Perturbative Unitarity Constraints on a SUSY Higgs portal Sonia El - - PowerPoint PPT Presentation

Perturbative Unitarity Constraints

• n a SUSY Higgs portal

Sonia El Hedri

with

Kassahun Betre, Devin Walker

ERC Workshop, Schloss Waldthausen

November 12, 2014

arXiv:1407.0395 arXiv:1410.1534

1 / 40

Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds

Unitarity and Perturbativity Unitarity and the NMSSM parameters

Relic density constraints Parameter scan and results

2 / 40

Finding New Energy Scales Application to the NMSSM Parameter scan and results

3 / 40

H W , Z J

H W

0 1 GeV 10 GeV 103 GeV 10 GeV 106 GeV 10

GeV 109 GeV 10 GeV 1012 GeV

1015 GeV 10 GeV 1018 GeV 10 GeV 1021 GeV

Planck scale

New scales?

EW ? } EW scale

Heavy pions QCD

4 / 40

Finding new energy scales

How to look for the next energy scale?

I Break down of the theory?

∆ SM perturbative up to the GUT scale ∆ Electroweak vacuum metastable

Degrassi, Di Vita, Elias-Miró, Espinosa, Giudice, Isidori, Strumia, [arXiv:1205.6497] I New observations

∆ Evidence for Dark Matter, neutrino masses, . . . ∆ Unknown/too high energy scale

I Naturalness arguments

∆ Upper bounds depend on the fine-tuning

I Other possibilities??

5 / 40

Finding new energy scales

How to look for the next energy scale?

I Break down of the theory?

∆ SM perturbative up to the GUT scale ∆ Electroweak vacuum metastable

Degrassi, Di Vita, Elias-Miró, Espinosa, Giudice, Isidori, Strumia, [arXiv:1205.6497] I Look for new phenomena

∆ Evidence for Dark Matter, neutrino masses, . . . ∆ Unknown/too high energy scales

I Naturalness arguments

∆ Avoid fine-tuning of the Higgs mass ∆ Upper bounds depend on the tolerated fine-tuning

I Perturbative Unitarity

6 / 40

Unitarity in the Standard Model

I Breaking of perturbative unitarity is a sign for new physics

I Light pion effective theory: unitarity violated around

1.2 GeV ∆ Axial and vector resonances at 800 MeV

I Fermi theory: Unitarity violated around 350 GeV

∆ W boson at 80 GeV

I Electroweak theory: unitarity violated around 1 TeV

∆ Higgs boson at 125 GeV

7 / 40

Effects of unitarity on couplings

ReTii < 1 2 Dimensionless Unitarity Dimensionful Unitarity

~λ2

Aκ φ1

1 φ2 2A2 1 φ2 2A2

Aκ φ1

2 φ3

∝ g Aλ A2

123

s − mφ2

3

A Bounds on quartic couplings

Lee, Quigg, Thacker [Phys. Rev. D 16, 1519 (1977)]

Bounds on mass ratios

Schuessler, Zeppenfeld [arXiv:0710.5175]

8 / 40

Anchoring the spectrum: Low Energy Observables

I Unitarity constrains BSM theories

∆ Upper bounds on dimensionless couplings ∆ Upper bounds on ratios of scales

I Does not prevent decoupling

What if new phenomena are observed?

I Couple unitarity to low energy observables

9 / 40

Unitarity and Dark Matter

I Dark Matter is one of the only evidences of new physics beyond

the SM

I Unknown mass, known relic density I Only gravitational couplings observed

Thermal Dark Matter

I Dark Matter relic density is obtained through annihilation to

lighter particles

I Dark Matter cannot decouple from the light sector I Relic Density known as a function of DM couplings

10 / 40

Thermal Dark Matter

Heavy dark matter requires large couplings ∆ Unitarity violation at large mass

g2 ˜ χ0 SM g2 ˜ χ0 SM

∝ g

. λ2

123 φ1

s − m SM 2

123 φ1

GeV Ge

3

∝ g

I Existing Unitarity Bound : 120 TeV for λ = 4π Griest and

Kamionkowski, 1990

I Much tighter bounds for specific theories!

11 / 40

A recipe for constraining new models

I Applies to

I Models predicting a Dark Matter candidate I Known production and annihilation mechanisms

I Dimensionful unitarity: upper bounds on the mass ratios

I Contracted spectrum

I Dimensionless unitarity: upper bounds on dimensionless

couplings

I Tension with Relic Abundance constraints for heavy Dark

Matter

Unitarity and Relic Abundance set an upper bound

• n the masses of the new particles!

I Unitarity constraints on the Higgs portal ∆ 10 TeV bounds Walker [arXiv:1310.1083]

12 / 40

Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results

13 / 40

Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results

14 / 40

The NMSSM Higgs sector

I Focus on NMSSM Higgs Sector

WNMSSM = ≠λˆ S ˆ Hu.ˆ Hd + 1 3κˆ S3 Vsoft = m2

HdH† dHd + m2 HuH† uHu + m2 SS†S

≠

3

λAλSHuHd ≠ 1 3κAκS3 + h.c.

4

I Winos, Binos and Sfermions decoupled I Six parameters after EWSB

λ, κ, tan β, µ, Aλ, Aκ

15 / 40

NMSSM spectrum: Decoupling limit

I One light Higgs, mh = 125 GeV I Heavy Higgs masses depending on

µ2, Aλµ and Aκµ

I Higgsino/Singlino Dark Matter

mDM ≥ µ

I DM annihilation governed by λ and/or κ

16 / 40

Upper Bounds on the NMSSM

I Tree-level study

m2

Z cos2 2β + λv 2 sin2 2β Ø (125 GeV)2

λ Ø 0.7

I Using unitarity + Relic abundance measurements I We want to obtain

∆ Upper bounds on λ, κ ∆ Upper bounds on Aλ,κ/µ ∆ Upper bound on µ

17 / 40

Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds

Unitarity and Perturbativity Unitarity and the NMSSM parameters

Relic density constraints Parameter scan and results

18 / 40

NMSSM and Unitarity

S S S S S S S S S

∝ g

µ +

λ κ2

µ + κ2A2

κ

s − m2

S

I Lee-Quigg-Thacker type bounds on λ and κ

If s ≥ 5m2

S

A Ã κ2 + O

Aκ2Aκ

µ

B

I All heavy particle masses are of order µ or less

19 / 40

Perturbative Unitarity

Constrains a given scattering matrix S = 1 + iT Optical theorem S†S = I ∆ 1 2(T ≠ T †) = |T 2

ii |

Use Partial Wave Decomposition ˜ T J

ij = λ1/4 i

λ1/4

f

32πs

⁄ 1

−1

TijPJ(cos θ)d cos θ We find Im ˜ Tii = | ˜ Tii|2 ∆ |Re ˜ Tii| < 1 2

20 / 40

Perturbative Unitarity: a Geometric view

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Exact Matrix Element

SM 1 2 SM 1 2

• Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)]

21 / 40

Perturbative Unitarity: a Geometric view

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Tree Level nth-loop

Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)]

22 / 40

Perturbativity breakdown

EW ? }

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

− | dmin

min xTL

2 | − |

TL a = dmin

|xTL|

Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)]

23 / 40

Perturbativity breakdown

I Conservative estimate of loop corrections

0.0 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3 0.4 0.5 Tii

Tree

a'

41% 1/2

Schuessler and Zeppenfeld [arXiv:07105175, Schuessler thesis (2005)]

24 / 40

Large s study: Quartic Couplings

Constraints on dimensionless couplings

1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Λ Κ

For large s, only quartic couplings remain lims→∞|Re ˜ Tii| < 1 2

λ, κ . 3

25 / 40

Unitarity and SUSY breaking scales

• , µ, Aλ, Aκ

electroweak scale

I mH, mA, mχ depend on Aλ,

Aκ, µ

I Trilinear couplings

∆ vanish at high energy

I Energy-dependent scattering

amplitudes ∆ Scan over s

26 / 40

General Optimal s

b 20 40 60 80 100 120 0.0 0.5 1.0 1.5 2.0 2.5 s TeV 5 mh Max Eigenvalue

27 / 40

Unitarity: Summary

I Upper bounds on λ and κ

λ, κ . 3

I Optimal bounds for

s ≥ 5m2

H I Upper bounds on ratios of scales

Aλ µ and Aκ µ ≥ O(1)

I µ is the only scale left unconstrained ∆ Need to constrain the

DM mass!

28 / 40

Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results

29 / 40

Relic density Relic density anchors the heavy spectrum

˜ χ ˜ χ

h, H12, A12

h, H, A, SM h, H, A, SM

∝ λ, κ

I λ and κ increase with the DM mass I Maximal mass when λ or κ hits the unitarity bound

30 / 40

Loopholes in Fine-Tuned Regions

I Higgs funnels: s-channel resonances when

R = mini |2mχ ≠ mHi| mHi . 0.1

I t-channel resonances: not in our model but can exist if

mχ0 ≥ mW + mχ±

I Sommerfeld enhanced regions: for low Higgsino-Chargino

splitting

˜ H0 ˜ H± ˜ H0 ˜ H±

. . . H0 . . . H0

−

S

W ± −

S

W ±

31 / 40

Finding New Energy Scales Application to the NMSSM Parameter scan and results

32 / 40

Finding upper bounds: procedure

I Uniform scan over 6 parameters with the 125 GeV Higgs mass

constraint λ, |κ| < 4, |Ai|, |µ| < 40 TeV

I Apply vacuum constraints Kanehata, Kobayashi, Konishi, Seto, Shimomura [arXiv:1103.5109] I Unitarity: allow for at most 40% loop corrections to tree-level

amplitudes |ReTij| Æ 1 2

I Compute relic density using MicrOmegas and NMSSMTools

Ωh2 < 0.1199 + 0.0081 (Planck measurement)

33 / 40

Results: Dark Matter

I Fine Tuning Factor R = mini

|2mDM ≠ mHi| mHi

34 / 40

Results: Higgs sector

35 / 40

Summary

I Need to find new energy scales for future experiments I Unitarity reliably indicates when new physics will appear I Unitarity + Thermal Dark Matter hypothesis can give upper

bounds on models of new physics

I 12 TeV bounds on DM mass in the NMSSM I All masses are of order the Dark Matter mass or less I New Higgs fields below 20 TeV

36 / 40

Backup

37 / 40

Ratios of SUSY Breaking Scales: tighter unitarity bounds

Outside Higgs funnel (R > 10%)

38 / 40

Ratios of SUSY Breaking Scales

Outside Higgs funnel (R > 10%)

39 / 40

Vacuum constraints

I NMSSM has unrealistic vacua

Kanehata, Kobayashi, Konishi, Seto, Shimomura [arXiv:1103.5109]

I |Hu| = |Hd| ”= 0, |S| ”= 0 I |H|u,d = 0 or |S| = 0

I Require that the EW breaking vacua is the deepest

ÈH0

uÍ =

Ô 2mZ g sin β ÈH0

dÍ =

Ô 2mZ g cos β ÈSÍ = µ λ

I Require no CP violation in the Higgs sector

40 / 40