in Particle Physics and Cosmology Warsaw, Poland, October 12, 2019

[Yusuf Buyukdag, TG, Andrew Miller: 1811.12388]

1 Gherghetta_Warsaw - 12 October 2019 SUPERSYMMETRY: complete theoretical framework for Beyond the Standard Model • Stabilizes Planck/weak scale hierarchy • Origin of electroweak symmetry breaking • Dark matter • Gauge coupling uniﬁcation • Low-energy limit of string theory

BUT where are the superpartners?!?

LHC: gluino: mg˜ & 1970 GeV stop: mt˜ & 1120 GeV

2 Gherghetta_Warsaw - 12 October 2019 [Giudice, Strumia 1108.6077]

7 SUSY breaking scale . 10 GeV

3 Gherghetta_Warsaw - 12 October 2019 Minimal SUSY requirements: • Higgs mass [Pardo Vega, Villadoro 1504.05200]

Requires ~10 TeV stops or large A-terms

C. FCNC’s

2 The soft mass matrices m˜ ij that will arise from the 5D calculation are of a diagonal, nondegenerate form. The same is true for the D-term contributions to scalar masses that 2 occur after EWSB. On the other hand, the F-term contributions are of the form (⌅†⌅)ijv , the square of the 4D Yukawa couplings. This is the only source of mixing, say between ˜ dL-s˜L. Th• Supersymmetricus, we can replace the ﬂavorconstra problemints of Eq. (4.18) of ALT by: 2 3 ⇤m˜ ds 2 (F/M) Requires heavy sfermions e.g. K Kmixing:¯ < 10 (4.3) (10 TeV)2 (10 TeV)3 m˜ 1,2 & 100 TeV 2 2 Recall that F/M is of order 100 TeV. Also, ⇤m˜ ds is much less than (100GeV ) , because of small Yukawa coupling suppression for the light generations. Thus we avoid the bounds on FCNC’s by more than ﬁve orders of magnitude. Renormalization eects are not of any

concern because SUSY is broken at 100 TeV, rather4 than a high scale. Gherghetta_Warsaw - 12 October 2019 The fact that we avoid FCNC’s can be traced to the fact that our SUSY-breaking is transmitted through the deformed metric. This is a flavor diagonal eect, and does not generate mixing in the 4D theory. On the other hand, one might imagine a more generic 5D action that would mimick the operators considered in Eq. (4.16) of ALT. However, these speculations are beyond the scope of the present work. In the model that we present, one should assume that there is an unspecified (symmetry) mechanism at work in the string theory vacuum that suppresses such operators. That is, we restrict to a class of vacua with good properties vis-á-vis FCNC’s. [* Could this be an anthropic “decision”? What would happen to us if FCNC’s were large? *]

D. Bulk soft masses

For tan = 10, we obtain the bulk soft mass spectrum shown in Table IV. These are the

masses obtained for the lightest modes, zero modes in the AdS5 limit, from the classical 5D calculation. They represent bona ﬁde nonperturbative masses in the 4D dual theory.

V. LHC PHENOMENOLOGY lhc Here we present the results of a preliminary LHC study of the pp 2⇥+ E signal in ⇥ ⇤ T the single-sector model we are studying. The diphoton signal has been studied as a probe

13 A possible minimal SUSY scenario: ⇤ M UV ⇠ P

“Big” hierarchy m(˜q1,2) TeV “Little” hierarchy ( & 10) 5D metric (“split” families) [Dimopoulos, Guidice 95; Pomarol, Tommasini 95; Cohen, Kaplan, Nelson 96] m(˜q3),m(˜g) & TeV

m 125 GeV h ⇠

m 1,2 10 Can sfermion mass hierarchy m & be related ✓ 3 ◆ em t 105 to fermion mass hierarchy m e . ? Yes! ✓ e,µ ◆

5 Gherghetta_Warsaw - 12 October 2019 e.g. MSUGRA Pre-LHC small squark hierarchy

light sleptons Universal boundary condition

Post LHC heavy sleptons L˜1,2

Q˜1,2 ˜ large squark L3 hierarchy Flavor-dependent boundary conditions! Q˜3 Determined by fermion masses!

[Related ideas: Dudas, Grojean, Pokorski, Savoy ’96; 104 1016 Nelson, Strassler ’00; GeV } Badziak, Dudas, Olechowski, Pokorski ’12]

6 Gherghetta_Warsaw - 12 October 2019 Partial Compositeness [Kaplan 91]

SM gauge ﬁeld, Higgs strongly-coupled and matter sector Aµ,H, i = + g AµJ i Lmix F O V µ O

relative admixture controlled by dim Oi a elementary + a composite | i⇠ e| i c| i couples to elementary Higgs couples to supersymmetry breaking from strong dynamics

Cases: ae ac dim( ) > 4 “irrelevant” mixing O ae ac dim( ) < 4 “relevant” mixing ⌧ O + [Similar to ⇢ mixing which explains ⇢ e e in QCD!] !

7 Gherghetta_Warsaw - 12 October 2019 Example: Fermion mixing

anomalous dimension 3 (dim c = + ) O 2

mass

⇤IR ⇤UV } mixing! ⌧ } Depends on (1) = g ⇤IR

Mass eigenstate is partially composite!

8 Gherghetta_Warsaw - 12 October 2019 Explains the fermion mass hierarchy:

L x L R v mf LRv x H = ⇠ h i p2 5 x dim L,R R L ⇤ O 2 where IR L,R ⇠ ⇤ R ✓ UV ◆

• Light fermions are mostly composite! 3 5 3 dim L,R < (or 0 L,R < 1) (dim L,R = + L,R) 2  O 2  O 2 • Top quark is elementary 5 dim > (or L,R > 1) OL.R 2

9 Gherghetta_Warsaw - 12 October 2019 Supersymmetry breaking Assume strong sector breaks supersymmetry: = ✓✓F X X GAUGINO: linear supermultiplet

partially composite gaugino

SUSY breaking mass: }

4D gauge coupling

10 Gherghetta_Warsaw - 12 October 2019 SFERMION:

(dim c =1+) O

partially composite sfermion

SUSY breaking:

Hierarchical sfermion masses!

However for sufﬁciently large i.e. radiative corrections dominate

Critical value (m2 m2) '

e e

11 Gherghetta_Warsaw - 12 October 2019 GRAVITINO:

W = constant superpotential

where

HIGGSINO: [Kim, Nilles 84]

where

12 Gherghetta_Warsaw - 12 October 2019 Sfermion mass hierarchy:

m v “relevant” mixing (0 < e < 1) “composite” electron e ⌧ mt v “irrelevant” mixing ( > 1) ⇠ t “elementary” top quark

Yukawa couplings at IR scale: Partial compositeness explains Yukawa coupling hierarchy!

top quark Partial compositeness predicts selectron inverted sfermion mass hierarchy! electron stop

13 Gherghetta_Warsaw - 12 October 2019 Anomalous dimension contours [Buyukdag, TG, Miller: 1812.12388]

18 ⇤UV = 10 GeV, tan =3

MSUSY = 50 TeV

14 Gherghetta_Warsaw - 12 October 2019 Partially Composite Spectrum [Buyukdag, TG, Miller: 1811.12388]

Fermions Bosons

15 Gherghetta_Warsaw - 12 October 2019 To model strong dynamics use AdS/CFT:

Partial 5D Localization in Compositeness a slice of AdS

5D Model: (k = AdS curvature)

16 Gherghetta_Warsaw - 12 October 2019 Fermion mass hierarchy: [TG, Pomarol 00]

UV brane localized Higgs }

cL,cR = bulk mass parameters Yukawa coupling contours

⇤ =2 1016 GeV IR ⇥ tan =3 (5) Yij k =1

17 Gherghetta_Warsaw - 12 October 2019 Supersymmetry breaking

IR brane spurion superﬁeld: 2⇡kR X = ✓✓FX SUSY breaking scale: F = FX e

Gaugino masses:

X = singlet

4D gauge coupling }

X = non singlet

F Extra suppression 2 ⇤IR

18 Gherghetta_Warsaw - 12 October 2019 Gravitino mass:

where for vanishing cosmological constant

Sfermion masses:

Flavor-dependent masses

1 Matches partial composite result using AdS/CFT dictionary: = c i | i ± 2|

19 Gherghetta_Warsaw - 12 October 2019 One-loop sfermion radiative corrections [Buyukdag, TG, Miller: 1811.12388]

IR localized UV localized

UV localized sfermions dominated by radiative corrections

20 Gherghetta_Warsaw - 12 October 2019 Higgs sector: Soft terms generated at one-loop (since Higgs is UV localized)

EWSB:

21 Gherghetta_Warsaw - 12 October 2019 One-loop Higgs soft mass radiative corrections [Buyukdag, TG, Miller: 1811.12388]

IR localized UV localized

22 Gherghetta_Warsaw - 12 October 2019 Charge and Color breaking minima Sfermions can receive negative mass-squared corrections from: • Weak hypercharge D-term

where • Bulk D-term (and Yukawa couplings)

where

• 2-loop gauge boson [Arkani-Hamed, Murayama ’97]

where

23 Gherghetta_Warsaw - 12 October 2019 Phenomenological constraints

Higgs mass m 125 GeV • h '

• Supersymmetric ﬂavor problem m˜ 1,2 & 100 TeV

Gauge coupling uniﬁcation µ M 100 TeV • | | ⇠ .

• Gravitino Dark Matter

Charge and color breaking minima 2 • m˜ > 0

constrains pF,⇤IR

24 Gherghetta_Warsaw - 12 October 2019 Parameter space constraints (singlet X spurion) [Buyukdag, TG, Miller: 1811.12388]

25 Gherghetta_Warsaw - 12 October 2019 Parameter space constraints (non-singlet X spurion) [Buyukdag, TG, Miller: 1811.12388]

26 Gherghetta_Warsaw - 12 October 2019 Two benchmark scenarios

27 Gherghetta_Warsaw - 12 October 2019 Superpartner spectrum [Buyukdag, TG, Miller: 1811.12388

hatched: singlet X solid: nonsinglet X

mu˜ /m˜ 3 (18) m /m 13 (35) for singlet (non-singlet) 6 t1 ⇠ u˜6 ⌧˜1 ⇠

28 Gherghetta_Warsaw - 12 October 2019 2

Charged Lepton Flavor Violation † m} Lsoft ij i j Mu2e experiment not (ﬂavor) diagonal CLFV! e

Current limits: + + 13 BR(µ e ) < 5.7 10 [MEG 2013] ! ⇥ 13 BR(µ Au e Au) < 7 10 [SINDRUM-II 2006] ! ⇥ [compared to capture rate µ N ⌫ N 0 ] ! µ

17 BR(µ Al e Al) 10 ! ⇠ 104 improvement! ⇠ • Mu2e will probe values: 2000 TeV . ⇤ . 10000 TeV

(µ e) dipole contact (µ e) ! term term !

29 Gherghetta_Warsaw - 12 October 2019 µ e !

m2 eµ 1 eg2 e 2 2 2 ✓eµ ⇤ ⇠ 16⇡ MSUSY 2 meµ where ✓eµ 2 ⇠ MSUSY e m2 m 2 Mu2e ⇤ 2000 TeV eµ 3 m2 ' 100 TeV ⇠ ✓ ◆ e e Partially-Composite Supersymmetry: e 2 Can relate meµ to fermion mass hierarchy — much more predictive!

1 3 e2 2 [in preparation] mij 1 ⇠ 0 3 2 1 1 e @ A

30 Gherghetta_Warsaw - 12 October 2019 µ e !

Note: Penguin contributions are log enhanced

[Altmannshofer et al 1308.3653]

Anarchic sfermion mass matrix: 111 2 m˜ ij 111 ⇠ 0 1111 @ A Mu2e can probe (300 TeV) sleptons! O

Partially Composite [in preparation] Supersymmetry:

31 Gherghetta_Warsaw - 12 October 2019 Summary • Partial compositeness relates fermion and sfermion mass spectrum --- Higgs/top quark = elementary --- First two generations = partly composite --- Hierarchies arise from order one anomalous dimensions • Predicts inverted sfermion spectrum or --- 20(65) TeV . mt˜1 . 27(80) TeV 150(250) TeV . me˜6 . 180(330) TeV --- gravitino = dark matter --- long-lived (stau or neutralino) NLSP decay • Sfermion flavor structure leads to specific flavor- violation processes (e.g Mu2e) or EDM --- work in progress

32 Gherghetta_Warsaw - 12 October 2019