TH-Institute25-July-2016
Effective-Field-TheoryApproachofthe
anomalousTripleGaugeCouplings
attheLHC
MinhoSon
KAIST
Greljo,Gonzalez-Alonso,Falkowski,Marzoca,SONinprogress
Lesson from Run1, part of Run 2
> 𝒪(TeV)
: cut-off scale
extracted from data
Higgs Effective Field Theory
Widely separated two scales, or seemingly un-natural
hierarchy offers a remarkable bonus
StoletextfromthetalkbyRattazzi
ℒ)*+, = ℒ/0123. + 𝐻𝑖𝑔𝑔𝑠
1
1
= ℒ (:;<) +
ℒ +
ℒ +⋯
Λ ?)@ (A) ΛB?)@ (C)
Structural picture of EFT Racco,Wulzer,Zwirner 15’
Contino,Falkowski,Goertz,Grojean,Riva16’
𝑔∗
𝑀FGH
𝑔∗
𝑀∗ =
𝑚
𝑀FGH
𝑔∗
Interaction scale
Structural picture of EFT Racco,Wulzer,Zwirner 15’
Contino,Falkowski,Goertz,Grojean,Riva16’
𝑔∗
𝑀FGH
𝑔∗
𝑀∗ =
𝑚
𝑀FGH
𝑔∗
Interaction scale
: the only scale accessible to
a low-E observer
Typical interaction in EFT is
controlled by the effective coupling,
𝐸
𝑔 𝐸 =
𝑀∗
𝑀FGH
≤
= 𝑔∗
𝑀∗
Structural picture of EFT Racco,Wulzer,Zwirner 15’
Contino,Falkowski,Goertz,Grojean,Riva16’
𝑔∗
𝜓
𝜓
𝜓
𝜓
𝑀FGH
→ 𝑚N
𝑔∗
𝑔O
𝜓
𝜓
𝑀FGH
𝑀∗ =
𝑔∗
𝑚
Interaction scale
: the only scale accessible to
a low-E observer
𝜓
B
𝑔O
∼ B
𝑚O
Typical interaction in EFT is
controlled by the effective coupling,
𝐸
𝑔 𝐸 =
𝑀∗
𝑀FGH
≤
= 𝑔∗
𝑀∗
→
𝑚N
1
=
𝑔O
𝐺Q
𝜓
→ 𝑚R
𝑔O
𝑔𝐸 =
𝐸
𝑚O
Structural picture of EFT Racco,Wulzer,Zwirner 15’
Contino,Falkowski,Goertz,Grojean,Riva16’
𝑔∗
𝑀FGH
𝑔∗
𝑀∗ =
𝑚
𝑀FGH
𝑔∗
Interaction scale
Typical interaction in EFT is
controlled by the effective coupling,
𝐸
𝑔 𝐸 =
𝑀∗
𝑀FGH
≤
= 𝑔∗
𝑀∗
Unitarity violation in EFT
𝑆𝑀
𝑆𝑀
𝑔∗
𝑆𝑀
𝑀FGH
𝑔∗
𝑆𝑀
𝑀FGH
𝑔∗
𝑀∗ =
𝑆𝑀
𝑀FGH
𝑔∗
𝑆𝑀
𝒜]^
𝑆𝑀
𝑆𝑀
𝑔∗B 𝑠
∝
B
𝑠 − 𝑀FGH
→ const. as𝑠 → ∞
𝑔B∗ 𝑠
𝑠B
= B +𝑂
<
𝑀FGH
𝑀FGH
What if our collider was not strong
enoug h to produce 𝑴𝒄𝒖𝒕 ?
𝒜[Q\ ∼
𝑠
𝑀∗B
E-growing
→ ∞as𝑠 → ∞
vs.
Validity of EFT
EarlynewphysicshintinEFTapproachreliesontheE-growingfeatureduetodecent𝑆/ 𝐵.
However,thisbenefitshouldcutoffatacertainenergyscale,𝐸 < 𝑀FGH
Constraining HEFT via VV processes
WewillparameterizeBSMintheHiggsbasis
See“LHC HiggsCrossSectionWorkingGroup”note
Data
Newinteractionsbeyond SM
ℒ/0123 [Q\ = ℒlm + Δℒ
ℒo[Q\ = ℒlm
•
•
shiftofthecoupling strengthawayfromSMpredictions
newtensorstructuresofinteractionabsentinSM
𝒪rtruvC
+ ∑𝑐sr
𝑣B
Warsaw,SILHbasesetc with
SU(2)doublet HiggsH
BSM
𝑔B (𝐸) ∼
𝑂
B
𝑔lm
𝐸B
𝑐̅
𝑚BN
Constraining HEFT via VV processes
ℒ\yz = 𝑖𝑒 𝑊}~• 𝑊}€ − 𝑊}~€ 𝑊}• 𝐴~ + 1 + 𝛿𝜅 „ 𝐴}~ 𝑊}• 𝑊~€
• 𝑊 € − 𝑊 € 𝑊 • 𝑍 + 1 + 𝛿𝜅 𝑍 𝑊 • 𝑊 €
+𝑖𝑔… 𝑐𝑜𝑠𝜃 1 + 𝛿𝑔ˆ,Š 𝑊}~
}
}~ }
~
Š }~ }
~
+𝑖𝑒
TreatLEPmeasurementsasinputs
𝜆„
𝑚BN
€𝐴
𝑊}~• 𝑊~•
•} +𝑖𝑔… 𝑐𝑜𝑠𝜃
𝑔ŽB
𝛿𝜅 Š = 𝛿𝑔ˆ,Š − B 𝛿𝜅 „
𝑔…
𝜆Š • €
𝑊 𝑊 𝑍
𝑚BN }~ ~• •}
𝜆Š = 𝜆„
→Three variables for VV
{𝜆 Š , 𝛿𝑔ˆ,Š , 𝛿𝜅„ }
A difficulty of EFT approach:
Many parameters lead to a degeneracy
Decay vs 2-to-2 scattering process
𝛿𝑐
𝑔∗
∼
𝑐lm
𝑔lm
Main focus of Run 1
Parameters in HEFT
are 𝜃, 𝑠̂ -dependent
B
𝛿𝜎B→B 𝑔B (𝐸)
𝑔∗
∼ B ∼
𝜎lm
𝑔lm
𝑔lm
𝑚B0
B
𝑀FGH
B
𝐸B
B
𝑀FGH
Important item of Run 2
𝑑𝜎
𝑑 𝑠̂ ,
𝑑𝜎
,
𝑑𝑐𝑜𝑠𝜃
𝑑𝜎
𝑑 𝑠̂ Can see more microscopic
structure of BSM
ˆ”,•–
˜
𝑑𝜎
𝑑 𝑠̂ —,•–
Decay vs 2-to-2 scattering process
𝛿𝑐
𝑔∗
∼
𝑐lm
𝑔lm
B
𝛿𝜎B→B 𝑔B (𝐸)
𝑔∗
∼ B ∼
𝜎lm
𝑔lm
𝑔lm
𝑚B0
B
𝑀FGH
Main focus of Run 1
B
𝐸B
B
𝑀FGH
Important item of Run 2
𝑑𝜎
Parameters in HEFT
are 𝜃, 𝑠̂ -dependent
𝑑 𝑠̂ ,
𝑑𝜎
,
𝑑𝑐𝑜𝑠𝜃
𝑑𝜎
𝑑 𝑠̂ ˆ”,•–
˜
Can see more microscopic
structure of BSM
Accessing to the truth-level
is non-trivial
Whatwewanttoknow
𝑠̂
= 𝑚NN, 𝑚N™
𝑠̂
vs.
Whatwecurrentlymeasure
𝑚šš ,𝑚\N™ , 𝑝\ etc
𝑑𝜎
𝑑 𝑠̂ —,•–
Accessing to the truth-level
𝑠̂ is non-trivial
SM WZ→ lνll, 8TeV
1000
104
900
800
3
10
700
600
500
102
400
300
10
200
100
0
100
200
300
400
500
600
700
800
900
1000
mWW [GeV]
What we want to know
1
mWZ
[GeV]
T
1000
What is measured
mll [GeV]
What is measured
SM WW→ lνlν, 8TeV
104
900
800
103
700
600
500
102
400
300
10
200
100
0
100
200
300
400
500
600
700
800
900
1000
1
mWZ [GeV]
What we want to know
Pollution from the wrong events
:yourhypothesis
𝑚NN < 𝑚uœ•
NN
Theory
𝑑𝜎
𝑑𝑚NN
EFT works
EFT beaks down
Events beyond
EFT regime
bin1
bin2
…
𝑚NN
Data
𝑑𝜎
𝑑𝑚šš
bin1
bin2
…
𝑚šš <
FGH
𝑀žrŸ
𝑚šš
Removal of the healthy events
:yourhypothesis
𝑚NN < 𝑚uœ•
NN
Theory
𝑑𝜎
𝑑𝑚NN
EFT works
EFT beaks down
Events beyond
EFT regime
bin1
bin2
…
𝑚NN
Data
𝑑𝜎
𝑑𝑚šš
bin1
bin2
…
𝑚šš <
FGH
𝑀žrŸ
𝑚šš
You wrongly kill healthy events
mll [GeV]
What is measured
SM WW→ lνlν, 8TeV
1000
104
900
800
103
700
600
500
102
Youcuthereon 𝑚šš
400
300
10
200
100
0
100
200
300
400
500
600
700
800
900
1000
1
mWW [GeV]
You fail to remove these wrong events
𝑚uœ•
NN
What controls EFT validity
u£¤¥
¢¢
¦
𝑑𝜎
𝑑𝑚^^
≠
𝑑𝑚^^
ª«¬
m§¨©
¦
𝑑𝑚žrŸ
𝑑𝜎
𝑑𝑚žrŸ
Cutting on 𝑚𝑙𝑙 is not justified.
What do we do?
In principle, if we can access to 𝑚^^ ≡ 𝑠̂
(𝜎lm +𝜎®lm )(𝑚^^ < 𝑚uœ•
^^ )
𝜎3°Ÿ (𝑚^^ < 𝑚uœ•
^^ )
In mass situations, we do not have access to 𝑚𝑉𝑉 ≡ 𝑠²
We only hope to set a conservative bound
(𝜎3°Ÿ −𝜎lm) − Δ𝜎 ≤ 𝜎®lm ≤ (𝜎3°Ÿ −𝜎lm ) + Δ𝜎
u¢¢³u£¤¥
𝜎®lm ¢¢
+
u¢¢´u£¤¥
𝜎®lm ¢¢
InspiredbyRacco,Wulzer,Zwirner 15’
ForgeneraldiscussionforValidityofEFT
Biekötter, Krämer,Liu,Riva15’
Contino,Falkowski,Goertz,Grojean,Riva16’
setting a conservative bound
(𝜎3°Ÿ −𝜎lm) − Δ𝜎 ≤ 𝜎®lm ≤ (𝜎3°Ÿ −𝜎lm ) + Δ𝜎
u¢¢³u£¤¥
𝜎®lm ¢¢
u
³u£¤¥
¢¢
¢¢
If𝜎®lm
u
´u£¤¥
¢¢
¢¢
> 0 &&𝜎®lm
𝜎3°Ÿ − 𝜎lm − Δ𝜎 ≤
+
u¢¢´u£¤¥
𝜎®lm ¢¢
> 0 &&Noexcess
u¢¢³u£¤¥
𝜎®lm ¢¢
≤ (𝜎3°Ÿ −𝜎lm) + Δ𝜎
InspiredbyRacco,Wulzer,Zwirner 15’
ForgeneraldiscussionforValidityofEFT
Biekötter, Krämer,Liu,Riva15’
Contino,Falkowski,Goertz,Grojean,Riva16’
setting a conservative bound
(𝜎3°Ÿ −𝜎lm) − Δ𝜎 ≤ 𝜎®lm ≤ (𝜎3°Ÿ −𝜎lm ) + Δ𝜎
u¢¢³u£¤¥
𝜎®lm ¢¢
u
³u£¤¥
¢¢
¢¢
If𝜎®lm
u
´u£¤¥
¢¢
¢¢
> 0 &&𝜎®lm
𝜎3°Ÿ − 𝜎lm − Δ𝜎 ≤
+
InspiredbyRacco,Wulzer,Zwirner 15’
ForgeneraldiscussionforValidityofEFT
Biekötter, Krämer,Liu,Riva15’
Contino,Falkowski,Goertz,Grojean,Riva16’
u¢¢´u£¤¥
𝜎®lm ¢¢
> 0 &&Noexcess
u¢¢³u£¤¥
𝜎®lm ¢¢
≤ (𝜎3°Ÿ −𝜎lm) + Δ𝜎
ü Intheabsenceofthe interferencebetweenSMandBSM
ü Inthepresenceofthe interference
•
Incompletejustification
𝜎®lm ∝ (𝒜 ∗lm𝒜®lm + ℎ. 𝑐. ) + 𝒜 ®lm
𝒜 ®lm
𝑔∗
∼
𝒜 lm
𝑔lm
B
B
B
𝐸
>1
𝑚uœ•
^^
for𝐸 > 𝑚uœ•
^^
Ifatheoryisstronglycoupled, 𝑔∗ ≫ 𝑔lm
•
Suppression ofinterferencebyhidden selectionrules
𝜎®lm ∝
(𝒜 ∗lm𝒜 ®lm +
ℎ. 𝑐. ) + 𝒜 ®lm
B
∼ 𝒜 ®lm
B
-> This is what’s
happening in aTGC
No excess scenario
:yourhypothesis
𝑚NN < 𝑚uœ•
NN
Theory
𝑑𝜎
𝑑𝑚NN
Valid EFT regime
What we propose
EFT beaks down
1.Assumepossible
cut-offscale
2.Removeevents
u¢¢´u£¤¥
from𝜎®lm ¢¢ in
bin1
bin2
yoursimulation
…
𝑚NN
Data
3.recastdata
inentire𝑚 šš distribution
4.Repeat1-3for
differentchoiceofcutoffscales
𝑑𝜎
𝑑𝑚šš
bin1
bin2
…
𝑚šš
u
³u£¤¥
¢¢
¢¢
𝜎3°Ÿ − 𝜎lm − Δ𝜎 ≤ 𝜎®lm
≤ (𝜎3°Ÿ −𝜎lm) + Δ𝜎
Complication in Resonance scenario
:yourhypothesis
𝑚NN <
Theory
𝑑𝜎
𝑑𝑚NN
𝑚uœ•
NN
EFT assumes
no resonance
bin1
Resonance
bin2
…
𝑚NN
Data
𝑑𝜎
𝑑𝑚šš
EFT behavior
Data includes
whole events
bin1
bin2
…
𝑚šš
→Unphysical Fit
u
¢¢
𝜎3°Ÿ − 𝜎lm − Δ𝜎 ≤ 𝜎®lm
³u£¤¥
¢¢
≤ (𝜎3°Ÿ −𝜎lm ) + Δ𝜎
ü
*Canbefixedifwerecoverfull 𝑠̂ = 𝑚NN
Inthiscase,wemightjustswitchto
resonancesearchthanrelyingon EFT
aTGC Amplitude
aTGC in WW
T, U channels participate in
Unitarity restoration in SM
Anomalous TripleGaugecouplings
𝑊•
𝑢
𝑢
𝑊•
𝑑
𝑢¿
𝑊€
𝑢¿
𝑊€
Perfect cancellation of E-growing pieces
S-channel
𝒜 lm
¦,¦
sin𝜃
∼
2
(𝑇G”
−
𝑠»B¼ 𝑄G )𝑔 B
T
+ 𝑒 B 𝑄G
𝑔B 𝑠
−
=0
2 𝑚BN
Imperfect cancellation picks up E-growing behavior
sin𝜃 B ”
𝑠
𝒜 ¦,¦ ∼
𝑔 𝑇G − 𝑠»B¼ 𝑄G 𝛿𝜅 Š + 𝑒 B 𝑄G 𝛿𝜅 „ B
2
𝑚N
𝒜 …/À,¦ ∼
∓1 − cos𝜃
2 2
𝑔 B 𝑇G” − 𝑠»B¼ 𝑄G (𝛿𝑔ˆŠ + 𝛿𝜅 Š + 𝜆 Š ) + 𝑒 B 𝑄G (𝛿𝜅 „ + 𝜆 „ )
𝑠
𝑚N
aTGC in WZ
T, U channels participate in
Unitarity restoration in SM
Anomalous TripleGaugecouplings
𝑢
𝑢
𝑊•
𝑊•
𝑢
𝑑
𝑍
𝑑̅
𝑊•
𝑢
𝑑̅
𝑑̅
𝑍
𝑍
Perfect cancellation of E-growing pieces
𝒜 lm
¦,¦ ∼ sin𝜃
𝑔B
S-channel
2 2𝑐»¼
T
U
c B»¼ + (𝑇t” −𝑠»B¼ 𝑄t ) − (𝑇G” −𝑠»B¼ 𝑄G )
𝑠
=0
𝑚N 𝑚™
Imperfect cancellation picks up E-growing behavior
𝒜 ¦,¦ ∼ sin𝜃
𝑔B
c»B¼ 𝛿𝑔ˆ,Š
𝑠
𝑚N 𝑚™
ü Accessing to the polarizations
could give us further
discriminating power
2 2𝑐»¼
𝑐»¼ 𝑔 B
𝑠
𝒜 …/À,À/… ∼ −sin𝜃
𝜆Š B
𝑚N
2 2
𝑔B
𝑠
𝒜 …/À,¦ ∼ ±1 + cos𝜃
2c»B¼ 𝛿𝑔ˆ,Š + 𝜆 Š
4c»¼
𝑚™
𝒜 ¦,À/…
𝑔B
𝑠
∼ ∓1 + cos𝜃
c»B¼ (𝛿𝑔ˆ,Š + 𝛿𝜅 Š + 𝜆 Š )
4c»¼
𝑚N
Quadratic vs Linear fit
𝜎Í𝜎 = 1 + 𝐵 𝜅 + 𝐶 𝜅 𝜅
œ œ
œ° œ °
lm
Linear: dim-6*SM
∼ 𝒪 Λ€B
Quadratic : dim-6*dim-6
∼ 𝒪 Λ€<
𝜅 œ = {𝜆 Š ,𝛿𝑔ˆ,Š , 𝛿 𝜅 „ }
[ dim-8*SM ∼ 𝒪(Λ€<) ]
Inclusivecrosssections
VaryingoneaTGC atatime(nocross-term included)
�� ���
� =� ���
�� ���
����
𝜆Š
����
����
𝛿𝑔ˆ,Š
����
𝛿𝜅 „
����
SolidLines: 𝑠̂ < ∞
����
DashedLines: 𝑠̂ < 600GeV
����
:Quadratictermsstaybeing
dominant foranycutvalueon 𝑠̂-cut
����
����
����
����
-���
σ /σ��
σ /σ��
����
����
� =� ���
����
����
-���
���
���
���
-���
-���
{λ�� δ����� δκγ }
���
���
{λ�� δ����� δκγ }
Interference terms appear to be suppressed
Deeper insight comes from Helicity Amplitude
Structural difference between WW and WZ
���
Helicity Amplitude
Deeper insight into the suppressed interference
Azatov,Contino,Machado, Riva16’
Cheung, Shen15’
Inthemasslesslimit
I. Gluing amplitudes to get n-pt amplitude
±
∓
ℎ 𝐴2 = ℎ 𝐴u + ℎ(𝐴uÙ )
𝐴uØ
𝐴u
II. 3-pt amplitude
LittleGroupscalinguniquely fixesthe3-pointamplitudes
2
1
𝑔
3
E.g.
𝐴” 10Ï 20Ð 30Ò = 𝑔 Ó
Littlegroup+NDA
𝑆𝑀
𝒪”N = tr(𝑊 ”)
12 0Ò€0Ï €0Ð 13 0Ѐ0Ï €0Ò 23 0Ï€0Ð €0Ò for∑ℎr < 0
[12]0Ï•0Ð €0Ò [13]0Ï•0Ò €0Ð [23]0Е0Ò €0Ï for∑ℎr > 0
→ ∑ℎr ≡ ℎ = 1 − [𝑔]
ℎ(𝐴lm
” ) =1− 𝑔 = 1
ℎ(𝐴®lm
) = 1 − 𝑐”N = 3
”
III. Some of SM 4-pt amplitude with |ℎ 𝐴lm
| = 2 vanish
<
𝐴< 𝑉• 𝑉• 𝑉• 𝑉€ = 𝐴< 𝑉• 𝑉• 𝜓 • 𝜓 € = 𝐴< 𝑉• 𝑉• 𝜙𝜙 = 𝐴< 𝑉• 𝜓 • 𝜓€ 𝜙 = 0
Azatov,Contino,Machado, Riva16’
Illustrative example
Helicity selection rule: total helicity should match
𝜓±
𝜓∓
𝜓±
+
− +
ℎ
−
𝐴lm
<
=0
𝜓∓
+
− +
+
Azatov,Contino,Machado,Riva16’
ℎ 𝐴®lm
=2
<
BSM amplitude
with insertion of 𝒪”N ∼ tr(𝑊 ” )
SM amplitude
How to interfere? Flip the helicity via VEV insertion (finite mass effect)
+
𝜓±
𝜓∓
− +
0
VEV
0
VEV
ℎ
𝐴lm
C
=2
𝑚N
∝
𝐸
B
+
Azatov,Contino,Machado,Riva16’
EFT interpretation of LHC data
Available analyses
Butteretal.16’
EFT interpretation of LHC data
Available analyses
Butteretal.16’
CMS-SMP-14-016
Events / (75 GeV)
Recasting WW-lvlv
CMS analysis at 8TeV
CMS
19.4 fb-1 (8 TeV)
Preliminary
4
Data
WW
WZ/ZZ/VVV
10
Top
DY
W+jets
cW/Λ2 = 20 TeV-2
3
cWWW/Λ2 = 20 TeV-2
10
cB/Λ2 = 55 TeV-2
102
10
100
200
300
400
500
600
mll (GeV)
ü WeakcorrelationamongaTGC
ü 𝑚^^ < ∞ isroughlysimilarto𝑚^^ < 𝒪(TeV).Weakening ispronounced for𝑚^^ < 𝒪(sub-TeV)
CMS-SMP-14-016
Events / (75 GeV)
Recasting WW-lvlv
CMS analysis at 8TeV
CMS
19.4 fb-1 (8 TeV)
Preliminary
4
Data
WW
WZ/ZZ/VVV
10
Top
DY
W+jets
cW/Λ2 = 20 TeV-2
3
cWWW/Λ2 = 20 TeV-2
10
cB/Λ2 = 55 TeV-2
102
10
100
200
300
400
500
600
mll (GeV)
ü WeakcorrelationamongaTGC
ü 𝑚^^ < ∞ isroughlysimilarto𝑚^^ < 𝒪(TeV).Weakening ispronounced for𝑚^^ < 𝒪(sub-TeV)
Recasting WZ-lvll
ATLAS analysis at 8TeV
ATLASarXiv:1603.02151
ü StrongcorrelationamongaTGC
ü 𝑚^^ < ∞ isroughlysimilarto𝑚^^ < 𝒪(TeV).Weakening ispronounced for𝑚^^ < 𝒪(sub-TeV)
WW
CMS-SMP-14-016
WZ
ATLAS
1603.02151
ü 𝛿𝜅 „ isstronglyconstrainedbyWW,notbyWZ
‘First’ recasting of 13TeV data on aTGC
WZ
arXiv:1606.04017
ATLAS analysis
ü Nodramaticimprovement.Moreorless similarto8TeV case.
Combine all (8TeV CMS + ATLAS and 13TeV ATLAS)
Profiled95%CLboundsontheeachaTGC
fromourcombinedfitwithdiff.mVV cut
Combine all (8TeV CMS + ATLAS and 13TeV ATLAS)
Profiled95%CLboundsontheeachaTGC
fromourcombinedfitwithdiff.mVV cut
Can be widely different
EFT vs UV model
𝑆𝑈 2
…
Contino,Falkowski,Goertz,Grojean,Riva16’
forsimilardiscussion
triplet+singlet
𝑖
𝑔 Ø œ}
𝑖
𝑔
}
ℒr2H = 𝑉}œ 𝑔𝜅Øo 𝐽oœ} + 𝜅Þß
𝐽Þ + 𝑉}¦ − 𝑔𝜅o 𝐽o
+ 𝜅Þß 𝐽Þ}
2
2
2
2
Integrate out Triplet and Singlet and match to
EFT coefficients
𝑐N®
𝛿𝑔ˆ,Š =
𝑔B + 𝑔Ø B
𝑔B − 𝑔Ø B
Ø
𝑐oš
ˆˆ
𝑐šš
𝛿𝑚 =
=
1
𝑔B
−
𝑔Ø B
𝑐\ − 𝛿𝑣
1 Ø
𝛿𝑣 =
𝑐 oš
2
Ø
𝑐oš
BB
=
ˆBBˆ
𝜅 Bo 𝑚BN
3𝜅′o 𝑚BN
𝑚BN
𝑚BN
B
B
= 0 𝑐\ =
𝑐 =
𝑐 = −4𝜆𝜅′o B 𝑐R = 𝜅′o B
2 𝑚B^ o
2 𝑚B^ C
𝑚^
𝑚^
=
−2𝜅 Øš B
−𝜅′o 𝜅 Øš
ˆˆ +
𝑐Ø
oš BB
𝑚BN
𝑚B^
𝑚BN
+ Δ = 0
𝑚B^
1
− 𝑐šš
4
ˆBBˆ
𝑚BN
o 𝜅′ š
𝑚B^
Assumed LEP
bound is perfect
𝑔 B 𝑐\ − 𝑔 Ø B𝛿𝑣 = 0 → 𝜅′o 𝜅′Þ = −
Both triplet and singlet are
required to have dm = 0
=
−𝜅 Ø
𝑔B
B
B 𝜅o
Ø
2𝑔
𝛿𝑔ˆ,Š =
𝑔
−𝜅Bo
𝛿𝜅„ = 𝜆 Š = 0
B
+ 𝑔′B 𝑚BN
2𝑔′B 𝑚B^
EFT vs UV model
𝑆𝑈 2
…
(strongly vs weakly)
triplet+singlet
𝑖
𝑔 Ø œ}
𝑖
𝑔
ℒr2H = 𝑉}œ 𝑔𝜅 Øo 𝐽oœ} + 𝜅Þß
𝐽Þ
+ 𝑉}¦ − 𝑔𝜅 o 𝐽o} + 𝜅Þß 𝐽Þ}
2
2
2
2
𝛿𝑔ˆ,Š =
−𝜅 Bo
𝑔 B + 𝑔 Ø B 𝑚BN
𝜅 Bo
∝− B
𝑚^
2𝑔 Ø B 𝑚B^
𝛿𝑔ˆ,Š = −0.009
↔
𝜅o
0.75
1.5
4.5
= = = 𝑚^
1TeV
2TeV
6TeV
Weakly
coupled
Strongly
coupled
EFT works better for
a strong coupling
SimilarexerciseforWh appeared in
Contino,Falkowski,Goertz,Grojean,Riva16’
Illustration of EFT vs Direct
𝑆𝑈 2
…
triplet+singlet
𝑖
𝑔 Ø œ}
𝑖
𝑔
ℒr2H = 𝑉}œ 𝑔𝜅 Øo 𝐽oœ} + 𝜅Þß
𝐽Þ
+ 𝑉}¦ − 𝑔𝜅 o 𝐽o} + 𝜅Þß 𝐽Þ}
2
2
2
2
𝛿𝑔ˆ,Š =
−𝜅 Bo
𝑔 B + 𝑔 Ø B 𝑚BN
𝜅 Bo
∝− B
𝑚^
2𝑔 Ø B 𝑚B^
: EFT constrains
𝜿𝑯
⁄𝒎𝑽
WZ-lvll @8TeV
Will become more
conservative with cuts
SimilarexerciseforWh appeared in
Contino,Falkowski,Goertz,Grojean,Riva16’