After the discovery of a Higgs boson(-like) particle a theorists - - PowerPoint PPT Presentation

SLIDE 1

After the discovery

• f

a Higgs boson(-like) particle – a theorist’s perspective

Heidi Rzehak

Albert-Ludwigs-Universit¨ at Freiburg

February 21, 2014

SLIDE 2

Discoveries at the LHC

Expectations (2008): ’t Hooft: “A Higgs, or more” Gross: “A super world” Veltman: “The unexpected”

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 3

Discoveries at the LHC

Expectations (2008): ’t Hooft: “A Higgs, or more” Gross: “A super world” Veltman: “The unexpected” . . . I I I I

• Nov. 2011

13 Dec. 2011 4 July 2012 8 Oct. 2013 HCP 2011: Exclusion of a wide Higgs mass range, some theorists’ thought: “complete exclusion until the end of 2011” ATLAS & CMS report an excess

• f events:

Too early to draw conclusions ATLAS & CMS announce the discovery of a Higgs-like particle Nobel prize: for the theoret. discovery of a mechanism that contributes to our understanding

• f the origin of

mass . . .

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 4

How was it discovered?

Discovery channels (LHC: p p collider, p = proton): pp → H → ZZ ∗ → 4ℓ: pp → H → γγ:

(here: ℓ = µ, µ = muon) g g H t t t Z Z ℓ ℓ ℓ ℓ g g H t t t W W W γ γ

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 5

How was it discovered?

Discovery channels (LHC: p p collider, p = proton): pp → H → ZZ ∗ → 4ℓ: pp → H → γγ + 2 jets:

(here: ℓ = µ, µ = muon) g g H t t t Z Z ℓ ℓ ℓ ℓ q q′ H q′′ q′′′ V V W W W γ γ

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 6

Is it “the” Higgs boson?

• Mass: free parameter in the Standard Model

expectation from precision measurements: O(100 GeV) (e.g. mass of the W boson) Moriond ’13: CMS: mH = 125.7 ± 0.3 (stat) ± 0.3 (syst) GeV ATLAS: mH = 125.5 ± 0.2 (stat) +0.5

−0.6 (syst) GeV

• Spin? Landau-Yang theorem:

Massive spin-1 particle cannot decay into two photons: Decay into photons observed ⇒ spin = 1 Moriond ’13: spin = 2: Excluded with > 99% confidence level spin = 0: compatible

• CP?

Moriond ’13: CP-even: compatible CP-odd: Exclusion with 98% confidence level

model dependent spin = 0

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 7

Is it “the” Higgs boson?

• Couplings? so far compatible with the Standard Model:

– Measurement of further production und decay channels: pp → H → WW (compatible with SM) pp → H → ττ (Evidence!) pp → H → bb . . . – still relatively large errors (∼ 20 %) – not all couplings accessible Signal strengths:

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 8

Is it “the” Higgs boson?

• Mass: free parameter in the Standard Model

expectation from precision measurements: O(100 GeV) (e.g. mass of the W boson) Moriond ’13: CMS: mH = 125.7 ± 0.3 (stat) ± 0.3 (syst) GeV ATLAS: mH = 125.5 ± 0.2 (stat) +0.5

−0.6 (syst) GeV

• Spin? Landau-Yang theorem:

Massive spin-1 particle cannot decay into two photons: Decay into photons observed ⇒ spin = 1 Moriond ’13: spin = 2: Excluded with > 99% confidence level spin = 0: compatible

• CP?

Moriond ’13: CP-even: compatible CP-odd: Exclusion with 98% confidence level

model dependent spin = 0

O t h e r m

• d

e l s : H i g g s m a s s c a n b e g i v e n b y

• t

h e r p a r a m e t e r s . a mixture of CP-odd and

• even?

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 9

Is it “the” Higgs boson?

• Couplings? so far compatible with the Standard Model:

– Measurement of further production und decay channels: pp → H → WW (compatible with SM) pp → H → ττ (Evidence!) pp → H → bb . . . – still relatively large errors (∼ 20 %) – not all couplings accessible Signal strengths: Could be affected by an extended Higgs sector

• r other unknown particles:

how much?

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 10

Further Results of the LHC

Supersymmetric partner particles:

• not found yet
• strongest constraints:

colour charged particles: gluinos and first generation of squarks signature: jets and missing energy

• much less constrained:

⋆ top squarks ⋆ purely electroweak particles signature: three charged leptons

Mass scales [GeV] 200 400 600 800 1000 1200 1400

χ ∼ l → l ~ χ ∼ χ ∼ ν τ τ τ →

±

χ ∼

2

χ ∼ χ ∼ χ ∼ ν τ ll →

±

χ ∼

2

χ ∼ χ ∼ χ ∼ H W →

2

χ ∼

±

χ ∼ χ ∼ χ ∼ W Z →

2

χ ∼

±

χ ∼ χ ∼ χ ∼ ν ν

• l

+

l →

• χ

∼

+

χ ∼ χ ∼ χ ∼ ν lll →

±

χ ∼

2

χ ∼ χ ∼ bZ → b ~ χ ∼ tW → b ~ χ ∼ b → b ~ H G) → χ ∼ ( χ ∼ t b → t ~ ) χ ∼ W →

±

χ ∼ b ( → t ~ ) χ ∼ W →

+

χ ∼ b( → t ~ χ ∼ t → t ~ χ ∼ t → t ~ χ ∼ q → q ~ χ ∼ q → q ~ )) χ ∼ W →

±

χ ∼ t( → b ~ b( → g ~ ) χ ∼ γ →

2

χ ∼ qq( → g ~ ) χ ∼ W →

±

χ ∼ | χ ∼ γ →

2

χ ∼ qq( → g ~ ) χ ∼ W →

±

χ ∼ qq( → g ~ ) χ ∼ Z →

2

χ ∼ qq ( → g ~ ) χ ∼ ν

±

l →

±

χ ∼ qq( → g ~ ) χ ∼ t → t ~ t( → g ~ ) χ ∼ | χ ∼ W →

±

χ ∼ qq( → g ~ ) χ ∼ | χ ∼ τ τ →

2

χ ∼ qq( → g ~ ) χ ∼

• l

+

l →

2

χ ∼ qq ( → g ~ χ ∼ tt → g ~ χ ∼ bb → g ~ χ ∼ qq → g ~ χ ∼ qq → g ~ SUS-13-006 L=19.5 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-011 L=19.5 /fb

x = 0.25 x = 0.50 x = 0.75

SUS-13-008 L=19.5 /fb SUS-12-001 L=4.93 /fb SUS-11-010 L=4.98 /fb SUS-13-006 L=19.5 /fb

x = 0.05 x = 0.50 x = 0.95

SUS-13-006 L=19.5 /fb SUS-13-012 SUS-12-028 L=19.5 11.7 /fb SUS-12-005 SUS-11-024 L=4.7 /fb SUS-12-028 L=11.7 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-014 L=19.5 /fb SUS-13-004 SUS-13-007 SUS-13-008 SUS-13-013 L=19.4 19.5 /fb SUS-13-013 L=19.5 /fb

x = 0.20 x = 0.50

SUS-13-004 SUS-12-024 SUS-12-028 L=19.3 19.4 /fb SUS-12-001 L=4.93 /fb SUS-13-012 SUS-12-028 L=19.5 11.7 /fb SUS-12-010 L=4.98 /fb

x = 0.25 x = 0.50 x = 0.75

SUS-12-005 SUS-11-024 L=4.7 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-017 L=19.5 /fb SUS-12-004 L=4.98 /fb SUS-13-006 L=19.5 /fb SUS-11-011 L=4.98 /fb SUS-13-011 SUS-13-004 L=19.5 19.3 /fb

left-handed top unpolarized top right-handed top

SUS-11-024 SUS-12-005 L=4.7 /fb SUS-11-021 SUS-12-002 L=4.98 4.73 /fb

x = 0.25 x = 0.50 x = 0.75

SUS-13-006 L=19.5 /fb

x = 0.05 x = 0.50 x = 0.95

SUS-13-006 L=19.5 /fb SUS-11-030 L=4.98 /fb gluino production squark stop sbottom EWK gauginos slepton

Summary of CMS SUSY Results* in SMS framework CMS Preliminary

m(mother)-m(LSP)=200 GeV m(LSP)=0 GeV

SUSY 2013

= 7 TeV s = 8 TeV s

lsp

m ⋅

• (1-x)

mother

m ⋅ = x

intermediate

m For decays with intermediate mass, Only a selection of available mass limits *Observed limits, theory uncertainties not included Probe *up to* the quoted mass limit

Note specific assumptions: simplified models, . . .

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 11

Further Results of the LHC

Further particles:

• not found yet

Mass scale [TeV]

• 1

10 1 10

2

10

Other Excit. ferm. New quarks LQ V' CI Extra dimensions

Magnetic monopoles (DY prod.) : highly ionizing tracks Multi-charged particles (DY prod.) : highly ionizing tracks

jj

m Color octet scalar : dijet resonance,

ll

m ), µ µ ll)=1) : SS ee ( →

L ± ±

(DY prod., BR(H

L ± ±

H

Zl

m (type III seesaw) : Z-l resonance,

±

Heavy lepton N

• Major. neutr. (LRSM, no mixing) : 2-lep + jets

WZ

m ll), ν Techni-hadrons (LSTC) : WZ resonance (l

µ µ ee/

m Techni-hadrons (LSTC) : dilepton,

γ l

m resonance, γ Excited leptons : l-

Wt

m Excited b quark : W-t resonance,

jj

m Excited quarks : dijet resonance,

jet γ

m

• jet resonance,

γ Excited quarks :

q ν l

m Vector-like quark : CC, Ht+X → Vector-like quark : TT

,miss T

E SS dilepton + jets + → 4th generation : b'b' WbWb → generation : t't'

th

4 jj ν τ jj, τ τ =1) : kin. vars. in β Scalar LQ pair ( jj ν µ jj, µ µ =1) : kin. vars. in β Scalar LQ pair ( jj ν =1) : kin. vars. in eejj, e β Scalar LQ pair (

tb

m tb, LRSM) : → (

R

W'

tq

m =1) :

R

tq, g → W' (

µ T,e/

m W' (SSM) :

tt

m l+jets, → t Z' (leptophobic topcolor) : t

τ τ

m Z' (SSM) :

µ µ ee/

m Z' (SSM) :

,miss T

E uutt CI : SS dilepton + jets +

ll

m , µ µ qqll CI : ee & )

jj

m ( χ qqqq contact interaction : )

jj

m (

χ

Quantum black hole : dijet, F

T

p Σ =3) : leptons + jets,

D

M /

TH

M ADD BH (

• ch. part.

N =3) : SS dimuon,

D

M /

TH

M ADD BH (

tt

m l+jets, → t (BR=0.925) : t t t →

KK

RS g

lljj

m Bulk RS : ZZ resonance,

ν l ν ,l T

m RS1 : WW resonance,

ll

m RS1 : dilepton,

ll

m ED : dilepton,

2

/Z

1

S

,miss T

E UED : diphoton +

/ ll γ γ

m Large ED (ADD) : diphoton & dilepton,

,miss T

E Large ED (ADD) : monophoton +

,miss T

E Large ED (ADD) : monojet + mass

862 GeV , 7 TeV [1207.6411]

• 1

=2.0 fb L

mass (|q| = 4e)

490 GeV , 7 TeV [1301.5272]

• 1

=4.4 fb L

Scalar resonance mass

1.86 TeV , 7 TeV [1210.1718]

• 1

=4.8 fb L

) µ µ mass (limit at 398 GeV for

L ± ±

H

409 GeV , 7 TeV [1210.5070]

• 1

=4.7 fb L

| = 0)

τ

| = 0.063, |V

µ

| = 0.055, |V

e

mass (|V

±

N

245 GeV , 8 TeV [ATLAS-CONF-2013-019]

• 1

=5.8 fb L

) = 2 TeV)

R

(W m N mass (

1.5 TeV , 7 TeV [1203.5420]

• 1

=2.1 fb L

))

T

ρ ( m ) = 1.1

T

(a m ,

W

m ) +

T

π ( m ) =

T

ρ ( m mass (

T

ρ

920 GeV , 8 TeV [ATLAS-CONF-2013-015]

• 1

=13.0 fb L

)

W

) = M

T

π ( m ) -

T

ω /

T

ρ ( m mass (

T

ω /

T

ρ

850 GeV , 7 TeV [1209.2535]

• 1

=5.0 fb L

= m(l*)) Λ l* mass (

2.2 TeV , 8 TeV [ATLAS-CONF-2012-146]

• 1

=13.0 fb L

b* mass (left-handed coupling)

870 GeV , 7 TeV [1301.1583]

• 1

=4.7 fb L

q* mass

3.84 TeV , 8 TeV [ATLAS-CONF-2012-148]

• 1

=13.0 fb L

q* mass

2.46 TeV , 7 TeV [1112.3580]

• 1

=2.1 fb L

)

Q

/m ν =

qQ

κ VLQ mass (charge -1/3, coupling

1.12 TeV , 7 TeV [ATLAS-CONF-2012-137]

• 1

=4.6 fb L

T mass (isospin doublet)

790 GeV , 8 TeV [ATLAS-CONF-2013-018]

• 1

=14.3 fb L

b' mass

720 GeV , 8 TeV [ATLAS-CONF-2013-051]

• 1

=14.3 fb L

t' mass

656 GeV , 7 TeV [1210.5468]

• 1

=4.7 fb L

• gen. LQ mass

rd

3

534 GeV , 7 TeV [1303.0526]

• 1

=4.7 fb L

• gen. LQ mass

nd

2

685 GeV , 7 TeV [1203.3172]

• 1

=1.0 fb L

• gen. LQ mass

st

1

660 GeV , 7 TeV [1112.4828]

• 1

=1.0 fb L

W' mass

1.84 TeV , 8 TeV [ATLAS-CONF-2013-050]

• 1

=14.3 fb L

W' mass

430 GeV , 7 TeV [1209.6593]

• 1

=4.7 fb L

W' mass

2.55 TeV , 7 TeV [1209.4446]

• 1

=4.7 fb L

Z' mass

1.8 TeV , 8 TeV [ATLAS-CONF-2013-052]

• 1

=14.3 fb L

Z' mass

1.4 TeV , 7 TeV [1210.6604]

• 1

=4.7 fb L

Z' mass

2.86 TeV , 8 TeV [ATLAS-CONF-2013-017]

• 1

=20 fb L

(C=1) Λ

3.3 TeV , 8 TeV [ATLAS-CONF-2013-051]

• 1

=14.3 fb L

(constructive int.) Λ

13.9 TeV , 7 TeV [1211.1150]

• 1

=5.0 fb L

Λ

7.6 TeV , 7 TeV [1210.1718]

• 1

=4.8 fb L

=6) δ (

D

M

4.11 TeV , 7 TeV [1210.1718]

• 1

=4.7 fb L

=6) δ (

D

M

1.5 TeV , 7 TeV [1204.4646]

• 1

=1.0 fb L

=6) δ (

D

M

1.25 TeV , 7 TeV [1111.0080]

• 1

=1.3 fb L

mass

KK

g

2.07 TeV , 7 TeV [1305.2756]

• 1

=4.7 fb L

= 1.0)

Pl

M / k Graviton mass (

850 GeV , 8 TeV [ATLAS-CONF-2012-150]

• 1

=7.2 fb L

= 0.1)

Pl

M / k Graviton mass (

1.23 TeV , 7 TeV [1208.2880]

• 1

=4.7 fb L

= 0.1)

Pl

M / k Graviton mass (

2.47 TeV , 8 TeV [ATLAS-CONF-2013-017]

• 1

=20 fb L

• 1

~ R

KK

M

4.71 TeV , 7 TeV [1209.2535]

• 1

=5.0 fb L

• 1
• Compact. scale R

1.40 TeV , 7 TeV [1209.0753]

• 1

=4.8 fb L

=3, NLO) δ (HLZ

S

M

4.18 TeV , 7 TeV [1211.1150]

• 1

=4.7 fb L

=2) δ (

D

M

1.93 TeV , 7 TeV [1209.4625]

• 1

=4.6 fb L

=2) δ (

D

M

4.37 TeV , 7 TeV [1210.4491]

• 1

=4.7 fb L

Only a selection of the available mass limits on new states or phenomena shown *

• 1

= ( 1 - 20) fb Ldt

∫

= 7, 8 TeV s

ATLAS

Preliminary

ATLAS Exotics Searches* - 95% CL Lower Limits (Status: May 2013)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 12

Reasons for further investigations

• Main question: What is the underlying theory?
• Reasons to search for beyond the Standard Model Physics

From experiments: ⋆ dark matter ⋆ matter-antimatter asymmetry in the universe ⋆ neutrino oscillations From theory: ⋆ grand unification ⋆ embedding of gravity ⋆ Higgs mass MH: sensitive to physics at high energy scales Λ quantum corrections: δM2

H ∼ Λ2 (hierarchy problem)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 13

Minimal Supersymmetric Standard Model (MSSM)

MSSM: ⋆ Extension of the Standard Model (SM) ⋆ Further symmetry: Supersymmetry (SUSY): Q|Boson = |Fermion, Q|Fermion = |Boson Q = supersymmetry generator Recipe: • Standard Model particles + 2nd Higgs doublet (2HDM) (Generation of fermion masses, anomaly cancelations)

• Superpartners
• Explicit soft SUSY-breaking ⇒ many new (complex) parameters

(Else: masssuperpartner = mass2HDM-particle ← exp. excluded)

• R-Parity: discrete symmetry

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 14

Minimal Supersymmetric Standard Model (MSSM)

Particle content: (2HDM)-Particle Quarks Leptons Gauge bosons Higgs boson s Superpartner Squarks Sleptons Gauginos Higgsinos Particles with same quantum numbers can mix: charged Higgsinos and Gauginos → Charginos neutral Higgsinos and Gauginos → Neutralinos

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 15

Higgs Sector at Born Level

Higgs potential: gauge couplings VHiggs = g2 + g′2 8 (H+

d Hd − H+ u Hu)2 + g2

2 |H+

d Hu|2

+ |µ|2(H+

d Hd + H+ u Hu)

µ: coupl. betw. Higgs superfields + (m2

1H+ d Hd + m2 2H+ u Hu)

soft breaking terms + (ǫij|m2

12|e iϕm2

12Hi

dHj u + h.c.)

Hd, Hu: Higgs doublets

• one phase in the Higgs potential: ϕm2

12

can be rotated away

• phase difference of Higgs doublets ξ

vanishes because of minimum condition

}

non-vanishing phases: ⇒ maybe CP- or T-violation? (Time reversal-operator is antiunitary ⇒ complex conjugation

• f parameters)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 16

Higgs Sector at Born Level

Higgs potential: gauge couplings VHiggs = g2 + g′2 8 (H+

d Hd − H+ u Hu)2 + g2

2 |H+

d Hu|2

+ |µ|2(H+

d Hd + H+ u Hu)

µ: coupl. betw. Higgs superfields + (m2

1H+ d Hd + m2 2H+ u Hu)

soft breaking terms + (ǫij|m2

12|e iϕm2

12Hi

dHj u + h.c.)

Hd, Hu: Higgs doublets

• one phase in the Higgs potential: ϕm2

12

can be rotated away

• phase difference of Higgs doublets ξ:

vanishes because of minimum condition

}

no CP violation at Born level in the Higgs sector

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 17

Higgs Sector at Born Level

Physical mass eigenstates (at Born level):

• 5 Higgs bosons:

3 neutral H, h, A; 2 charged H± Masses of the Higgs bosons:

• not all independent:
• ften: Mass MA or MH± (and tan β) as free parameter

tan β = v2

v1 : ratio of the Higgs vac. expect. values

• lightest Higgs boson: h

Upper theoretical Born mass bound: Mh ≤ MZ = 91 GeV with quantum corrections of higher orders: Mh 140 GeV dependent on the MSSM parameters

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 18

Why a precise Higgs mass prediction?

• Needed as consistent input for the calculation of

cross sections and decay widths in the MSSM

• experimentally

measured value

⇒

constraint on viable MSSM parameter space A precise theoretical prediction is needed to fully exploit this constraint: ∆Mexp.

H

< 1 GeV vs ∆Mtheory

H

≈ 3 GeV

• In the discussion of the amount of fine-tuning of the MSSM

the precise theoretical prediction of the Higgs boson mass enters.

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 19

Contributions to the Higgs boson masses

Quantum corrections:

h h t t

+...

h0 h0 t ˜ tj ˜ g t ˜ ti

+... One-loop level O(αt): Two-loop level O(αtαs): αt ∼ (top Yukawa coupl.)2 Real parameters:

h0 A0 t ˜ tj ˜ g t ˜ ti

=0 no mixing between CP-even and CP-odd states ⇒ Lightest Higgs boson is CP-even.

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 20

Implications of a 125.5 GeV Higgs boson (MSSM)

80 90 100 110 120 130 140

• 4
• 3
• 2
• 1

1 2 3 4

Xt/TeV Mh/GeV Born 1-loop 2-loop

generated using FeynHiggs

[Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams]

1-loop [Frank, Hahn, Heinemeyer,

Hollik, H.R., Weiglein]

2-loop O(α{t,b}αs, α2

{t,b}, αtαb)

[Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Heinemeyer, Hollik, H.R., Weiglein; Dedes, Degrassi, Slavich]

, Xt = squark mixing parameter

• A 125.5 ± 3 GeV mass constrains the parameter space but

does not exclude the MSSM. (theory uncertainty ≈ 3 GeV)

• here: no known 3-loop contributions included [Martin; Harlander, Kant,

Mihaila, Steinhauser]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 21

Implications of a 125.5 GeV Higgs boson (MSSM)

80 90 100 110 120 130 140

• 4
• 3
• 2
• 1

1 2 3 4

Xt/TeV Mh/GeV Born 1-loop 2-loop

generated using FeynHiggs

[Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams]

1-loop [Frank, Hahn, Heinemeyer,

Hollik, H.R., Weiglein]

2-loop O(α{t,b}αs, α2

{t,b}, αtαb)

[Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Dedes, Degrassi, Slavich]

, Xt = squark mixing parameter For parameter scans, see e.g.

[Heinemeyer, St˚ al, Weiglein, arXiv:1112.3026; Arbey, Battaglia, Djouadi, Mahmoudi, Quevillon, arXiv:1112.3028]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 22

Higgs boson mass and CP-violating phases

110 115 120 125 130 135 140 0.5 1 1.5 2

ϕXt/π Mh1/GeV

1-loop 2-loop O(αtαs) 2-loop (interpol.)

generated using FeynHiggs

[Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams]

1-loop [Frank, Hahn, Heinemeyer,

Hollik, H.R., Weiglein]

2-loop O(αtαs) [Heinemeyer,

Hollik, H.R., Weiglein]

2-loop (interpol.): corrections for real parameters are interpolated

[Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Dedes, Degrassi, Slavich]

• The Higgs mass does depend on

the squark mixing phase ϕXt.

• For ϕXt = nπ, n ∈ N0,

h1 is not a CP-eigenstate. (no resummation)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 23

Higgs boson mass and CP-violating phases

110 115 120 125 130 135 140 0.5 1 1.5 2

ϕXt/π Mh1/GeV

1-loop 2-loop O(αtαs) 2-loop (interpol.)

generated using FeynHiggs

[Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams]

1-loop [Frank, Hahn, Heinemeyer,

Hollik, H.R., Weiglein]

2-loop O(αtαs) [Heinemeyer,

Hollik, H.R., Weiglein]

2-loop (interpol.): corrections for real parameters are interpolated

[Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Dedes, Degrassi, Slavich]

• The Higgs mass does depend on

the squark mixing phase ϕXt.

• For ϕXt = nπ, n ∈ N0,

h1 is not a CP-eigenstate. To do: Implementation of O(α2

t ) contr. [Hollik, Passehr, arXiv:1401.8275]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 24

Higgs boson mass for large stop masses

Prediction obtained via Feynman diagrammatic approach: + all log and non-log terms are taken into account at a certain order of perturbation theory

• possible appearance of large logs:

∆MH ∼ log MS

mt

MS: SUSY particle mass scale mt: top quark mass

⇒ • good prediction for lower SUSY mass scales

• no reliable prediction for large SUSY mass scales

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 25

Higgs boson mass for large stop masses

Other approach: Renormalization Group Equation (RGE) approach: ⋆ assume: all SUSY particles are heavy of order ∼ MS: above MS: MSSM below MS: Standard Model match at scale MS: λMSSM(MS) = λStandard Model(MS) (as effective theory) quartic Higgs coupling ⋆ evolve λ to lower scale using Standard Model running (RGE) ⋆ the Higgs mass2 is then M2

h(mt) = 2λ(mt)v2

v ≈ 174 GeV ⇒ logs resummed to all orders: good prediction for large SUSY masses → Combine both approaches (now:only for real parameters)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 26

Higgs boson mass for large stop masses

5000 10000 15000 20000

MS [GeV]

115 120 125 130 135 140 145 150 155

Mh [GeV]

FH295 3-loop 4-loop 5-loop 6-loop 7-loop LL+NLL FeynHiggs 2.10.0 Xt = 0 Xt/MS = 2

Comparison of: ⋆ old FeynHiggs reliable up to Ms = O(1TeV) ⋆ analyt. solution of RGE: 3-loop . . . 7-loop level: Logs of order O(αtα2

s, α2 t αs, α3 t ) . . .

⋆ numerical solution: LL+NLL: logs resummed to all orders

MA = M2 = µ = 1 TeV, m˜

g = 1.6 TeV, tan β = 10

[T. Hahn, S. Heinemeyer, W. Hollik, H.R., G. Weiglein, arXiv:1312.4937]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 27

Higgs boson mass for large stop masses

5000 10000 15000 20000

MS [GeV]

115 120 125 130 135 140 145 150 155

Mh [GeV]

3-loop, O(αt αs

2)

3-loop full LL+NLL H3m FeynHiggs 2.10.0 A0 = 0, tanβ = 10

Comparison with H3m:

[Kant, Harlander, Mihaila, Steinhauser, arXiv:1005.5709]

3-loop: O(αtα2

s), O(α2 t αs), O(α3 t ),

⋆ only leading and next-to leading logs ⋆ single scale MS H3m: ⋆ complete O(αtα2

s) result

⋆ different scales At 2-loop: different ren. schemes

CMSSM: m0 = m1/2 = 200 . . . 15000 GeV, A0 = 0, tan β = 10, µ > 0, spectra generation with SoftSUSY [Allanach, hep-ph/0104145]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 28

Higgs boson mass for large stop masses

Similar findings for large SUSY masses (pure RGE approach):

[Draper, Lee, Wagner, arXiv:1312.5743]

1Σ, 2Σ ATLASCMS LEP exclusion 5000 10000 15000 20000 25000 30000 110 115 120 125 130 135

MS GeV Mh GeV

Mh, QRG Mt, XtMS 0, tanΒ 20, Μ MS

2-loop NNLL result 3-loop NNLL result 4-loop NNLL result resummed result Differences:

• 3-loop running for λ
• 2-loop matching
• not yet implemented

into a computer code

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 29

Deviations from the Standard Model?

[Frank Vincentz, http://de.wikipedia.org/wiki/Kleeblatt; Uwe Vogel, http://www.oldskoolman.de/] After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 30

Deviations from the Standard Model (SM)?

Needed:

• precise predictions of the signal cross sections in the SM

Calculation of higher-order corrections necessary

• precise determination of the background
• good error estimate

(e.g. including possible errors originating from a contamination

• f control regions by events of unknown particles

[Feigl, H.R., Zeppenfeld, arXiv:1205.3468])

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 31

Deviations from the Standard Model (SM)?

Where can they originate from?

• changes in loop-induced couplings due to unknown particles

γ γ h

• changes of couplings due to mixing effects

in an enlarged Higgs sector

• changes due to additional decay into invisible particles
• changes due to two degenerate Higgs bosons

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 32

Next-tominimal Supersymmetric Standardmodel (NMSSM)

In the MSSM: Parameter µ in the superpotential W, W = µH1H2+ . . . A priori: arbitrary value But: Order of the electroweak/SUSY-breaking scale In the NMSSM: Additional Higgs superfield singlet S: µ is generated via a vacuum expectation value of the scalar Higgs singlet, W = λSH1H2+ . . ., λ = new coupling

• 7 Higgs bosons: h1, h2, h3, A1, A2, H±
• CP-violation in the Higgs sector possible already at

Born level (complex parameters)

• Mass of the light CP-even MSSM-like Higgs boson

can be larger than in the MSSM

• 5 neutralinos (4 neutralinos in the MSSM)

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 33

Degenerate Higgs bosons

For illustration (one possibility):

MHi [GeV] Aκ [GeV] H1 tree-level H1 one-loop H2 tree-level H2 one-loop 20 40 60 80 100 120 140 160 180 200

• 350
• 300
• 250
• 200
• 150
• 100
• 50

[Ender, Graf, M¨ uhlleitner, H.R.]

In the NMSSM: 2 Higgs bosons could be nearly degenerate with masses of ∼ 125 GeV

[Gunion, Jiang, Kraml, arXiv:1207.1545]

Illustration: Cross-over region of H1 and H2 at Aκ ≈ −210 GeV:

• Masses MHi ∼ 125 GeV
• H1 and H2 interchange their role

trilinear, SUSY-breaking singlet coupling

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 34

Degenerate Higgs bosons

For illustration (one possibility):

(RS

i3)2

Aκ [GeV] H1 tree-level H1 one-loop H2 tree-level H2 one-loop 0.2 0.4 0.6 0.8 1

• 350
• 300
• 250
• 200
• 150
• 100
• 50

[Ender, Graf, M¨ uhlleitner, H.R.]

In the NMSSM: 2 Higgs bosons could be nearly degenerate with masses of ∼ 125 GeV ⇒ Change of the effective couplings

[Gunion, Jiang, Kraml, arXiv:1207.1545]

Illustration: Cross-over region of H1 and H2: Masses ∼ 125 GeV Aκ < −210 GeV: H1 singlet-like, H2 non-singlet like Aκ > −210 GeV: H1 non-singlet like, H2 singlet-like

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 35

Degenerate Higgs bosons

For illustration (one possibility):

(RS

i3)2

Aκ [GeV] H1 tree-level H1 one-loop H2 tree-level H2 one-loop 0.2 0.4 0.6 0.8 1

• 350
• 300
• 250
• 200
• 150
• 100
• 50

[Ender, Graf, M¨ uhlleitner, H.R.]

In the NMSSM: 2 Higgs bosons could be nearly degenerate with masses of ∼ 125 GeV ⇒ Change of the effective couplings

[Gunion, Jiang, Kraml, arXiv:1207.1545]

Illustration: • Higher-order corrections are necessary

• Implemented in NMSSMCalc: program for

evaluation of mass spectra and decay widths (allows also for complex parameters)

[Baglio, Gr¨

• ber,

M¨ uhlleitner, Nhung, H.R., Spira, Streicher, Walz]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 36

Degenerate Higgs bosons

[Gunion, Jiang, Kraml, arXiv:1207.1545]

0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Rh

gg (γγ)

Rh

gg (VV)

123<mh1,mh2<128 0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.4 Rh

gg (γγ)

(Ch

bb)2

123<mh1,mh2<128

Legend: mh2 − mh1 ≤ 1 GeV, 1 GeV < mh2 − mh1 ≤ 2 GeV, 2 GeV < mh2 − mh1 ≤ 3 GeV Signal ratio: Rh

gg(XX) = 2

• i=1

σ(gg → hi)BR(hi → XX) σSM(gg → h)BRSM(h → XX) with an effective SM Higgs mass (Parameter scans with NMSSMTools [Ellwanger, Gunion, Hugonie])

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 37

Degenerate Higgs bosons

[Gunion, Jiang, Kraml, arXiv:1207.1545]

0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Rh

gg (γγ)

Rh

gg (VV)

123<mh1,mh2<128 0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.4 Rh

gg (γγ)

(Ch

bb)2

123<mh1,mh2<128

• Enhancement of the h → γγ channel by a factor of 1.5

possible without enhancing h → VV

• Enhancement of the h → γγ channel is generally achieved

by reducing the average b¯ b coupling strength Ch

bb

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 38

Only a single Higgs boson discovery at the LHC?

[Gupta, H.R., Wells, arXiv:1206.3560, arXiv:1305.6397]

If no beyond Standard Model (SM) physics is seen at the LHC:

(related to electroweak symmetry breaking)

How large can deviations from the SM Higgs couplings be? How precisely do we need to measure the Higgs couplings at least? Which future collider and detectors?

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 39

Only a single Higgs boson discovery at the LHC?

[Gupta, H.R., Wells, arXiv:1206.3560, arXiv:1305.6397]

No completely model independent answer possible:

• MSSM
• Mixed-in singlet model = Standard Model + exotic Higgs boson singlet S:

Scalar fields mix via |HSM|2|S|2

[Schabinger, Wells, hep-ph/0509209; Bowen, Cui, Wells, hep-ph/0701035]

⇒ 2 CP-even mass eigenstates: SM-like h, heavier H with couplings2 g2

h = c2 h g2 SM and g2 H = s2 h g2 SM

ch = cos θh sh = sin θh θh = mix. angle

• Composite Higgs models: SM-like Higgs boson = pseudo-Goldstone:

SM vector bosons and fermions + strong sector with Higgs multiplet in terms of an effective field theory for a strong interacting light Higgs (SILH) boson

[Guidice, Grojean, Pomarol, Rattazzi, hep-ph/0703164]

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 40

Only a single Higgs boson discovery at the LHC?

[Gupta, H.R., Wells, arXiv:1206.3560, arXiv:1305.6397]

Take into account: ⋆ discovery potential of the LHC for further particles related to electroweak symmetry breaking ⋆ constraints from electroweak precision tests

• MSSM:

Deviations constrained mainly by discovery potential

• Mixed-in singlet model:

Deviations constrained by discovery potential electroweak precision tests

• Composite Higgs models:

Deviations constrained by electroweak precision tests

10 20 30 40 50 100 200 300 400 500 600 700 800 900 1000 tan β MA/GeV

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 41

Only a single Higgs boson discovery at the LHC?

[Gupta, H.R., Wells, arXiv:1206.3560, arXiv:1305.6397]

Maximal deviations from the SM Higgs couplings? (no new physics at the LHC) |∆hVV| |∆h¯ tt| |∆h¯ bb| |∆hhh|

• c. to gauge
• c. to top
• c. to bottom

triple bosons V quarks t quarks b Higgs coupl. MSSM

< 1% 3% 10%, 100% 2%, 15%

Mixed-in Singlet

6% 6% 6% 18%

Composite Higgs

8% tens of % tens of % tens of % tan β > 20 no superpartners all other cases ⇒ a challenge for the future!

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014

SLIDE 42

Summary

• Exciting times: Discovery of a Higgs boson
• Still exciting: What is its true nature?
• At the moment: compatible with the Standard Model
• Constraints on the parameter space of extension of

the Standard Model (e.g. coming from the Higgs mass)

• Precise measurement of its couplings can help

with the complete identification of the particle

• Program development:

⋆ FeynHiggs: Higgs mass prediction for large stop masses improved ⋆ NMSSMCALC: New program for the NMSSM Higgs masses/decay widths

After the discovery of a Higgs boson(-like) particle – a theorist’s perspective Heidi Rzehak February 21, 2014