EFT-Naturalness:
an effective field theory analysis
of Higgs naturalness
EPS-HEP2015, Vienna, July 22-29
Shaouly Bar-Shalom
Technion, Israel
([email protected])
arXiv/1405.2924 [PRD 2015]
SBS (Technion), A. Soni (BNL) & J. Wudka (UCR)
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Shaouly Bar-Shalom
Higgs Physics
outline
• Naturalness …
• “EFT naturalness”:
a complete parameterization of all higher dimensional
effective operators (@ any dim.!) that can potentially
“soften” the 2 behavior of mh2
 look for naturalness conditions in the heavy underlying theory
•
Constraints, signals of EFT naturalness & concluding remarks
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t
Naturalness
The “master equation”:
driving force behind search for NP
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t
Naturalness
The “master equation”:
driving force behind search for NP
The hierarchy/naturalness problem:
mh2 ( physical mass)  mh2 (tree)  mh2 ( SM )  126 GeV
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New Physics
NP particle masses are lighter than 

SM is not a complete description of the heavy physics
below ; there being other particles yet to be discovered
with masses below 
 The parameters of the theory are such that there are
cancellations between the SM and NP contributions
to mh (symmetries/accidental) …
e.g., SUSY, little Higgs/composite models …
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Shaouly Bar-Shalom
All NP particle masses are heavier than 

 = the scale of the effective action
use EFT techniques
Higgs Physics
EFT Naturalness:
A modest goal:
acquire insight regarding the underlying new physics which
can potentially alleviate the little hierarchy problem in the
SM Higgs sector up to the scale of the effective action 
Exploit: EFT techniques
Assume: underlying physics lies above !
Ask: what are the “EFT naturalness” conditions?
 the conditions for the physics above  that can soften
naturalness in the Higgs sector
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EFT Naturalness:
Ask: what are the “EFT naturalness” conditions?
 the conditions for the physics above  that can soften
naturalness in the Higgs sector
The EFT-naturalness conditions are most likely due to a
higher symmetry of the underlying physics …
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Underlying setup:
E
new heavy physics
M ~ O(10 TeV)

 = the scale of the effective action (Wilsonian-like)
EFT naturalness:
conditions among
fi for theory to be
natural at  < M
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Shaouly Bar-Shalom
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Underlying setup:
E
new heavy physics
M ~ O(10 TeV)

 = the scale of the effective action (Wilsonian-like)
EFT naturalness:
conditions among
fi for theory to be
natural at  < M
Below M:
SM +
(SM fields and symmetries …)
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The “roadmap” to EFT naturalness:
a taste of the problem …
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The “roadmap” to EFT naturalness:
a taste of the problem …
h 
mh2
mh2
2
( eff )

F
 8.2
2 2
16 mh
A theory, F(eff), for
which h~1 is natural
while one with
h~10(100) suffers
from fine-tuning of
10%(1%)
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natural
1%
10%
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The EFT contribution to the Higgs mass:
Integrating out the heavy fields (M);
generates an infinite series of vertices suppressed by inverse powers of  (< M)
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The EFT contribution to the Higgs mass:
Integrating out the heavy fields (M);
generates an infinite series of vertices suppressed by inverse powers of  (< M)
EFT naturalness: what eff. interactions can tame the little hierarchy problem?
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To Calculate
We need the set of operators which give
the leading contribution to
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EFT:
Its a mess in general – underlying physics not known,
too many operators …
needs some guiding principles !
set the “rules of the game” …
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EFT framework:
Assume: physics at E  M is described by
 “light fields” [@ E  M] = SM fields
 Gauge-symmetry [@ E  M] = SM: SU(3)xSU(2)xU(1)
(useful for classifying the higher dim operators)
 Underlying NP (heavy) is weakly coupled, renormalizable, obeys
gauge-invariance & preserves symmetries of the known dynamics (SM)
(useful for classifying the higher dim operators)
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EFT framework:
Assume: physics at E  M is described by
 “light fields” [@ E  M] = SM fields
 Gauge-symmetry [@ E  M] = SM: SU(3)xSU(2)xU(1)
(useful for classifying the higher dim operators)
 Underlying NP (heavy) is weakly coupled, renormalizable, obeys
gauge-invariance & preserves symmetries of the known dynamics (SM)
(useful for classifying the higher dim operators)
Many operators can be constructed under these conditions, O(50)
BUT: only very few can balance the SM’s 1-loop quadratic terms !
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EFT corrections to Higgs mass
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EFT corrections to Higgs mass
From heavy scalar exchanges: singlets or triplets
From heavy vector exchanges: singlets or triplets
From heavy fermion exchanges: singlets, doublets or triplets
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EFT corrections to Higgs mass
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Higgs Physics
EFT corrections to Higgs mass
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EFT naturalness upshot:
h 
mh2
mh2
2

F ( eff )  8.2
2 2
16 mh
Provides the necessary conditions in the underlying theory
(i.e., in terms of the coefficients of the higher dim. operators)
for the theory to be natural (or to have a certain degree of fine-tuning)
  h  f ( h , f i , M )
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 natural  f (1, f i , M )
Shaouly Bar-Shalom
Higgs Physics
Less ignorance
More insight regarding the heavy new physics for naturalness
explicitly calculating the higher-dim coefficients …
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Less ignorance:
examples of interactions of the new heavy particles that can address naturalness
heavy scalars  = singlets & triplets:
heavy vectors X = singlets & triplets:
heavy fermions  = singlets, doublets & triplets:
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Less ignorance:
examples of interactions of the new heavy particles that can address naturalness
heavy scalars  = singlets & triplets:
heavy vectors X = singlets & triplets:
heavy fermions  = singlets, doublets & triplets:
Integrate out heavy fields (,X,) &
allowing for the more general case of different scales
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Matching the effective theory @ 
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Matching the effective theory @ 
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
F(eff) >Higgs
0 !Physics
EFT naturalness conditions – a simple example:
Assume that the heavy masses are clustered around a value M:
expected values:
e.g., u ~ 3M and/or a triplet heavy vector-like (colored) quark with y ~ 1
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EFT naturalness conditions – a simple example:
find the values of () for which EFT corrections to mh can “soften” naturalness in
the Higgs sector at a certain  for some value of M of the NP threshold …
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Shaouly Bar-Shalom
Higgs Physics
EFT naturalness conditions – a simple example:
find the values of () for which EFT corrections to mh can “soften” naturalness in
the Higgs sector at a certain  for some value of M of the NP threshold …
Regions in the  plane which corresponds to h=1 (natural) and
h=10 (10% fine-tuning) for an EFT-naturalness scale 3 <  < 10 TeV &  < M < 3
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EFT naturalness conditions – a simple example:
Example: extensions of the SM with a typical mass scale of
M ~ 7 TeV and with  ~ 9 &  ~ 5
will yield an effective action which is natural up to  ~ 5 TeV
(an order of magnitude improvement over the pure SM …)
Regions in the  plane which corresponds to h=1 (natural) and
h=10 (10% fine-tuning) for an EFT-naturalness scale 3 <  < 10 TeV &  < M < 3
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Constraints from current data
EFT naturalness operators can cause 2 types of effects:
• A shift to the -parameter
M(scalar triplet,vectors) > ~ 10 TeV
• A shift of the Higgs couplings
to SM fermions & gauge-bosons
no useful limit …
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Expected signals of EFT-Naturalness
vertices involving Higgs, gauge-bosons and fermions from
the EFT-naturalness higher-dim operators
Tail of new physics responsible for EFT-naturalness can be searched for
in multi-boson scattering processes of the form:
VV  nh+m V+X (n,m=0,1,2, …)
e.g., pp Wh+X, Zh+X
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Summary
• There is a UV completion to the SM which is
natural up to some scale !
• What do we know about the underlying NP?
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Shaouly Bar-Shalom
Higgs Physics
Summary
• There is a UV completion to the SM which is
natural up to some scale !
• What do we know about the underlying NP?
• Our EFT-naturalness analysis:
• provides insight about this theory:
relations among parameters of the UV theory (for naturalness)
• signals expected in multi-boson scattering processes, e.g., pp Wh+X, Zh+X
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Shaouly Bar-Shalom
Higgs Physics
Summary
• There is a UV completion to the SM which is
natural up to some scale !
• What do we know about the underlying NP?
• Our EFT-naturalness analysis:
• provides insight about this theory:
relations among parameters of the UV theory (for naturalness)
• signals expected in multi-boson scattering processes, e.g., pp Wh+X, Zh+X
• Naturalness in the UV is not that complicated:
need new singlet(s) or triplet(s) bosons or else singlet, doublet or triplet fermion(s)
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THANK YOU!
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backups
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Loop calculations
fermions loop
vectors loop
scalars loop
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Signals of potential heavy natural NP
• deviations in Higgs pair production
V
• VV  hh (s-channel exchange of heavy bosons)
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
D
V
• qq,ee  hh (t-channel exchange of heavy fermions)

• Higgs+jet/lepton production via off-shell heavy fermion ``decay”

• *  h ( = quark or lepton)
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