Characterisation of vector-like fermions at the LHC Luca Panizzi - - PowerPoint PPT Presentation

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Characterisation of vector-like fermions at the LHC Luca Panizzi - - PowerPoint PPT Presentation

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Characterisation of vector-like fermions at the LHC Luca Panizzi University of Pisa, Italy Beyond the Higgs boson open problems The Standard Model is complete but are we happy with it? Observations Matter-antimatter Dark Matter Neutrino

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Characterisation of vector-like fermions at the LHC

Luca Panizzi

University of Pisa, Italy

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Beyond the Higgs boson

  • pen problems

The Standard Model is complete but are we happy with it?

Observations Dark Matter Matter-antimatter asymmetry Neutrino masses Theoretical issues

Fermion mass hyerarchies Origin of flavour families Gauge coupling unification . . .

There must be new physics

and most probably it’s already in our reach! And if there’s new physics we should be able to observe new particles (hopefully soon!)

Luca Panizzi Characterisation of vector-like fermions at the LHC 1 / 46

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Looking for new physics at the LHC

Signature 2 Signature 1 Signature 3 Signature 4 Model 1 Model 2 Model 3 Model 4

TH EXP

Designing searches or simulating signals to test specific models is a risky bet

Luca Panizzi Characterisation of vector-like fermions at the LHC 2 / 46

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SLIDE 4

Looking for new physics at the LHC

Signature 2 Signature 1 Signature 3 Signature 4 Model 1 Model 2 Model 3 Model 4 EFT Operator 1 Simplified models with a Z′ EFT Operator 2 Simplified models with a t′

TH EXP PH

Designing searches or simulating signals to test specific models is a risky bet

Model-independent approach

EFTs: higher dimension operators where heavy d.o.f. are integrated out Simplified models: minimal extensions of the SM with new states Approximate description of classes of theoretical models

Luca Panizzi Characterisation of vector-like fermions at the LHC 2 / 46

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SLIDE 5

Characterisation of new physics

Signature 2 Signature 1 Signature 3 Signature 4 Model 1 Model 2 Model 3 Model 4 EFT Operator 1 Simplified models with a Z′ EFT Operator 2 Simplified models with a t′

Suppose Signature 1 is discovered Is it possible to distinguish between Model 1 and Model 2?

Answer 1

Look for Signature 2 or Signature 3

Implies further experimental effort and it takes an indefinite time

Luca Panizzi Characterisation of vector-like fermions at the LHC 3 / 46

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SLIDE 6

Characterisation of new physics

Signature 2 Signature 1 Signature 3 Signature 4 Model 1 Model 2 Model 3 Model 4 EFT Operator 1 Simplified models with a Z′ EFT Operator 2 Simplified models with a t′

Suppose Signature 1 is discovered Is it possible to distinguish between Model 1 and Model 2?

Answer 1

Look for Signature 2 or Signature 3

Implies further experimental effort and it takes an indefinite time

Answer 2

Try to characterise Signature 1

Implies a detailed analysis of available data which can be done immediately (though success is not always guaranteed)

Luca Panizzi Characterisation of vector-like fermions at the LHC 3 / 46

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SLIDE 7

Characterisation of new physics

Signature 2 Signature 1 Signature 3 Signature 4 Model 1 Model 2 Model 3 Model 4 EFT Operator 1 Simplified models with a Z′ EFT Operator 2 Simplified models with a t′

Suppose Signature 1 is discovered Is it possible to distinguish between Model 1 and Model 2?

Answer 1

Look for Signature 2 or Signature 3

Implies further experimental effort and it takes an indefinite time

Answer 2

Try to characterise Signature 1

Implies a detailed analysis of available data which can be done immediately (though success is not always guaranteed)

Let’s focus on new fermions (quarks and leptons)!

Luca Panizzi Characterisation of vector-like fermions at the LHC 3 / 46

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SLIDE 8

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 4 / 46

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SLIDE 9

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 5 / 46

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SM and new fermions

They can mix with SM fermions through Yukawa couplings

Q′ qi × L′ li ×

Dangerous FCNCs − → strong bounds on mixing parameters They can couple without mixing

Q′ li SLQ L′ qi VLQ

Non-minimal scenarios e.g. with lepto-quarks There can be SM partners (t′, e′) or fermions with exotic charges (X5/3, E−−. . . )

Luca Panizzi Characterisation of vector-like fermions at the LHC 6 / 46

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SLIDE 11

SM and new fermions

They can mix with SM fermions through Yukawa couplings

Q′ qi × L′ li ×

Dangerous FCNCs − → strong bounds on mixing parameters They can couple without mixing

Q′ li SLQ L′ qi VLQ

Non-minimal scenarios e.g. with lepto-quarks There can be SM partners (t′, e′) or fermions with exotic charges (X5/3, E−−. . . )

A special case

They can mediate dark matter production

Q′, L′ qi, li SDM Q′, L′ qi, li VDM

Only SM partners are allowed (up to 4-dim operators) They must be odd under the Z2 parity of DM − → they cannot mix with SM states

Luca Panizzi Characterisation of vector-like fermions at the LHC 6 / 46

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SM and new fermions

They can mix with SM fermions through Yukawa couplings

Q′ qi × L′ li ×

Dangerous FCNCs − → strong bounds on mixing parameters They can couple without mixing

Q′ li SLQ L′ qi VLQ

Non-minimal scenarios e.g. with lepto-quarks There can be SM partners (t′, e′) or fermions with exotic charges (X5/3, E−−. . . )

A special case

They can mediate dark matter production

Q′, L′ qi, li SDM Q′, L′ qi, li VDM

Only SM partners are allowed (up to 4-dim operators) They must be odd under the Z2 parity of DM − → they cannot mix with SM states

If new fermions exist what can they be?

Luca Panizzi Characterisation of vector-like fermions at the LHC 6 / 46

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New fermions: the chiral hypothesis

aka adding a fourth chiral family to the SM

u

d

  • νe

e

  • c

s

  • νµ

µ

  • t

b

  • ντ

τ

  • t′

b′

  • ν′

l′

  • both quarks and leptons for

anomaly cancellation Tr[Q] = 3( 2

3 − 1 3 ) + (0 − 1) = 0

Modifications to observed processes g g t, t′ H t, t′, l′ γ γ, Z

Luca Panizzi Characterisation of vector-like fermions at the LHC 7 / 46

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New fermions: the chiral hypothesis

aka adding a fourth chiral family to the SM

19.35 0.45 0.15 7.08 0.33 10.85

pp → H → γγ pp → H → WW pp → H → ZZ p¯ p → H → b¯ b pp → H → b¯ b pp → H → ττ −2 −1 +1 +2 +3 +4

∆χ2 SM SM4 before ICHEP’12 SM4 after ICHEP’12

(Oexp − Ofit)/∆Oexp

  • O. Eberhardt, et al.

Impact of a Higgs boson at a mass of 126 GeV on the standard model with three and four fermion generations Phys.Rev.Lett. 109 (2012) 241802, arXiv:1209.1101

400 GeV < mt′,b′ < 800 GeV ml′ > 100 GeV and mν′ > MZ/2

A chiral 4th generation is excluded at 4.8σ (or 5.3σ including H → b¯ b at Tevatron)

in the context of a simplified model where only the new family is added to the SM

Let’s go for vector-like fermions

Luca Panizzi Characterisation of vector-like fermions at the LHC 8 / 46

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Vector-like fermions

A fermion is vector-like under a gauge group if its left-handed and right-handed chiralities transform in the same way

e.g. SM quarks are vector-like under SU(3)c but are chiral under SU(2) × U(1)Y

Luca Panizzi Characterisation of vector-like fermions at the LHC 9 / 46

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Vector-like fermions

A fermion is vector-like under a gauge group if its left-handed and right-handed chiralities transform in the same way

e.g. SM quarks are vector-like under SU(3)c but are chiral under SU(2) × U(1)Y

Why “vector-like”?

LW = g/ √ 2 jµ±W±

µ

Charged current Lagrangian

SM Chiral fermions

jµ

L = ¯

fLγµf ′

L

jµ

R = 0

jµ = jµ

L + jµ R = ¯

fγµ(1 − γ5)f ′ V-A structure

Vector-like fermions

jµ

L = ¯

fLγµf ′

L

jµ

R = ¯

fRγµf ′

R

jµ = jµ

L + jµ R = ¯

fγµf ′ V structure

Luca Panizzi Characterisation of vector-like fermions at the LHC 9 / 46

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SLIDE 17

Vector-like fermions

A fermion is vector-like under a gauge group if its left-handed and right-handed chiralities transform in the same way

e.g. SM quarks are vector-like under SU(3)c but are chiral under SU(2) × U(1)Y

Why “vector-like”?

LW = g/ √ 2 jµ±W±

µ

Charged current Lagrangian

SM Chiral fermions

jµ

L = ¯

fLγµf ′

L

jµ

R = 0

jµ = jµ

L + jµ R = ¯

fγµ(1 − γ5)f ′ V-A structure

Vector-like fermions

jµ

L = ¯

fLγµf ′

L

jµ

R = ¯

fRγµf ′

R

jµ = jµ

L + jµ R = ¯

fγµf ′ V structure

Peculiar Properties

LM = −M ¯ ψψ Gauge invariant mass term without the Higgs No need to add both quarks and leptons: axial anomalies are automatically absent

Luca Panizzi Characterisation of vector-like fermions at the LHC 9 / 46

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SLIDE 18

Vector-like quarks

Vector-like quarks in many models of New Physics

Warped or universal extra-dimensions: KK excitations of bulk fields Composite Higgs models: excited resonances of the bound states which form SM particles Little Higgs models: partners of SM fermions in larger group representations which ensure the cancellation of divergent loops Non-minimal SUSY extensions: increase corrections to Higgs mass without affecting EWPT

Luca Panizzi Characterisation of vector-like fermions at the LHC 10 / 46

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Vector-like quarks

Vector-like quarks in many models of New Physics

Warped or universal extra-dimensions: KK excitations of bulk fields Composite Higgs models: excited resonances of the bound states which form SM particles Little Higgs models: partners of SM fermions in larger group representations which ensure the cancellation of divergent loops Non-minimal SUSY extensions: increase corrections to Higgs mass without affecting EWPT Intense experimental effort CMS-B2G-16-024 (t′) ATLAS twiki: summary plots (t′)

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Unphysical = 1150 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 1200 GeV T m 0.2 0.4 0.6 0.8 1 Unphysical = 1300 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 1000 GeV T m Unphysical = 1050 GeV T m Unphysical = 1100 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 900 GeV T m Unphysical = 950 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 800 GeV T m Unphysical = 850 GeV T m 1

Wb) → BR(T Ht) → BR(T ATLAS Preliminary

  • 1
= 13 TeV, 3.2-36.1 fb s SU(2) doublet SU(2) singlet
  • Exp. limit
  • Obs. limit
[EXOT-2016-14]
  • 1
Wb+X - 36.1 fb [CONF-2016-104]
  • 1
Ht+X - 13.2 fb [arxiv:1705.10751]
  • 1
)t+X - 36.1 fb ν ν Z( [CONF-2016-032]
  • 1
Same-sign - 3.2 fb

Characterising VLQ properties if a discovery is made would be essential for embedding them into some scenarios (and exclude others!)

Luca Panizzi Characterisation of vector-like fermions at the LHC 10 / 46

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Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 11 / 46

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Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 12 / 46

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VLQ chirality

Minimal SM extensions with one VLQ representation interacting through Yukawa terms

Mixing in left- and right-handed sectors behaves differently: L = ¯ qSM ¯ QVLQ

  • L V†

L MVR

qSM

QVLQ

  • R

Singlets, triplets. . .

tan θR tan θL = mSM

q

MVLQ dominantly left-handed MVLQ ≫ mSM

q

Doublets, quadruplets. . .

tan θL tan θR = mSM

q

MVLQ dominantly right-handed

VLQ couplings always have a dominant chirality, which depends on their representation

Luca Panizzi Characterisation of vector-like fermions at the LHC 13 / 46

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Discriminating the chirality of a VLQ

Polarisation of the gauge boson P P T ¯ T b ¯ b W+ W−

500 600 700 800 900 1000 1100 0.01 0.02 0.03 0.04 0.05 MT [GeV] |ML

2 / |Mtot 2

Wb decay: T singlet, (X T) doublet and triplets

sin θR

d = 0

sin θR

d = 0.02

sin θR

d = 0.1

|ML

2/|Mtot 2

|MR

2/|Mtot 2

500 600 700 800 900 1000 1100 0.00 0.05 0.10 0.15 0.20 0.25 0.30 MT [GeV] sin θR

u

Wb decay: (T B) Doublet

0.01 0.02 0.03 0.03 0.01 0.02 . 3 0.05 0.01 0.02 0.03 0.04 0.01 0.02 0.01 0.02 0.03 0.03

For a T singlet: |M|2

L = g2 2 sin2 θu L(m2 T − m2 W)

|M|2

0 = g2 4 m2

T

m2

W sin2 θu

L

  • m2

T − m2 W

  • |M|2

R = 0

The W boson is always mainly longitudinally polarised for both L and R chiralities O(1)% transverse component Same for Z polarisation in the T → tZ decay Higgs does not provide any information as it is a scalar

Luca Panizzi Characterisation of vector-like fermions at the LHC 14 / 46

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SLIDE 24

Discriminating the chirality of a VLQ

Polarisation of the top P P T ¯ T t ¯ t Z, H Z, H P P X ¯ X t ¯ t W+ W−

200 400 600 800 1000 0.00 0.05 0.10 0.15 pT

l [GeV]

Left Right

The polarisation of the top is transmitted to the leptons after W decay. The right-handed pT distribution of the leading lepton is harder than the left-handed one. This information can be exploited to discriminate left from right chiralities!

Slightly higher reach for right-handed chirality

Luca Panizzi Characterisation of vector-like fermions at the LHC 15 / 46

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SLIDE 25

Recasting experimental data

Pair production of a VLQ with charge 2/3 decaying exclusively to Zt: pp → T¯ T → ZtZ¯ t

Exclusion and discovery reach of a single lepton ATLAS search

ATLAS CONF-2017-015 1 lepton ≥4 jets

  • ET ≥350GeV

100 1000 20 200 3000 50 500 900 1000 1100 1200 1300 1400 L [1/fb] mT [GeV] TT→ZtZt ϵsyst=31% Left Right

2σ 13 TeV 36.1/fb 2σ limit

100 1000 20 200 3000 50 500 900 1000 1100 1200 1300 1400 1500 L [1/fb] mT [GeV] TT→ZtZt ϵsyst=10% Left Right

2σ 5σ 13 TeV 36.1/fb 2σ limit

High ET cut: the Z goes mostly invisible and the lepton comes from top decay Depending on the uncertainty on the background, a discovery can be made in the HL phase If it cannot be reduced, only exclusion bounds will be possible with this selection

Luca Panizzi Characterisation of vector-like fermions at the LHC 16 / 46

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SLIDE 26

Discrimination at higher luminosities

pp → T¯ T → ZtZ¯ t

Discrimination method on the leading lepton pT distribution

χ2 =

  • bins

(L − R)2/ max(L, R) We assume that the background can be neglected at discovery and only consider the poisson uncertainties on the signal for each bin The discrimination will depend on the number of bins (i.e. d.o.f. for the χ2)

pT of leading lepton after the cuts with different binning bin=20 GeV

Left Right

ATLAS atlas_conf_2017_015 @13TeV

200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 pTl[0] [GeV]

bin=50 GeV

Left Right

ATLAS atlas_conf_2017_015 @13TeV

200 400 600 800 1000 1200 1400 0.000 0.001 0.002 0.003 0.004 0.005 0.006 pTl[0] [GeV]

bin=100 GeV

Left Right

ATLAS atlas_conf_2017_015 @13TeV

200 400 600 800 1000 1200 1400 0.000 0.001 0.002 0.003 0.004 0.005 pTl[0] [GeV]

Luca Panizzi Characterisation of vector-like fermions at the LHC 17 / 46

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SLIDE 27

Discrimination at higher luminosities

pp → T¯ T → ZtZ¯ t

ϵL for both ϵR for both ϵL for L, ϵR for R 100 1000 20 200 3000 50 500 900 1000 1100 1200 1300 1400 1500 L [1/fb] mT [GeV] TT→ZtZt ϵsyst=10% Left Right 50 GeV binning

5σ 13 TeV 36.1/fb 2σ limit

Current exclusion limit @ 36.1 fb−1: 1.16 TeV

A discrimination can be done above ∼700 fb−1

ϵL for both ϵR for both ϵL for L, ϵR for R 100 1000 20 200 3000 50 500 900 1000 1100 1200 1300 1400 1500 L [1/fb] mT [GeV] TT→ZtZt ϵsyst=10% Left Right 100 GeV binning

5σ 13 TeV 36.1/fb 2σ limit

ϵL for both ϵR for both ϵL for L, ϵR for R 100 1000 20 200 3000 50 500 900 1000 1100 1200 1300 1400 1500 L [1/fb] mT [GeV] TT→ZtZt ϵsyst=10% Left Right 200 GeV binning

5σ 13 TeV 36.1/fb 2σ limit

A larger binning of the distribution allows a discrimination for smaller values of masses and luminosities

Luca Panizzi Characterisation of vector-like fermions at the LHC 18 / 46

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SLIDE 28

Discrimination at higher energies

13 TeV 27 TeV 33 TeV 100 TeV σQ Q

__ @ NNLO with HATHOR

PDF MSTW2008nnlo68

1 2 3 4 5 6 7 8 10-9 10-6 10-3 1 MQ [TeV] σ [pb]

Higher energies mean (potentially) higher reach!

Luca Panizzi Characterisation of vector-like fermions at the LHC 19 / 46

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SLIDE 29

Discrimination at higher energies

Pair production of a VLQ with charge 5/3 decaying exclusively to Wt: pp → X¯ X → WtW¯ t

Considering same-sign di-lepton final state For discrimination we must be able to identify the lepton from top decay

500 1000 1500 2000 0.0 0.1 0.2 0.3 0.4 pT [GeV] X→W(→e+ν)t→e+νW(→μ+ν)b e+ mu+ 1st lep: blue dashed 2nd lep: red dashed

The leading lepton comes from W decay The sub-leading lepton comes from top decay Distributions after the cuts (SR defined in arXiv:1309.2234 for HE-LHC at 33 TeV) Leading lepton similar shapes

500 1000 1500 2000 2500 0.00 0.02 0.04 0.06 0.08 0.10 0.12 pT

l [GeV]

Leading Lepton Left Right 200 400 600 800 1000 1200 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 pT

l [GeV]

Second Lepton Left Right

Sub-leading lepton different shapes

Luca Panizzi Characterisation of vector-like fermions at the LHC 20 / 46

slide-30
SLIDE 30

Discrimination at higher energies

pp → X¯ X → WtW¯ t

33 TeV

ϵL for both ϵR for both ϵL for L, ϵR for R 1000 200 3000 500 2100 2200 2300 2400 2500 2600 2700 2800 L [1/fb] mX [GeV] XX→WtWt, s =33TeV, ϵsyst=20% Left Right 5σ 200 GeV binning

100 TeV

1000 3000 500 4000 4200 4400 4600 4800 5000 L [1/fb] mX [GeV] XX→WtWt, s =100 TeV, ϵsyst=20% Left Right

5σ

300 GeV binning

Promising perspectives for discrimination of coupling chiralities at high energy hadron collider prototypes! Update for 27 TeV in progress

Luca Panizzi Characterisation of vector-like fermions at the LHC 21 / 46

slide-31
SLIDE 31

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 22 / 46

slide-32
SLIDE 32

Lagrangians

Interactions between the new lepton and a singlet dark matter

LS

1 =

  • f=e,µ,τ
  • λf

11¯

EPRef + λf

21 (¯

N ¯ E) PL νf ef

  • S0

DM + h.c.

LV

1 =

  • f=e,µ,τ
  • gf

11¯

EγµPRef + gf

21 (¯

N ¯ E) γµPL νf ef

  • V0µ

DM + h.c.

The new lepton can be either singlet or doublet Since the lepton is vector-like, its couplings are either purely left or purely right

Interactions between the new lepton and the SM gauge bosons

LAXL = −eAµ¯ EγµE LZXL = Zµ¯ Eγµ

  • gZEE

L

PL + gZEE

R

PR

  • E + Zµ ¯

Nγµ

  • gZNN

L

PL + gZNN

R

PR

  • N

LWXL = W+µ ¯ Nγµ

  • gWLN

L

PL + gWLN

R

PR

  • E + h.c

The couplings with the Z and W boson depend on the VLL representation

(in simplified scenarios)

focus on charged leptons

Luca Panizzi Characterisation of vector-like fermions at the LHC 23 / 46

slide-33
SLIDE 33

Collider signatures

LEP , LHC and future linear colliders

Tree-level

Z, γ E+ E− S0

DM, V0 DM

S0

DM, V0 DM

l+

i

l−

j

}

ET {PP, e+e−} → Z, γ → l+

i l− j

+ ET

In the NWA, only the ZEE coupling affects the bounds: the E decay can be factorized by its BR

Luca Panizzi Characterisation of vector-like fermions at the LHC 24 / 46

slide-34
SLIDE 34

Collider signatures

LEP , LHC and future linear colliders

Tree-level

Z, γ E+ E− S0

DM, V0 DM

S0

DM, V0 DM

l+

i

l−

j

}

ET {PP, e+e−} → Z, γ → l+

i l− j

+ ET

In the NWA, only the ZEE coupling affects the bounds: the E decay can be factorized by its BR

One-loop

Z, γ E+ E−

S0 DM, V0 DM

l+

i

l−

j

{PP, e+e−} → Z, γ → l+

i l− j

Z, γ l±

i /E±

E±/l±

j

l±

i /E±

S0

DM, V0 DM

S0

DM, V0 DM

{PP, e+e−} → Z, γ → invisible

Luca Panizzi Characterisation of vector-like fermions at the LHC 24 / 46

slide-35
SLIDE 35

Testing against data

Combination of ATLAS and CMS searches @ 8 TeV VLL coupling to DM and SM electron Bounds for the process of pair production of VL leptons via DY and decay into SM leptons and DM with different spin Different gauge couplings between singlet and doublet VL leptons allow a potential discrimination between scenarios based on different cross-sections

and by the way, the spin of DM cannot be distinguished

Luca Panizzi Characterisation of vector-like fermions at the LHC 25 / 46

slide-36
SLIDE 36

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 26 / 46

slide-37
SLIDE 37

Searches at the LHC

CMS (t′)

CMS-B2G-16-024

ATLAS (t′)

ATLAS twiki: summary plots

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8

Unphysical = 1150 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 1200 GeV T m 0.2 0.4 0.6 0.8 1 Unphysical = 1300 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 1000 GeV T m Unphysical = 1050 GeV T m Unphysical = 1100 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 900 GeV T m Unphysical = 950 GeV T m 0.2 0.4 0.6 0.8 Unphysical = 800 GeV T m Unphysical = 850 GeV T m 1

Wb) → BR(T Ht) → BR(T ATLAS Preliminary

  • 1
= 13 TeV, 3.2-36.1 fb s SU(2) doublet SU(2) singlet
  • Exp. limit
  • Obs. limit
[EXOT-2016-14]
  • 1
Wb+X - 36.1 fb [CONF-2016-104]
  • 1
Ht+X - 13.2 fb [arxiv:1705.10751]
  • 1
)t+X - 36.1 fb ν ν Z( [CONF-2016-032]
  • 1
Same-sign - 3.2 fb

Common assumptions

  • nly one extra quark mixing with one generation only

σ × BR assuming NWA . . . at least until recently!

  • nly interactions with the visible sector

Luca Panizzi Characterisation of vector-like fermions at the LHC 27 / 46

slide-38
SLIDE 38

Going beyond to find a signal

1

There can be multiple VLQs, with general mixing structure (third generation, light generations, universal couplings. . . ) Recasting tools (with different degrees of accuracy-vs-speed optimisations)

  • ur one is XQCAT: JHEP 1412 (2014) 080, arXiv:1405.0737 and Comput. Phys. Commun. 197 (2015) 263, arXiv:1409.3116

Luca Panizzi Characterisation of vector-like fermions at the LHC 28 / 46

slide-39
SLIDE 39

Going beyond to find a signal

1

There can be multiple VLQs, with general mixing structure (third generation, light generations, universal couplings. . . ) Recasting tools (with different degrees of accuracy-vs-speed optimisations)

  • ur one is XQCAT: JHEP 1412 (2014) 080, arXiv:1405.0737 and Comput. Phys. Commun. 197 (2015) 263, arXiv:1409.3116

2

Single production can be the dominant channel in the region where experiments are setting current mass bounds It is possible to describe single production channels in a model-independent way

  • M. Buchkremer, G. Cacciapaglia, A. Deandrea and LP, Nucl.Phys. B876 (2013) 376-417, arXiv:1305.4172

J.A. Aguilar-Saavedra, R. Benbrik and S. Heinemeyer, Phys.Rev. D88 (2013) no.9, 094010, arXiv:1306.0572 Luca Panizzi Characterisation of vector-like fermions at the LHC 28 / 46

slide-40
SLIDE 40

Going beyond to find a signal

1

There can be multiple VLQs, with general mixing structure (third generation, light generations, universal couplings. . . ) Recasting tools (with different degrees of accuracy-vs-speed optimisations)

  • ur one is XQCAT: JHEP 1412 (2014) 080, arXiv:1405.0737 and Comput. Phys. Commun. 197 (2015) 263, arXiv:1409.3116

2

Single production can be the dominant channel in the region where experiments are setting current mass bounds It is possible to describe single production channels in a model-independent way

  • M. Buchkremer, G. Cacciapaglia, A. Deandrea and LP, Nucl.Phys. B876 (2013) 376-417, arXiv:1305.4172

J.A. Aguilar-Saavedra, R. Benbrik and S. Heinemeyer, Phys.Rev. D88 (2013) no.9, 094010, arXiv:1306.0572

3

VLQs may have large width so that the NWA is not applicable

Luca Panizzi Characterisation of vector-like fermions at the LHC 28 / 46

slide-41
SLIDE 41

Going beyond to find a signal

1

There can be multiple VLQs, with general mixing structure (third generation, light generations, universal couplings. . . ) Recasting tools (with different degrees of accuracy-vs-speed optimisations)

  • ur one is XQCAT: JHEP 1412 (2014) 080, arXiv:1405.0737 and Comput. Phys. Commun. 197 (2015) 263, arXiv:1409.3116

2

Single production can be the dominant channel in the region where experiments are setting current mass bounds It is possible to describe single production channels in a model-independent way

  • M. Buchkremer, G. Cacciapaglia, A. Deandrea and LP, Nucl.Phys. B876 (2013) 376-417, arXiv:1305.4172

J.A. Aguilar-Saavedra, R. Benbrik and S. Heinemeyer, Phys.Rev. D88 (2013) no.9, 094010, arXiv:1306.0572

3

VLQs may have large width so that the NWA is not applicable

4

VLQs may mediate interactions with DM

I will focus on points 3 and 4

Can we reinterpret current data? What are the bounds in these scenarios? Can searches be sensitive to large widths (for visible and/or DM decays)?

Luca Panizzi Characterisation of vector-like fermions at the LHC 28 / 46

slide-42
SLIDE 42

Going to large width regime

example for DM decay QCD pair production and decay of on-shell VLQs

P P T ¯ T t ¯ t DM DM σX = σ2→2 × BR(T)BR(¯ T)

Production and decays are factorized Basically no information on the spin of DM

Full signal g g t T t t DM DM ¯ t q ¯ q ¯ t t T b DM DM σS = σ2→4 with any allowed topology

Topologies with ≥ 1 VLQ propagator (generally subleading in the NWA) More sensitivity to the coupling structure between T and DM

If the width of the T mediator is large the kinematics will be different from NWA!

Luca Panizzi Characterisation of vector-like fermions at the LHC 29 / 46

slide-43
SLIDE 43

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 30 / 46

slide-44
SLIDE 44

How large the width can be

example with a T singlet

LTsinglet = κWV4i

L/R

g √ 2 [¯ TL/RW+

µ γµdi L/R] + κZV4i L/R

g 2cW [¯ TL/RZµγµui

L/R] − κHV4i L/R

M v [¯ TR/LHui

L/R] + h.c.

Width expressions

Γ(T → Wdi) = κ2

W|V4i L/R|2 M3g2

64πm2

W

λ

1 2 (1,

m2

q

M2 , m2

W

M2 )

  • 1 −

m2

q

M2 2 + m2

W

M2 − 2 m4

W

M4 + m2

Wm2 q

M4

  • Γ(T → Zui) = κ2

Z|V4i L/R|2 M3g2

64πm2

W

1 2 λ

1 2 (1,

m2

q

M2 , m2

Z

M2 )

  • 1 −

m2

q

M2 2 + m2

Z

M2 − 2 m4

Z

M4 + m2

Zm2 q

M4

  • Γ(T → Hui) = κ2

H|V4i L/R|2 M3g2

64πm2

W

1 2 λ

1 2 (1,

m2

q

M2 , m2

H

M2 )

  • 1 +

m2

q

M2 − m2

H

M2

  • ΓT,total = Γ(T → Wdi) + Γ(T → Zui) + Γ(T → Hui)

To obtain a large width:

Increase couplings − → bounds from other observables (flavour, EWPT); perturbativity − → non-minimal extensions which allow to escape bounds while enlarging couplings Increase number of decay channels − → new physics, non-minimal extension

Luca Panizzi Characterisation of vector-like fermions at the LHC 31 / 46

slide-45
SLIDE 45

How large the width can be

Increasing the couplings T singlet

0.001 0.01 600 800 1000 1200 1400 1600 1800 2000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 MT [GeV] Sin(θ) T singlet mixing with 3rd gen.

(T B) doublet

0.001 600 800 1000 1200 1400 1600 1800 2000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 MT [GeV] Sin(θ) T in TB doublet ( sin(θb)=0 ) mixing with 3rd gen.

(X T) doublet

600 800 1000 1200 1400 1600 1800 2000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 MT [GeV] Sin(θ) T in XT doublet mixing with 3rd gen.

Bounds from C.-Y. Chen, S. Dawson, and E. Furlan, Vector-like Fermions and Higgs Effective Field Theory Revisited, Phys. Rev. D 96 (2017) no.1, 015006.

Simplified models with large couplings already excluded by other observables New physics has to be invoked

Luca Panizzi Characterisation of vector-like fermions at the LHC 32 / 46

slide-46
SLIDE 46

Ratio of cross-sections

(σLW − σNWA)/σNWA “Diagonal” final states WbWb ZtZt HtHt

400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' . WbWb . 13 TeV 400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' .

ZtZt

. 13 TeV
  • 400
600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' .

HtHt

. 13 TeV

“Off-diagonal” final states WbZt WbHt ZtHt

400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' .

WbZt

. 13 TeV 400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' .

WbHt

. 13 TeV
  • 0.3
400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4

MT [GeV] ΓT/MT

(σS-σX')/σX' .

ZtHt

. 13 TeV

Effects of “subleading” topologies is very large! How do kinematical cuts of current searches modify the picture?

Luca Panizzi Characterisation of vector-like fermions at the LHC 33 / 46

slide-47
SLIDE 47

LHC bounds

T mixing with third SM generation ATLAS @ 8 TeV combination of searches implemented in CheckMATE

Bounds weakly dependent on the width! Increase of cross-section somehow compensated by decrease of search efficiencies in the region of the bound

Luca Panizzi Characterisation of vector-like fermions at the LHC 34 / 46

slide-48
SLIDE 48

LHC bounds

T mixing with first SM generation Topologies not present for mixing with third generation ATLAS @ 8 TeV combination of searches implemented in CheckMATE

Bounds strongly depend on the width! For mixing with first generation current searches may be able to characterise the width of the T

Luca Panizzi Characterisation of vector-like fermions at the LHC 35 / 46

slide-49
SLIDE 49

A parametrisation for single production

also in collaboration with CMS

g ¯ b b T t Z W q q

Single T: Phys. Lett. B 781 (2018) 574 arXiv:1708.01062 Single B: arXiv:1802.01486. in the narrow-width approximation (NWA)

σ(C1, C2, mQ, ΓQ) = σP(C1, mQ)BRQ→decay channel = C2

1 ˆ

σNWA(mQ)BRQ→decay channel

Luca Panizzi Characterisation of vector-like fermions at the LHC 36 / 46

slide-50
SLIDE 50

A parametrisation for single production

also in collaboration with CMS

g ¯ b b T t Z W q q

Single T: Phys. Lett. B 781 (2018) 574 arXiv:1708.01062 Single B: arXiv:1802.01486. in the narrow-width approximation (NWA)

σ(C1, C2, mQ, ΓQ) = σP(C1, mQ)BRQ→decay channel = C2

1 ˆ

σNWA(mQ)BRQ→decay channel

in the finite width regime (FW) and assuming negligible interference contributions

σ(C1, C2, mQ, ΓQ) = C2

1 C2 2 ˆ

σ(mQ, ΓQ)

Luca Panizzi Characterisation of vector-like fermions at the LHC 36 / 46

slide-51
SLIDE 51

A parametrisation for single production

also in collaboration with CMS

g ¯ b b T t Z W q q

Single T: Phys. Lett. B 781 (2018) 574 arXiv:1708.01062 Single B: arXiv:1802.01486. in the narrow-width approximation (NWA)

σ(C1, C2, mQ, ΓQ) = σP(C1, mQ)BRQ→decay channel = C2

1 ˆ

σNWA(mQ)BRQ→decay channel

in the finite width regime (FW) and assuming negligible interference contributions

σ(C1, C2, mQ, ΓQ) = C2

1 C2 2 ˆ

σ(mQ, ΓQ)

600 800 1000 1200 1400 1600 1800 2000 0.1 0.5 1 5 10 MT [GeV] ΓT/MT (%) T3: σ S [pb] for pp → Wbj

+

3.6 3.6 3.2 3.2 2.5 2.5 2.3 2.3 2.4 2.4 2.3 2.3 2.3 2.3 2.1 2.1 2.1 2.1 2. 2. 1.9 1.9 2. 2. 1.8 1.8 2. 2. 1.7 1.7 1.8 1.8 1.9 1.9 1.6 1.6 1.7 1.7 1.6 1.6 1.5 1.5 1.8 1.8 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.2 1.2 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.1 1.1 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3

600 800 1000 1200 1400 1600 1800 2000 10 20 30 40 MQ [GeV] ΓQ/MQ [%] CMS-recast Wbj T ~2.3 fb-1 (13 TeV)

Luca Panizzi Characterisation of vector-like fermions at the LHC 36 / 46

slide-52
SLIDE 52

A parametrisation for single production

also in collaboration with CMS

If interference contributions are non negligible signal with itself σS = C2

2 ˆ

σS(C1..., MQ, ΓQ, χQ) signal with background σint

SB = C2 ˆ

σint

SB(C1..., MQ, ΓQ, χQ)

Model-dependency is unavoidable Fiducial cross-section

S + B = L(σSǫS + σint

SBirrǫint SBirr) + Birr+red ≡ Lσeff + B

Suppose the VLQ interacts only with one gauge boson: σeff = C4

2 ˆ

σS ǫS + C2

2 ˆ

σint

SBirr ǫint SBirr ≡ C4 2 ˆ

σS,eff + C2

2 ˆ

σint

SBirr,eff Luca Panizzi Characterisation of vector-like fermions at the LHC 37 / 46

slide-53
SLIDE 53

A parametrisation for single production

Recast of CMS-B2G-16-006

Folding search efficiencies into the reduced cross-section: Signal

600 800 1000 1200 1400 1600 1800 2000 0.1 0.5 1 5 10 MT [GeV] ΓT/MT (%) T3: σ S [pb] for pp → Wbj 600 800 1000 1200 1400 1600 1800 2000 0.1 0.5 1 5 10 MT [GeV] ΓT/MT (%) T3: σ Seff [pb] for pp → Wbj SRe

Interference with SM

600 800 1000 1200 1400 1600 1800 2000 0.1 0.5 1 5 10 MT [GeV] ΓT/MT (%) T3 L: σ SBirr

int

[pb] for pp → Wbj 600 800 1000 1200 1400 1600 1800 2000 0.1 0.5 1 5 10 MT [GeV] ΓT/MT (%) T3 L: σ SBirr,eff

int

[pb] for pp → Wbj SRe

Luca Panizzi Characterisation of vector-like fermions at the LHC 38 / 46

slide-54
SLIDE 54

Development of new strategies

Preliminary results @NLO in LH proceedings arXiv:1803.10379

Effects at NLO pp → Tj(+b) with T → Wb Width effects (still only LO)

Γ/M = 1% Γ/M = 10%

T→bW, M=1200GeV

η(j0) 5FS 4FS

  • 4
  • 2

2 4 0.00 0.02 0.04 0.06 0.08

η dσ/dη (normalised units)

pp → Wbj(+b) via T

Luca Panizzi Characterisation of vector-like fermions at the LHC 39 / 46

slide-55
SLIDE 55

Outline

1

Adding extra-fermions to the SM

2

Chirality of vector-like fermions VL quarks interacting with SM

D.Barducci and LP, JHEP 1712 (2017) 057

VL leptons interacting with DM

D.Barducci, A.Deandrea, S.Moretti, LP, H.Prager, Phys. Rev. D 97 (2018) no.7, 075006

3

Width of vector-like fermions VLQs decaying to SM states

(1) S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.7, 075035 (2) A.Carvalho, S.Moretti, D.O’Brien, LP and H.Prager, arXiv:1805.06402

VLQs decaying to dark matter

S.Moretti, D.O’Brien, LP, H.Prager, Phys. Rev. D 96 (2017) no.3, 035033 Luca Panizzi Characterisation of vector-like fermions at the LHC 40 / 46

slide-56
SLIDE 56

Width dependence of bounds

combination of ATLAS searches @ 13 TeV The bounds weakly depend on the width for light DM, somewhat more if the DM mass increases

Luca Panizzi Characterisation of vector-like fermions at the LHC 41 / 46

slide-57
SLIDE 57

Kinematics of the signal

Scalar DM: MT=1100 GeV and MDM=10 GeV

MET [GeV] 200 400 600 800 1000 1200 1400 1600 1800 2000 /dMET [fb/GeV/bin] σ d 1 2 3 4 5 6 7 8

Missing Transverse Energy

NWA = 20%

T

/M

T

Γ = 40%

T

/M

T

Γ

Missing Transverse Energy

[GeV]

T

p 200 400 600 800 1000 1200 1400 [fb/GeV/bin]

T

/dp σ d 1 2 3 4 5 6 T

Leading jet p

NWA = 20%

T

/M

T

Γ = 40%

T

/M

T

Γ T

Leading jet p

The distributions of ET and transverse momentum of the leading jet depend significantly on the width along the bound Need to look at the performance of the searches

Luca Panizzi Characterisation of vector-like fermions at the LHC 42 / 46

slide-58
SLIDE 58

Cross-sections and efficiencies

SR tN_high of ATLAS CONF-2016-050 for scalar DM

← − region where tN_high is the best SR

Cross-section weakly dependent on the width in the region of the bound Light DM: the efficiency

  • f the best SR in the

bound region depends in a complementary way, almost compensating the cross-section increase Heavier DM: the efficiency stays almost constant, as well as the cross-section

For vector DM results are qualitatively analogous

Luca Panizzi Characterisation of vector-like fermions at the LHC 43 / 46

slide-59
SLIDE 59

Interactions with light quarks

In this case the DM can interact directly with the initial state

The bound strongly depends on the width It is possible to distinguish scalar from vector DM

Different behaviour due to interplay between cross-sections and (shape-dependent) efficiencies

Luca Panizzi Characterisation of vector-like fermions at the LHC 44 / 46

slide-60
SLIDE 60

Exclusion limits

MT vs MDM plane In the small splitting region, the width dependence is always large For coupling with first generation, width effects are always sizable

considering pair production final states and with the selections of current searches A shape analysis of the signal would provide information about different scenarios

Luca Panizzi Characterisation of vector-like fermions at the LHC 45 / 46

slide-61
SLIDE 61

Conclusions and perspectives

Discovery of new physics may be (hopefully) around the corner and it is paramount to be ready to characterise new signals Characterisation of new fermions at the LHC and future colliders in different channels would be very useful to narrow down the theoretical possibilities however Any new signal may possibly be used to discriminate between classes of models if effective strategies are developed

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-62
SLIDE 62

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-63
SLIDE 63

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-64
SLIDE 64

Backup

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-65
SLIDE 65

Representations and lagrangian terms

Minimal extension of the SM with just one vector-like quark SM Singlets Doublets Triplets X   X   u c t (t′) t′ t′ t′   t′   d s b (b′) b′ b′ b′ b′ Y Y SU(2)L 2 and 1 1 2 3 U(1)Y qL = 1/6 uR = 2/3 dR = −1/3 2/3

  • 1/3

7/6 1/6

  • 5/6

2/3

  • 1/3

LY −yi

u¯

qi

LHcui R

−yi

d¯

qi

LVi,j CKMHdj R

−λi

u¯

qi

LHct′ R

−λi

d¯

qi

LHb′ R

−λi

uψLH(c)ui R

−λi

dψLH(c)di R

−λi¯ qi

Lτ aH(c)ψa R

Lm −M ¯ ψψ

(gauge invariant since vector-like)

Free parameters 4 M + 3 × λi 4 or 7 M + 3λi

u + 3λi d

4 M + 3 × λi

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-66
SLIDE 66

Mixing between VL and SM quarks

Ly+M =

  • ¯

˜ u ¯ ˜ c ¯ ˜ t ¯ U

  • L Mu

   ˜ u ˜ c ˜ t U   

R

+ ¯ ˜ d ¯ ˜ s ¯ ˜ b ¯ D

  • L Md

    ˜ d ˜ s ˜ b D    

R

+ h.c.

Mass matrices depend on representations

Singlets and triplets: Mu =     ˜ mu x1 ˜ mc x2 ˜ mt x3 M     Md =     ˜ VCKM

L

  ˜ md ˜ ms ˜ mb   ˜ VCKM

R

x1 x2 x3 M     Doublets: M4I

u,d ↔ MI4 u,d

Flavour and mass eigenstates

   ˜ u ˜ c ˜ t U   

L,R

= Vu

L,R

   u c t t′    and     ˜ d ˜ s ˜ b D    

L,R

= Vd

L,R

   d s b b′    The exotics X5/3 and Y−4/3 do not mix → no distinction between flavour and mass eigenstates

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-67
SLIDE 67

A key property of mixing matrices

Lm =

  • ¯

u ¯ c ¯ t ¯ t′

L (Vu L)†Mu(Vu R)

  u c t t′  

R

+ ¯ d ¯ s ¯ b ¯ b′

L (Vd L)†Md(Vd R)

  d s b b′  

R

+ h.c. (Vu

L)†Mu(Vu R) = diag (mu, mc, mt, mt′)

(Vd

L)†Md(Vd R) = diag (md, ms, mb, mb′)

Mixing in left- and right-handed sectors behave differently

  • (Vq

L)†(MM†)(Vq L) = diag

(Vq

R)†(M†M)(Vq R) = diag

q I

L,R

q J

L,R

× Vq

L,R

Singlets and triplets (case of up-type quarks) Vu

L =

⇒ Mu · M†

u =

    ˜ m2

u + |x1|2

x∗

1 x2

x∗

1 x3

x∗

1 M

x∗

2 x1

˜ m2

c + |x2|2

x∗

2 x3

x∗

2 M

x3x1 x3x2 ˜ m2

t + x2 3 x3M

x1M x2M x3M M2     mixing in the left sector present also for ˜ mq → 0 flavour constraints for qL are relevant Vu

R =

⇒ M†

u · Mu =

    ˜ m2

u

x∗

1 ˜

m2

u

˜ m2

c

x∗

2 ˜

m2

c

˜ m2

t

x3˜ m2

t

x1˜ mu x2˜ mc x3˜ mt 3

i=1 |xi|2 + M2

    mq ∝ ˜ mq mixing is suppressed by quark masses Doublets: other way round

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46

slide-68
SLIDE 68

Couplings

With Z

gIJ

ZL = g cW

Tq

3 − Qqs2 w

δIJ+ g

cW (Tq′ 3 − Tq 3 )(V∗ L )q′IVq′J L

gIJ

ZR = g cW

−Qqs2

w

δIJ+ g

cW Tq′ 3 (V∗ R )q′IVq′J R

With W±

gWL = g √ 2 (Vu

L)†

    ˜ VCKM 1     Vd

L

gWR = g √ 2 (Vu

R)†

   1    Vd

R

With Higgs

CIJ = 1 v mIδIJ− M v (V∗

R )q′IVq′J L

Singlet T t′

S,L

× uL Z uL ∝ (VL)t′u Doublet (T B) t′

D,R

× b′

D,R

dR W ∝ (Vd

R)b′J

Triplet (X T B) t′

T,L

× uL uR H ∝ Vt′u

L

VLQ couplings always have a dominant chirality, which depends on their representation

Luca Panizzi Characterisation of vector-like fermions at the LHC 46 / 46