Precision observables of compositeness Roman Pasechnik Dept. of - - PowerPoint PPT Presentation

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Precision observables of compositeness Roman Pasechnik Dept. of - - PowerPoint PPT Presentation

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Precision observables of compositeness Roman Pasechnik Dept. of Astronomy and Theoretical physics, Lund University HP2, September 5 th , 2014 Dynamical electroweak symmetry breaking Many attractive features EWSB is triggered by a

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SLIDE 1

Precision observables of compositeness

Roman Pasechnik

  • Dept. of Astronomy and Theoretical physics, 



 Lund University

HP2, September 5th, 2014

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SLIDE 2

Dynamical electroweak symmetry breaking

✓ EWSB is triggered by a new strongly-coupled dynamics more than one confinement scale in Nature? Higgs mechanism is effective?

  • ✓ No fundamental scalars 


composite Higgs? Higgs “partners”?

  • ✓ No hierarchy problem, no fine-tuning

a best alternative to SUSY with fewer free parameters?

  • ✓ A plenty of new hadron-like objects, difficult to find/treat though

composite Dark Matter? LHC phenomenology? ..etc Many attractive features Evolutions of DEWSB ideas/realizations Technicolor Extended TC Walking TC Bosonic TC Composite Higgs EFT’s e.g. MCHM SO(5)/SO(4) ??? No consistent UV completion has yet been proposed….

2

Hill & Simmons, Phys. Rept. 381, 235 (2003) Sannino, Acta Phys. Polon. B40, 3533 (2009), etc

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SLIDE 3

A new energy scale from confinement?

The energy scale of both EW theory (SM) and new strongly-coupled dynamics has a common

  • rigin: the Tquark-Tgluon condensate

QCD “T-QCD”

3

Simplistic approach: one employs a direct analogy with QCD Static properties of light hadrons can be completely determined by two dimensionful vacuum parameters:

gluon condensate: light quark condensate:

Well-known example: QCD at low momentum scales Spectrum of light composites (incl. Higgs) is governed by

working hypothesis:

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SLIDE 4

4

Issues of Technicolor: oblique corrections

New Physics must come in loops

Generic parameterization

  • f NP effects is EW observables

in terms of S,T,U parameters

should not disturb EW obs too much!

Peskin&Takeuchi PRL’90 M2

Z = M2 Z0

1 − α(MZ)T 1 − GF M2

Z0S/2

√ 2π

  • −

M2

W = M2 W 0

1 1 − GF M2

W 0(S + U)/2

√ 2π

ΓZ = M3

ZβZ

1 − α(MZ)T ,

S = 0.00+0.11

−0.10,

T = 0.02+0.11

−0.12,

U = 0.08 ± 0.11,

PDG’13 Extra chiral heavy family doublet brings up

e 2/3π

Standard QCD-like TC

] S ∼ 0.45

EW precision constraints on New Physics

S = C 3π

  • i
  • t3L(i) − t3R(i)

2 , = 4

vector SU(2) breaking axial SU(2) breaking Non-QCD-like (Walking) TC still survives but has other issues…

  • Flavour-Changing neutral-currents
  • Too-light quarks
  • Too many unobserved pseudo-Goldstone states

Is a new QCD-like dynamics completely dead?

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SLIDE 5

5

Vector-like weak interactions

Which confined symmetry enables to transform a chiral UV completion into a vector-like one?

At the fundamental level, we arrive at the simplest possible VLTC Lagrangian: RP et al, arXiv:1407.2392

˜ Q =

  • U

D

  • ,

Y ˜

Q =

  • 0,

if NTC = 2 , 1/3, if NTC = 3 .

y SU(NTC)TC (A = 1, 2)

start with two generations

  • f CHIRAL fields

˜ Qaα′

L(A) = ˜

Qaα

L(A) + i

2gWθkτ ab

k ˜

Qbα

L(A)

+ i 2gT Cϕkτ αβ

k

˜ Qaβ

L(A) ,

) of left-handed T-qua e SU(2)W ⊗ SU(2)TC

ˆ CQaα

L(2) = QCaα L(2) ,

QCaα′

L(2) = QCaα L(2) − i

2gWθk(τ ab

k )∗QCbα

L(2)

− i 2gT Cϕk(τ αβ

k )∗QCaβ

L(2) .

charge conjugation

  • f the SECOND

generation

Qaα

R(2) ≡ εabεαβQCbβ L(2)

new R-handed WEAK DOUBLET We end up Dirac WEAK DOUBLET

Qaα = Qaα

L(1) + Qaα R(2)

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SLIDE 6

Toy-model of DEWSB: SU(2)LxSU(2)R LσM

pseudoscalar T-pions (adjoint rep.) scalar T-sigma (singlet rep.)

ms:

lightest T-glueball collective excitation

  • f T-quark condensate

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LσM in QCD hadron physics:

a model for constituent quark-meson interactions ¯ QQ → ⟨ ¯ QQ⟩ + ¯ QQ

−gTC ¯ Q(S + iγ5P a)Q → −gTC

  • ⟨ ¯

QQ⟩S + ¯ Q(S + iγ5P aτ a)Q

  • the source term

global chiral SSB

QGC formation

1 2µ2

S(S2 + P 2) + µ2 HH2 − 1

4λTC(S2 + P 2)2 − λHH4 + λH2(S2 + P 2)

Potential

⟨H⟩ = 1 √ 2

  • v
  • Spontaneous

EWSB

u = λH δ 1/3 ¯ g1/3

TC ,

v = ξλ λH 1/2 λH δ 1/3 ¯ g1/3

TC

  • Both chiral and EW SSB are dynamically linked to T-quark condensate
  • T-pion gets mass via T-sigma interaction with T-quark condensate
  • T-pions remain physical, the Higgs-like mechanism becomes effective

SU(2)L ⊗ SU(2)R → SU(2)V≡L+R

mQ mπ =

= −gTC⟨ ¯ ˜ Q ˜ Q⟩ u

T-pion mass

f µS,H m˜

π

S = u + σ

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SLIDE 7
  • nly gauge interactions
  • f light T-pions remain…

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SU(2)LxSU(2)R: parameter space

0.01 0.1 1

  • 40
  • 20

20 40 |sin θ| ∆mσ

~ (GeV)

hσ ~ mixing mπ

~ = 80 GeV

mπ

~ = 150 GeV

mπ

~ = 300 GeV

0.01 0.1 1

  • 40
  • 20

20 40 v/u ∆mσ

~ (GeV)

v/u ratio mπ

~ = 80 GeV

mπ

~ = 150 GeV

mπ

~ = 300 GeV

RP et al, PRD88, 075009 (2013) 150, 250, 350 GeV, √

  • m˜

π =

bsolute value of sine o

  • f ∆m˜

σ ≡ m˜ σ −

√ 3m˜

π

it M˜

σ →

√ 3m˜

π, w

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SLIDE 8

NEW! NEW! Modified SM + T-sigma!

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SU(2)LxSU(2)R: oblique corrections

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SLIDE 9

T-pion and Dirac T-quark contributions

can be large in the T-parameter only!

give vanishing contributions to all oblique corrections for any VLTC parameters!

T-pion/T-quark loops

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Vector-like weak interactions of the UV completion preserve Technicolor!

RP et al, PRD88, 075009 (2013)

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SLIDE 10

T-parameter: constraint on σh-mixing and σ-mass

a small mixing angle and/or small σ-mass are preferable!

Given by scalar contribution ONLY

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RP et al, PRD88, 075009 (2013)

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SLIDE 11

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SU(2)LxSU(2)R: Higgs signal rates

+ + f, ˜ Q f, ˜ Q f, ˜ Q γ γ (c) + ˜ π− γ γ (d) γ γ (e) ˜ π+ π+ ˜ π+ ˜ π− W W W h, ˜ σ γ γ (a) W W γ γ (b) h, ˜ σ h, ˜ σ h, ˜ σ h, ˜ σ

d gTC = 2, 8, 15,

500 600 700 800 MΣ

, GeV

0.5 1.0 1.5 2.0 ΜΓΓ

res res

500 600 700 800 MΣ

, GeV

0.5 1.0 1.5 2.0 ΜΓΓ

res res

) m˜

π = 350 GeV, M ˜ Q = 500 GeV,

d M ˜

Q = 400, 500, 700 GeV,

) gTC = 8,

t) m˜

π = 350 GeV,

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SLIDE 12

12

SU(2)LxSU(2)R: search for T-pions

˜ Q ˜ π0,± γ, Z, W ± ˜ Q ˜ Q γ, Z, W ± ˜ Q ˜ π0,± ˜ Q

T-pion decay

f YQ ̸= 0,

e YQ = 0

p1 p2 p′

2

p′

1

q0 q1 q2 γ γ γ γ γ γ u, d

0.01 0.1 1 160 180 200 220 240 260 280 300 σ(pp -> X + jj + π ~0) (pb) mπ

~ (GeV)

T-pion production cross section Epp=14 TeV MQ

~ = 300 GeV, gTC = 10, CTEQ5L quark PDFs

γ and Z γ only

γ γ γ γ ˜ π0 γ γ ˜ π0 U, D U, D

Signal Background

(GeV)

γ γ

M

200 400

(fb/GeV)

γ γ

/dM σ d

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 1 p γ γ p → pp = 14 TeV s

| < 2.5

γ

η | via gg

no Sudakov ff’s

γ γ via

(GeV)

Q ~

m

200 300 400 500

(fb) σ

  • 2

10

  • 1

10 1 10 π ∼ pp → pp = 14 TeV s fusion γ γ

= 10

TC

g = 100, 200 GeV

π ∼

M

RP et al, NP881, 288 (2014)

0.01 0.1 1 150 200 250 300 350 400 450 500 BR(π ~ -> VV) mπ

~ (GeV)

T-pion branching ratios γγ γZ ZZ γW ZW

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SLIDE 13

13

SU(3)LxSU(3)R composite Higgs model: content

ˆ Φ = 1 √ 2 ⎛ ⎜ ⎜ ⎝

1 √ 2a0 + 1 √ 6f + 1 √ 3σ

a+ H+ a− − 1

√ 2a0 + 1 √ 6f + 1 √ 3σ

H0 H− ¯ H0 −

  • 2

3f + 1 √ 3σ

⎞ ⎟ ⎟ ⎠ − − i √ 2 ⎛ ⎜ ⎜ ⎝

1 √ 2π0 + 1 √ 6η + 1 √ 3η′

π+ K+ π− − 1

√ 2π0 + 1 √ 6η + 1 √ 3η′

K0 K− ¯ K0 −

  • 2

3η + 1 √ 3η′

⎞ ⎟ ⎟ ⎠

e accounts for the s QL = (U, D, S)L ing groups

d QR = (U, D, S)R

LT C = −1 4T n

µνT µν n + i ¯

Qγµ

  • ∂µ − i

2gWW

A

µ τA − i

2gT CT n

µ τn

  • Q − mQ ¯

QQ+ +i ¯ Sγµ

  • ∂µ + i

2g1Bµ − i 2gT CT n

µ τn

  • S − mS ¯

SS Fundamental Lagrangian chiral Dirac T-quarks in SU(2)TC pseudo-Goldstones:

π+, π0, π−; K+, K0, ¯ K0, K−; η

their chiral partners:

a+, a0, a−; H+, H0, ¯ H0, H−; f ,

3σ

⎟ ⎟ ⎠

3η′

⎟ ⎟ ⎠

+

components of the bi-fundamental rep:

Lσ = i ¯ Qγµ∂µQ − √ 6κ( ¯ QLΦQR + ¯ QRΦ+QL) + ∂µ ˆ Φ+ · ∂µ ˆ Φ+ +µ2ˆ Φ+ ˆ Φ − λ1(ˆ Φ+ ˆ Φ)2 − 3λ2ˆ Φ+ ˆ Φˆ Φ+ ˆ Φ + 2 √ 6Λ3Re detΦ .

Generic global LσM Lagrangian:

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SLIDE 14

14

SU(3)LxSU(3)R CHM: EW interactions of composites

Additional EW-invariant piece to the Higgs-less SM Lagrangian:

Lσ = i ¯ Qγµ

  • ∂µ − i

2gWW a

µτa

  • Q + i ¯

Sγµ

  • ∂µ + i

2g1Bµ

  • S −

√ 6κ( ¯ QLΦQR + ¯ QRΦ+QL)+ 1 2(Dµπa · Dµπa + Dµaa · Dµaa) + (DµK)+ · DµK + (DµH)+ · DµH+ 1 2(∂µη · ∂µη + ∂µη0 · ∂µη0 + ∂µf · ∂µf + ∂µσ · ∂µσ)+ µ2ˆ Φ+ ˆ Φ − λ1(ˆ Φ+ ˆ Φ)2 − 3λ2ˆ Φ+ ˆ Φˆ Φ+ ˆ Φ + 2 √ 6Λ3Re detΦ− (Y l

mn ¯

LmHEn + Y d

mn ¯

QmHDn + Y u

mn ¯

Qm ˜ HUn + h.c.)− (Y

l mn ¯

LmKEn + Y

d mn ¯

QmKDn + Y

u mn ¯

Qm ˜ KUn + h.c.) ,

Structure of the theory has certain similarities to the class of THDMs!

Dµπa = ∂µπa + gWeabcW b

µπc,

Dµaa = ∂µaa + gWeabcW b

µac ,

DµK = ∂µK − i 2g1Bµ − i 2gWW a

µτaK,

DµH = ∂µH − i 2g1Bµ − i 2gWW a

µτaH .

where

composite Higgs-like kinetic terms replaces Higgs potential to be constrained by FCNC etc

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SLIDE 15

15

SU(3)LxSU(3)R composite Higgs model: spectrum

Unbroken EW phase:

⟨0| : ¯ DS + ¯ SD : |0⟩ = 0.

⟨0| : ¯ UU : |0⟩ = ⟨0| : ¯ DD : |0⟩ = ⟨0| : ¯ SS : |0⟩ = −ℓT C⟨0| : αT C π T n

µνT µν n

: |0⟩ diagonal T-quark and T-gluon condensates

  • nly!

Two scalar mass scales:

M2

σ(0) = 2(λ1 + λ2)u2 − Λ3u + M2 π(0)

M2

a(0) = M2

H(0) = M2

f(0) = 2λ2u2 + 2Λ3u + M2 π(0)

Two pseudoscalar mass scales:

M2

η′(0) = 3Λ3u + M2 π(0)

M2

π(0) = M2

K(0) = M2

η(0) = −κ

u ⟨0| : ¯ QQ : |0⟩

Broken EW phase:

d H = (H+, H0) h

= 1 √ 2

  • v + h
  • ает автоматически, если

ат ⟨0| : ¯ DS + ¯ SD : |0⟩ ̸= 0. о it mS ≃ mQ ΛTC H = ( ¯ SQ)

v ≈ −

  • 3

2 · κ⟨0| : ¯ DS + ¯ SD : |0⟩ M 2

H(0)

Vacuum is stable!

a0 + f0 √ 2 + …

M2

σ = M2 σ(0)

, M2

H = M2 H(0)

κ

M2

a0 = M2

H(0) − κ2

3 √ 2 δ

, M2

f0 = M2

H(0) + κ2

3 √ 2 δ

Only five free parameters!

⎝ re δ ≡ v/u

+

0}

ll δ 1

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SLIDE 16

16

SU(3)LxSU(3)R CHM: oblique corrections

0.04 0.06 0.08 0.10 vêu 0.02 0.04 0.06 0.08 0.10 0.12 0.14 T

a noticeable decoupling of the T-confinement scale from the EWSB scale is favoured! S,U parameters are vanishingly small!

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SLIDE 17

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Fine structure of the Higgs signal in SU(3)LxSU(3)R

The main signature of the Higgs compositeness in this scenario – a fine structure of the Higgs signal with nearly-degenerate Higgs-like resonances!

(η

+ π0) +

(a0

+ f0) +

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 100 110 120 130 140 150 gg-> (pb) m (GeV) LO parton-level gg-> =0.05 CHM CHM+SM

ξ ζ

η0

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SLIDE 18

18

(GeV)

H

m

110 115 120 125 130 135 140 145 150

SM

σ '/ σ 95% CL limit on

0.5 1 1.5 2 2.5 3

(7 TeV)

  • 1

(8 TeV) + 5.1 fb

  • 1

19.7 fb

CMS

γ γ → H

Observed Median expected 68% expected 95% expected

0.6 0.8 1 1.2 1.4 1.6 1.8 2 100 110 120 130 140 150 CHM/SM m (GeV) LO CHM/SM ratio (CHM+SM)/SM

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 100 110 120 130 140 150 pp->+X (pb) m (GeV) LO hadron-level pp->+X, =0.05 via gg-> only, 7 TeV, CTEQ10 with Gaussian detector smearing, =2 GeV CHM CHM+SM

Composite Higgs model vs observations

sensitivity to the second resonance is severely degraded!

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SLIDE 19

Summary

  • The vector-like nature of weak interactions in the T-quark sector,

naturally emerging in SU(2)TC theory, along with a SM-like Higgs mechanism, eliminates all the known troubles of previous TC-based models

  • As a possible mechanism dynamical EWSB, the VLTC model naturally

leads to an effective Higgs mechanism of the SM, composite Higgs bosons, potentially predicts a plenty of extra Higgs-like states, and evades EW precision constraints

  • Remarkably, the composite Higgs model with three T-flavors provides

an extremely rich LHC phenomenology of light composites and predicts a double-hump fine structure of the Higgs signal, discovery of which may require a dedicated high-precision study of the low mass region at high statistics.

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