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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 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]
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 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]
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 (×) pre-LHCdata-driven (×) (×)theory-driven (×) pre-LHC
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]
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 (×) 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
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]
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
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]
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
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)
– 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
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)
– actual basis after equation of motion, etc
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
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)
– actual basis after equation of motion, etc
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
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)
– 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
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)
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
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)
Run 1 legacy
– kinematics: pT ,V ,∆φjj [#2 solved]
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
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)
Run 1 legacy
– kinematics: pT ,V ,∆φjj [#2 solved]
– 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
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)
Run 1 legacy
– kinematics: pT ,V ,∆φjj [#2 solved]
– 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
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)
Run 1 legacy
– kinematics: pT ,V ,∆φjj [#2 solved]
– 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
, 68% CL: ATLAS + CMS
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
, 68% CL: ATLAS + CMS
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
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
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
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
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
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
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
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
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
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
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
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
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
]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
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
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
]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
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
– 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
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
– combined LHC channels
– 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
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
– combined LHC channels
– affecting Higgs-sector correlations
⇒ 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
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
– combined LHC channels
– affecting Higgs-sector correlations
⇒ 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
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]
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
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]
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
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
– 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
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
– 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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
Triplet gauge extension [Brehmer, Biekotter, TP]
– 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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
Triplet gauge extension [Brehmer, Biekotter, TP]
– 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
– 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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
Triplet gauge extension [Brehmer, Biekotter, TP]
– 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
– 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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
Triplet gauge extension [Brehmer, Biekotter, TP]
– 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
– 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...
Higgs singlet/doublet extensions [Higgs portal]
– mixing with SM-like Higgs, not too interesting
Scalar top partners [simplified supersymmetry]
– loop contributions everywhere, small, not too interesting
Triplet gauge extension [Brehmer, Biekotter, TP]
– 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
– 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
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)
– 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
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)
– 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 = 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
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)
– 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 = 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
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)
– 4-fermion operator for Njets = 2, 3gluon operator for Njets ≥ 5 [Sherpa]
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
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)
– 4-fermion operator for Njets = 2, 3gluon operator for Njets ≥ 5 [Sherpa]
– 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
D6 dark matter operators
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
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
– 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
D6 dark matter operators
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
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
– 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
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
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
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
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
– 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
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
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
– tree-level vector s-channel mediator [Z′ mediator]
relic density pushing LHC into poles
– 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
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
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
– tree-level vector s-channel mediator [Z′ mediator]
relic density pushing LHC into poles
– 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...
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
– 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...
Tree-level scalar in t-channel [squarks]
– relic density for mχ < mu
– two effective Lagrangians
Leff ⊃cuχ
Λ2(uRχ) (χuR) Leff ⊃
cΛ3
(χχ) GµνGµν
– not valid for correct relic density...
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...
Tree-level scalar in t-channel [squarks]
– relic density for mχ < mu
– two effective Lagrangians
Leff ⊃cuχ
Λ2(uRχ) (χuR) Leff ⊃
cΛ3
(χχ) GµνGµν
– not valid for correct relic density...
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
– only 4-fermion operator
– not valid for correct relic density...
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...
Tree-level scalar in t-channel [squarks]
– relic density for mχ < mu
– two effective Lagrangians
Leff ⊃cuχ
Λ2(uRχ) (χuR) Leff ⊃
cΛ3
(χχ) GµνGµν
– not valid for correct relic density...
Tree-level vector in s-channel
– relic density for mχ < mV
– only 4-fermion operator
– not valid for correct relic density...
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
=100 GeVχm=200 GeVχm
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
– two effective Lagrangians
Leff ⊃cuχ
Λ2(uRχ) (χuR) Leff ⊃
cΛ3
(χχ) GµνGµν
– not valid for correct relic density...
Tree-level vector in s-channel
– relic density for mχ < mV
– only 4-fermion operator
– not valid for correct relic density...
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
=100 GeVχm=200 GeVχm
– two good effective Lagrangians
Leff ⊃ct
S
Λ2(t t) (χχ) Leff,3 ⊃
cgχ
Λ3(χχ) GµνGµν
– not valid for correct relic density...
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
10-2
1
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
