LHC Physics in a Data-Driven Era · Tilman Plehn Higgs Coupl’s Higgs EFT Consistency QCD EFT Top...
Transcript of LHC Physics in a Data-Driven Era · Tilman Plehn Higgs Coupl’s Higgs EFT Consistency QCD EFT Top...
![Page 1: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/1.jpg)
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
![Page 2: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/2.jpg)
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]
![Page 3: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/3.jpg)
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 (×)
![Page 4: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/4.jpg)
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
![Page 5: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/5.jpg)
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
![Page 6: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/6.jpg)
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]
![Page 7: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/7.jpg)
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
![Page 8: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/8.jpg)
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
![Page 9: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/9.jpg)
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
![Page 10: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/10.jpg)
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
![Page 11: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/11.jpg)
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)
![Page 12: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/12.jpg)
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
![Page 13: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/13.jpg)
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 + · · ·
![Page 14: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/14.jpg)
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
![Page 15: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/15.jpg)
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
![Page 16: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/16.jpg)
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
![Page 17: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/17.jpg)
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
![Page 18: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/18.jpg)
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
![Page 19: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/19.jpg)
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
![Page 20: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/20.jpg)
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
![Page 21: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/21.jpg)
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
![Page 22: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/22.jpg)
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
![Page 23: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/23.jpg)
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
![Page 24: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/24.jpg)
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
)
![Page 25: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/25.jpg)
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
]
![Page 26: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/26.jpg)
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)
![Page 27: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/27.jpg)
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
![Page 28: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/28.jpg)
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
![Page 29: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/29.jpg)
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
![Page 30: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/30.jpg)
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
![Page 31: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/31.jpg)
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]
![Page 32: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/32.jpg)
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
![Page 33: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/33.jpg)
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]
![Page 34: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/34.jpg)
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
![Page 35: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/35.jpg)
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]
![Page 36: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/36.jpg)
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
![Page 37: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/37.jpg)
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
)
![Page 38: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/38.jpg)
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
![Page 39: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/39.jpg)
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
![Page 40: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/40.jpg)
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
![Page 41: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/41.jpg)
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
![Page 42: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/42.jpg)
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
![Page 43: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/43.jpg)
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
![Page 44: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/44.jpg)
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
![Page 45: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/45.jpg)
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
![Page 46: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/46.jpg)
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
![Page 47: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/47.jpg)
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
![Page 48: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/48.jpg)
Tilman Plehn
Higgs Coupl’s
Higgs EFT
Consistency
QCD EFT
Top EFT
DM EFT
DUH!
![Page 49: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/49.jpg)
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)
![Page 50: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/50.jpg)
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
![Page 51: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/51.jpg)
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
![Page 52: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/52.jpg)
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
![Page 53: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/53.jpg)
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
![Page 54: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/54.jpg)
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)
![Page 55: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/55.jpg)
Tilman Plehn
Higgs Coupl’s
Higgs EFT
Consistency
QCD EFT
Top EFT
DM EFT
YEAH!
![Page 56: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/56.jpg)
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
![Page 57: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/57.jpg)
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
![Page 58: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/58.jpg)
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
![Page 59: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/59.jpg)
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
![Page 60: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/60.jpg)
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...
![Page 61: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/61.jpg)
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
![Page 62: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/62.jpg)
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
![Page 63: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/63.jpg)
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
![Page 64: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/64.jpg)
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
![Page 65: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/65.jpg)
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
![Page 66: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/66.jpg)
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
![Page 67: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/67.jpg)
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
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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
![Page 69: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/69.jpg)
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
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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
![Page 71: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/71.jpg)
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
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Tilman Plehn
Higgs Coupl’s
Higgs EFT
Consistency
QCD EFT
Top EFT
DM EFT
SIGH...
![Page 73: LHC Physics in a Data-Driven Era · 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¨](https://reader034.fdocuments.us/reader034/viewer/2022042803/5f471396916cb03b377dac9f/html5/thumbnails/73.jpg)
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