Download HiggsIdentity_Part1

Higgs Identity @ the LHC, Part I:
Compositeness and Naturalness
1.
2.
3.
R. Dermisek and I. L., hep-ph/0701235
I. L. and S. Shalgar: arXiv:0901.0266
I. L., R. Rattazzi, and A. Vichi: arXiv:0907.5413
Ian Low
Argonne National Lab and Northwestern U.
Outline
•
•
•
•
•
Mysteries at the TeV scale
Higgs search @ the LHC
Gluon fusion production
Size of effects
Summary and outlook
Mysteries at the TeV Scale
• Electroweak symmetry is broken, but we don’t
know how.
• W and Z bosons have masses, but we don’t
know where they came from.
• Electroweak scale (v=246 GeV) is much
smaller than the next energy scale we know,
Mp=1019 GeV. Why this big hierarchy?
• Is there a stable neutral particle (dark
matter)? There’s none in the SM…
• etc.
Understanding these mysteries requires new
dynamics at the TeV scale, and possibly new
physical principles associated with it.
•
•
•
•
•
•
Supersymmetry?
Extra dimensions?
New (global or gauge) symmetries?
Grand unification?
All of the above?
None of the above?
The landsacpe of models is huge:
Drawing by H. Murayama
However, message from LEP is loud and clear:
Precision electroweak measurements favor a weaklycoupled description at the TeV scale!
If the dynamics responsible
for EWSB were stronglycoupled at the TeV
scale, the induced
quantum effects at low
energies would be large.
Then we should have seen
sizable deviations at the
LEP!!
QuickTime™ and a
decompressor
are needed to see this picture.
• The only known way to construct a model of
EWSB that is weakly-coupled at the TeV scale is
through the Higgs mechanism:
An electroweak doublet scalar
receives a vacuum expectation
value, v=246 GeV, and breaks
SU(2)LxU(1)Y spontaneously.
Searching for the Higgs at the LHC is among its
top priorities!
However, having a description based on the
Higgs mechanism raises more questions:
• We have never observed a fundamental scalar in
nature so far. Is the Higgs fundamental?
• A scalar mass is “fine-tuned” in quantum field theory,
unless it is “cut off” by new physics. Is there new
physics at the TeV scale in addition to the Higgs?
• How do we know the new physics, if any, reduces the
fine-tuning in the Higgs mass?
• If we observe one or more scalars, how do we know it
has a VEV that breaks the electroweak symmetry?
All these questions are not necessarily
“problems” if we could figure out easily that
which one of the 10,000 models gives us the
signals.
eg, if we know it’s MSSM that gives us the multijet, multi-lepton, and missing ET, then we have
answers to all the above problems
immediately.
There are discussions of discovering SUSY within a
matter of weeks of turning on the LHC…
Unfortunately, it’s not going to be that straightforward…
Typical signatures for SUSY events are isolated leptons,
missing ET, plus jets.
They actually have nothing to do with SUSY!!
A computer simulation of SUSY events.
Any model with a new conserved parity at the TeV scale
gives such signals:
R-parity (SUSY), KK-parity (extra-dimension), T-parity (little Higgs)
A computer simulation of UED events.
Given the huge degeneracy, it is then important
to ask global and structural questions first:
• Is the Higgs fundamental or composite?
• Is the new physics at the TeV scale, if any, follows
from naturalness principle?
• If we observe new particles, who ordered them? Does
any of them reduce the fine-tuning in the Higgs mass?
• If we observe one or more scalars, how do we know it
has a VEV that breaks the electroweak symmetry?
• Do the W and Z bosons get their masses from the
Higgs mechanism?
We need to answer them in order to navigate the infinite
space of models!!
I will try to provide answers to some of these
questions, by looking into two particular
processes:
•
Gluon-fusion production of the Higgs:
could tell us whether the Higgs is a composite
particle like the  in low-energy QCD, and whether
there exists new particle canceling the quadratic
divergence in the Higgs mass.
•
Decay of a resonance into ZZ final states:
could tell us whether it is a scalar with couplings
following from the Higgs mechanism
• Part I is mostly motivational:
I want to convince you the wealth of
information hidden behind (ggh). Thus it’s
worth putting in resources to extract it with
precision!
• Part II is very specific:
I will suggest smoking-gun signals in h ZZ
that have not attracted enough attention until
perhaps recently.
Higgs search at the LHC
The Higgs boson is the last particle in the standard
model that hasn’t been observed directly!
The History:
Legacy of LEP -precision electroweak
measurements
LEPEWWG as of
August 2009:
Minimal chi-square at
Higgs mass = 87 GeV
with an uncertainty of
+35 GeV and -26 GeV
LEP did not see the SM
Higgs before it was shut
down in 2000.
. combined four
The
LEP experiments put
a lower bound on
the Higgs mass at
114.4 GeV at the
95% confidence
Level.
(hep-ex/0306033)
The latest -- Legacy of Tevatron ??
Combined CDF and D0 in January of 2010:
A SM Higgs in the mass range of 162-166 GeV is now ruled out at
95% C.L.
All eyes on the LHC now for the discovery of the Higgs.
Main production mechanisms of the Higgs at hadron
colliders:
Ref: A. Djouadi,
hep-ph/0503172
Among them gluon fusion is the dominant mechanism!
At Tevatron:
Ref: A. Djouadi, hep-ph/0503172
At the LHC:
Decay channels depend on the Higgs mass:
Ref: A. Djouadi, hep-ph/0503172
• For low Higgs mass mh  150 GeV, the Higgs mostly
decays to two b-quarks, two tau leptons, two gluons
and etc.
• In hadron colliders these modes are difficult to extract
because of the large QCD jet background.
• The silver detection mode in this mass range is the
two photons mode: h   , which like the gluon
fusion is a loop-induced process.
Higgs mass can be measured very precisely by, for
example, looking at the invariant mass of the di-photon.
Ref: CMS physics TDR
Furthermore, it is possible to extract individual partial widths of
the Higgs boson.
LHC at 200 fb-1
D. Zeppenfeld, hep-ph/0203123
Gluon Fusion Production
• gg  h is the dominant production
mechanism at the LHC.
• gg  h is a loop-induced process, and hence
very sensitive to new physics running in the
loop.
Thus, this particular channel provides a unique
window into new physics at higher energy
scales.
We will analyze ways new physics could enter
into this production channel.
In the SM the dominant contribution comes from
the top loop.
Since the top is “heavy”, the loop can be shrunk
to a point and approximated by a dim-5
operator:
QuickTime™ and a
decompressor
are needed to see this picture.
In this diagram alone, there are two ways new
physics could enter:
1. The Higgs-fermion-fermion coupling could be
modified by new physics:
(roughly) scale of
new physics
QuickTime™ and a
decompressor
are needed to see this picture.
In this diagram alone, there are two ways new
physics could enter:
2. The definition of the Higgs field may be
modified:
QuickTime™ and a
decompressor
are needed to see this picture.
Finally, there could a new loop diagram in
addition to the SM top loop:
1. For non-supersymmetric theories, it could be
a new top-like fermion, the top partner .
2. For supersymmetric theories, it could be a
new top-like scalar, the stop .
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
When the new particle in the loop is heavy, the
new contribution is encoded in the
parameter cg:
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Summarizing these three effects, we have
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Quite amazingly, the sign of all three
parameters are correlated with the identity of
the Higgs boson, whether it is a fundamental
or composite particle like the pion in QCD.
In addition, the sign of cg is correlated with
whether the Higgs mass is “natural” or not.
First let’s consider the sign of cH, cy, and cH+2cy.
(The latter controls the Higgs-fermion-fermion coupling.)
We have the following “robust” positivity
constraints:
• cH>0 except when there exists electroweak
triplet scalars, regardless of whether the
Higgs is a fundamental or composite scalar.
• cH+2cy >0 when the Higgs is fundamental,
even in the presence of a triplet.
On the other hand, the following positivity
constraint is “almost robust,” and holds for all
known models:
cH+2cy >0 in models where the Higgs is a
composite scalar (Goldstone boson) like the
pion in QCD.
There are several contributions to this
coefficient in composite Higgs models. We
proved rigorously the positivity of all but one
of them.
The remaining one turns out to be positive as
well in known models.
Next we consider the sign of cg, which is the
relative sign between the SM top loop and
the new loop diagram.
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
We first consider the sign of cg for a new top-like
fermion, the top partner. We will establish that
If the Higgs quadratic divergence in the top sector is
cancelled, the interference between the SM top and
the top partner is destructive.
 cg > 0 in our sign convention
Conversely, if the quadratic divergence is enhanced,
the interference is constructive.
 cg < 0
• There’s a simple diagrammatic argument:
The interaction of the Higgs with the top quark induces a
quadratically divergent contribution in the Higgs mass:
Q: How do we use another fermion to cancel the above
divergence?
• There’s a simple diagrammatic argument:
The interaction of the Higgs with the top quark induces a
quadratically divergent contribution in the Higgs mass:
Q: How do we use another fermion to cancel the above
divergence?
Wrong answer: another fermion T with only Yukawa coupling to
the Higgs wouldn’t work. The divergences always add up!
• There’s a simple diagrammatic argument:
The interaction of the Higgs with the top quark induces a
quadratically divergent contribution in the Higgs mass:
Q: How do we use another fermion to cancel the above
divergence?
Correct answer: always need a dimension-five coupling with the
Higgs!
• If the following two diagrams have a relative minus
sign, then Higgs quadratic divergence is cancelled.
Otherwise, the divergences add up.
Now let’s massage the diagrams a little bit:
Now let’s massage the diagrams a little bit:
-- First putting one of the Higgs field in its VEV.
Now let’s massage the diagrams a little bit:
-- First putting one of the Higgs field in its VEV.
-- Next let’s insert two gluons into the fermion line.
These are exactly the two diagrams contributing to
gluon fusion from the top quark and the new state!
Because we have the same number of insertions along
the fermion line, the relative sign between the diagrams
is preserved!
In other words, if the Higgs divergence is cancelled, the new
state would interfere destructively with the top quark.
But if the divergence is NOT canceled, the new state would
interfere constructively with the top quark.
The only assumption here is there is a new degree of freedom
that is colored and has a significant coupling to the Higgs.
Otherwise, our statement is completely general, model
independent, and applies to any non-supersymmetric theories.
The diagrammatic arguments can be formalized using
the low-energy Higgs theorem, where the coefficient
cg is related to the one-loop QCD beta function.
Taking into account all the effects discussed so
far
QuickTime™ and a
decompressor
are needed to see this picture.
We conclude the gluon fusion production rate
is reduced in composite Higgs models!
• The same diagrammatic argument can be
extended to the case of MSSM. The
difference is the pattern of interference is
reversed because of the opposite spin of stop
to the top.
Size of Effects
• cH and cy, roughly speaking, is a measure of
the compositeness of the Higgs (in the sense
of the pion in QCD.)
If the Higgs is fundamental, we expect their
effects to be small.
• cg is suppressed by the mass of the new
particles, relative the SM contribution.
Examples: In SUSY or flat extra-dimensional
theories, where the Higgs is a fundamental
scalar, the partial width is then dominated by
the cg term, which is in the order
So the effects could be sizable if the top partner
or the stop is light, and/or when there’s more
than one new particles contributing
coherently.
The ratio of the gluon fusion rate in the MSSM over the SM:
The right panel is the region where the Higgs mass in the MSSM is
least fine-tuned, and the rate is reduced!
QuickTime™ and a
decompressor
are needed to see this picture.
Gluon Fusion Rate in the Universal Extra-Dimension (UED):
The Higgs scalar is fundamental and its mass unnatural (finetuned). The rate is enhanced over the SM!
QuickTime™ and a
decompressor
are needed to see this picture.
F. Petriello, hep-ph/0204067
In composite Higgs models, such as the little
Higgs or the holographic Higgs, all three
terms, cH, cy, and cg, contribute (somewhat!)
equally. The generic size varies:
However, in this case all three terms go in the
same direction of reducing the rate!
So the pile-up effect could be important.
Gluon Fusion Rate in the littlest Higgs with T-parity (LHT):
The Higgs is a composite scalar like the pion and the rate is
reduced!
QuickTime™ and a
decompressor
are needed to see this picture.
Chuan-Ren Chen et al, hep-ph/0602211
Gluon Fusion Rate in the littlest Higgs (without T-parity):
The Higgs is a composite scalar like the pion and the rate is
reduced!
QuickTime™ and a
decompressor
are needed to see this picture.
T. Han et al, hep-ph/0302188
Summary and Outlook
• We found the gluon fusion production rate is
a unique handle into the compositeness of
the Higgs boson as well as the naturalness of
the mass.
• Composite Higgs models generally have a
reduced gluon fusion rate.
• Unnatural models tend to have an enhanced
production rate.
• The size of effects depends on the underlying
models, ranging from modest, in the order of
10-30 %, to as small as SM one-loop effect.
• Given the wealth of information that could be
revealed, there’s strong motivation to improve
on measurements at the LHC both
theoretically and experimentally.
For example, some advocate that the theoretical
uncertainties should be smaller than it is often quoted:
QuickTime™ and a
decompressor
are needed to see this picture.
C. Anastasiou, et al, hep-ph/0509014
Last but not the least:
If the LHC sees the Higgs and nothing else, in
my mind there is still a strong scientific case
for building a precision machine such as the
linear (or muon) collider!