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

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

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 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

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

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

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

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

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 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 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

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

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

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

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

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...

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]

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’

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’

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

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

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?

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

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

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]

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

?

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+

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

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

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

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

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

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

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

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

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

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!

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

Higgs Physics

Tilman Plehn

Weak interaction

Higgs boson

Discovery

Lagrangian

Couplings

Meaning

FW moments