Download Little Higgs dark matter and its collider signals

Little Higgs Dark Matter & Its Collider Signals
Shigeki Matsumoto
(University of Toyama)
～ Papers ～
・ E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki,
Y. Takubo, and H. Yamamoto, PRD 79, 2009.
・ S. M, T. Moroi and K. Tobe, PRD 78, 2008.
・ S. M, M. M. Nojiri and D. Nomura, PRD 75, 2007.
・ M. Asano, S. M., N. Okada and Y. Okada, PRD 75, 2007.
～ Contents ～
1.
2.
3.
Little Higgs Scenario
Little Higgs signals at LHC & ILC
Summary
1/11
1. Little Hierarchy Scenario
Corrections to mh
EW Observables
Kolde & Murayama, hep-ph/0003170
Barbieri & Strumia, 1998
If coefficient ci is O(1),
ΛSM > O(10)TeV (mh = 120 GeV)
When the tuning < 10%,
ΛSM < O(1)TeV (mh = 120 GeV)
Little Hierarchy Problem
1 TeV
???
E
10 TeV
Need some mechanism to control the Higgs mass!
1. Little Hierarchy Scenario
Little Higgs Scenario
・
Higgs boson = Pseudo NG boson
・ Explicit breaking = Collective symmetry breaking
E
10 TeV
1 TeV
100 GeV
Generation of mh
New Physics with
G ( ⊃ Gauge group ),
which is slightly broken
SSB: G  G’, where
G’ ( ⊃ SU(2) x U(1)Y )
Electroweak breaking
SU(2) x U(1)Y  U(1)EM
(Standard Model)
Origin of mh =
Interactions which break G.
Usual breaking:
When the interaction
“L1“
breaks the symmetry G,
and generates mh, then
(mh)2 ～ (ΛSM)2/(16π2)
～ (1 TeV)2
(1-loop diagrams)
2/11
1. Little Hierarchy Scenario
2/11
Little Higgs Scenario
・
Higgs boson = Pseudo NG boson
・ Explicit breaking = Collective symmetry breaking
E
10 TeV
Generation of mh
New Physics with
G ( ⊃ Gauge group ),
which is slightly broken
1 TeV
SSB: G  G’, where
G’ ( ⊃ SU(2) x U(1)Y )
100 GeV
Electroweak breaking
SU(2) x U(1)Y  U(1)EM
(Standard Model)
Origin of mh =
Interactions which break G.
Collective symmetry breaking:
When the Interactions
“L1“ & “L2“
(partially) break G,
and the Higgs boson is
“pseudo” NG boson when both
interactions exist,
(mh)2 ～ (ΛSM)2/(16π2)2
～ (100 GeV)2
(2-loop diagrams)
3/11
1. Little Hierarchy Scenario
Diagrammatic view point
・ Global symmetry imposed
・ Collective sym. breaking
New particles introduced.
(Little Higgs partners)
W,Z
WH,ZH
+
h
h
t
h
t
+ h
T
+ h
t
T
Quadratically divergent corrections to mh are
completely cancelled at 1-loop level!
Constructing models
SM
Nonlinear sigma model
E
100 GeV
1 TeV
10 TeV
4/11
1. Little Hierarchy Scenario
-
-
-
H
-
H
H
SU(5)
 SO(5)
[SU(2)xU(1)]2 SU(2)xU(1)
-
-
-
-
-
T+Triplet
Lagrangian
– F2/4 + LYukawa – V(H, F)
+ Kinetic terms of fermions
No quadratically divergent |H|2 term at 1-loop level.
4/11
1. Little Hierarchy Scenario
H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003)
T-parity
T+
-
-
-
H
-
-
-
H
-
-
-
H
-
-
Triplet
Constraints from EWPM
Littlest Higgs model suffers from EWP constraints.
～ Imposition of the Z2-symmetry (T-parity) ～
1. SM particles & Top partner T+ are even
2. Heavy Gauge bosons are odd.
3. T-odd partners of matter fields introduced.
T–
4/11
1. Little Hierarchy Scenario
H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003)
T-parity
T+
-
-
-
H
-
-
-
H
-
-
-
H
-
-
Triplet
Constraints from EWPM
Model Parameters of the LHT
f : VEV of the SU(5)  SO(5) breaking
l2 : Mass of the top-partners (in units of f)
kx : Mass of the T-odd partner of “x”(in units of f)
Higgs mass mh is treated as a free parameter
T–
1. Little Hierarchy Scenario
H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003)
O (f)
O (v)
Masses of new particles
are proportional to f.
Masses of SM particles
are proportional to v.
Constraints from EWPM
Model Parameters of the LHT
f : VEV of the SU(5)  SO(5) breaking
l2 : Mass of the top-partners (in units of f)
kx : Mass of the T-odd partner of “x”(in units of f)
Higgs mass mh is treated as a free parameter
4/11
1. Little Hierarchy Scenario
Lightest T-odd Particle is stable due to the T-parity conservation.
 Little Higgs Dark Matter! (Heavy photon in the LHT)
J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005)
Main annihilation mode: AH AH  h  WW or ZZ
1. AHAHh vertex is given by the SM gauge coupling.
2. Annihilation cross section depends on mAH & mh.
 Relic abundance of AH: Wh2(mAH(f), mh)
Little Higgs dark matter is
singlet and spin 1 particle.
1.
The dark matter mass:
80-400 GeV
Wh2 of dark matter
2.
The Higgs mass:
110-800 GeV
Asano, S.M, N.Okada, Y.Okada (2006)
5/11
1. Little Hierarchy Scenario
Constraints from EWPM?
U-branch
6/11
1. Little Hierarchy Scenario
Constraints from EWPM?
L-branch
6/11
1. Little Hierarchy Scenario
Constraints from EWPM?
L-branch
f = 580 GeV
l2 = 1.15
mh = 134 GeV
mT+ = 834 GeV
mT- = 664 GeV
mAH = 81.9 GeV
mWH = 368 GeV
mZH = 369 GeV
Representative point
1. Masses of top partners are
about (or less than) 1 TeV!
 copiously produced at the LHC.
2. Masses of heavy gauge bosons
are several hundred GeV!
 can be produced at the ILC.
6/11
2. Littlest Higgs Signals at LHC & ILC
Top partner productions
LHC is a hadron collider, so
that colored new particles
are copiously produced!
 T+ & T- productions!
S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008)
MadGraph/Event (Event generation)
PYTHIA
PDG4
(Hadronization)
(Detector Response)
T+ pair production
Reconstructing two
T+-system, T+(lep) & T–(had)
Determination of T+ Mass
(with ±20 GeV uncertainty)
7/11
2. Littlest Higgs Signals at LHC & ILC
Top partner productions
LHC is a hadron collider, so
that colored new particles
are copiously produced!
 T+ & T- productions!
S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008)
MadGraph/Event (Event generation)
PYTHIA
PDG4
(Hadronization)
(Detector Response)
Single T+ production
Reconstructing bW system
# of the signal depends on NP!
(σ determined with 20% accuracy.)
7/11
2. Littlest Higgs Signals at LHC & ILC
Top partner productions
LHC is a hadron collider, so
that colored new particles
are copiously produced!
 T+ & T- productions!
MadGraph/Event (Event generation)
PYTHIA
S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008)
PDG4
(Hadronization)
(Detector Response)
T- pair production
H1
H2
Top reconstruction via
hemisphere analysis.
S.M., Nojiri, Nomura (2007)
0 100 200
End points of MT2 depend on mT- & mAH
(within about 20 GeV accuracy.)
7/11
2. Littlest Higgs Signals at LHC & ILC
From T+ pair prod.
From T+ single prod.
From T- pair prod.
l2
3s
1s
f (GeV)
f = 580 ± 33 GeV
 Cosmological connections
8/11
2. Littlest Higgs Signals at LHC & ILC
9/11
Heavy gauge boson productions
ILC is a e+e- collider, so that
heavy particles are produced
with clean environment.
 WH, ZH, AH productions!
E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M.,
R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009.
Physsim (Event generation)
PYTHIA (Hadronization)
JSF Q-sim. (Detector Response)
ZHAH production @ 500 GeV
500 fb-1
s = 1.9 fb
Energy distribution of h
 End points depend on mAH & mZH
mAH = 83.2 ± 13.3 GeV
mZH = 366. ± 16. GeV
 f = 576. ± 25. GeV
2. Littlest Higgs Signals at LHC & ILC
9/11
Heavy gauge boson productions
ILC is a e+e- collider, so that
heavy particles are produced
with clean environment.
 WH, ZH, AH productions!
E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M.,
R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009.
Physsim (Event generation)
PYTHIA (Hadronization)
JSF Q-sim. (Detector Response)
ZHAH production @ 1 TeV
500 fb-1
s = １２１ fb
Energy distribution of W
 End points depend on mAH & mZH
mAH = 81.58 ± 0.67 GeV
mWH = 368.3 ± 0.63 GeV
 f = 580± 0.69 GeV
10/11
2. Littlest Higgs Signals at LHC & ILC
Probability density
Simulation results
+ Higgs mass
Planck
WMAP
Annihilation X-section
<sv>(mAH, mh)  WDMh2
Probability density of
the dark matter relics
ILC(1000)
LHC
ILC(500)
WDMh2
LHC: Abut 10% accuracy (Model-dependent analysis)
ILC(500): Better than 10% accuracy (Model-independent analysis)
ILC(1000): 2% accuracy!! (Model-independent analysis)
3. Summary
•
Little Higgs model with T-parity is one of attractive scenario
describing New Physics at TeraScale.
•
It contains a candidate for cold dark matter whose stability is
guaranteed by the T-parity (Little Higgs dark matter).
•
The property of the dark matter can be investigated at collider
experiments such as LHC & ILC.
•
At LHC, top partners can be detected. From their data, the property
of the dark matter can be estimated with a model dependent way.
•
At ILC with s1/2 = 500 GeV, the property of the dark matter can be
determined with model-independent way. Also, the relic abundance
can be determined with the accuracy comparable to the WMAP.
•
AT ILC with s1/2 = 1 TeV, the property of the dark matter can be
determined very accurately. For instance, the relic abundance will
be determined with the accuracy comparable to PLANCK
experiment.
11/11
Back Up
The LH Lagrangian
– F2/4 + LYukawa – V(H, F)
+ Kinetic terms of fermions
Non-linear s field
Pseudo NG bosons
Breaking directions
The LH Lagrangian
– F2/4 + LYukawa – V(H, F)
Gauge interactions [SU(2) x U(1)]2
Gauge couplings: g1, g’1, g2, g’2
The LH Lagrangian
– F2/4 + LYukawa – V(H, F)
Top Yukawa interactions
tR
tL
Top Yukawa: l1
U quark mass: l2
Particle contents in Gauge,
Higgs, and top sectors
4 gauge bosons : B1, W1 , B2, W2
Σ= (24 – 10) pions :
After breakings
SM gauges : A, W±, Z
Heavy gauges : AH, WH±, ZH
SM Higgs : h
Triplet Higgs : Φ
Parameters
SM top quark : t ,
Heavy top : T = (U , UR)T
g1, g’1, g2, g’2
f l1, l2
Little Higgs Dark Matter
Lightest T-odd Particle is stable due to the T-parity conservation.
 Little Higgs Dark Matter! (Heavy photon in the LHT)
[J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) ]
Main annihilation mode: AH AH  h  WW or ZZ.
1. AHAHh vertex is given by the SM gauge coupling.
2. Annihilation cross section depends on mAH & mh.
 Relic abundance of AH: Wh2(mAH(f), mh)
Wh2(mAH(f), mh)
[Asano, S.M, N.Okada, Y.Okada (2006)]
When mh < 150 GeV,
then 550 < f < 750 GeV.
Masses of heavy gauge bosons
are several hundred GeV.
 can be produced at ILC.
Masses of top partners are
about (or less than) 1 TeV
 copiously produced at LHC.
Representative point for simulation study
Considering EW precision & WMAP constraints
[J. Hubisz, P. Meade, A. Noble, M. Perelstein, JHEP0601 (2006)]
(1) Observables (mw sinqW, Gl, WDMh2) vs. Model parameters (f, l2, mh)
(2) 2mh2/mt > O(0.1-1), where mt is the top-loop contribution to mh.
f = 580 GeV
l2 = 1.15
mh = 134 GeV
mAH = 81.9 GeV
mWH = 368 GeV
mZH = 369 GeV
mT+ = 834 GeV
mT- = 664 GeV
mF = 440 GeV
(mLH = 410 GeV)
T+ pair production at the LHC
SM BG: tt–production! (460 pb)
At the parton- level
Signal = bbqqlν
~ Output ~
Distribution of
~ Strategy to reduce BG ~
Reconstruct Two T+-system: T+(lep) & T–(had)
using the fact that the missing momentum
pT is due to the neutrino emission and
(pl + pν)2 = mW2. There are 6-fold ambiguity
in the reconstruction of T+-system.
The combination to minimize
T+ pair production at the LHC
~ Results ~
~ Cut used in the analysis ~
~ Discussion ~
The distributions have distinguishable
peaks at around the T+ mass. SM BG
are well below the signal.
 From the distribution, we will be able
to study the properties of T+.
T+ pair production at the LHC
~ Accuracy of the mT+ determination ~
We consider the bin
~ Conclusion ~
Then, we calculate the # of events in the bin
as a function of
with
being fixed.
The peak of the distribution is determined
by
maximizing the # of events in the
bin. We applied the procedure for
~ Results ~
The difference between the
position of the peak and the
input value of mT+ is,
typically, 10-20 GeV!
T+ single production at the LHC
SM BG: tt & single t productions!
At the parton level
Signal = bqlν
~ Output ~
Distribution of
~ Strategy to reduce BG ~
Existence of very energetic jet (b from T+)!
With the leading jet, reconstruct T+-system.
There are 2-fold ambiguity to reconstruct
neutrino momenta 
&
Reject events unless
is small.
Jet mass is also used to reduce the BG.
T+ single production at the LHC
~ Results ~
~ Cut used in the analysis ~
~ Discussion ~
Single T+ production occurs not
through a QCD process but through
a EW process (e.g. W-exchange).
Distributions have distinguishable
peaks at around the T+ mass when
sin2β is large enough!
 From the cross section, we will be
able to determine sinβ.
T+ single production at the LHC
~ Accuracy of sinβ determination ~
We use the side-band method to extract the
# of the single production events,
(L)
(C)
(R)
after imposing the cuts. Then, cross section
for the single T+ production can be obtained
from the # of events in the signal region.
~ Results (Point 2) ~
~ Conclusion ~
The cross section, which is
proportional to sin2β, will be
determined with 10-20%.
Parameter “sinβ”, which is
given by a combination
of f & λ2, will be determined
with 5-10% accuracy!
T– pair production at the LHC
H1
H2
T– decays into t + AH with
100 % branching ratio
SM BG: tt–production! (460 pb)
At the parton level
Signal = (bqqAH)×2
~ Output ~
Distribution of MT2
~ Strategy to reduce BG ~
1. Large missing momentum is expected in the
signal event due to dark matter emissions.
2. Use the hemisphere analysis to reconstruct
the top quark [S.M., Nojiri, Nomura (2007)].
3. Since AH is undetectable, direct masurements
of T– & AH are difficult.  MT2 variable!
T– pair production at the LHC
~ Results (Point 2) ~
0 100
~ Cut used in the analysis ~
200
~ Discussion ~
“MT2 variable” is a powerful tool to determine mT+ and mAH, which is defined by
with
being the postulated AH mass. Then, the end point of MT2 distribution is
T– pair production at the LHC
~ Accuracy MT2(max) determination ~
End-point of the distribution of MT2 is
determined by a combination of mT+ , mAH,
and the postulate mass
.
By looking at the position of the end-point
with an appropriate value of
, it is
possible to get information of mAH & mT+!
We have also checked that there is no
contamination of the BG around End-point!
~ Conclusion ~
Using the distribution of the
MT2 with
,
the upper end-point will be
determined with 10-20 GeV
accuracy (at Point 2)!
~ Results (Point 2) ~
With the use of quadratic function to estimate the end-point,
using
using
when
. Theoretically, the end-point is 664 GeV.