A Theorist's Take on Higgs Physics -...
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![Page 1: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/1.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
A Theorist’s Take on Higgs Physics
Tilman Plehn
Universitat Heidelberg
Nordic Physics Days, 6/2013
![Page 2: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/2.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Weak interaction
Massive exchange bosons
– Fermi 1934: weak interactions [n → pe−νe ]
point-like (2→ 2) amplitude A ∝ GF E2
unitarity violation [E < 600 GeV]
pre-80s effective theory– Yukawa 1935: massive particles
Fermi’s theory for E Mmodified amplitude A ∝ g2E2/(E2 −M2)unitarity violation in WW → WW [E < 1.2 TeV]
pre-LHC effective theory
– Higgs 1964: spontaneous symmetry breakingunitary through Higgs particleparticle masses allowedfundamental weak-scale scalar
– ’t Hooft & Veltman 1971: renormalizabilityno 1/M couplings allowedtheory valid to high energyStandard Model with Higgs fundamental
![Page 3: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/3.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
![Page 4: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/4.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
![Page 5: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/5.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
![Page 6: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/6.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
![Page 7: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/7.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
![Page 8: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/8.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
![Page 9: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/9.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
– 1976 etc: collider phenomenology
![Page 10: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/10.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
– 1976 etc: collider phenomenology
![Page 11: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/11.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
– 1966: original Higgs phenomenology
– 1976 etc: collider phenomenology
⇒ Higgs boson predicted from mathematical field theory
![Page 12: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/12.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs boson
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theoremSU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theoriesmassive gauge bosons have 3 polarizations, and 3 6= 2
In terms of Higgs potential
V =− µ2|φ|2 + λ|φ|4
minimum at φ =v√2
∂V∂ |φ|2 =− µ2 + 2λ|φ|2 ⇒ v2
2=µ2
2λ
excitation φ =v + H√
2
m2H =
∂2V∂H2
∣∣∣∣∣minimum
= 2λv2
![Page 13: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/13.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs signatures
Higgs decays easy
– weak-scale scalar coupling proportional to mass
– off-shell decays below threshold
– decay to γγ via W and top loop [destructive interference]
⇒ mH = 125 GeV perfectBR(H)
bb_
τ+τ−
cc_
gg
WW
ZZ
tt-
γγ Zγ
MH [GeV]50 100 200 500 1000
10-3
10-2
10-1
1
![Page 14: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/14.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs signatures
Higgs decays easy
– weak-scale scalar coupling proportional to mass
– off-shell decays below threshold
– decay to γγ via W and top loop [destructive interference]
⇒ mH = 125 GeV perfect
Higgs production hard [7-8 TeV, 5-15/fb]
– quantum effects neededgluon fusion production loop induced [σ ∼ 15000 fb]
weak boson fusion production with jets [σ ∼ 1200 fb]
t W,Z
b,tW,Z
![Page 15: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/15.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs signatures
Higgs decays easy
– weak-scale scalar coupling proportional to mass
– off-shell decays below threshold
– decay to γγ via W and top loop [destructive interference]
⇒ mH = 125 GeV perfect
Higgs production hard [7-8 TeV, 5-15/fb]
– quantum effects neededgluon fusion production loop induced [σ ∼ 15000 fb]
weak boson fusion production with jets [σ ∼ 1200 fb]
t W,Z
b,tW,Z
– easy channels for 2011-2012pp → H → ZZ → 4` fully reconstructedpp → H → γγ fully reconstructedpp → H → WW → (`−ν)(`+ν) large BR
![Page 16: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/16.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs signatures
Higgs decays easy
– weak-scale scalar coupling proportional to mass
– off-shell decays below threshold
– decay to γγ via W and top loop [destructive interference]
⇒ mH = 125 GeV perfect
Higgs production hard [7-8 TeV, 5-15/fb]
– quantum effects neededgluon fusion production loop induced [σ ∼ 15000 fb]
weak boson fusion production with jets [σ ∼ 1200 fb]
t W,Z
b,tW,Z
– easy channels for 2011-2012pp → H → ZZ → 4` fully reconstructedpp → H → γγ fully reconstructedpp → H → WW → (`−ν)(`+ν) large BR
⇒ fun still waitingpp → H → ττ plus jetspp → ZH → (`+`−)(bb) boostedpp → t tH waiting for a good idea...
![Page 17: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/17.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs discovery
4th of July fireworks [no theory input needed beyond basic Pythia]
– ‘silver channel’ H → γγ
local significance 4.5σ (ATLAS), 4.1σ (CMS)
– ‘golden channel’ H → ZZ → 4`local significance 3.4σ (ATLAS), 3.2σ (CMS)
– WW and ττ, bb adding little (CMS)
– combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ]
![Page 18: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/18.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs discovery
4th of July fireworks [no theory input needed beyond basic Pythia]
– ‘silver channel’ H → γγ
local significance 4.5σ (ATLAS), 4.1σ (CMS)
– ‘golden channel’ H → ZZ → 4`local significance 3.4σ (ATLAS), 3.2σ (CMS)
– WW and ττ, bb adding little (CMS)
– combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ]
⇒ Rolf Heuer: ‘We have him’
![Page 19: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/19.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Higgs discovery
4th of July fireworks [no theory input needed beyond basic Pythia]
– ‘silver channel’ H → γγ
local significance 4.5σ (ATLAS), 4.1σ (CMS)
– ‘golden channel’ H → ZZ → 4`local significance 3.4σ (ATLAS), 3.2σ (CMS)
– WW and ττ, bb adding little (CMS)
– combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ]
⇒ Rolf Heuer: ‘We have it’
![Page 20: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/20.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Questions
1. What is the ‘Higgs’ Lagrangian?
– psychologically: looked for Higgs, so found a Higgs
– CP-even spin-0 scalar expectedspin-1 vector unlikelyspin-2 graviton unexpected
![Page 21: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/21.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Questions
1. What is the ‘Higgs’ Lagrangian?
– psychologically: looked for Higgs, so found a Higgs
– CP-even spin-0 scalar expectedspin-1 vector unlikelyspin-2 graviton unexpected
2. What are the coupling values?
– ‘coupling’ after fixing operator basis
– Standard Model Higgs vs anomalous couplings
![Page 22: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/22.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Questions
1. What is the ‘Higgs’ Lagrangian?
– psychologically: looked for Higgs, so found a Higgs
– CP-even spin-0 scalar expectedspin-1 vector unlikelyspin-2 graviton unexpected
2. What are the coupling values?
– ‘coupling’ after fixing operator basis
– Standard Model Higgs vs anomalous couplings
3. What does all this tell us?
– models predicting weak-scale new physics?
– renormalization group based Hail-Mary passes?
![Page 23: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/23.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
cos θe = pe− · pZµ
∣∣∣Ze
cos θµ = pµ− · pZe
∣∣∣Zµ
cos θ∗ = pZe · pbeam
∣∣∣X
cosφe = (pbeam × pZµ ) · (pZµ × pe− )∣∣∣
Ze
cos ∆φ = (pe− × pe+ ) · (pµ− × pµ+ )∣∣∣
X
µ
µ+j↵
j`
h
X
Z Z
p
p
ez
ez0
?
1
p
p
W ±, Z
W !, ZH
(")
q(")
Q
(")
q#(")
Q#
!, Z
Z, !H
(")
q(")
Q
(")
q#(")
Q#
g
gH
(")
q(")
q
(")
q#(")
q#
g
gH
(")
q(")
q
g
gg
g H
g
g
g
g W±,Z
W!,ZH
(")
q(")
Q
(")
q#(")
Q#
!,Z
Z,!H
(")
q(")
Q
(")
q#(")
Q#
g
gH
(")
q(")
q
(")
q#(")
q#
g
gH
(")
q(")
q
g
gg
gH
g
g
g
g
e
e+
µ+
µµ
e
e
![Page 24: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/24.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
cos θe = pe− · pZµ
∣∣∣Ze
cos θµ = pµ− · pZe
∣∣∣Zµ
cos θ∗ = pZe · pbeam
∣∣∣X
cosφe = (pbeam × pZµ ) · (pZµ × pe− )∣∣∣
Ze
cos ∆φ = (pe− × pe+ ) · (pµ− × pµ+ )∣∣∣
X
µ
µ+j↵
j`
h
X
Z Z
p
p
ez
ez0
?
1
p
p
W ±, Z
W !, ZH
(")
q(")
Q
(")
q#(")
Q#
!, Z
Z, !H
(")
q(")
Q
(")
q#(")
Q#
g
gH
(")
q(")
q
(")
q#(")
q#
g
gH
(")
q(")
q
g
gg
g H
g
g
g
g W±,Z
W!,ZH
(")
q(")
Q
(")
q#(")
Q#
!,Z
Z,!H
(")
q(")
Q
(")
q#(")
Q#
g
gH
(")
q(")
q
(")
q#(")
q#
g
gH
(")
q(")
q
g
gg
gH
g
g
g
g
e
e+
µ+
µµ
e
e
![Page 25: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/25.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
– Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like]
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
![Page 26: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/26.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
– Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like]
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
cos θ1 = pj1 · pV2
∣∣∣V1Breit
cos θ2 = pj2 · pV1
∣∣∣V2Breit
cos θ∗ = pV1 · pd
∣∣∣X
cosφ1 = (pV2 × pd ) · (pV2 × pj1 )∣∣∣
V1Breit
cos ∆φ = (pq1 × pj1 ) · (pq2 × pj2 )∣∣∣
X.
W±,Z
W!,Z
H
(")
q
(")
Q (")
q#
(")
Q#
!,ZZ,!
H
(")
q
(")
Q (")
q#
(")
Q#
g
g
H
(")
q
(")
q (")
q#
(")
q#
g
g
H
(")
q
(")
q g
g
g
g
H
g
g
g
g
W±
,Z W!
,Z
H
(") q
(") Q
(") q#
(") Q#
!,Z
Z,!
H
(") q
(") Q
(") q#
(") Q#
g
g
H
(") q
(") q
(") q#
(") q#
g
g
H
(") q
(") q
g
g
g
g
H
g
gg
g
1
2
j1
j2
V1
V2
d
?
![Page 27: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/27.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
– Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like]
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
– possible scalar couplings
L ⊃ (φ†φ)WµWµ1
Λ2(φ†φ)WµνWµν
1Λ2
(φ†φ)εµνρσWµνWρσ
⇒ different channels, same physics
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
Γ d∆φ1 dΓ
0-
D5
0+
D5
0+
SM
2+
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
σ d∆φ1 dσ
0-
D5
0+
D5
0+
SM
2+
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
σ d∆φjj
1 dσ
0-
D5
0+
D5
0+
SM
2+
![Page 28: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/28.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Lagrangian
Angular correlations
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Englert, Spannowsky, Takeuchi]
– Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like]
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
– possible scalar couplings
L ⊃ (φ†φ)WµWµ1
Λ2(φ†φ)WµνWµν
1Λ2
(φ†φ)εµνρσWµνWρσ
⇒ different channels, same physics
![Page 29: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/29.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Couplings
Standard-Model-inspired model
– assume: narrow CP-even scalarStandard Model operatorscouplings proportional to masses?
– couplings from production & decay rates
t W,Z
b,tW,Z
gg → Hqq → qqHgg → t tHqq′ → VH
←→ gHXX = gSMHXX (1 + ∆X ) ←→
H → ZZH → WWH → bbH → τ+τ−
H → γγ
![Page 30: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/30.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Couplings
Standard-Model-inspired model
– assume: narrow CP-even scalarStandard Model operatorscouplings proportional to masses?
– couplings from production & decay rates
t W,Z
b,tW,Z
gg → Hqq → qqHgg → t tHqq′ → VH
←→ gHXX = gSMHXX (1 + ∆X ) ←→
H → ZZH → WWH → bbH → τ+τ−
H → γγ
⇒ almost too exactly the prediction of 1964?
-0.5
0
0.5
1
∆H
∆V
∆f
∆W
∆Z
∆t
∆b
∆τ
∆γ
∆Z/W
∆τ/b
∆b/W
gx = gxSM
(1+∆x)
L=4.6-5.1(7 TeV)+12-21(8 TeV) fb-1
, 68% CL: ATLAS + CMS
SM exp.
data
data (+∆γ)
Moriond 2013
![Page 31: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/31.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Meaning
TeV-scale scenarios
– fourth chiral generation excluded
– strongly interacting models retreating [Goldstone protection]
– extended Higgs sectors wide open
– no final verdict on the MSSM
– hierarchy problem worse than ever [light fundemental scalar discovered]
⇒ do not know
![Page 32: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/32.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Meaning
TeV-scale scenarios
– fourth chiral generation excluded
– strongly interacting models retreating [Goldstone protection]
– extended Higgs sectors wide open
– no final verdict on the MSSM
– hierarchy problem worse than ever [light fundemental scalar discovered]
⇒ do not know
High scales
– Planck-scale extrapolation [Holthausen, Lim, Lindner]
d λd log Q2
=1
16π2
[12λ2 + 6λλ2
t − 3λ4t −
32λ(
3g22 + g2
1
)+
316
(2g4
2 + (g22 + g2
1 )2)]
– vacuum stability right at edge
– IR fixed point for λ/λ2t fixing m2
H/m2t [with gravity: Shaposhnikov, Wetterich]
mH = 126.3+mt − 171.2
2.1×4.1−αs − 0.1176
0.002×1.5
⇒ do not know
![Page 33: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/33.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Fox-Wolfram moments
Weighted series in spherical harmonics [Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
HT` =
4π2` + 1
∑m=−`
∣∣∣∣∣N∑
i=1
Y m` (Ωi )
pT ,i
pT ,tot
∣∣∣∣∣2
=N∑
i,j=1
pT ,i pT ,j
p2T ,tot
P`(cos Ωij )
–
– tunable for forward jets
r
00.10.2
0.30.40.50.6
0.70.80.91]π[Ω
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1H
r
00.10.2
0.30.40.50.6
0.70.80.91]π[Ω
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
4H
r
00.10.2
0.30.40.50.6
0.70.80.91]π[Ω
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
5H
r
00.10.2
0.30.40.50.6
0.70.80.91]π[Ω
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
19H
H` < 0.3 0.3 < H` < 0.7 0.7 < H` < 1even ` forbidden democratic ordered, collinear, back-to-backodd ` back-to-back democratic collinear, ordered
![Page 34: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/34.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Fox-Wolfram moments
Weighted series in spherical harmonics [Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
HT` =
4π2` + 1
∑m=−`
∣∣∣∣∣N∑
i=1
Y m` (Ωi )
pT ,i
pT ,tot
∣∣∣∣∣2
=N∑
i,j=1
pT ,i pT ,j
p2T ,tot
P`(cos Ωij )
–
– tunable for forward jets
– applied to tagging jets in WBF [mjj > 600 GeV]
0 0.2 0.4 0.6 0.8 10
0.005
0.01
0.015
0.02
T3H
T3dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.02
0.04
0.06
T4H
T4dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.005
0.01
0.015
0.02
T8H
T8dH
dN N1
![Page 35: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/35.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Fox-Wolfram moments
Weighted series in spherical harmonics [Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
HT` =
4π2` + 1
∑m=−`
∣∣∣∣∣N∑
i=1
Y m` (Ωi )
pT ,i
pT ,tot
∣∣∣∣∣2
=N∑
i,j=1
pT ,i pT ,j
p2T ,tot
P`(cos Ωij )
– tunable for forward jets
– applied to tagging jets in WBF [mjj > 600 GeV]
– applied to all jets in WBF
0 0.2 0.4 0.6 0.8 10
0.005
0.01
0.015
0.02
T3H
T3dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.02
0.04
0.06
T4H
T4dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.005
0.01
0.015
0.02
T8H
T8dH
dN N1
![Page 36: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/36.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Fox-Wolfram moments
Weighted series in spherical harmonics [Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
HT` =
4π2` + 1
∑m=−`
∣∣∣∣∣N∑
i=1
Y m` (Ωi )
pT ,i
pT ,tot
∣∣∣∣∣2
=N∑
i,j=1
pT ,i pT ,j
p2T ,tot
P`(cos Ωij )
– tunable for forward jets
– applied to tagging jets in WBF [mjj > 600 GeV]
– applied to all jets in WBF
– applied to all jets after WBF cuts
0 0.2 0.4 0.6 0.8 10
0.01
0.02
T3H
T3dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.02
0.04
0.06
T4H
T4dH
dN N1
0 0.2 0.4 0.6 0.8 10
0.005
0.01
0.015
0.02
T8H
T8dH
dN N1
![Page 37: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/37.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Fox-Wolfram moments
Weighted series in spherical harmonics [Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
HT` =
4π2` + 1
∑m=−`
∣∣∣∣∣N∑
i=1
Y m` (Ωi )
pT ,i
pT ,tot
∣∣∣∣∣2
=N∑
i,j=1
pT ,i pT ,j
p2T ,tot
P`(cos Ωij )
– tunable for forward jets
– applied to tagging jets in WBF [mjj > 600 GeV]
– applied to all jets in WBF
– applied to all jets after WBF cuts
⇒ might be useful, bachelor project!
![Page 38: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/38.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments
Exciting times...
...for LHC physicists
– Higgs discovery after almost 50 years [waiting since Fermi]
– detailed studies just starting
– all open physics territory
– many Higgs analysis challenges ahead
– technical expertize the key
– QCD always helpful
⇒ young and bright ideas in high demand
Lectures on LHC Physics, Springer, arXiv:0910.4182 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
![Page 39: A Theorist's Take on Higgs Physics - thphys.uni-heidelberg.deplehn/includes/talks/2013/nordic_13.pdf · cc _ gg WW ZZ tt-## Z# M H [ GeV] 1000 10-3 10-2 10-1 1. Higgs Physics Tilman](https://reader030.fdocuments.in/reader030/viewer/2022041204/5d55b7b188c993ce518b745b/html5/thumbnails/39.jpg)
Higgs Physics
Tilman Plehn
Weak interaction
Higgs boson
Discovery
Lagrangian
Couplings
Meaning
FW moments