Heavy Vector T riplets: Bridging Theory and Data Andrea Thamm - - PowerPoint PPT Presentation

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Heavy Vector T riplets: Bridging Theory and Data Andrea Thamm - - PowerPoint PPT Presentation

Jun 21, 2023 515 likes •799 views

Benasque, 17 April 2014 Heavy Vector T riplets: Bridging Theory and Data Andrea Thamm cole Polytechnique Fdrale de Lausanne in collaboration with D. Pappadopulo, R. Torre, A. Wulzer based on arXiv:1402.4431 Outline 1. Motivations

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SLIDE 1

Heavy Vector T riplets: Bridging Theory and Data

Andrea Thamm

Benasque, 17 April 2014 École Polytechnique Fédérale de Lausanne in collaboration with D. Pappadopulo, R. Torre, A. Wulzer based on arXiv:1402.4431

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SLIDE 2

Outline

Andrea Thamm 3

  • 1. Motivations
  • 2. Simple Simplified Model
  • 3. Limit setting procedure
  • 4. Data and Bounds
  • 5. Conclusions
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SLIDE 3

Motivation

Andrea Thamm 3

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SLIDE 4

✤ aim: phenomenological Lagrangian for heavy spin-1 resonances


to bridge between experimental data and theoretical models

✤ idea:

present bounds in terms of simplified model parameters any model can be matched to simplified Lagrangian

Motivation

Theory yDatay Ls ⃗ c(⃗ p) L(⃗ c)

✤ indirect probes of new physics very important ✤ at LHC also many direct probes, for example:

Weakly coupled Strongly coupled SPIN 1 Z’ models,
 sequential W’ ,… Composite Higgs models very difficult to reinterpret

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SLIDE 5

A Simple Simplified Model

Andrea Thamm 3

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SLIDE 6

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0
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SLIDE 7

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0
slide-8
SLIDE 8

∼ gV cH Vµ

WL , ZL, h WL , ZL, h

Coupling to SM Vectors

Vµ f ¯ f ∼ g2 gV cF

cF V · JF → clV · Jl + cqV · Jq + c3V · J3 Jµ a

F

= X

f

f Lγµτ afL

Coupling to SM fermions

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0
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SLIDE 9

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0

Couplings among Vectors

✤ do not contribute to V decays ✤ do not contribute to single production ✤ only effects through (usually small) VW mixing

  • irrelevant for phenomenology only need (cH, cF )
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SLIDE 10

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0

typical strength of V interactions gV gV ∼ g ∼ 1 Weakly coupled model Strongly coupled model gV ≤ 4π dimensionless coefficients ci cH ∼ cF ∼ 1 cH ∼ −g2/g2

V

and cF ∼ 1

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SLIDE 11

Production Rates

1 2 3 4 5 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 s ` = MV @TeVD dLêds ` @pbD WL

+ZL HV+L

WL

+WL

  • HV0L

WL

  • ZL HV-L

8 TeV

CTEQ6L1 Hm2 = MW

2 L

1 2 3 4 5 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 s ` = MV @TeVD dLêds ` @pbD uid j HV+L uiuj HV0L did j HV0L diuj HV-L

8 TeV

CTEQ6L1 Hm2 = s `L

✤ DY and VBF production

model
 independent model
 dependent

✤ can compute production rates analytically! ✤ easily rescale to different points in parameter space ✤ VBF subleading in motivated part of parameter space

σDY = X

i,j ∈ p

ΓV → ij MV 4π2 3 dLij dˆ s

  • ˆ

s=M 2

V

σV BF = X

i,j ∈ p

ΓV → WL iWL j MV 48π2 dLWL iWL j dˆ s

  • ˆ

s=M 2

V

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SLIDE 12

Decay widths

ΓV±→ff

0 ' 2 ΓV0→ff ' Nc[f]

✓g2cF gV ◆2 MV 96π , ΓV0→W +

L W − L

' ΓV±→W ±

L ZL

' g2

V c2 HMV

192π ⇥ 1 + O(ζ2) ⇤ ΓV0→ZLh ' ΓV±→W ±

L h

' g2

V c2 HMV

192π ⇥ 1 + O(ζ2) ⇤

500 1000 1500 2000 2500 3000 3500 4000 0.02 0.04 0.06 0.08 0.10 0.12

M0 @GeVD BRHV0 Æ 2 XL

W+W- Zh uu dd ll è nn bb tt è gV = 1 Model A 500 1000 1500 2000 2500 3000 3500 4000 10-3 10-2 10-1

M0 @GeVD BRHV0 Æ 2 XL

W+W- Zh uu dd ll è nn bb tt è gV = 3 Model B

✤ relevant decay channels: di-lepton, di-quark, di-boson

gV cH ' g2cF /gV ' g2/gV gV cH ' gV , g2cF /gV ' g2/gV

Weakly coupled model Strongly coupled model

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SLIDE 13

Data and Bounds

Andrea Thamm 3

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SLIDE 14

Limit setting

✤ want limits on since model-independent ✤ must stay in a window around the peak,


  • therwise finite widths effects must be considered

σ × BR

  • 1. distortion from Breit-Wigner 


due to steep fall of parton luminosities at large energies

Effect of interference -1 < y < 1 SM + BW Hwêo interferenceL sHpp Æ V0L â BRHV0 Æ l+l-L + sSMHpp Æ l+l-L SM + Signal Hwêo interferenceL sHpp Æ V0 Æ l+l-L + sSMHpp Æ l+l-L Signal BW sHpp Æ V0L â BRHV0 Æ l+l-L Signal only sHpp Æ V0 Æ l+l-L SM sSMHpp Æ l+l-L ✤ large distortion for non-negligible widths ✤ still under control in window around the peak ✤ but large tail

Di-lepton searches for

2600 2800 3000 3200 3400 3600 3800 1 2 3 4 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 15
  • 10
  • 5

y 1-sFullêsBW H%L

LHCû8TeV MV = 3.5 TeV GêMV = 11 %

BW 2 → 2 V0

1200 1400 1600 1800 2000 2200 2 4 6 8 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 10

10 20 y 1-sFullêsBW H%L

LHCû8TeV MV = 2 TeV GêMV = 10 %

[M − Γ, M + Γ]

[Accomando, Becciolini, Balyaev, Moretti, Shepherd, arXiv:1304.6700 ] [Accomando, Becciolini, de Curtis, Dominici, Fedeli, Shepherd, arXiv:1110.0713]

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SLIDE 15

Limit setting

σ × BR

  • 2. interference with SM background

Effect of interference -1 < y < 1 SM + BW Hwêo interferenceL sHpp Æ V0L â BRHV0 Æ l+l-L + sSMHpp Æ l+l-L SM + Signal Hwêo interferenceL sHpp Æ V0 Æ l+l-L + sSMHpp Æ l+l-L Signal BW sHpp Æ V0L â BRHV0 Æ l+l-L Signal only sHpp Æ V0 Æ l+l-L SM sSMHpp Æ l+l-L ✤ depends on S/B ratio ✤ can be a large effect ✤ tail strongly model dependent, not

V0 σ × BR

✤ want limits on since model-independent ✤ must stay in a window around the peak,


  • therwise finite widths effects must be considered

Di-lepton searches for

2600 2800 3000 3200 3400 3600 3800 1 2 3 4 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 15
  • 10
  • 5

y 1-sFullêsBW H%L

LHCû8TeV MV = 3.5 TeV GêMV = 11 %

1200 1400 1600 1800 2000 2200 2 4 6 8 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 10

10 20 y 1-sFullêsBW H%L

LHCû8TeV MV = 2 TeV GêMV = 10 %

constructive destructive background

[Accomando, Becciolini, Balyaev, Moretti, Shepherd, arXiv:1304.6700 ] [Accomando, Becciolini, de Curtis, Dominici, Fedeli, Shepherd, arXiv:1110.0713]

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SLIDE 16

1200 1400 1600 1800 2000 2200 2 4 6 8 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 10

10 20 y 1-sFullêsBW H%L

LHCû8TeV MV = 2 TeV GêMV = 10 %

Limit setting

σ × BR

✤ searches only sensitive to the peak can be easily reused


(give bounds on )

✤ searches sensitive to the tail only valid in the assumed model, not reusable Effect of interference -1 < y < 1 SM + BW Hwêo interferenceL sHpp Æ V0L â BRHV0 Æ l+l-L + sSMHpp Æ l+l-L SM + Signal Hwêo interferenceL sHpp Æ V0 Æ l+l-L + sSMHpp Æ l+l-L Signal BW sHpp Æ V0L â BRHV0 Æ l+l-L Signal only sHpp Æ V0 Æ l+l-L SM sSMHpp Æ l+l-L

V0 σ × BR

✤ want limits on since model-independent ✤ must stay in a window around the peak,


  • therwise finite widths effects must be considered

Di-lepton searches for

2600 2800 3000 3200 3400 3600 3800 1 2 3 4 Ml+ l- @GeVD dsêdMl+ l- @10-7pbêGeVD

  • 1.0 -0.5

0.0 0.5 1.0

  • 20
  • 15
  • 10
  • 5

y 1-sFullêsBW H%L

LHCû8TeV MV = 3.5 TeV GêMV = 11 %

[Accomando, Becciolini, Balyaev, Moretti, Shepherd, arXiv:1304.6700 ] [Accomando, Becciolini, de Curtis, Dominici, Fedeli, Shepherd, arXiv:1110.0713]

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SLIDE 17

Limit setting: example

ATLAS CMS

both neglect interference effects bounds set assuming a Z’ tail Gaussian shape around the peak for very narrow resonance not ok, since tail is considered

  • k

reusable for very narrow resonance

  • nly valid in the assumed model

no bound on σ × BR

[ATLAS-CONF-2013-017] [CMS-PAS-EXO-12-061]

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SLIDE 18

Limit setting: example

✤ ATLAS di-boson search using the simplified model ✤ ideally, also bounds on model parameters should be given

slide-19
SLIDE 19

Taking the current bounds at face value…

Andrea Thamm 3

slide-20
SLIDE 20

LHC Bounds

1000 2000 3000 4000 10-4 10-3 10-2 10-1 100 101 102 103 104 MV @GeVD sHpp Æ VL @pbD

theoretically excluded

CMS AgV=1

Weakly coupled model Strongly coupled model

similar bounds for ATLAS

✤ excluded for masses < 3 TeV ✤ di-lepton most stringent ✤ di-boson searches < 1-2 TeV ✤ reach of LHC at 14 TeV: 6 TeV ✤ reach of FCC at 100 TeV: 30 TeV ✤ excluded for masses < 1.5 TeV


unconstrained for larger

✤ di-boson most stringent ✤ in excluded region , not

reproduced

✤ reach of LHC at 14 TeV: 3-4 TeV ✤ reach of FCC at 100 TeV: 15-20 TeV

1000 2000 3000 4000 10-4 10-3 10-2 10-1 100 101 102 103 104 MV @GeVD sHpp Æ VL @pbD

theoretically excluded

CMS BgV=3

gV

pp Æ V0 pp Æ V+ V0 Æ tt V0 Æ WW Æ jj V0 Æ WW Æ lnqq

_'

V±Æ W±Z Æ 3l±n V±Æ W±Z Æ jj V0 Æ ll V±Æ l±n V0 Æ tt V± Æ tb

GF mZ

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SLIDE 21

Limits on parameter space

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 6
  • 4
  • 2

2 4 6

cH cF

*

BgV=1

ú

AgV=1 MV = 2 TeV gV=1

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 6
  • 4
  • 2

2 4 6

cH cF

*

BgV=3

ú

AgV=3 MV = 2 TeV gV=3

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 6
  • 4
  • 2

2 4 6

cH cF

*

BgV=6

ú

AgV=6 MV = 2 TeV gV=6

✤ experimental limits converted into plane

(cH, cF )

yellow: CMS analysis dark blue: CMS light blue: CMS black: bounds from EWPT WZ → jj WZ → 3lν l+ν

✤ dominates ✤ EWPT not competitive ✤ only


allowed lν −1 . cF . 1

✤ EWPT become comparable ✤ di-bosons more and more relevant ✤ strongly coupled model evades bounds from


direct searches

[Pappadopulo, Thamm, Torre, Wulzer, arXiv:1402.4431 ]

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SLIDE 22

Limits on parameter space

500 1000 1500 2000 2500 3000 3500 1 2 3 4 5

MV @GeVD gV

Model A 500 1000 1500 2000 2500 3000 3500 1 2 3 4 5

MV @GeVD gV

Model B

theoretically excluded

yellow: CMS analysis dark blue: CMS light blue: CMS black: bounds from EWPT WZ → jj WZ → 3lν l+ν

✤ experimental limits converted into plane

(MV , gV )

✤ similar exclusions at low , leptonic final state dominates ✤ very different for larger coupling

gV

[Pappadopulo, Thamm, Torre, Wulzer, arXiv:1402.4431 ]

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SLIDE 23

Conclusions

  • 1. If possible, experimental bounds should be presented in a

model-independent, reusable way.

  • 2. Limits should be set on by focussing only on the on-

shell signal region.

  • 3. It would be useful to present results in terms of simplified

model parameters which can be easily matched to any preferred model. σ × BR

slide-24
SLIDE 24

Back-up

slide-25
SLIDE 25

Phenomenological Lagrangian

LV = −1 4D[µV a

ν]D[µV ν] a + m2 V

2 V a

µ V µ a

+ i gV cHV a

µ H†⌧ a ↔

D

µ

H + g2 gV cF V a

µ Jµ a F

+ gV 2 cV V V ✏abcV a

µ V b ν D[µV ν] c + g2 V cV V HHV a µ V µ aH†H − g

2cV V W ✏abcW µ ν aV b

µV c ν

V =

  • V +, V −, V 0

✤ including only dim-4 operators is well justified in: 


weakly coupled models
 strongly coupled models that obey SILH power counting

✤ if higher dim. operators are unsuppressed:


parametrisation insufficient

slide-26
SLIDE 26

Relations and EWPT

✤ generalised custodial relation after rotation to mass basis

m2

W M 2 + = cos2 θW m2 ZM 2 0 .

mW,Z M+,0 . 10−1 ⌧ 1

✤ require hierarchy

M 2

+ = M 2 0 (1 + O(%))

✤ degeneracy


expect comparable production rates
 phase space suppressed cascade decays

✤ naturally small mixing angles
 ✤ EWPT to ensure compatibility with experiment

θN,C ' cH gV ˆ v 2 mW,Z m2

V

. 10−1 g|exp = g + O( ˆ m2

W /µ2 V ),

g0|exp = g0 + O( ˆ m2

W /µ2 V )

v2|expˆ v2 ✓ 1 − c2

H

g2

V ˆ

v2 4µV ◆ ˆ S = γ2

Hz2 ˆ

m2

W

µ2

V

− γHγF ˆ m2

W

µ2

V

, W = γ2

F

g2 g2

V

m2

W

µ2

V

✤ to include corrections we fix

(mZ, M0, GF ) → (v, mV , g)

slide-27
SLIDE 27

Limits on parameter space

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 1.0
  • 0.5

0.0 0.5 1.0

cH cVVW

MV = 2 TeV cF = 4 gV = 3

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 1.0
  • 0.5

0.0 0.5 1.0

cH cVVV

MV = 2 TeV cF = 4 gV = 3

  • 1.0
  • 0.5

0.0 0.5 1.0

  • 1.0
  • 0.5

0.0 0.5 1.0

cH cVVHH

MV = 2 TeV cF = 4 gV = 3

yellow: CMS analysis dark blue: CMS light blue: CMS black: bounds from EWPT WZ → jj WZ → 3lν l+ν

✤ experimental limits converted into plane

(cH, cV V V )

✤ affect exclusion only marginally

cV V W , cV V V and cV V HH

[Pappadopulo, Thamm, Torre, Wulzer, arXiv:1402.4431 ]