higgs physicsshaouly bar-shalom1 arxiv/1405.2924 [prd 2015] sbs (technion), a. soni (bnl) & j....
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Higgs PhysicsShaouly Bar-Shalom1
arXiv/1405.2924 [PRD 2015]
SBS (Technion), A. Soni (BNL) & J. Wudka (UCR)
Shaouly Bar-ShalomTechnion, Israel
(shaouly@physics.technion.ac.il)
EFT-Naturalness: an effective field theory analysis
of Higgs naturalness EPS-HEP2015, Vienna, July 22-29
Higgs PhysicsShaouly Bar-Shalom2
outline
• Naturalness …
• “EFT naturalness”: a complete parameterization of all higher dimensional effective operators (@ any dim.!) that can potentially “soften” the 2 behavior of mh
2 look for naturalness conditions in the heavy underlying theory
• Constraints, signals of EFT naturalness & concluding remarks
Higgs PhysicsShaouly Bar-Shalom3
NaturalnessThe “master equation”:
t
driving force behind search for NP
Higgs PhysicsShaouly Bar-Shalom4
NaturalnessThe “master equation”:
t
driving force behind search for NP
The hierarchy/naturalness problem:
GeVSMmtreemmassphysicalm hhh 126)()()( 222 GeVSMmtreemmassphysicalm hhh 126)()()( 222 GeVSMmtreemmassphysicalm hhh 126)()()( 222 GeVSMmtreemmassphysicalm hhh 126)()()( 222 GeVSMmtreemmassphysicalm hhh 126)()()( 222 GeVSMmtreemmassphysicalm hhh 126)()()( 222
New Physics
Shaouly Bar-Shalom5
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 …
All NP particle masses are heavier than
= the scale of the effective action
use EFT techniques
Higgs Physics
Higgs PhysicsShaouly Bar-Shalom6
Underlying setup:
E
new heavy physics
SM +
(SM fields and symmetries …)
Below M:
M ~ O(10 TeV)
Higgs PhysicsShaouly Bar-Shalom7
Underlying setup:
E
new heavy physics
SM +
(SM fields and symmetries …)
EFT naturalness: conditions among fi for theory to be natural at < M
= the scale of the effective action (Wilsonian-like)
Below M:
M ~ O(10 TeV)
Higgs PhysicsShaouly Bar-Shalom8
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 …
EFT Naturalness :
Higgs PhysicsShaouly Bar-Shalom9
The “roadmap” to EFT naturalness: a taste of the problem …
Higgs PhysicsShaouly Bar-Shalom10
The “roadmap” to EFT naturalness: a taste of the problem …
2.816
)(22
2
2
2
eff
hh
h
h Fmm
m
10%
1%
naturalA theory, F(eff), for which h~1 is natural
while one with
h~10(100) suffers from fine-tuning of
10%(1%)
Higgs PhysicsShaouly Bar-Shalom11
Integrating out the heavy fields (M); generates an infinite series of vertices suppressed by inverse powers of (< M)
The EFT 1-loopv contribution to the Higgs mass:
Higgs PhysicsShaouly Bar-Shalom12
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?
The EFT contribution to the Higgs mass:
Higgs PhysicsShaouly Bar-Shalom13
We need the set of operators which give
the leading contribution to
To Calculate
Higgs PhysicsShaouly Bar-Shalom14
EFT:
Its a mess in general – underlying physics not known, too many operators …
needs some guiding principles !
set the “rules of the game” …
Higgs PhysicsShaouly Bar-Shalom15
EFT framework:
“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)
Assume: physics at E M is described by
Higgs PhysicsShaouly Bar-Shalom16
“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 !
Assume: physics at E M is described by
EFT framework:
Higgs PhysicsShaouly Bar-Shalom17
EFT corrections to Higgs mass
Higgs PhysicsShaouly Bar-Shalom18
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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EFT corrections to Higgs mass
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EFT naturalness upshot:
),,( Mff ihh ),,1( Mff inatural
2.816
)(22
2
2
2
eff
hh
h
h Fmm
m
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)
Higgs PhysicsShaouly Bar-Shalom22
Less ignorance
More insight regarding the heavy new physics for naturalness
explicitly calculating the higher-dim coefficients…
Higgs PhysicsShaouly Bar-Shalom23
Less ignorance: examples of interactions of the new heavy particles that can address naturalness
heavy fermions = singlets, doublets & triplets:
heavy scalars = singlets & triplets:
heavy vectors X = singlets & triplets:
Higgs PhysicsShaouly Bar-Shalom24
Less ignorance: examples of interactions of the new heavy particles that can address naturalness
Integrate out heavy fields (,X,) & allowing for the more general case of different scales
heavy fermions = singlets, doublets & triplets:
heavy scalars = singlets & triplets:
heavy vectors X = singlets & triplets:
Higgs PhysicsShaouly Bar-Shalom25
Matching the effective theory @
Higgs PhysicsShaouly Bar-Shalom26 F(eff) > 0 !
Matching the effective theory @
Higgs PhysicsShaouly Bar-Shalom27
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
EFT naturalness conditions – a simple example:
Higgs PhysicsShaouly Bar-Shalom28
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 …
Higgs PhysicsShaouly Bar-Shalom29
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
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 …
EFT naturalness conditions – a simple example:
Higgs PhysicsShaouly Bar-Shalom30
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
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 …)
EFT naturalness conditions – a simple example:
Higgs PhysicsShaouly Bar-Shalom31
EFT naturalness operators can cause 2 types of effects:
• A shift to the -parameter
• A shift of the Higgs couplings to SM fermions & gauge-bosons
M(scalar triplet,vectors) > ~ 10 TeV
no useful limit…
Constraints from current data
Higgs PhysicsShaouly Bar-Shalom32
Expected signals of EFT-Naturalness
Modified 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 associated production of the form:
VV nh+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?
Higgs PhysicsShaouly Bar-Shalom34
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
Higgs PhysicsShaouly Bar-Shalom35
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)
Higgs PhysicsShaouly Bar-Shalom36
THANK YOU!
Higgs PhysicsShaouly Bar-Shalom37
backups
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vectors loopscalars loop
fermions loop
Loop calculations
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Signals of potential heavy natural NP
• Higgs+jet/lepton production via off-shell heavy fermion ``decay”
• * h ( = quark or lepton)
• deviations in Higgs pair production
• VV hh (s-channel exchange of heavy bosons)
• qq,ee hh (t-channel exchange of heavy fermions)
V
V
2D
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