a light composite higgs and its heavy vector partners

A Light Composite Higgs and its Heavy Vector Partners

Kenneth Lane, with Lukas Pritchett Boston University

A Light Composite Higgs and its Heavy Vector Partners

Kenneth Lane, with Lukas Pritchett Boston University

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The data

The light composite Higgs model

Tests for Run 2

⇢H , aH ! V V, V H cross sections

•

⇢H , aH ! V V, V H decays

1.5 2 2.5 3 3.5

Even

ts /

100

GeV

1−10

1

10

210

310

410DataBackground model1.5 TeV EGM W', c = 12.0 TeV EGM W', c = 12.5 TeV EGM W', c = 1Significance (stat)Significance (stat + syst)

ATLAS-1 = 8 TeV, 20.3 fbs

WZ Selection

[TeV]jjm1.5 2 2.5 3 3.5

Sign

ifica

nce

2−1−0123

Run 1

ATLAS “WZ” nonleptonic

[TeV]W' m1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

WZ)

[fb]

→ B

R(W

' ×

W')

→(p

p σ

1−10

1

10

210

310

410 Observed 95% CL

Expected 95% CL

uncertaintyσ 1±

unceirtaintyσ 2±

EGM W', c = 1

ATLAS-1 = 8 TeV, 20.3 fbs

Run 1

ATLAS “WZ” nonleptonic

[GeV]GM1000 1500 2000 2500

ZZ)

[pb]

→ bu

lk B

R(G

× 95

%σ

-310

-210

-110

1

600

observedS

Frequentist CL

σ 1± expected S

Frequentist CL

σ 2± expected S

Frequentist CL

= 0.5PlM/k ZZ), → bulk

x BR(GTHσ

= 0.2PlM/k ZZ), → bulk

x BR(GTHσ

CMS = 8 TeVs at -1L = 19.7 fb

Run 1

CMS “ZZ” semileptonic

[GeV]GM1000 1500 2000 2500

) [pb

]bu

lk G

→ (p

p 95

%σ

-310

-210

-110

1 observedS

Frequentist CL

σ 1± expected S

Frequentist CL

σ 2± expected S

Frequentist CL

= 0.5PlM/k), bulk G→ (pp THσ

I II III

CMS = 8 TeVs at -1L = 19.7 fb

600

Run 1

CMS “WW” semileptonic

(GeV)W'M1000 1500 2000

WH

) (pb

)→

*BR

(W'

95%

σ

-310

-210

-110

1

10

800

ObservedSFull CLσ 1± Expected SFull CLσ 2± Expected SFull CL

WH)→ * BR(W' W'

HVT B(gv=3):xsec WH)→ * BR(W' W'LH model:xsec

(8 TeV)-119.7 fbCMS combinedµPreliminary e+

Run 1

CMS “WH” semileptonic

Run 2

ATLAS “WH” semileptonic

Mass[TeV]1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Sigm

a

2−

1−

0

1

2

3

4

5ATLAS Dijet

ATLAS All-Hadronic WZ

ATLAS Dilepton plus Jet(s)

ATLAS Lepton plus Jet(s) WZ

CMS Dijet

CMS All-Hadronic WZ

CMS Dilepton plus Jet(s)

CMS Lepton plus Jet(s)

CMS WR

“WZ” resonance significances

Run 1

Mass[TeV]1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Sigm

a

2−

1−

0

1

2

3

4

5 ATLAS DijetATLAS DileptonATLAS All-Hadronic WWATLAS All-Hadronic ZZATLAS Dilepton plus Jet(s)ATLAS Lepton plus Jet(s) WWCMS DijetCMS DileptonCMS All-Hadronic WWCMS All-Hadronic ZZCMS Dilepton plus Jet(s)CMS Lepton plus Jet(s)

“WW,ZZ” resonance significances

Run 1

Mass[TeV]1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Sigm

a

2−

1−

0

1

2

3

4

5ATLAS Dilepton bb

ATLAS Lepton, MET bb

CMS Ditau Jet(s)

CMS All-Hadronic WH

CMS All-Hadronic ZH

CMS Lepton, MET bb

WH resonance significances

Run 1

• ALL models for H(125) are finely-tuned:

-> The SM (of course) -> SUSY -> even composite Higgs models! They require top, W-partners — none have been found. (see, e.g., Guidice 1307.7879 Bellazzini, Csaki, Serra 1401.2457, Barnard, et al. 1409.7391)

A new composite Higgs model

models for H(125) are finely-tuned:

-> The SM (of course) -> SUSY -> even composite Higgs models! They require top, W-partners — none have been found. (see, e.g., Guidice 1307.7879 Bellazzini, Csaki, Serra 1401.2457, Barnard, et al. 1409.7391)

Do we need top, W partners?

ALL•


TC models (Yamawaki, et al., Sannino, et al.)

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No plausible explanation why H(125) is so light (dilaton??)

No plausible explanation why H(125) is so much lighter than other technihadrons — where is ⇢T ??


(KL, PRD 90, (2014) 9, 09525; arXiv:1407:2270; KL + Luke Pritchett, in preparation; see also Chivukula, Cohen, KL NPB 343 (1990) 554)

(inspired by BHL PRD41, 1647 (1989))


A fine-tuned solution

NJL applied to strong ETC:

Strong ETC, not TC, drives EWSB!•

(KL, PRD 90, (2014) 9, 09525; arXiv:1407:2270; see also Chivukula, Cohen, KL NPB 343 (1990) 554)

(BHL PRD41, 1647 (1989))




Strong ETC, not TC, drives EWSB!•

• ETC coupling is fine-tuned to be near the critical value for EWSB.

(KL, PRD 90, (2014) 9, 09525; arXiv:1407:2270; see also Chivukula, Cohen, KL NPB 343 (1990) 554)




Strong ETC, not TC, drives EWSB!

The fine tuning: in the large-N approximation,

(BHL PRD41, 1647 (1989))

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ETC coupling is fine-tuned to be near the critical value for EWSB.

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(a physical cut-off)mf ,MH ' 2mf ⌧ ⇤ETC = ⇤


• WEAK TC binds T-fermions to make technihadrons with

M⇢H ,MaH , · · · = O(⇤TC) = 1 � 2TeV � MH , but ⌧ ⇤

⇢H , aH , . . .




⇢H , aH , . . .

(this slide is too small to hold the argument)




⇢H , aH , . . .

The Higgs is much lighter than • ⇢H , aH , . . .




⇢H , aH , . . .

The Higgs is much lighter than • ⇢H , aH , . . .

and there are no top, W-partners!•

a simplest TC-ETC model:

LETC = G1 qiaL tRa tbR qLib + G3 T

i↵L UR↵ U�

R TLi�

+G2

�qiaL tRa U↵

R TLi↵ + h.c.�

consider this model in the limit of large-N and weak-TC

qL = (t, b)L 2 (2, 16, 3C , 1TC), tR 2 (1, 2

3, 3C , 1TC), bR 2 (1,�1

3, 3C , 1TC)

TL = (U,D)L 2 (2, 0, 1C , dTC), UR 2 (1, 12, 1C , dTC), DR 2 (1,�1

2, 1C , dTC)

In the limit of large N and weak TC:

A magic relation that makes everything else work— including disappearance of -divergence!

mt =G1NCmt

8⇡2

⇣⇤2 � m2

t ln⇤2

m2t

⌘

+G2dTCmU

8⇡2

⇣⇤2 � m2

U ln ⇤2

m2U

⌘

mU = G2NCmt

8⇡2

⇣⇤2 � m2

t ln⇤2

m2t

⌘

+G3dTCmU

8⇡2

⇣⇤2 � m2

U ln ⇤2

m2U

⌘

⇤2

Independence of NC and dTC = dim(dTC)

) G2 = (mU/mt)G1 = (mt/mU)G3

This has a pole at

##2mU2mt

mt(⇤) = 118GeV,mU(⇤) = 126GeVat ⇤ = 500TeVNC = 3, NTC = 15) MH = 250GeV

p = MH(⇤) = 250GeV

MH⇠= 2

sNCm4

t + dTCM4U

NCm2t + dTCM2

U

�tt!tt0+ (p) = m

2t

m

2tNC(p2 � 4m2

t )

8⇡2

Z 1

0dx ln

✓⇤2

m

2t � p

2x(1 � x)

◆

+m

2UNTC(p2 � 4m2

U)

8⇡2

Z 1

0dx ln

✓⇤2

m

2U � p

2x(1 � x)

◆��1

This has a pole at

##2mU2mt

mt(⇤) = 118GeV,mU(⇤) = 126GeVat ⇤ = 500TeVNC = 3, NTC = 15) MH = 250GeV

p = MH(⇤) = 250GeV

MH⇠= 2

sNCm4

t + dTCM4U

NCm2t + dTCM2

U

�tt!tt0+ (p) = m

2t

m

2tNC(p2 � 4m2

t )

8⇡2

Z 1

0dx ln

✓⇤2

m

2t � p

2x(1 � x)

◆

+m

2UNTC(p2 � 4m2

U)

8⇡2

Z 1

0dx ln

✓⇤2

m

2U � p

2x(1 � x)

◆��1

N.B.: These are masses at !scale — to be renormalized to

⇤⇤EW

⇢H and aHThe Higgs’ heavy vector partners —

• ⇢H and aH are the most accessible technihadron partners of H(125)

Describe them via Hidden Local Symmetry as the gauge bosons of an flavor symmetry.SU(2)L ⌦ SU(2)R

•

KL & Luke Pritchett, PLB 753, 211-214; 1507.07102

⇢H and aH

! gL = gR ⌘ g⇢H = 3 � 5

! ⇢0H ! W+

L W�L , ⇢±

H ! W±L ZL

! a0H ! ZLH, a±

H ! W±L H

TC interactions are vectorial, isospin and parity-invariant: ⇢H and aH(minimizes S from too!)

The Higgs’ heavy vector partners —

• ⇢H and aH are the most accessible technihadron partners of H(125)

• Describe them via Hidden Local Symmetry as the gauge bosons of an flavor symmetry.SU(2)L ⌦ SU(2)R

KL & Luke Pritchett, PLB 753, 211-214; 1507.07102

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(the Goldstone bosons of EWSB)

) M⇢H⇠= MaH

Decay rates and Cross sections

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�(⇢0H ! W+W�) ⇠= �(⇢±H ! W±Z) ⇠=g2⇢H

M⇢H

48⇡

�(a0 ! ZH) ⇠= �(a± ! W±H) ⇠=g2⇢H

MaH

48⇡

�(a0H ! W+W�) ⇠= �(a±H ! W±Z) ⇠=g2⇢H

M2WM3

aH

24⇡M4⇢H

H,W±L , ZL

⇢H and aH are parity-doubled isotriplets

Near the EW phase transition are a degenerate (2,2) quartet => equal decay rates!

M⇢H(MaH

= 1.05M⇢H) �(⇢H ! V V ) (GeV) �(aH ! V H) (GeV) �(aH ! V V ) (GeV)

1800 178 184 0.82

1900 188 196 0.78

2000 198 208 0.74

for g⇢H= 3.86

M⇢H(MaH

= 1.05M⇢H) �(⇢H ! V V ) (GeV) �(aH ! V H) (GeV) �(aH ! V V ) (GeV)

1800 178 184 0.82

1900 188 196 0.78

2000 198 208 0.74

N.B.: These widths may be significantly depleted (⇠ 1/4?)

by the content of tt, tb H,WL, ZL


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⇢H , aH are mainly produced at LHC via Drell-Yan.

⇢HLarge VV coupling of

aH

=> appreciable VBF too.

=> NO appreciable VBF. Small VV coupling of

ps (TeV) M⇢H (GeV) �(⇢±

H) (fb)(DY + V BF )

�(⇢0H) (fb)

(DY + V BF ) �(a±H) (fb) �(a0

H) (fb)

8 1800 1.53+0.36 0.74+0.18 0.71 0.37

8 1900 1.05+0.24 0.50+0.12 0.51 0.27

8 2000 0.73+0.15 0.36+0.08 0.36 0.17

13 1800 7.61+3.67 3.74+1.93 4.65 2.23

13 1900 5.74+2.62 2.81+1.37 3.16 1.69

13 2000 4.37+1.90 2.16+0.99 2.39 1.27

for g⇢H= 3.86, MaH

= 1.05M⇢H, YTL

= 0, YUR= �YDR

=

12


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⇢H , aH are mainly produced at LHC via Drell-Yan.

⇢HLarge VV coupling of

aH

=> appreciable VBF too.

=> NO appreciable VBF.

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�DY (aH) ' 0.5�DY (⇢H)

�DY (13TeV) = 5� 7 �DY (8TeV)

�V BF (aH) < 0.01 �V BF (⇢H)

rising to about

12�DY (⇢H) at 13TeV

�V BF (⇢H) ' 14�DY (⇢H) at

ps = 8TeV,

proton pdf’s

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Small VV coupling of

) �(⇢±H) ' �(⇢+H) ' 2�(⇢0H) uniformly

ditto for aH) W+Z � W�Z, W+H � W�H

!!

• VV production from W±Z,W+W�⇢H only: but NO ZZ !

=> Distinguish W from Z — using leptonic decays.

Predictions & recommendations for Run 2-300 fb�1!

W±Z,W+W�⇢H only: but NO ZZ !•

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=> Distinguish W from Z — using leptonic decays. VV production from

aH ⇢H . How to distinguish if degenerate?VH due to not


W±Z,W+W�⇢H only: but NO ZZ !•

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aH ⇢H . How to distinguish if degenerate?VH due to not 1/3 of VV, not VH, production is VBF, with forward jets!


W±Z,W+W�⇢H only: but NO ZZ !

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aH ⇢H . How to distinguish if degenerate?VH due to not 1/3 of VV, not VH, production is VBF, with forward jets!


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Difficult to explain DY+VBF > few fb at 8 TeV. Therefore, Run 1 was an up-fluctuation — like H(125)! This was confirmed (!!) last December.

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W±Z,W+W�⇢H only: but NO ZZ !

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aH ⇢H . How to distinguish if degenerate?VH due to not 1/3 of VV, not VH, production is VFB, with forward jets!


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Difficult to explain DY+VBF > few fb at 8 TeV. Therefore, Run 1 was an up-fluctuation — like H(125)! This was confirmed (!!) last December.

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• There will be NO top & W partners. Our model doesn’t need them!

That’s all, Folks!

a light composite higgs and its heavy vector partners

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