INDUCED EWSB GGI, Florence September 21, 2015 Jamison Galloway - - PowerPoint PPT Presentation

INDUCED EWSB

Based on work with:

• A. Azatov, S. Chang, M. Luty, E. Salvioni,
• Y. Tsai,
• Y. Zhao

GGI, Florence September 21, 2015 Jamison Galloway

• utline
• Introduction/Motivation
• Modeling, take one: realization with strong dynamics
• Modeling, take two: realization with perturbative dynamics
• Implications: phenomenology at the LHC
• A conclusion or two

introduction

h mass: h couplings:

Examples:

• v/f in comp. H

(MCHM4)

• ‘non-alignment’

in type-1 2HDM at large tan β

• Higgs mixing with

singlet (tree-level)

*ref: M. Pieri @ LHCP 2015

introduction

h mass: h couplings:

Examples:

• type-1 2HDM

at variable tan β (tree-level)

*ref: M. Pieri @ LHCP 2015

δκV . 0.08 δκF . 0.16

introduction

h mass: h couplings:

Examples:

• light top partners
• charged Higgses

(loop-level)

*ref: M. Pieri @ LHCP 2015

δκγ,g . 0.14

takeaway (and assumptions going forward)

• h confirmed at 125 GeV
• Tree-level couplings are already at ~SM ± 10%
• Loop-level at ~SM ± 15%, consistent with…
• …null results from partner searches up to ~600 GeV

• h confirmed at 125 GeV
• Tree-level couplings are already at ~SM ± 10%
• Loop-level at ~SM ± 15%, consistent with…
• …null results from partner searches up to ~600 GeV

**~ SUSYish** **composite H tuned at least at 10%** **~inconclusive**

I’ll take this circumstantial evidence for an elementary Higgs seriously; assume SUSY stabilization and focus on the question of mass

takeaway (and assumptions going forward)

**still room for (somewhat) natural elementary H**

SUSY Higgs and its mass

High SUSY scale (and thus pressure on naturalness) boils down to very special role of quartic (and very ‘special’ smallness of it) unavoidable consequence of V(H) with negative quadratic

m2

h = 2λv2

λ ≤ 1 8(g2 + g02)

SUS’ic relation for H quartic is too small by a factor of 2… ⇒ need an order one breaking! Can be done with spectrum, but not very naturally

mh ≤ mZ

tan β 1 2 4 50

3 × 107 mSUSY(GeV) 106 35 × 103 104

δm2

H ∝ m2 SUSY

problem:

*ref: Vega, Villadoro (JHEP 2015)

M1 = M2 = M3 = m = 1 TeV tan b = 50 tan b = 4 tan b = 2 tan b = 1

mh = 125 GeV 4 6 8 10 12 14 16 18 110 120 130 140 150 160

log10 mSUSY @GeVD mh results from SUSY HD

induced EWSB: a strong model

[ turn that frown upside down ]

V (H) ∼ + (125)2 |H|2 + λ |H|4

what if… naively:

• EW intact
• massless W, Z, fermions
• physical mass approximately independent of quartic

{

less naively:

• EW broken by QCD
• W, Z acquire mass
• electron mass

{

∼ gfπ/2 ∼ 50 MeV

me ∼ yeyq × 4πf 3

π/m2 h ∼ 10−5 eV

~1.5 yes votes 4 strong NO votes (consensus may well be misguided;

• cf. Trump leading GOP)

induced EWSB: a strong model

“v” ∼ yuΛ3

QCD

16π2m2

h

→ λΛ3

TC

16π2m2

h

ΛTC = TeV “v” → λ × TeV

}

Higgs ‘VEV’ in previous example fixed by QCD… …consider instead a TC-like sector

∆VUV = m2

H |H|2 − (λHψψ0 + h.c.);

ψ = (⇤, 2)0, ψ0 = (⇤, 1)1/2

∆V (µ < TeV) = m2

H |H|2 − c1

✓λΛ3

TC

16π2 H + h.c. ◆

*contrast e.g. SILH

induced EWSB: a strong model

“v” ∼ yuΛ3

QCD

16π2m2

h

→ λΛ3

TC

16π2m2

h

ΛTC = TeV “v” → λ × TeV

}

Higgs ‘VEV’ in previous example fixed by QCD… …consider instead a TC-like sector

∆VUV = m2

H |H|2 − (λHψψ0 + h.c.);

ψ = (⇤, 2)0, ψ0 = (⇤, 1)1/2

∆V (µ < TeV) = m2

H |H|2 − c1

✓λΛ3

TC

16π2 H + h.c. ◆

Upshot:

• Confining dynamics induces .
• Elementary Higgs VEV naturally right size.
• Elementary Higgs mass is independent of quartic.
• New isotriplet (minimally) of scalars exists below ~TeV.

hHi 6= 0

*

* Corrections from quartic < 20%

induced EWSB: a strong model

EFT coupling H to TeV scale strong sector (w/ nonlinear sigma field)

∆L = f 2

TC

4 tr ⇥ (DµΣ)†(DµΣ) ⇤ + 1 2 tr ⇥ (DµH)†(DµH) ⇤

⇒ m2

W = g2

4 (f 2

TC + v2 h)

“bipartisan EWSB” kinetic: interaction:

✏ ⌘ vh Λ ⌧ 1

controlled expansion parameter

∆L = X

n≥1

cn Λ4−n 16π2 tr

• H†λΣ

n

✏ . 0.1 with vh = 230 GeV, λ = 0.5

constraint from Higgs @ LHC:

δgV V H g(SM)

V V H

. 0.08

⇒ f < v × p (2 − δ)δ ≈ 95 GeV

*ref: Azatov, Galloway, Luty (PRL 2012)

induced EWSB: a strong model

vh ∼

Recap: an ‘induced’ VEV for the elementary field

[sensible for λ = O(1), Λ ∼ TeV] λ 4π Λ2 m2

h

× f vh ∼

…(recklessly) reimagine as a linear sigma model [ i.e. treat ]

Λ ∼ 4πf → mσ

⇒ ✏ ≡ vh Λ → v2

h

f 2 m2

h

m2

σ

λ 4π m2

σTC

m2

h

× fσTC

induced EWSB: a strong model

vh ∼

Recap:

[sensible for λ = O(1), Λ ∼ TeV] λ 4π Λ2 m2

h

× f vh ∼

…(recklessly) reimagine [ i.e. treat ]

Λ ∼ 4πf → mσ

⇒ ✏ ≡ vh Λ → v2

h

f 2 m2

h

m2

σ

λ 4π m2

σTC

m2

h

× fσTC

Criteria for generalized induced EWSB

• H in isolation does NOT break EW
• EW broken appreciably by heavy fields
• i.e. EW nonlinearly realized at scales > 125
• coupling H to heavy EWSB source induces <H>
• can be realized in 2HDM (with weaker couplings)…

|{z}

|{z}

(f ∼ vh) (mσ mh)

induced EWSB: a perturbative model

10% 30% 50% 65%

VACUUM STABILITY

mS ` mh

LIGHT HIGGS COUPLINGS H95% CLL

Contours: FT -1 Hsee textL decoupling

mh < 125 GeV

120 140 160 180 200 220 240 0.5 1.0 1.5 2.0 2.5 3.0

f @GeVD lS

TREE-LEVEL TUNING HSimplified ModelL

⇒ δm2

h ∝

λ 16π2 m2

σ (×mixing angles)

Higgs mass corrected via coupling to Σ: [ considering a single H doublet ] (reminiscent of corrections from stops with important distinction that σ needn’t be pushed to >>TeV scales)

V = m2

H|H|2 − m2 Σ|Σ|2 − κ2(H†Σ + h.c.) + λΣ|Σ|4

‘auxiliary Higgs’ λΣ λH

small mixing ) hΣi = f / |mΣ| pλΣ , m2

σ / λΣf 2 m2 h

Veff(h) = 1 2m2

Hh2 − κ2fh + O(κ4) ⇒ vh ∝ κ2f

m2

H

, →

*ref: Galloway, Luty, Tsai, Zhao (PRD 2014); Alves, Fox, Weiner (PRD 2015)

phenomenology: TC-like model

     H±

2 , A0 2

H0

1, H± 1 , A0 1

h G±, G0     

{

}π(1,2,3)

TC

MSSM (Hu, Hd, Σ) ⇒ 8 physical scalars:

Heavy Higgses (pions) produced by, decay to, SM via mixing

• r through auxiliary fields’ SU(2) couplings

UNIQUE signals: compare with MSSM (H couples to f ), NMSSM (“S” inherits *all* quantum numbers from mixing),

∆L ⊃ (vh + H) 0 ⇒ m2

π ∼ (uvu + dvd) × Λ

≡ (✏u + ✏d) × Λ2 ≈ (500 GeV)2

phenomenology: TC-like model

[ examples, exclusions ]

• Decouple second H (to simplify)
• sub-TeV pseudoscalar remains

from TC sector

• couples to fermions only through

mixing: Zh persists even at m>350

*ref: Chang, Galloway, Luty, Salvioni, Tsai (JHEP 2015)

• A > Zh to cover most space @ LHC
• powerful exclusion for strong

model due to small ff couplings

phenomenology: 2HDM-like model

[ illustrating possibility of reduced trilinear ]

• direct searches exclude up to m ~ 400
• 50% reduction in H trilinear remains

possible (!)

• even at large tan β significant

reduction persists (~30%) for large ‘auxiliary’ self-interactions

conclusions

• h @ LHC still allows ~1/3 of W mass to be generated elsewhere
• If excitations of this other EWSB source are heavy and

couple to H, the Higgs EFT contains a tadpole

• non-zero Higgs VEV may not require negative quadratic;

H may not break EW at all *in isolation*

• Higgs quartic is consequently untethered from mass

> may provide breathing room in SUSY theories especially > can generate large deviations in Higgs self-couplings

• appearance of light stops will require explanation of Higgs mass;

physical mass is essentially free parameter in induced EWSB

• rich spectrum contains sub-TeV scalars with unique

(i.e. non-MSSM) footprints

• Nonstandard Higgs and add’l scalars still in play…

…any surprise is welcome; many nicely motivated, *and* still viable!

BACKUP

coincidence issue

ψ ψ0 ⇤ 1 ⇤ 1 1 ⇤

The active participants:

SU(2)TC SU(2)L

SU(2)R

⇤ ⇤ ⇤

with potential plus two sterile flavors:

b = N

IR fixed point

• Strongly coupled
• Self-dual

= ⇒ H

∆W = λHψψ0

µ

gTC

m(ψ) ∼ TeV

g∗

b = N

b ≥ 5 3N

• Phase transition induced by

SUSY breaking

• STRONG fixed point above

sets without conspiracy

• As in the QCD toy case:

is *free*, independent of quartic at leading order ΛTC ∼ mh

m0

mh

(RG induced by soft masses)

EWPT and strong model

∆S(IR)

TC '

1 12π log ✓ Λ2 m2

h

◆ | {z }

∼16π2

∆S(IR)

• Ind. '

1 12π log ✓ Λ2 m2

π

◆ | {z }

∼4π

vs. S Parameter: T Parameter:

λuvu = λdvd ⇒ custodial limit

, → T corresponds to a variable parameter of the theory

• 0.3
• 0.2
• 0.1

0.0 0.1 0.2 0.3 0.4

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4

S T

↵T = (✏u − ✏d)2

[ Notice that increasing T tends to decrease S above]

mref = 120 GeV 120 350 H’less

‘universal’ phenomenology: H couplings

Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê

Ï

ATLAS + CMS H68, 95%L solid: 25 fb-1û7+8 TeV dashed: 300 fb-1û14 TeV

mA=250 GeV 300 400 600 mA=250 GeV 300 400 600

strong lS = 2

0.85 0.90 0.95 1.00 1.05 1.10 1.15 0.6 0.8 1.0 1.2 1.4

kV kf

generation of auxiliary quartics

D-Terms {

∆K = Σ†

u,d exp(gSV aT a)Σu,d; T a ∈ SU(2)S

Σ ∈ Ψ5; Ψ5 = T, Σ [SU(2)S broken by hΦi]

g1 g2 g3 gS

SUH2LS SUH3LS' 100 105 108 1011 1014 1 2 3 4

m @GeVD coupling

RUNNING COUPLINGS @ Extended D-Term Model D

running starts at two loops; some completion still required

{

(Ψ, ¯ Ψ, Φ, ¯ Φ) = 6 flavors

history of Higgs @ LHC

¯

Jamboree

• Dec. 2011

Moriond

• Mar. 2012

Observation

• Jul. 2012

HCP

• Nov. 2012

SM

Moriond

• Mar. 2013

Run 1 combination 0.90 0.95 1.00 1.05 1.10 1.15 1.20 0.6 0.8 1.0 1.2

a c

Higgs û LHC: the road so far

H carries all light scalars of the theory. Self-interactions modified by , :

(H†H)3 (∂µ(H†H))2

mh = 125 l3êSM > 1+c6 = SM = SM ± 25%

0.6 0.8 1.0 1.2 1.4

• 0.3
• 0.2
• 0.1

0.0 0.1 0.2 0.3

ltreeêSM c6

HIGGS SELF-INTERACTIONS: h3

mh = 125 l4êSM > 1+15c6ê2 = SM = SM ± 25%

0.6 0.8 1.0 1.2 1.4

• 0.3
• 0.2
• 0.1

0.0 0.1 0.2 0.3

ltreeêSM c6

HIGGS SELF-INTERACTIONS: h4

Small cubic implausible: M < 500 GeV for vectors! hVV and hff ~ SM *does* paint us into a corner

Higgs self-interaction: comparison with SILH