plehn/includes/talks/... · Tilman Plehn Higgs Coupl’s Higgs EFT Consistency QCD EFT Top EFT DM...

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT LHC Physics in a Data-Driven Era

Tilman Plehn

Universitat Heidelberg

PPP12, May 2017

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Theory in a data-driven era

Same old theory motivation

– dark matter still not understood [WIMP still best choice]

– hierarchy problem (probably) a problem

– but: data in driving seat [remember 750]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT






Theory tool box

– Lagrangian language obvious after Higgs discovery

1 full new physics model [built to solve problems, last lecture]

2 simplified models [Feynman diagrams for experimental features, theoretically poor at best]

3 effective Lagrangians [symmetries and particles fixed, non-renormalizable operators, SMEFT]

⇒ matter of experimental needs, convenience and taste

effective Lagrangian simplified models full modelsagnostic (×)data-driven (×) (×)theory-driven (×)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT






Theory tool box






effective Lagrangian simplified models full modelsagnostic (×) pre-LHCdata-driven (×) (×)theory-driven (×) pre-LHC

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT






Theory tool box






effective Lagrangian simplified models full modelsagnostic (×) dishonest pre-LHCdata-driven boring (×) (×)theory-driven pointless (×) pre-LHC

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Higgs questions

1. What is the ‘Higgs’ field?

– psychologically: looked for Higgs, so found a Higgs

– CP-even spin-0 scalar expected, which operators?spin-1 vector unlikelyspin-2 graviton unexpected

– ask LHCb [Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles, not part of lecture]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Higgs questions





2. What is the Higgs Lagrangian?

– naive-but-useful: set of ‘couplings’ given Lagrangian

– bottom-up: effective theory [simplified models?]

– top-down: modified Higgs sectors

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Higgs questions





2. What is the Higgs Lagrangian?

– naive-but-useful: set of ‘couplings’ given Lagrangian

– bottom-up: effective theory [simplified models?]

– top-down: modified Higgs sectors

3. What does all this tell us? [not part of lecture]

– strongly interacting models?

– weakly interacting extensions?

– TeV-scale physics, hierarchy problem, vacuum stability, Higgs inflation, etc

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Higgs Couplings

Standard Model operators [historic slide]

– assume: narrow CP-even scalarStandard Model operators

– couplings proportional to masses?– fundamental physics in terms of Lagrangian

L = LSM + ∆W gmW H WµWµ + ∆Zg

2cwmZ H ZµZµ −

∑τ,b,t

∆fmf

vH(fR fL + h.c.

)+ ∆gFG

Hv

GµνGµν + ∆γFAHv

AµνAµν + invisible + unobservable

t W,Z

b,tW,Z

gg → Hgg → H + j (boosted)gg → H∗ (off-shell)qq → qqHgg → t tHqq′ → VH

←→ gHXX = gSMHXX (1 + ∆X ) ←→

H → ZZH → WWH → bbH → τ+τ−

H → γγH → invisible

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Higgs Couplings

Standard Model operators [historic slide]

– assume: narrow CP-even scalarStandard Model operators

– couplings proportional to masses?– fundamental physics in terms of Lagrangian

L = LSM + ∆W gmW H WµWµ + ∆Zg

2cwmZ H ZµZµ −

∑τ,b,t

∆fmf

vH(fR fL + h.c.

)+ ∆gFG

Hv

GµνGµν + ∆γFAHv

AµνAµν + invisible + unobservable

t W,Z

b,tW,Z

Great Run I results, but issues... [Corbett, Eboli, Goncalves, Gonzalez-Fraile, TP, Rauch]

1 electroweak renormalizability broken

2 total rates only

3 hard to relate to gauge, flavor sectors

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

∆W

∆Z

∆t

∆b

∆τ

∆γ

∆g

BRinv

∆γSM

+NP

∆gSM

+NP

∆Z/W

∆b/τ

∆b/W

gx = gxSM

(1+∆x)

L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb-1

, 68% CL: ATLAS + CMS

SM exp.

data

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators

D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal]

– set of Higgs operators [renormalizable, #1 solved]

OGG = φ†φGa

µνGaµν OWW = φ†WµνWµν

φ OBB = · · ·

OBW = φ†BµνWµν

φ OW = (Dµφ)†Wµν(Dνφ) OB = · · ·

Oφ,1 = (Dµφ)† φ φ†(Dµφ

)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3

Oφ,4 = (Dµφ)†(Dµφ

) (φ†φ)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

– actual basis after equation of motion, etc

LHVV =−αsv8π

fgΛ2OGG +

fBB

Λ2OBB +

fWW

Λ2OWW +

fBΛ2OB +

fWΛ2OW +

fφ,2Λ2Oφ,2

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)


LHVV =−αsv8π

fgΛ2OGG +

fBB

Λ2OBB +

fWW

Λ2OWW +

fBΛ2OB +

fWΛ2OW +

fφ,2Λ2Oφ,2

– Higgs couplings to SM particles [derivatives = momentum, #2 solved]

LHVV = gg HGaµνGaµν + gγ HAµνAµν

+ g(1)Z ZµνZµ∂νH + g(2)

Z HZµνZµν + g(3)Z HZµZµ

+ g(1)W

(W +µνW−µ∂νH + h.c.

)+ g(2)

W HW +µνW−µν + g(3)

W HW +µW−µ + · · ·

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)


LHVV =−αsv8π

fgΛ2OGG +

fBB

Λ2OBB +

fWW

Λ2OWW +

fBΛ2OB +

fWΛ2OW +

fφ,2Λ2Oφ,2

– Higgs couplings to SM particles [derivatives = momentum, #2 solved]

LHVV = gg HGaµνGaµν + gγ HAµνAµν

+ g(1)Z ZµνZµ∂νH + g(2)

Z HZµνZµν + g(3)Z HZµZµ

+ g(1)W

(W +µνW−µ∂νH + h.c.

)+ g(2)

W HW +µνW−µν + g(3)

W HW +µW−µ + · · ·

– plus Yukawa structure fτ,b,t– 7 ∆-like coupling modifications

4 new Lorentz structures

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

– linking couplings and operators

gg =fGGvΛ2≡ −

αs

8πfgvΛ2

gγ = −g2vs2

w

2Λ2

fBB + fWW

2

g(1)Z =

g2v2Λ2

c2w fW + s2

w fB2c2

wg(1)

W =g2v2Λ2

fW2

g(2)Z = −

g2v2Λ2

s4w fBB + c4

w fWW

2c2w

g(2)W = −

g2v2Λ2

fWW

g(3)Z =

g2v4c2

w

(1−

v2

2Λ2fφ,2

)g(3)

W =g2v

4

(1−

v2

2Λ2fφ,2

)

gf = −mf

v

(1−

v2

2Λ2fφ,2

)+

v2

√2Λ2

ff

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

Run 1 legacy

– kinematics: pT ,V ,∆φjj [#2 solved]

102

103

0 25 50 75 100 125 150 175 200 225 250

pT

V(GeV)

Ev

ents

/bin

SM(SM Higgs) x 70

(fW

/Λ2 =20TeV

-2) x 70

2leptons

0 50 100 150 200 250

103

102

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

Run 1 legacy


20

30

40

50

60

70

80

90

100

0 1.0472 2.0944 3.1416

∆Φjj

Ev

ents

/bin

SM Higgs

fWW

/Λ2=-f

BB/Λ

2=20TeV

-2

fWW

/Λ2=-f

BB/Λ

2=-20TeV

-2

γγ jj

0 π/3 2π/3 π10

102

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

Run 1 legacy


– with impact...

fW/Λ2 [TeV

-2]

fB/Λ2

[TeV-2

]

-20 -10 0 10 20 30-80

-60

-40

-20

0

20

40

-20 -10 0 10 20 30-80

-60

-40

-20

0

20

40

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

Run 1 legacy


– with impact...

...in last bin

fW/Λ2 [TeV

-2]

fB/Λ2

[TeV-2

]

-20 -10 0 10 20 30-80

-60

-40

-20

0

20

40

-20 -10 0 10 20 30-80

-60

-40

-20

0

20

40

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs operators



OGG = φ†φGa


φ OBB = · · ·




)Oφ,2 =

12∂µ(φ†φ)∂µ(φ†φ)

Oφ,3 =13

(φ†φ)3


) (φ†φ)

Run 1 legacy


– with impact...

...in last bin

– Run I limits

-50

-40

-30

-20

-10

0

OGG

OW

W

OBB

OW

OB

Oφ2

0.15

0.2

0.25

0.3

0.5∞

0.5

f/Λ2

[TeV-2

]Λ/√|f|[TeV]

L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb-1


rate only

rate+distributions

-15

-10

-5

0

5

Ot

Ob

Oτ

0.3

0.4

0.5

1∞1

0.5

f/Λ2

[TeV-2

]Λ/√|f|[TeV]

L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb-1


Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Exercise: higher-dimensional operators

Higgs sector including dimension-6 operators

LD6 =2∑

i=1

fiΛ2Oi with Oφ,2 =

12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3

first operator, wave function renormalization

Oφ,2 =12∂µ(φ†φ) ∂µ(φ†φ)=

12

(H + v)2∂µH ∂

µH

proper normalization of combined kinetic term [LSZ]

Lkin =12∂µH ∂

µH

(1 +

fφ,2v2

Λ2

)!

=12∂µH ∂

µH ⇔ H = H

√1 +

fφ,2v2

Λ2

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3


Oφ,2 =12∂µ(φ†φ) ∂µ(φ†φ)=

12

(H + v)2∂µH ∂

µH


Lkin =12∂µH ∂

µH

(1 +

fφ,2v2

Λ2

)!

=12∂µH ∂

µH ⇔ H = H

√1 +

fφ,2v2

Λ2

second operator, minimum condition giving v

v2 = −µ2

λ−

fφ,3µ4

4λ3Λ2

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3


Oφ,2 =12∂µ(φ†φ) ∂µ(φ†φ)=

12

(H + v)2∂µH ∂

µH


Lkin =12∂µH ∂

µH

(1 +

fφ,2v2

Λ2

)!

=12∂µH ∂

µH ⇔ H = H

√1 +

fφ,2v2

Λ2

second operator, minimum condition giving v

v2 = −µ2

λ−

fφ,3µ4

4λ3Λ2

both operators contributing to Higgs mass

Lmass = −µ2

2H2 −

32λv2H2 −

fφ,3Λ2

1524

v4H2 != −

m2H

2H2

⇔ m2H = 2λv2

(1−

fφ,2v2

Λ2+

fφ,3v2

2Λ2λ

)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3

Higgs self couplings momentum dependent

Lself =−m2

H

2v

[(1−

fφ,2v2

2Λ2+

2fφ,3v4

3Λ2m2H

)H3 −

2fφ,2v2

Λ2m2H

H ∂µH ∂µH

]

−m2

H

8v2

[(1−

fφ,2v2

Λ2+

4fφ,3v4

Λ2m2H

)H4 −

4fφ,2v2

Λ2m2H

H2∂µ H∂µH

]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3


Lself =−m2

H

2v

[(1−

fφ,2v2

2Λ2+

2fφ,3v4

3Λ2m2H

)H3 −

2fφ,2v2

Λ2m2H

H ∂µH ∂µH

]

−m2

H

8v2

[(1−

fφ,2v2

Λ2+

4fφ,3v4

Λ2m2H

)H4 −

4fφ,2v2

Λ2m2H

H2∂µ H∂µH

]alternatively, strong multi-Higgs interactions

H =

(1 +

fφ,2v2

2Λ2

)H +

fφ,2v2Λ2

H2 +fφ,26Λ2

H3 +O(H4)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT



LD6 =2∑

i=1


12∂µ(φ†φ) ∂µ(φ†φ) , Oφ,3 = −

13

(φ†φ)3


Lself =−m2

H

2v

[(1−

fφ,2v2

2Λ2+

2fφ,3v4

3Λ2m2H

)H3 −

2fφ,2v2

Λ2m2H

H ∂µH ∂µH

]

−m2

H

8v2

[(1−

fφ,2v2

Λ2+

4fφ,3v4

Λ2m2H

)H4 −

4fφ,2v2

Λ2m2H

H2∂µ H∂µH

]alternatively, strong multi-Higgs interactions

H =

(1 +

fφ,2v2

2Λ2

)H +

fφ,2v2Λ2

H2 +fφ,26Λ2

H3 +O(H4)

⇒ operators and distributions linked to (poor) UV behavior

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 Higgs-gauge operators

Triple gauge couplings

– one more Higgs-gauge operator [#3 solved]

OW = (Dµφ)†Wµν(Dνφ) OB= (Dµφ)†Bµν(Dνφ) OWWW = Tr(

WµνWνρWµρ

)– kinematics: pT ,` in VV production

1

10

102

103

104

100 200 300 400 500 600 700 800 900 1000

pT

lead(GeV)

Ev

ents

/bin

BackgroundSM WW

Data

fW

/Λ2=25TeV

-2

fB/Λ

2=25TeV

-2

fWWW

/Λ2=25TeV

-2

100 300 500 700 900

104

103

102

10

1

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT





WµνWνρWµρ


– combined LHC channels

]-2 [TeV2ΛWf

30− 20− 10− 0 10 20 30

]-2

[TeV

2ΛBf

80−60−40−20−0

20

40

60

80

7 WZ

7 semi

8 WW

8 WZ

ATLASCMS

combined

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT





WµνWνρWµρ



– affecting Higgs-sector correlations

]-2 [TeV2ΛWf

20− 15− 10− 5− 0 5 10 15 20

]-2

[TeV

2ΛBf

60−

40−

20−

0

20

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT





WµνWνρWµρ




⇒ complete Higgs-gauge analysis

-50

-40

-30

-20

-10

0

10

20

OGG

OW

W

OBB

OW

OB

Oφ2

OW

WW

0.15

0.2

0.250.3

0.5∞

0.5

0.30.25

f/Λ2

[TeV-2

]Λ/√|f|[TeV]

LHC-Higgs, 95% CL

LHC-Higgs + LHC-TGV + LEP-TGV, 95% CL

-20

-15

-10

-5

0

5

10

15

Ot

Ob

Oτ

0.25

0.3

0.5

∞

0.5

0.3

f/Λ2

[TeV-2

]Λ/√|f|[TeV]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT





WµνWνρWµρ




⇒ complete Higgs-gauge analysis

LHC vs LEP

– triple gauge vertices g1, κ, λ vs operators

– LEP limits from precisionLHC limits from energy

– semileptonic analyses missing for 8 TeV

⇒ LHC beating LEP, but what does it mean?

]-2 [TeV2ΛWf

10− 5− 0 5 10 15 20 25 30 35

]-2

[TeV

2ΛBf

80−

60−

40−

20−

0

20

40

LHC

LEP

LHC+LEP

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Self consistency

Ideal LEP and flavor worlds

– unique EFT Lagrangian: linear realization matching unbroken phase

– chain of well separated energy scales E Λ1 ... ΛN

⇒ systematic expansions in E/Λ and α [example: ew precision data]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Self consistency





Rotten LHC world [Brehmer, Freitas, Lopez-Val, TP]

– range of (partonic) energy scales [H+jets production]

– electroweak symmetry breaking at v ∼ ELHC

– low precision, reach from energy∣∣∣∣∣ σ × BR(σ × BR)SM

− 1

∣∣∣∣∣ =g2m2

h

Λ2≈ 10%

g=1⇐⇒ Λ ≈ 400 GeV

⇒ D8 operators not obviously suppressed

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Self consistency





Rotten LHC world [Brehmer, Freitas, Lopez-Val, TP]

– range of (partonic) energy scales [H+jets production]

– electroweak symmetry breaking at v ∼ ELHC

– low precision, reach from energy∣∣∣∣∣ σ × BR(σ × BR)SM

− 1

∣∣∣∣∣ =g2m2

h

Λ2≈ 10%

g=1⇐⇒ Λ ≈ 400 GeV

⇒ D8 operators not obviously suppressed

Task for LHC theory

– develop a working D6 framework

– keep theorist’s self respect

– validate as representation of full models [forget D8 estimates]

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Matching matters

Example: oblique parameters from Higgs portal vs D6 [Freitas, Lopez-Val, TP]

– operators

LEFT ⊃cH

2Λ2∂µ(φ†φ)∂µ(φ†φ) +

cT

2Λ2(φ†←→D µ

φ)(φ†←→D µφ) +

igcW

2Λ2(φ†σk←→D µ

φ)DνW kµν

– predictions of Higgs portal model [mH ≈ 2λ2v2s , s2

α ≈ λ23v2/(2λ2m2

H )]

S ≈λ2

3

24πλ2

v2

m2H

logm2

H

m2h

T ≈−3λ2

3v2

32π s2w λ2 m2

W

(m2

Z

m2H

−m2

W

m2H

)log

m2H

m2h

– leading log with tree-insertion of loop operators OT ,B,W [Λ2 = 2λ2v2s ]

cT

Λ2= −

3αews2wλ

23

32πc2wλ2Λ2

logΛ2

µ2

cB,W

Λ2=

λ23

192π2λ2Λ2log

Λ2

µ2

– including weak-scale loops with OH

cH

Λ2=

λ23

2λ2Λ2.

– v -improvement: Λ = mH and full model in terms of cα [resumming VEV insertions?]

cH

Λ2=

2(1− cα)

v2

cT

Λ2= −

3αews2w (1− cα)

8πc2w v2

logm2

H

µ2

cB,W

Λ2=

1− cα48π2v2

logm2

H

µ2

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Matching matters


– operators

LEFT ⊃cH

2Λ2∂µ(φ†φ)∂µ(φ†φ) +

cT

2Λ2(φ†←→D µ

φ)(φ†←→D µφ) +

igcW


φ)DνW kµν

– v -improvement: Λ = mH and full model in terms of cα [resumming VEV insertions?]

cH

Λ2=

2(1− cα)

v2

cT

Λ2= −

3αews2w (1− cα)

8πc2w v2

logm2

H

µ2

cB,W

Λ2=

1− cα48π2v2

logm2

H

µ2

– broken-phase matching: systematically all terms v/Λ

cT

Λ2= −

αews2w (1− cα)

8πc2w v2

(−

52

+ 3 logm2

H

µ2

)cB,W

Λ2=

1− cα144π2v2

(−

52

+ 3 logm2

H

µ2

)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Matching matters


– operators

LEFT ⊃cH

2Λ2∂µ(φ†φ)∂µ(φ†φ) +

cT

2Λ2(φ†←→D µ

φ)(φ†←→D µφ) +

igcW


φ)DνW kµν

– numerical comparison [tan β = v/vs ]

400 500 600 700 800 900

mH

[GeV]

1.4×10-3

4.1×10-3

Γ (

H >

hh)

[GeV

]

FullLL-LLL-TLLL-TLvBP-TLBP-TLv

10 15 20 25 30tanβ

10-1

100

δr[%

]S parameter

λ1 = 1.8x10

-1

sin α

λ2 = 6.6x10

-3

S3

S3

I

I400 500 600 700 800 900

mH

[GeV]

-1.0×10-2

-5.0×10-3

Γ (

H >

hh

) [G

eV

]

FullLL-LLL-TLLL-TLvBP-TLBP-TLv

10 15 20 25 30tanβ

10-1

100

δr[%

]

T parameter

λ2 = 6.6x10

-3

sinα

λ1 = 1.8x10

-1

S3

S3

I

I

– similar analysis for loop-induced H → γγ [Trott etal]

⇒ D6 Lagrangian systematically improved

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

EFT strategy at LHC

What does the D6 analysis at LHC mean? [Brehmer, Freitas, Lopez-Val, TP]

– phenomenology: does D6 capture features of model classes at LHC?theory: how do D6 vs EFT vs full model differences appear?

1 push (simplified) models to visible deviations at LHCHiggs portal, 2HDM, stops, vector triplet [weakly interacting]

2 construct and match D6-Lagrangian to modelcoupling modifications v2/Λ2 vs new kinematics ∂/Λ?v -improved and broken phase matching

3 LHC simulations: D6-Lagrangian vs full modelproduction: WBF, VH, HHdecays: H → γγ, 4`

⇒ check for differenceskinematic distributions like pT ,j or mVH?resonance peaks of new states?

⇒ consider uncertainties as matching uncertainties

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...

Higgs singlet/doublet extensions [Higgs portal]

– mixing with SM-like Higgs, not too interesting

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...



Scalar top partners [simplified supersymmetry]

– loop contributions everywhere, small, not too interesting

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...





Triplet gauge extension [Brehmer, Biekotter, TP]

– additional vector triplet field Vµ– Lagrangian modulo UV completion

L ⊃−14

V aµν Vµνa +

M2V

2V aµVµa + i

gV

2cH V a

µ

[φ†σ

a←→D µφ]

+g2

w

2gVV aµ

∑fermions

cF F Lγµσ

aFL

+gV

2cVVV εabc V a

µV bνD[µVν]c + g2

V cVVHH V aµVµa(φ†φ)−

gw

2cVVW εabcWµν V b

µV cν

– new states, mixing with W± and Zweak gauge coupling to W ,Z mass eigenstates

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...






– additional vector triplet field Vµ– new states, mixing with W± and Z

weak gauge coupling to W ,Z mass eigenstatesTriplet model EFT

MV gV cH cF cVVHH mξ cW cH c6 cf

591 3.0 −0.47 −5.0 2.0 1200 −0.044 0.000 0.000 0.000946 3.0 −0.47 −5.0 1.0 1200 −0.017 0.000 0.000 0.000941 3.0 −0.28 3.0 1.0 1200 0.006 0.075 0.100 0.025

1246 3.0 −0.50 3.0 −0.2 1200 0.006 0.103 0.138 0.034846 1.0 −0.56 −1.32 0.08 849 −0.007 −0.020 −0.027 −0.007

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...









591 3.0 −0.47 −5.0 2.0 1200 −0.044 0.000 0.000 0.000946 3.0 −0.47 −5.0 1.0 1200 −0.017 0.000 0.000 0.000941 3.0 −0.28 3.0 1.0 1200 0.006 0.075 0.100 0.025

1246 3.0 −0.50 3.0 −0.2 1200 0.006 0.103 0.138 0.034846 1.0 −0.56 −1.32 0.08 849 −0.007 −0.020 −0.027 −0.007

– effects in Vh and WBF [f

b/bi

n]σ

1

10

210

310

V h (T4)→p p

)ξfull (no EFT

full

SM

[GeV]Vhm500 1000

full

σfu

llσ

-

EF

Tσ

1−

0

1

EFT error

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...









591 3.0 −0.47 −5.0 2.0 1200 −0.044 0.000 0.000 0.000946 3.0 −0.47 −5.0 1.0 1200 −0.017 0.000 0.000 0.000941 3.0 −0.28 3.0 1.0 1200 0.006 0.075 0.100 0.025

1246 3.0 −0.50 3.0 −0.2 1200 0.006 0.103 0.138 0.034846 1.0 −0.56 −1.32 0.08 849 −0.007 −0.020 −0.027 −0.007

– effects in Vh and WBF [f

b/bi

n]σ

1−10

1

10

210

V h (T4')→p p

)ξfull (no EFT

full

SM

[GeV]Vhm500 1000

full

σfu

llσ

-

EF

Tσ

1−

0

1

EFT error

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...









591 3.0 −0.47 −5.0 2.0 1200 −0.044 0.000 0.000 0.000946 3.0 −0.47 −5.0 1.0 1200 −0.017 0.000 0.000 0.000941 3.0 −0.28 3.0 1.0 1200 0.006 0.075 0.100 0.025

1246 3.0 −0.50 3.0 −0.2 1200 0.006 0.103 0.138 0.034846 1.0 −0.56 −1.32 0.08 849 −0.007 −0.020 −0.027 −0.007

– effects in Vh and WBF

⇒ D6 Lagrangian okay, if away from poles

[fb/

bin]

σ

1−10

1

10

210

u d h (T5)→u d

)ξfull (no EFT

full

SM

[GeV]T,j1

p200 400 600 800 1000

full

σfu

llσ

-

EF

Tσ

1−

0

1EFT error

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...









591 3.0 −0.47 −5.0 2.0 1200 −0.044 0.000 0.000 0.000946 3.0 −0.47 −5.0 1.0 1200 −0.017 0.000 0.000 0.000941 3.0 −0.28 3.0 1.0 1200 0.006 0.075 0.100 0.025

1246 3.0 −0.50 3.0 −0.2 1200 0.006 0.103 0.138 0.034846 1.0 −0.56 −1.32 0.08 849 −0.007 −0.020 −0.027 −0.007

– effects in Vh and WBF

⇒ D6 Lagrangian okay, if away from poles

[fb/

bin]

σ

1−10

1

10

210

u d h (T5')→u d

)ξfull (no EFT

full

SM

[GeV]T,j1

p200 400 600 800 1000

full

σfu

llσ

-

EF

Tσ

1−

0

1EFT error

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

DUH!

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators

Ubiquitous QCD operator [TP, Krauss, Kuttimalai]

– anomalous gluon coupling

cGOG =gs cG

Λ2fabcGρaνGνbλGλcρ with Gρνa = ∂

ρGνa − ∂νGρa − igs fabcGbρGcν

– affecting multi-jet production [CMS black hole search]

ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators



cGOG =gs cG




ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)

– 4-fermion operator for Njets = 2, 3gluon operator for Njets ≥ 5 [Sherpa]

10−2

10−1

100

101

102

103

104

Even

tspe

rbi

n

Njet = 2 Λ√cG

= 5 TeV

CMS dataSMSM + OG

2000 3000 4000 5000 6000 7000ST [GeV]

0.51.01.52.0

Rat

ioto

SM SHERPA

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators



cGOG =gs cG




ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)


10−2

10−1

100

101

102

103

104

Even

tspe

rbi

n

Njet = 3 Λ√cG

= 5 TeV

CMS dataSMSM + OG

2000 3000 4000 5000 6000 7000ST [GeV]

0.51.01.52.0

Rat

ioto

SM SHERPA

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators



cGOG =gs cG




ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)


10−2

10−1

100

101

102

103

104

Even

tspe

rbi

n

Njet = 4 Λ√cG

= 5 TeV

CMS dataSMSM + OG

2000 3000 4000 5000 6000 7000ST [GeV]

0.51.01.52.0

Rat

ioto

SM SHERPA

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators



cGOG =gs cG




ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)


10−1

100

101

102

103

104

Even

tspe

rbi

n

Njet ≥ 5 Λ√cG

= 5 TeV

CMS dataSMSM + OG

2000 3000 4000 5000 6000 7000ST [GeV]

0.51.01.52.0

Rat

ioto

SM SHERPA

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 QCD operators



cGOG =gs cG




ST =

Njets∑j=1

ET ,j + ( /pT > 50 GeV)


– 4-fermion operators from ATLAS Λ/√

c > 4.8 ... 6.8 TeV

⇒ gluon operator Λ/√

c > 5.2 TeV ∼ Smax

5.0 5.2 5.4 5.6 5.8 6.0Λ/√

cG [TeV]

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

CL s

Njet ≥ 5 L = 2.2 fb−1

Observed

Expected (±σ)

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

YEAH!

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 top operators

Effective Lagrangian for tops@LHC [TopFitter: Buckley, Englert, Ferrando, Miller, Moore, Russell, White]

– single, pair-wise, and associated top production [plus decays]

– including anomalous AFB from Tevatron– 4-quark, Yang-Mills, electroweak operators

Oqq = qγµq tγµt OG = fABCGAνµ GBλ

ν GCµλ OφG = φ

†φGa

µνGaµν · · ·

– profile likelihoods and individual limits

⇒ generic D6 reach ∼ 500 GeV [C = 1]

-1 -0.5 0 0.5 1Ci = Civ

2/Λ2

individualmarginalizedCG

C33uG

C1u

C2u

C1d

C2d

C33uW

Ct

C3φq

C33uB

Cφu

C1φq

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 top operators

Effective Lagrangian for tops@LHC [TopFitter: Buckley, Englert, Ferrando, Miller, Moore, Russell, White]

– single, pair-wise, and associated top production [plus decays]

– including anomalous AFB from Tevatron– 4-quark, Yang-Mills, electroweak operators

Oqq = qγµq tγµt OG = fABCGAνµ GBλ

ν GCµλ OφG = φ

†φGa

µνGaµν · · ·

– profile likelihoods and individual limits

⇒ generic D6 reach ∼ 500 GeV [C = 1]

-1 -0.5 0 0.5 1Ci = Civ

2/Λ2

individualmarginalizedCG

C33uG

C1u

C2u

C1d

C2d

C33uW

Ct

C3φq

C33uB

Cφu

C1φq

For theorists: in terms of models

– axigluon: MA > 1.4 TeV [t t resonance]

– SM-like W ′: MW ′ > 1.2 TeV [t-channel,...]

⇒ models less sensitive to correlations

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

D6 dark matter operators

Combining direct, indirect, collider results for WIMPs [Tait etal]

– choose dark matter candidate [Majorana/Dirac fermion, scalar, dark photon]

– consider D6 scattering process χχ→ SM SM

– relic density from annihilation [mχ/T ∼ 30]

– indirect detection even later

– direct detection non-relativistic [E ∼ 10 MeV]

– LHC tricky: single scale mχ mmediator?

– example: scalar dark matterLabelCoefficient Operator σSI〈σannv〉

Real scalar

R1 λ1 ∼ 1/(2M2) mqχ2 qq X s-waveR2 λ2 ∼ 1/(2M2) imqχ2 qγ5q s-waveR3 λ3 ∼ αs/(4M2)χ2GµνGµν X s-waveR4 λ4 ∼ αs/(4M2)iχ2Gµν Gµν s-wave

Complex scalar

C1 λ1 ∼ 1/(M2) mqχ†χqq X s-waveC2 λ2 ∼ 1/(M2) imqχ†χqγ5q s-waveC3 λ3 ∼ 1/(M2) χ†∂µχqγµq X p-waveC4 λ4 ∼ 1/(M2) χ†∂µχqγµγ5q p-waveC5 λ5 ∼ αs/(8M2)χ†χGµνGµν X s-waveC6 λ6 ∼ αs/(8M2)iχ†χGµν Gµν s-wave

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT


Relic density plus Hooperon [Liem, Bertone, Calore, Ruiz de Austri, Tait, Trotta, Weniger]

– default input: relic density

– scalar dark matterLabelCoefficient Operator σSI〈σannv〉

Real scalar


– profile likelihood

– flat prior on logλi [prior 1/λi ]

– Dirichlet prior preferingsimilar-sized Wilson coefficients

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT


Relic density plus Hooperon [Liem, Bertone, Calore, Ruiz de Austri, Tait, Trotta, Weniger]

– default input: relic density

– scalar dark matterLabelCoefficient Operator σSI〈σannv〉

Real scalar


– profile likelihood

– flat prior on logλi [prior 1/λi ]

– Dirichlet prior preferingsimilar-sized Wilson coefficients

– Fermi: GCE plus dwarf galaxies

⇒ working in practice...

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Towards a global analysis?

Combination of measurements [Bauer, Butter, Desai, Gonzalez-Fraile, TP]

– relic density, annihilation in early universe [non-relativistic]

– indirect detection, annihilation today [very non-relativistic]

– direct detection [non-relativistic]

– collider searches [away from poles]

⇒ effective Lagrangian not obvious

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT








Representing models?

– relic density only actual measurementtypical mass scales m2

med/(g2mχ) ∼ 8 TeV

– tree-level colored t-channel mediator [squark-neutralino in MSSM]

relic density requiring light mediator, direct production at LHC

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT













– tree-level vector s-channel mediator [Z′ mediator]

relic density pushing LHC into poles

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT















– loop-mediated scalar s-channel mediator [heavy Higgs-neutralino in MSSM]

issues with mass effects and χχ→ t t annihilation

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT















– loop-mediated scalar s-channel mediator [heavy Higgs-neutralino in MSSM]

issues with mass effects and χχ→ t t annihilation

– loop-mediated scalar t-channel mediator [stop-neutralino in MSSM]

mediator pairs at LHC

⇒ relic density and LHC combination the challenge

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...

Tree-level scalar in t-channel [squarks]

– relic density for mχ < mu

[GeV]u~m

310

2 h

Ω

3−10

2−10

1−10

1

10

=10 GeVχm=50 GeVχm=100 GeVχm

=1u~

y

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...



[GeV]u~m

310

2 h

Ω

3−10

2−10

1−10

1

10

=10 GeVχm=50 GeVχm=100 GeVχm

=1u~

y

– two effective Lagrangians

Leff ⊃cuχ

Λ2(uRχ) (χuR) Leff ⊃

cΛ3

(χχ) GµνGµν

– not valid for correct relic density...

103

mu = Λ [GeV]

10−4

10−3

10−2

10−1

100

101

σpp→χχ

j[p

b]

EFT

simp.total

simp.single

simp.pair

mχ = 100 GeV , ET > 50 GeV

103

mu = Λ [GeV]

10−5

10−4

10−3

10−2

10−1

100

σpp→χχ

j[p

b] EFTsim

p.totalsim

p.single

simp.pair

mχ = 100 GeV , ET > 300 GeV

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...




Leff ⊃cuχ


cΛ3

(χχ) GµνGµν


Tree-level vector in s-channel

– relic density for mχ < mV

[GeV]Vm

210 310 410

2 h

Ω

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

=10 GeVχm

=50 GeVχm=100 GeVχm

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...




Leff ⊃cuχ


cΛ3

(χχ) GµνGµν




[GeV]Vm

210 310 410

2 h

Ω

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

=10 GeVχm


– only 4-fermion operator


103 104

mV = Λ [GeV]

10−5

10−4

10−3

10−2

10−1

100

101

102σ

pp→χχ

j[p

b]

EFT, cuχ =

1

EFT, cuχ =

1/4

simp. g

u,χ =1

simp. g

u,χ =1/2

mχ = 100 GeV , ET > 50 GeV

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...




Leff ⊃cuχ


cΛ3

(χχ) GµνGµν






Loop-mediated scalar in s-channel

– relic density for mχ < mS [GeV]Sm

210 310 410

2 h

Ω

4−10

3−10

2−10

1−10

1

10

210

310

410

510

=10 GeVχm


Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Model by model...




Leff ⊃cuχ


cΛ3

(χχ) GµνGµν






Loop-mediated scalar in s-channel

– relic density for mχ < mS [GeV]Sm

210 310 410

2 h

Ω

4−10

3−10

2−10

1−10

1

10

210

310

410

510

=10 GeVχm


– two good effective Lagrangians

Leff ⊃ct

S

Λ2(t t) (χχ) Leff,3 ⊃

cgχ

Λ3(χχ) GµνGµν


102 103 104 10510-10

10-8

10-6

10-4

10-2

1

102

simp.

EFT 1

EFT 2

EFT 3

simp.

EFT 2

EFT 2

simp.

10310-6

10-4

10-2

1

10310-6

10-4

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Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

SIGH...

Tilman Plehn

Higgs Coupl’s

Higgs EFT

Consistency

QCD EFT

Top EFT

DM EFT

Bottom line

Describing LHC data using effective Lagrangians

dimension-6 Higgs-gauge Lagrangian working

dimension-6 QCD Lagrangian excellent

dimension-6 top Lagrangian like Higgs

dark matter EFT not for global analyses

validation through full models

uncertainties part of matching

mostly tool for limit setting

⇒ Welcome to a data-driven era!

Lectures on LHC Physics and dark matter updated under www.thphys.uni-heidelberg.de/˜plehn/

Much of this work was funded by the BMBF Theorie-Verbund which is ideal for relevant LHC work

www.thphys.uni-heidelberg.de/~plehn/

plehn/includes/talks/... · Tilman Plehn Higgs Coupl’s Higgs EFT Consistency QCD EFT Top EFT DM...

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