Higgs Physics
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Random Thoughts about Higgs Measurements
Meaning
Tilman Plehn
Universität Heidelberg
Sussex, June 2014
Higgs Physics
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive gauge bosons have 3 polarizations, and 3 6= 2
Higgs Physics
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive gauge bosons have 3 polarizations, and 3 6= 2
Meaning
Higgs-related papers
[also Brout & Englert; Guralnik, Hagen, Kibble]
– 1964: combining two problems to one predictive solution
Higgs Physics
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive 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
Higgs boson
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Two problems for spontaneous gauge symmetry breaking
– problem 1: Goldstone’s theorem
SU(2)L × U(1)Y → U(1)Q gives 3 massless scalars
– problem 2: massive gauge theories
massive gauge bosons have 3 polarizations, and 3 6= 2
Meaning
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 based on field theory
Higgs Physics
Questions
Tilman Plehn
Higgs boson
1. What is the ‘Higgs’ Lagrangian?
Questions
– psychologically: looked for Higgs, so found a Higgs
Couplings
– CP-even spin-0 scalar expected, which operators?
spin-1 vector unlikely
spin-2 graviton unexpected
ggH vertex
MadMax
BSM
Meaning
– ask flavor colleagues
[Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles]
Higgs Physics
Questions
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
1. What is the ‘Higgs’ Lagrangian?
– psychologically: looked for Higgs, so found a Higgs
– CP-even spin-0 scalar expected, which operators?
spin-1 vector unlikely
spin-2 graviton unexpected
– ask flavor colleagues
[Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles]
Meaning
2. What are the coupling values?
– ‘coupling’ after fixing operator basis
– Standard Model Higgs vs anomalous couplings
Higgs Physics
Questions
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
1. What is the ‘Higgs’ Lagrangian?
– psychologically: looked for Higgs, so found a Higgs
– CP-even spin-0 scalar expected, which operators?
spin-1 vector unlikely
spin-2 graviton unexpected
– ask flavor colleagues
[Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles]
Meaning
2. What are the coupling values?
– ‘coupling’ after fixing operator basis
– Standard Model Higgs vs anomalous couplings
3. What does all this tell us?
– strongly interacting models?
– weakly interacting two-Higgs-doublet models?
– TeV-scale new physics?
Higgs Physics
Couplings
t
W,Z
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Standard Model operators
[SFitter: Klute, Lafaye, TP, Rauch, Zerwas]
– assume: narrow CP-even scalar
Standard Model operators
couplings proportional to masses?
b,t
W,Z
– couplings from production & decay rates
BSM
Meaning
gg → H
qq → qqH
gg → t t̄H
qq 0 → VH
←→
gHXX =
SM
gHXX
(1 + ∆X )
←→
H
H
H
H
H
→
→
→
→
→
ZZ
WW
bb̄
τ +τ −
γγ
Higgs Physics
Couplings
t
W,Z
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Standard Model operators
[SFitter: Klute, Lafaye, TP, Rauch, Zerwas]
– assume: narrow CP-even scalar
Standard Model operators
couplings proportional to masses?
b,t
W,Z
– couplings from production & decay rates
BSM
Meaning
gg → H
qq → qqH
gg → t t̄H
qq 0 → VH
←→
gHXX =
SM
gHXX
(1 + ∆X )
H
H
H
H
H
←→
→
→
→
→
→
Total width
– non-trivial scaling
gp2
g2
N = σ BR ∝ √
√d ∼
Γtot
Γtot
gives constraint from
P
g4
P
g2
Γi (g 2 )
+ Γunobs
g2
Γi (g 2 ) < Γtot → ΓH |min
SM
– WW → WW unitarity: gWWH . gWWH
→ ΓH |max [HiggsSignals]
P
– SFitter assumption Γtot = obs Γj [plus generation universality]
g 2 →0
−→ = 0
ZZ
WW
bb̄
τ +τ −
γγ
Higgs Physics
Couplings now and in the future
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Now
[Aspen/Moriond 2013; Lopez-Val, TP, Rauch; Cranmer, Kreiss, Lopez-Val, TP]
– focus SM-like
[secondary solutions possible]
– SFitter: correct theory uncertainties
L=4.6-5.1(7 TeV)+12-21(8 TeV) fb-1, 68% CL: ATLAS + CMS
Moriond 2013
– gg vs gt not yet possible
[similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal]
– poor man’s analyses: ∆H , ∆V , ∆f
⇒ six couplings and ratios from data
SM
gx = gx
SM exp.
data
data (+∆γ)
1
(1+∆x)
0.5
0
-0.5
b
/W
∆b
/W
∆ τ/
∆Z
∆γ
∆τ
∆b
∆t
∆Z
∆W
∆f
∆V
∆H
Higgs Physics
Couplings now and in the future
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Now
[Aspen/Moriond 2013; Lopez-Val, TP, Rauch; Cranmer, Kreiss, Lopez-Val, TP]
– focus SM-like
[secondary solutions possible]
– SFitter: correct theory uncertainties
– gg vs gt not yet possible
[similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal]
– poor man’s analyses: ∆H , ∆V , ∆f
⇒ six couplings and ratios from data
Future
– LHC extrapolations unclear
– interplay in loop-induced couplings
68% CL: 3000 fb-1, 14 TeV LHC and 500 fb-1, 500 GeV LC
0.2
0.15
3000 fb-1, 14 TeV LHC
500 fb-1, 500 GeV LC
HL-LHC + LC500
HL-LHC + LC500 (∆t ≠ ∆c)
gx = gSM
x (1+∆x)
0.1
0.05
0
-0.05
-0.1
-0.15
∆g
∆γ
∆τ
∆b
∆c
∆t
∆Z
∆W
∆H
Higgs Physics
Couplings now and in the future
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Now
[Aspen/Moriond 2013; Lopez-Val, TP, Rauch; Cranmer, Kreiss, Lopez-Val, TP]
– focus SM-like
[secondary solutions possible]
– SFitter: correct theory uncertainties
– gg vs gt not yet possible
[similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal]
– poor man’s analyses: ∆H , ∆V , ∆f
⇒ six couplings and ratios from data
Future
– LHC extrapolations unclear
– interplay in loop-induced couplings
– theory correlations protecting ratios?
68% CL: 14 TeV
0.25
0.2
gx = gSM
x (1+∆x)
3000 fb-1 uncorr. theory errors
3000 fb-1 corr. theory errors
-1
3000 fb no theory errors
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
b
/W
∆b
/W
∆ τ/
∆Z
∆g
∆γ
∆τ
∆b
∆t
∆Z
∆W
Higgs Physics
Couplings now and in the future
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Now
[Aspen/Moriond 2013; Lopez-Val, TP, Rauch; Cranmer, Kreiss, Lopez-Val, TP]
– focus SM-like
[secondary solutions possible]
– SFitter: correct theory uncertainties
– gg vs gt not yet possible
[similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal]
– poor man’s analyses: ∆H , ∆V , ∆f
⇒ six couplings and ratios from data
Future
– LHC extrapolations unclear
– interplay in loop-induced couplings
– theory correlations protecting ratios?
– obvious ILC case:
unobserved decays avoided
width measured from rates including σZH
H → c c̄ accessible
invisible decays hugely improved
QCD theory error bars avoided
Higgs Physics
Resolving the ggH vertex
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Non–pointlike-ness of ggH vertex
– loop–induced coupling
[Ellis, Hinchliffe, Soldate, v d Bij; Baur & Glover]
[τ = 4mt2 /m2 ]
H
αs
H
µν
G Gµν
τ [1 + (1 − τ )f (τ )]
v
8π
r !2
1
1
τ →∞ 1
on-shell
=
+
f (τ ) =
arcsin
τ
τ
3τ 2
LggH ⊃ −i
Meaning
– start with absorptive imaginary parts of loop integrals
[like thresholds]
Higgs Physics
Resolving the ggH vertex
Tilman Plehn
Higgs boson
Questions
Non–pointlike-ness of ggH vertex
– loop–induced coupling
Couplings
ggH vertex
[Ellis, Hinchliffe, Soldate, v d Bij; Baur & Glover]
[τ = 4mt2 /m2 ]
H
αs
H
µν
G Gµν
τ [1 + (1 − τ )f (τ )]
v
8π
r !2
1
1
τ →∞ 1
on-shell
=
+
f (τ ) =
arcsin
τ
τ
3τ 2
LggH ⊃ −i
MadMax
BSM
Meaning
– start with absorptive imaginary parts of loop integrals
10
dσ
dmHj
HEFT
SM
HEFTgq
SMgq
fb
GeV
10
[like thresholds]
dσ
dmHjj
HEFT
SM
HEFTqq
SMqq
fb
GeV
1
1.1280
300
320
340
360
380
SM/HEFT
400
420
440
460
10-1
280
300
320
340
360
380
SM/HEFT
400
420
440
460
1
1
0.8
0.9
300
350
400
450
mHj [GeV]
300
350
400
450
mHjj [GeV]
Higgs Physics
Resolving the ggH vertex
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Non–pointlike-ness of ggH vertex
– loop–induced coupling
[Ellis, Hinchliffe, Soldate, v d Bij; Baur & Glover]
[τ = 4mt2 /m2 ]
H
αs
H
µν
G Gµν
τ [1 + (1 − τ )f (τ )]
v
8π
r !2
1
1
τ →∞ 1
on-shell
=
+
f (τ ) =
arcsin
τ
τ
3τ 2
LggH ⊃ −i
Meaning
– start with absorptive imaginary parts of loop integrals
– high-pT logarithmic structure instead
2
[like thresholds]
[Banfi etal; Azatov etal; Grojean etal]
4
4
|MHj | ∝ mt log
pT2
mt2
Higgs Physics
Resolving the ggH vertex
Tilman Plehn
Higgs boson
Questions
Non–pointlike-ness of ggH vertex
– loop–induced coupling
Couplings
[Ellis, Hinchliffe, Soldate, v d Bij; Baur & Glover]
[τ = 4mt2 /m2 ]
H
αs
H
µν
G Gµν
τ [1 + (1 − τ )f (τ )]
v
8π
r !2
1
1
τ →∞ 1
on-shell
=
+
f (τ ) =
arcsin
τ
τ
3τ 2
LggH ⊃ −i
ggH vertex
MadMax
BSM
Meaning
– start with absorptive imaginary parts of loop integrals
– high-pT logarithmic structure instead
Higher multiplicity, more logs?
[Buschmann, Englert, Golcalves, TP, Spannowsky]
– check mjj , pz in Hjj production, nothing...
– instead same as Hj process
2
|MHjj | ∝
[like thresholds]
[Banfi etal; Azatov etal; Grojean etal]
2
2
m4
mt4
4 p
4 Q
∼ 4t log T2
log
Q4
mt2
pT
mt
Higgs Physics
Resolving the ggH vertex
Tilman Plehn
Higgs boson
Questions
Non–pointlike-ness of ggH vertex
– loop–induced coupling
[Ellis, Hinchliffe, Soldate, v d Bij; Baur & Glover]
[τ = 4mt2 /m2 ]
H
αs
H
µν
G Gµν
τ [1 + (1 − τ )f (τ )]
v
8π
r !2
1
1
on-shell
τ →∞ 1
f (τ ) =
arcsin
=
+
τ
τ
3τ 2
Couplings
LggH ⊃ −i
ggH vertex
MadMax
BSM
Meaning
– start with absorptive imaginary parts of loop integrals
– high-pT logarithmic structure instead
Higher multiplicity, more logs?
[Buschmann, Englert, Golcalves, TP, Spannowsky]
– check mjj , pz in Hjj production, nothing...
– instead same as Hj process
2
|MHjj | ∝
[like thresholds]
[Banfi etal; Azatov etal; Grojean etal]
2
2
mt4
m4
4 Q
4 p
log
∼ 4t log T2
Q4
mt2
pT
mt
– Hjj most promising with H → WW
⇒ Hjj with more events in relevant regime
[fb/GeV]
MCFM Hj inclusive
dσtt/dpT,H
dσtg/dpT,H
dσgg/dp
10-1
T,H
VBFNLO Hjj inclusive
dσtt/dp
T,H
dσtg/dpT,H
dσgg/dpT,H
10-2
10-3
10-4
10-5
0
200
400
600
800
p
T,H
1000
[GeV]
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Modern analyses vs phase space
– hardly any counting experiments left
[NN or BDT output instead]
– theory uncertainties increasingly relevant
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Modern analyses vs phase space
– hardly any counting experiments left
[NN or BDT output instead]
– theory uncertainties increasingly relevant
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Meaning
Differential significance distribution
[TP, Schichtel, Wiegand]
– Neyman–Pearson lemma
log-likelihood ratio the best discriminator
– maximum significance through PS integral
[Cranmer & TP]
q(r ) = −σtot,s L + log
– evaluated in parallel to cross sections
1+
dσs (r )
dσb (r )
[in Madgraph]
– translated into significance via LEPStats4LHC
[Cranmer etal]
.
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Modern analyses vs phase space
Questions
– hardly any counting experiments left
Couplings
– theory uncertainties increasingly relevant
ggH vertex
MadMax
BSM
[NN or BDT output instead]
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Meaning
– pT ,bb distributions
pb
10 GeV
– modern analyses imminent
T,bb
– boosted Higgs the key
[same for t t̄H]
dσ
dp
Link to Higgs couplings: ZH, H → bb̄
10-1
s = 14TeV
10-2
QCD
-3
10
ZH
10-4
-5
10
QED
-6
10
0
50
100
150
200 250
pT,bb GeV
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Modern analyses vs phase space
Questions
– hardly any counting experiments left
Couplings
– theory uncertainties increasingly relevant
ggH vertex
MadMax
BSM
[NN or BDT output instead]
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Meaning
– modern analyses imminent
– pT ,bb distributions
2
1
50 GeV
– boosted Higgs the key
[same for t t̄H]
significance
Link to Higgs couplings: ZH, H → bb̄
L = 50 fb-1
s = 14TeV
1.5
1
0.5
- 20% background
ZH
+ 20% background
0
0
100
200
300
400
pT,bb GeV
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Modern analyses vs phase space
Questions
– hardly any counting experiments left
Couplings
– theory uncertainties increasingly relevant
ggH vertex
MadMax
BSM
[NN or BDT output instead]
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Meaning
– boosted Higgs the key
– modern analyses imminent
– pT ,bb distributions
[same for t t̄H]
pb
dσ
dR bb 0.2
Link to Higgs couplings: ZH, H → bb̄
10-1
s = 14TeV
QCD
10-2
– Rbb distributions
-3
10
ZH
10-4
QED
-5
10
1
2
3
4
5
6
Rbb
Higgs Physics
MadMax-imizing theory understanding
Tilman Plehn
Higgs boson
Modern analyses vs phase space
Questions
– hardly any counting experiments left
Couplings
– theory uncertainties increasingly relevant
ggH vertex
MadMax
BSM
[NN or BDT output instead]
– relevant information still (mostly) in hard process
⇒ how do we understand experimental results?
Meaning
– modern analyses imminent
– pT ,bb distributions
– Rbb distributions
⇒ poor man’s MEM at parton level
2
1
50 GeV
– boosted Higgs the key
[same for t t̄H]
significance
Link to Higgs couplings: ZH, H → bb̄
L = 50 fb-1
s = 14TeV
1.5
1
0.5
- 20% background
ZH
+ 20% background
0
0
2
4
6
Rbb
Higgs Physics
2HDM as weakly interacting completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Extended Higgs models
[Lopez-Val, TP, Rauch; many, many, many papers, ask Dr No]
– assume the Higgs really is ‘a Higgs’
– allow for coupling modifications
⇒ how would 2HDMs look?
BSM
Meaning
i
h
2
2
2
Φ†1 Φ2 + h.c.
Φ†2 Φ2 − m12
Φ†1 Φ1 + m22
V (Φ1 , Φ2 ) = m11
λ1
λ2
(Φ†1 Φ1 )2 +
(Φ†2 Φ2 )2 + λ3 (Φ†1 Φ1 ) (Φ†2 Φ2 ) + λ4 |Φ†1 Φ2 |2
2
2
λ5
+
(Φ†1 Φ2 )2 + λ6 (Φ†1 Φ1 ) (Φ†1 Φ2 ) + λ7 (Φ†2 Φ2 ) (Φ†1 Φ2 ) + h.c.
2
+
Higgs Physics
2HDM as weakly interacting completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Extended Higgs models
[Lopez-Val, TP, Rauch; many, many, many papers, ask Dr No]
– assume the Higgs really is ‘a Higgs’
– allow for coupling modifications
⇒ how would 2HDMs look?
BSM
Meaning
Physical parameters
– angle β = atan(v2 /v1 )
angle α defining h0 and H 0
SM
gauge boson coupling gW ,Z = sin(β − α)gW
,Z
– type-I: all fermions with Φ2
type-II: up-type fermions with Φ2
lepton-specific: type-I quarks and type-II leptons
flipped: type-II quarks and type-I leptons
√
Yukawa aligned: yb cos(β − γb ) = 2mb /v
– compressed masses mh0 ∼ mH 0 [thanks to Berthold Stech]
single hierarchy mh0 mH 0 ,A0 ,H ± protected by custodial symmetry
PQ-violating terms m12 and λ6,7
Higgs Physics
2HDM as weakly interacting completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Extended Higgs models
[Lopez-Val, TP, Rauch; many, many, many papers, ask Dr No]
– assume the Higgs really is ‘a Higgs’
– allow for coupling modifications
⇒ how would 2HDMs look?
BSM
Meaning
Facing data
– fit including single heavy Higgs mass
– decoupling regime sin2 α ∼ 1/(1 + tan2 β)
⇒ 2HDMs generally good fit, but decoupling heavy Higgs
type-I
type-II
lepton–specific
flipped
Higgs Physics
2HDM as a consistent UV completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
How to think of SFitter coupling results
– ∆x 6= 0 violating renormalization, unitarity,...
– weak UV theory experimentally irrelevant, only QCD matters
theoretically (supposedly) of great interest
– EFT approach:
(1) define consistent 2HDM, decouple heavy states
(2) fit 2HDM model parameters, plot range of SM couplings
(3) compare to free SM couplings fit
Higgs Physics
2HDM as a consistent UV completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
How to think of SFitter coupling results
– ∆x 6= 0 violating renormalization, unitarity,...
– weak UV theory experimentally irrelevant, only QCD matters
theoretically (supposedly) of great interest
– EFT approach:
(1) define consistent 2HDM, decouple heavy states
(2) fit 2HDM model parameters, plot range of SM couplings
(3) compare to free SM couplings fit
Yukawa-aligned 2HDM
– ∆V ↔ (β − α)
∆b,t,τ ↔ {β, γb,τ }
∆γ ↔ mH ±
– ∆g not free parameter, top partner?
custodial symmetry built in at tree level ∆V < 0
– Higgs-gauge quantum corrections
enhanced ∆V < 0
– fermion quantum corrections
large for tan β 1
∆W 6= ∆Z > 0 possible
Higgs Physics
2HDM as a consistent UV completion
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
How to think of SFitter coupling results
– ∆x 6= 0 violating renormalization, unitarity,...
– weak UV theory experimentally irrelevant, only QCD matters
theoretically (supposedly) of great interest
– EFT approach:
(1) define consistent 2HDM, decouple heavy states
(2) fit 2HDM model parameters, plot range of SM couplings
(3) compare to free SM couplings fit
UV-complete vs SM coupling fits
– 2HDM close to perfect at tree level
– ∆W 6= ∆Z > 0 through loops
⇒ free SM couplings well defined
0.8
measured data
direct fit
direct fit (∆V<0)
aligned 2HDM
aligned 2HDM (constr.)
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
∆γ
∆τ
∆b
∆t
∆V
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
gV
ξ2
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
SM
2
2
gV
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
gV
ξ2
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
SM
2
2
gV
– dark singlet
Γinv = ξ 2 ΓSM
µp,d =
ΓSM
= 1 − ξ 2 + O(ξ 3 ) < 1
ΓSM + Γinv
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
gV
ξ2
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
SM
2
2
gV
– dark singlet
Γinv = ξ 2 ΓSM
– mixing singlet
µp,d =
ΓSM
= 1 − ξ 2 + O(ξ 3 ) < 1
ΓSM + Γinv
[Jose’s portal, no anomalous decays]
1 + ∆x = cos θ =
q
1 − ξ2
µp,d = 1 − ξ 2 + O(ξ 3 ) < 1
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
gV
ξ2
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
SM
2
2
gV
– dark singlet
Γinv = ξ 2 ΓSM
– mixing singlet
µp,d =
ΓSM
= 1 − ξ 2 + O(ξ 3 ) < 1
ΓSM + Γinv
[Jose’s portal, no anomalous decays]
1 + ∆x = cos θ =
– composite Higgs
v
ξ=
f
q
1 − ξ2
µWBF,d
=
µGF,d
µp,d = 1 − ξ 2 + O(ξ 3 ) < 1
(1 − ξ 2 )2
(1 − 2ξ 2 )2
= 1 + 2ξ 2 + O(ξ 3 ) > 1
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
gV
ξ2
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
SM
2
2
gV
– dark singlet
Γinv = ξ 2 ΓSM
– mixing singlet
µp,d =
ΓSM
= 1 − ξ 2 + O(ξ 3 ) < 1
ΓSM + Γinv
[Jose’s portal, no anomalous decays]
1 + ∆x = cos θ =
– composite Higgs
v
ξ=
f
– additional doublet
q
1 − ξ2
µWBF,d
=
µGF,d
[type-X fermion sector]
1 + ∆V = sin(β − α) =
q
1 − ξ2
µp,d = 1 − ξ 2 + O(ξ 3 ) < 1
(1 − ξ 2 )2
(1 − 2ξ 2 )2
= 1 + 2ξ 2 + O(ξ 3 ) > 1
Higgs Physics
Similar models
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
One-dimensional description of signal strengths Γp,d
[Cranmer, Kreiss, Lopez-Val, TP]
– decoupling defined through the massive gauge sector
ξ2
ξ2
gV
=1−
+ O(ξ 3 )
⇔
∆V = −
+ O(ξ 3 )
2
2
gVSM
– dark singlet
Γinv = ξ 2 ΓSM
Meaning
– mixing singlet
µp,d =
[Jose’s portal, no anomalous decays]
1 + ∆x = cos θ =
– composite Higgs
v
ξ=
f
– additional doublet
q
2
ξ ='
µp,d = 1 − ξ 2 + O(ξ 3 ) < 1
1 − ξ2
µWBF,d
=
µGF,d
(1 − ξ 2 )2
(1 − 2ξ 2 )2
[type-X fermion sector]
1 + ∆V = sin(β − α) =
– MSSM
q
1 − ξ2
[plus tan β]
mh2 (mZ2 − mh2 )
2
mA2 (mH
ΓSM
= 1 − ξ 2 + O(ξ 3 ) < 1
ΓSM + Γinv
−
mh2 )
∼
mZ4 sin2 (2β)
mA4
= 1 + 2ξ 2 + O(ξ 3 ) > 1
Higgs Physics
Extended Higgs sectors
Tilman Plehn
Questions
Couplings
ggH vertex
Effect on signal strengths
– decay–diagonal and production–diagonal correlations
– new physics scenarios in 2 dimensions
MadMax
2
ξ < 0.4
ξ = 0.2
ξ < 0.4
ξ = 0.2
Meaning
2
2
ξ < 0.4
BSM
ξ = 0.2
1.5
MSSM
1.5
1.5
2HDM II
2HDM II
1
MCHM5
µVV
VBF
µγγ
VBF
MCHM5
singlet
µττ
VBF
Higgs boson
1
singlet
1
2HDM I
2HDM I
MSSM
0.5
0.5
MSSM
0.5
2HDM I
0
0
singlet
MCHM5
0.5
1
1.5
µγγ
GF
2
0
0
0.5
1
1.5
µVV
GF
2
0
0
2HDM II
0.5
1
1.5
µττ
GF
2
Higgs Physics
Extended Higgs sectors
Tilman Plehn
Higgs boson
Effect on signal strengths
Questions
– decay–diagonal and production–diagonal correlations
Couplings
– new physics scenarios in 2 dimensions
ggH vertex
2
MadMax
2
2
ξ = 0.2
ξ = 0.2
1.5
Meaning
ξ < 0.4
ξ = 0.2
ξ < 0.4
ξ < 0.4
BSM
MSSM
1.5
1.5
2HDM II
2HDM II
MCHM5
singlet
µττ
VBF
1
µVV
VBF
µγγ
VBF
MCHM5
1
singlet
singlet
1
2HDM I
MSSM
0.5
0.5
MSSM
0.5
2HDM II
2HDM I
0.5
1
1.5
µγγ
GF
2
0
0
– theory uncertainties with direction
⇒ robustness measure
0.5
1
1.5
µVV
GF
0
0
2
Ri(ξ)
0
0
2HDM I
MCHM5
2
1
0.5
singlet
MCHM5
2HDM I
2HDM II
MSSM (ξ x5)
1.5
µττ
GF
2
QCD scale ggF inclusive
QCD scale ggF ≥ 2 jets
1
0
-1
-2
H → WW* → lν lν
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
ξ
Higgs Physics
Meaning
Tilman Plehn
Higgs boson
TeV scale
Questions
– fourth chiral generation excluded
Couplings
– strongly interacting models retreating
ggH vertex
MadMax
BSM
Meaning
[Goldstone protection]
– extended Higgs sectors wide open
– no final verdict on the MSSM
– hierarchy problem worse than ever
⇒ whatever...
[light fundemental scalar discovered]
Higgs Physics
Meaning
Tilman Plehn
Higgs boson
TeV scale
Questions
– fourth chiral generation excluded
Couplings
– strongly interacting models retreating
ggH vertex
– extended Higgs sectors wide open
MadMax
BSM
Meaning
[Goldstone protection]
– no final verdict on the MSSM
– hierarchy problem worse than ever
[light fundemental scalar discovered]
⇒ whatever...
High scales
– Planck-scale extrapolation
dλ
d log Q 2
[Holthausen, Lim, Lindner; Buttazo etal]
1
3 2
3 4
2
2
4
2
2
2 2
=
12λ + 6λλt − 3λt − λ 3g2 + g1 +
2g2 + (g2 + g1 )
16π 2
2
16
– vacuum stability right at edge
– λ = 0 at finite energy?
2 /m2
– IR fixed point for λ/λ2t fixing mH
t
[with gravity: Shaposhnikov, Wetterich]
mt − 171.2
αs − 0.1176
mH = 126.3 +
× 4.1 −
× 1.5
2.1
0.002
– IR fixed points phenomenological nightmare
⇒ whatever...
Higgs Physics
Exercise: top–Higgs renormalization group
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Running of coupling/mass ratios
[Wetterich]
Higgs self coupling and top Yukawa with stable zero IR solutions
dλ
1 2
2
4
=
12λ + 6λyt − 3yt
d log Q 2
16π 2
d yt2
9
4
=
y
d log Q 2
32π 2 t
Higgs Physics
Exercise: top–Higgs renormalization group
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
Running of coupling/mass ratios
[Wetterich]
Higgs self coupling and top Yukawa with stable zero IR solutions
d yt2
9
4
=
y
d log Q 2
32π 2 t
dλ
1 2
2
4
=
12λ + 6λyt − 3yt
d log Q 2
16π 2
MadMax
BSM
Meaning
running ratio R = λ/yt2
3λ
dR
!
2
=
8R + R − 2 = 0
d log Q 2
32π 2 R
⇔
R∗ =
√
65 − 1
' 0.44
16
Higgs Physics
Exercise: top–Higgs renormalization group
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
Running of coupling/mass ratios
[Wetterich]
Higgs self coupling and top Yukawa with stable zero IR solutions
d yt2
9
4
=
y
d log Q 2
32π 2 t
dλ
1 2
2
4
=
12λ + 6λyt − 3yt
d log Q 2
16π 2
MadMax
BSM
Meaning
running ratio R = λ/yt2
3λ
dR
!
2
=
8R + R − 2 = 0
d log Q 2
32π 2 R
⇔
numbers in the far infrared, better for Q ∼ v
λ
yt2
=
mH2 v 2 2
2
2v 2mt IR
=
mH2 2
4mt IR
= 0.44
⇔
R∗ =
√
65 − 1
' 0.44
16
mH mt IR
= 1.33
Higgs Physics
Questions
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
Big questions
– is it really the Standard Model Higgs?
– is there new physics outside the Higgs sector?
MadMax
BSM
Meaning
Small questions
– what are good alternative ‘Higgs’ test hypotheses?
– how can we improve the couplings fit precision?
– how can we measure the bottom Yukawa?
– how can we measure the top Yukawa?
– how can we measure the Higgs self coupling?
– how do we avoid theory dominating uncertainties
– can QCD really be fun?
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
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Higgs sector including dimension-6 operators
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
LD6 =
2
X
fi
Oi
2
Λ
i=1
with
O1 =
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Higgs sector including dimension-6 operators
Questions
Couplings
LD6 =
2
X
fi
Oi
2
Λ
i=1
with
O1 =
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
ggH vertex
MadMax
first operator, wave function renormalization
BSM
O1 =
Meaning
1
1
†
µ
†
2
µ
∂µ (φ φ) ∂ (φ φ)=
(H̃ + v ) ∂µ H̃ ∂ H̃
2
2
proper normalization of combined kinetic term
Lkin =
1
µ
∂µ H̃∂ H̃
2
2
1+
f1 v
Λ2
!
!
=
[LSZ]
1
µ
∂µ H ∂ H
2
s
⇔
H = H̃
1+
f1 v 2
Λ2
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Higgs sector including dimension-6 operators
Questions
Couplings
LD6 =
2
X
fi
Oi
2
Λ
i=1
with
O1 =
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
ggH vertex
MadMax
first operator, wave function renormalization
BSM
O1 =
Meaning
1
1
†
µ
†
2
µ
∂µ (φ φ) ∂ (φ φ)=
(H̃ + v ) ∂µ H̃ ∂ H̃
2
2
proper normalization of combined kinetic term
Lkin =
1
µ
∂µ H̃∂ H̃
2
2
1+
f1 v
Λ2
!
!
=
[LSZ]
1
µ
∂µ H ∂ H
2
s
⇔
H = H̃
1+
second operator, minimum condition to fix v

µ2
f2 µ4
µ2



−
+ O(Λ−4 ) = −
 −
v
2λ
8λ3 Λ2
2λ
=

2
2λΛ2


 − 2 + O(Λ0 )
f2
2
1+
f2 µ2
4λ2 Λ2
!
f1 v 2
Λ2
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
Higgs sector including dimension-6 operators
LD6 =
2
X
fi
Oi
Λ2
i=1
with
O1 =
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
first operator, wave function renormalization
MadMax
O1 =
BSM
Meaning
1
1
†
µ
†
2
µ
∂µ (φ φ) ∂ (φ φ)=
(H̃ + v ) ∂µ H̃ ∂ H̃
2
2
proper normalization of combined kinetic term
Lkin
1
µ
= ∂µ H̃∂ H̃
2
2
f1 v
1+ 2
Λ
!
[LSZ]
1
µ
= ∂µ H ∂ H
2
!
s
⇔
H = H̃
1+
second operator, minimum condition to fix v

µ2
f2 µ4
µ2



−
+ O(Λ−4 ) = −
 −
v
2λ
8λ3 Λ2
2λ
=

2
2λΛ2


 − 2 + O(Λ0 )
f2
2
1+
f2 µ2
4λ2 Λ2
!
physical Higgs mass
µ2 2
3 2 2
f2 15 4 2 !
m2 2
H̃ − λv H̃ − 2
v H̃ = − H H
2
2
Λ 24
2
!
f1 v 2
f2 v 2
2
2
mH = 2λv
1− 2 +
Λ
2Λ2 λ
Lmass = −
⇔
f1 v 2
Λ2
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Higgs sector including dimension-6 operators
Questions
Couplings
LD6 =
2
X
fi
Oi
2
Λ
i=1
with
O1 =
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
ggH vertex
MadMax
BSM
Meaning
Higgs self couplings momentum dependent
!
#
f1 v 2
2f2 v 4
2f1 v 2
3
µ
+
H
−
H
∂
H
∂
H
µ
2Λ2
3Λ2 mH2
Λ2 mH2
"
!
#
2
4
2
m
4f2 v
f1 v
4f1 v 2 2
4
µ
− H2
1− 2 + 2 2
H − 2 2 H ∂µ H∂ H .
8v
Λ
Λ mH
Λ mH
Lself = −
mH2
2v
"
1−
Higgs Physics
Exercise: what operators can do
Tilman Plehn
Higgs boson
Higgs sector including dimension-6 operators
Questions
Couplings
LD6 =
2
X
fi
Oi
2
Λ
i=1
O1 =
with
1
†
µ
†
∂µ (φ φ) ∂ (φ φ) ,
2
1 † 3
O2 = − (φ φ)
3
ggH vertex
MadMax
BSM
Meaning
Higgs self couplings momentum dependent
!
#
f1 v 2
2f2 v 4
2f1 v 2
3
µ
+
H
−
H
∂
H
∂
H
µ
2Λ2
3Λ2 mH2
Λ2 mH2
"
!
#
2
4
2
m
4f2 v
f1 v
4f1 v 2 2
4
µ
− H2
1− 2 + 2 2
H − 2 2 H ∂µ H∂ H .
8v
Λ
Λ mH
Λ mH
Lself = −
mH2
2v
"
1−
field renormalization, strong multi-Higgs interactions
H =
1+
f1 v 2
2Λ2
!
H̃ +
f1 v 2
f1
3
4
H̃ +
H̃ + O(H̃ )
2Λ2
6Λ2
Higgs Physics
Higher-dimensional operators
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Meaning
Light Higgs as a Goldstone boson
[Contino, Giudice, Grojean, Pomarol, Rattazzi, Galloway,...]
– strongly interacting models not looking like that
– light state if protected by Goldstone’s theorem
– interesting if v f < 4πf ∼ mρ
– adding specific D6 operator set
[Bardeen, Hill, Lindner]
[Georgi & Kaplan]
[little Higgs v ∼ g 2 f /(2π)]
Higgs Physics
Higher-dimensional operators
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Light Higgs as a Goldstone boson
[Contino, Giudice, Grojean, Pomarol, Rattazzi, Galloway,...]
– strongly interacting models not looking like that
– light state if protected by Goldstone’s theorem
– interesting if v f < 4πf ∼ mρ
[Bardeen, Hill, Lindner]
[Georgi & Kaplan]
[little Higgs v ∼ g 2 f /(2π)]
– adding specific D6 operator set
Meaning
←
→
cH µ † cT † ←
µ
† →
†
∂
H D µH
H H ∂µ H H + 2 H D H
2f 2
2f
cy yf †
c6 λ † 3
H H +
H H f̄L HfR + h.c.
− 2
2
f
f
→
→
icW g † i ←
icB g 0 † ←
µ
ν
i
µ
ν
+
H σ D H (D Wµν ) +
H D H (∂ Bµν )
2mρ2
2mρ2
LSILH =
+
icHW g
icHB g 0
µ
† i
ν
i
µ
†
ν
(D H) σ (D H)Wµν +
(D H) (D H)Bµν
2
2
16π f
16π 2 f 2
+
cγ g 0 2 g 2 †
cg gS2 yt2 †
µν
a
aµν
H HBµν B
+
H HGµν G
.
16π 2 f 2 gρ2
16π 2 f 2 gρ2
Higgs Physics
Higher-dimensional operators
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
BSM
Light Higgs as a Goldstone boson
[Contino, Giudice, Grojean, Pomarol, Rattazzi, Galloway,...]
– strongly interacting models not looking like that
– light state if protected by Goldstone’s theorem
– interesting if v f < 4πf ∼ mρ
[Bardeen, Hill, Lindner]
[Georgi & Kaplan]
[little Higgs v ∼ g 2 f /(2π)]
– adding specific D6 operator set
Meaning
←
→
cH µ † cT † ←
µ
† →
†
∂
H D µH
H H ∂µ H H + 2 H D H
f2
f
cy yf †
c6 † 3
H H +
H H f̄L HfR + h.c.
−
2
2
(3f )
f
→
→
icW † i ←
icB † ←
µ
ν
i
µ
ν
+
H σ D H (D Wµν ) +
H D H (∂ Bµν )
(16f )2
(16f )2
LSILH =
icHW
icHB
µ
†
ν
µ
† i
ν
i
(D H) (D H)Bµν
(D H) σ (D H)Wµν +
(16f )2
(16f 2 )
cγ
cg
†
µν
†
a
aµν
+
H HBµν B
+
H HGµν G
.
(256f )2
(256f )2
+
Higgs Physics
Higher-dimensional operators
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Light Higgs as a Goldstone boson
[Contino, Giudice, Grojean, Pomarol, Rattazzi, Galloway,...]
– strongly interacting models not looking like that
– light state if protected by Goldstone’s theorem
– interesting if v f < 4πf ∼ mρ
BSM
– adding specific D6 operator set
Meaning
– collider phenomenology of (H † H)
[Bardeen, Hill, Lindner]
[Georgi & Kaplan]
[little Higgs v ∼ g 2 f /(2π)]
Higgs Physics
Higher-dimensional operators
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
MadMax
Light Higgs as a Goldstone boson
[Contino, Giudice, Grojean, Pomarol, Rattazzi, Galloway,...]
– strongly interacting models not looking like that
– light state if protected by Goldstone’s theorem
– interesting if v f < 4πf ∼ mρ
BSM
– adding specific D6 operator set
Meaning
– collider phenomenology of (H † H)
Anomalous Higgs couplings
[Bardeen, Hill, Lindner]
[Georgi & Kaplan]
[little Higgs v ∼ g 2 f /(2π)]
[Hagiwara etal; Corbett, Eboli, Gonzales-Fraile, Gonzales-Garcia]
– assume Higgs is largely Standard Model
– additional higher-dimensional couplings
α s v fg
fWW †
†
µν
µν
(Φ Φ)Gµν G
+ 2 Φ Wµν W Φ
8π Λ2
Λ
fW
fB
fWWW
†
µν
† µν
νρ
µ
+ 2 (Dµ Φ) W (Dν Φ) + 2 (Dµ Φ) B (Dν Φ) +
Tr(Wµν W Wρ )
Λ
Λ
Λ2
fb
fτ
†
†
+ 2 (Φ Φ)(Q 3 ΦdR,3 ) + 2 (Φ Φ)(L3 ΦeR,3 )
Λ
Λ
Leff = −
– plus e-w precision data and triple gauge couplings
⇒ before measuring couplings remember what your operators are!
Higgs Physics
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
ggH vertex
(− )
q
(− )
q
g
g
H
g
p
Q#
q
✓?
(− )
(− )
g
g
++
µµ
p
q#
q
g
H
êz
(− )
(− )
g
g
H
✓e ✓h g
H
g
g
je↵
g
Q
q
#
(− )
q
(− )
#
γ, Z
Z
(− )
µµ
✓µ
✓`
Z
Z, γ
X
q
Q
(− )
(− )
−)
#
p
−)
êz0
g
Q
g
q
p
H
1e Z, γ
g
je+(−q )
(− )
Q#
γ, Z
X
X
(− )
q#
g
(− )
W ,Z
)
H
(− )
(
g
−#
cos φe = (p̂beam × p̂Zµ ) ·
× p̂e− ) Q
Ze
W ±, Z
cos ∆φ = (p̂e− × p̂e+ ) · (p̂µ− ∓× p̂µ+H)
#
(p̂Zq µ
g
(− )
∗
cos θ = p̂Ze · p̂beam Q
Zµ
g
cos θµ = p̂µ− · p̂Ze Ze
q
Meaning
cos θe = p̂e− · p̂Zµ (− )
BSM
H
MadMax
Higgs Physics
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
ggH vertex
(− )
q
(− )
q
g
g
H
g
g
p
p
Q#
q
✓?
(− )
(− )
H
g
++
µµ
q#
q
g
êz
(− )
(− )
g
g
H
✓e ✓h g
−)
#
g
g
je↵
g
Q
q#
(− )
(− )
q#
H
Z
(− )
µµ
✓µ
✓`
Z
γ, Z
X
Z, γ
Q
q
(− )
(− )
êz0
p
g
Q
p
H
g
q
g
γ, Z
H
(− )
Q#
1e Z, γ
X
X
(− )
q#
g
W ,Z
)
g
je+(−q )
(
g
(− )
)
−)
Zµ
(− )
(
H
Ze
−#
−
#
cos φe = (p̂beam × p̂Zµ ) · (p̂Zq µ × p̂e− ) Q
Ze
±
W ,Z
cos ∆φ = (p̂e− × p̂e+ ) · (p̂µ− ∓× p̂µ+H)
∗
cos θ = p̂Ze · p̂beam Q
cos θµ = p̂µ− · p̂Ze g
Meaning
cos θe = p̂e− · p̂Zµ q
BSM
(− )
MadMax
Higgs Physics
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
ggH vertex
MadMax
BSM
Meaning
– 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
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
[Breit: boost into space-like]
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
(−
q
)
g
Meaning
q#
(−
g
)
H
X
(−
)
V1 Breit
q
(−
)
#
g
cos ∆φ = (p̂q1 × p̂j1 ) · (p̂q2 × p̂j2 ) .
H
g
g
(−
q
g
g
W
W
g
,Z
∓
✓1
g
)
H
(−
)
q
g
g
X
q
j1
Q
H
(−
)
Q
g
d
H
(−
g
g
g
q
(−
)
q#
,Z
±
g
g
V1
)
q
)
(−
γ
Z,
Z
g
)
g
γ,
(−
q#
Z
)
H
(−
Q
j2
Q
)
(−
q
W
Z
∓
)
(−
)
#
Q
,Z
(−
H
Q#)
#
q
)
#
q
(−
)
✓2
q
)
(−
H
#
Q
✓?
γ,
)
γ
g
(−
(−
Z,
g
Q#)
g
H
V2
(−
× p̂j1 )
)
V2 Breit
q
cos φ1 = (p̂V2 × p̂d ) · (p̂V2
∗
cos θ = p̂V1 · p̂d cos θ2 = p̂j2 · p̂V1 (−
V1 Breit
q
cos θ1 = p̂j1 · p̂V2 (−
BSM
)
MadMax
– Breit frame or hadron collider (η, φ) in WBF
(−
ggH vertex
Higgs Physics
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
ggH vertex
MadMax
BSM
Meaning
– 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
†
1
†
µν
(φ φ)W Wµν
Λ2
µ
L ⊃ (φ φ)W Wµ
1
†
µν
ρσ
(φ φ)µνρσ W W
Λ2
⇒ different
channels, same physics
0.5
0.5
1 dΓ
Γ d∆φ
0.4
0.5
1 dσ
σ d∆φ
0.4
1 dσ
σ d∆φjj
0.4
-
0.3
0D5
0.3
+
0 D5
-
0D5
0.3
+
0 SM
0D5
0.2
0.2
2
0
0
1
0 SM
0.2
+
+
+
0 D5
0.1
+
+
0 D5
2
2
3
4
0 SM
0.1
+
5
6
0
0
1
2
3
0.1
4
5
6
0
2
0
1
2
3
4
+
5
6
Higgs Physics
Angular Correlations
Tilman Plehn
Higgs boson
Questions
Couplings
ggH vertex
Measurements of operator structures
[learning from the flavor people]
– Cabibbo–Maksymowicz–Dell’Aquila–Nelson angles for H → ZZ
[Melnikov etal; Lykken etal; v d Bij etal; Choi etal; Fabio etal]
– Breit frame or hadron collider (η, φ) in WBF
[Breit: boost into space-like]
MadMax
[Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]
BSM
Meaning
– possible scalar couplings
†
µ
L ⊃ (φ φ)W Wµ
1
†
µν
(φ φ)W Wµν
Λ2
⇒ different channels, same physics
1
†
µν
ρσ
(φ φ)µνρσ W W
Λ2
Higgs Physics
Longitudinal WW scattering
Tilman Plehn
Higgs boson
Questions
Couplings
WW scattering at high energies
– historically alternative to light Higgs
– WW scattering at high energies [via Goldstones]
ggH vertex
MadMax
BSM
Meaning
[Tao etal; Dawson]
gV H
µ
µ
aL VLµ VL + aT VT µ VT
– still useful after Higgs discovery?
Higgs Physics
Longitudinal WW scattering
Tilman Plehn
Higgs boson
Questions
Couplings
WW scattering at high energies
– historically alternative to light Higgs
– WW scattering at high energies [via Goldstones]
ggH vertex
MadMax
[Tao etal; Dawson]
gV H
µ
µ
aL VLµ VL + aT VT µ VT
BSM
– still useful after Higgs discovery?
Meaning
– high energy signal reduced by Higgs
– tagging jets as Higgs pole observables instead
Higgs Physics
Longitudinal WW scattering
Tilman Plehn
Higgs boson
Questions
Couplings
WW scattering at high energies
– historically alternative to light Higgs
– WW scattering at high energies [via Goldstones]
ggH vertex
MadMax
[Tao etal; Dawson]
gV H
µ
µ
aL VLµ VL + aT VT µ VT
BSM
– still useful after Higgs discovery?
Meaning
– high energy signal reduced by Higgs
– tagging jets as Higgs pole observables instead
Tagging jet observables
[Brehmer, Jäckel, TP]
– polarization defined in Higgs frame
– transverse momenta
PT (x, pT ) ∼
PL (x, pT ) ∼
1 + (1 − x)2
pT3
2 + p 2 )2
x
((1 − x)mW
T
2
1−x
pT
2(1 − x)mW
2 + p 2 )2
x
((1 − x)mW
T
Higgs Physics
Longitudinal WW scattering
Tilman Plehn
Higgs boson
Questions
Couplings
WW scattering at high energies
– historically alternative to light Higgs
– WW scattering at high energies [via Goldstones]
ggH vertex
MadMax
[Tao etal; Dawson]
gV H
µ
µ
aL VLµ VL + aT VT µ VT
BSM
– still useful after Higgs discovery?
Meaning
– high energy signal reduced by Higgs
– tagging jets as Higgs pole observables instead
Tagging jet observables
[Brehmer, Jäckel, TP]
– polarization defined in Higgs frame
– transverse momenta
– azimuthal angle
Aφ =
σ(∆φjj <
σ(∆φjj <
π
2)
π
2)
− σ(∆φjj >
+ σ(∆φjj >
π
2)
π
2)
Higgs Physics
Longitudinal WW scattering
Tilman Plehn
Questions
Couplings
ggH vertex
WW scattering at high energies
[Tao etal; Dawson]
– historically alternative to light Higgs
– WW scattering at high energies [via Goldstones]
gV H
MadMax
µ
µ
aL VLµ VL + aT VT µ VT
BSM
– still useful after Higgs discovery?
Meaning
– high energy signal reduced by Higgs
– tagging jets as Higgs pole observables instead
Tagging jet observables
[Brehmer, Jäckel, TP]
– polarization defined in Higgs frame
aT
Higgs boson
2
Rate
– transverse momenta
1.5
p , Aφ
– azimuthal angle
– total rate σ ∼
(AL aL2
T,j
+
AT aT2 )
⇒ simple question, clear answer
1
Combined
0.5
95% CL, 300 fb-1
No systematics
0
0
0.5
1
1.5
2
aL
Higgs Physics
Fox-Wolfram moments
Tilman Plehn
Higgs boson
Questions
Weighted series in spherical harmonics
–
– originally alternative to event shapes
Couplings
ggH vertex
MadMax
BSM
[Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
T
H` =
2
`
N
N
X
X
X
pT ,i pT ,j
4π
pT ,i m
Y` (Ωi )
P` (cos Ωij )
=
2` + 1 m=−` i=1
pT ,tot pT2 ,tot
i,j=1
– tunable for forward jets
Meaning
H1
H4
1
1
0.9
0.8
0.8
0.6
0.7
0.6
0.4
0.5
0.2
0
0
0.1
0.2
0.3
0.4
0.5
Ω[π]
0.6
0.7
0.8
0.9
1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.2
0.3
0.1
0
0.4
0.3
0
r
0.1
0.2
0.3
0.4
0.5
Ω[π]
0.6
H5
0.8
0.9
1
1
0.9
1
1
0.9
0.7
0.8
0.6
0.5
0.4
0.3
0.2
0.1
0
r
H19
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
Ω[π]
even `
odd `
0.7
H` < 0.3
forbidden
back-to-back
0.6
0.7
0.8
0.9
1
1
0.9
0.8
0.3 < H` < 0.7
democratic
democratic
0.7
0.6
0.5
0.4
r
0.2
0.3
0.1
0
0.2
0
0
0.1
0.2
0.3
0.4
0.5
Ω[π]
0.6
0.7 < H` < 1
ordered, collinear, back-to-back
collinear, ordered
0.7
0.8
0.9
0.7
0.8
0.6
0.5
0.4
r
0.3
0.2
0.1
0
Higgs Physics
Fox-Wolfram moments
Tilman Plehn
Higgs boson
Questions
Weighted series in spherical harmonics
–
[Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
– originally alternative to event shapes
Couplings
T
ggH vertex
H` =
MadMax
2
N
`
N
X
X
X
pT ,i pT ,j
4π
pT ,i m
P` (cos Ωij )
Y` (Ωi )
=
2` + 1 m=−` i=1
pT ,tot pT2 ,tot
i,j=1
BSM
– tunable for forward jets
Meaning
– applied to tagging jets in WBF
0.02
1 dN
N dHT
0.06
[mjj > 600 GeV]
1 dN
0.02 N dHT8
1 dN
N dHT
4
3
0.015
0.015
0.04
0.01
0.01
0.02
0.005
0
0
0.005
0.2
0.4
0.6
0.8
HT3 1
0
0
0.2
0.4
0.6
0.8
HT4 1
0
0
0.2
0.4
0.6
0.8
HT8 1
Higgs Physics
Fox-Wolfram moments
Tilman Plehn
Higgs boson
Questions
Weighted series in spherical harmonics
– originally alternative to event shapes
Couplings
T
ggH vertex
H` =
MadMax
BSM
Meaning
[Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
2
N
`
N
X
X
X
pT ,i pT ,j
4π
pT ,i m
P` (cos Ωij )
Y` (Ωi )
=
2` + 1 m=−` i=1
pT ,tot pT2 ,tot
i,j=1
– tunable for forward jets
– applied to tagging jets in WBF
[mjj > 600 GeV]
– applied to all jets in WBF
0.02
0.06
1 dN
N dHT
3
0.02
1 dN
N dHT
1 dN
N dHT
8
4
0.015
0.015
0.04
0.01
0.01
0.02
0.005
0
0
0.005
0.2
0.4
0.6
0.8
HT3 1
0
0
0.2
0.4
0.6
0.8
HT4 1
0
0
0.2
0.4
0.6
0.8
HT8 1
Higgs Physics
Fox-Wolfram moments
Tilman Plehn
Higgs boson
Questions
Weighted series in spherical harmonics
– originally alternative to event shapes
Couplings
T
ggH vertex
H` =
MadMax
BSM
Meaning
[Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
2
N
`
N
X
X
X
pT ,i pT ,j
4π
pT ,i m
P` (cos Ωij )
Y` (Ωi )
=
2` + 1 m=−` i=1
pT ,tot pT2 ,tot
i,j=1
– 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
1 dN
N dHT
0.06
3
0.02
1 dN
N dHT
1 dN
N dHT
8
4
0.02
0.015
0.04
0.01
0.01
0.02
0
0
0.2
0.4
0.6
0.8
HT3 1
0
0
0.005
0.2
0.4
0.6
0.8
HT4 1
0
0
0.2
0.4
0.6
0.8
HT8 1
Higgs Physics
Fox-Wolfram moments
Tilman Plehn
Higgs boson
Questions
Weighted series in spherical harmonics
– originally alternative to event shapes
Couplings
ggH vertex
MadMax
BSM
Meaning
[Field, Kanev, Tayebnejad; Bernaciak, Buschmann, Butter, TP]
T
H` =
2
N
`
N
X
X
X
pT ,i pT ,j
4π
pT ,i m
P` (cos Ωij )
Y` (Ωi )
=
2` + 1 m=−` i=1
pT ,tot pT2 ,tot
i,j=1
– 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!