Indirect Studies of
Electroweakly Interacting Particles
at 100 TeV Hadron Colliders
So Chigusa
Department of Physics, University of Tokyo
July 23, Seminar @ Osaka University
SC, Yohei Ema, and Takeo MoroiPLB 789 (2019) 106 [arXiv:1810.07349]
Tomohiro Abe, SC, Yohei Ema, and Takeo Moroi(submitted to PRD) [arXiv:1904.11162]
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
ElectroWeakly Interacting Massive Particle (EWIMP)
EWIMP : massive particle with non-zero weak charges
Good dark matter (DM) candidate · · · “WIMP miracle”
MSSM
Lightest SUSY particle
Higgsino · · · 1 TeV
e.g. “natural SUSY”H. Baer, et al. [1203.5539], etc.
Wino · · · 3 TeV
e.g. “Mini-Split”A. Arvanitaki, et al. [1210.0555], etc.
Minimal Dark Matter
Large weak SU(2)L charge
Suppressed interaction with SM
5-plet fermion · · · 10 TeV
(7-plet scalar)
M. Cirelli, et al. [hep-ph/0512090], etc.
There are many search methods : BUT Higgsino is difficult2 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Indirect detection of DM
Look for EWIMP DM annihilation into SM particles in the sky
Wino Dark Matter Mass (GeV)210 310
)-1
s3v
(cm
σ
-2610
-2510
-2410
-2310
-2210 Expectation
4 years observation
SculptorSextans
Draco Ursa Minor
Combined (15 dSphs)
wino cross section
B. Bhattacherjee+ ’14
Wino (and MDM)
Already exclude mW in sub-TeV region and ∼ 2 TeV
Higgsino
Too small cross section to detect3 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Direct detection of DM
Look for recoiled nuclei by collision between EWIMP DM
101 102 103 104
WIMP mass [GeV/c2]
10−49
10−48
10−47
10−46
10−45
10−44
10−43
WIM
P-nu
cleo
nσ S
I[c
m2 ] XENON100 (2016)
LUX (2017)
PandaX (2017)
XENON1T (2017)
XENON1T (1 t year, this work)
XENONnT (20 t year Projection)
Billard 2013, neutrino discovery limit
XENON1T ’18
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J. Hisano+ ’15Wino & MDM
Region of future interest
Higgsino
Small cross section below neutrino bacground4 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Production at collider
Difficulty : event recognition
disappearing track search
⇔ requires long life time, small BG
ATLAS Simulation
π+
χ01
~χ+
1~︸ ︷︷ ︸
SCT 30∼52 cm
︸ ︷︷ ︸pixel 3∼12 cm
ATLAS [1712.02118]
CMS [1804.07321]
100 200 300 400 500 600 700 [GeV]±
1χ∼m
0.01
0.020.030.04
0.1
0.20.30.4
1
2
34
10
[ns]
± 1χ∼τ
)theory
σ1 ±Observed 95% CL limit ( )expσ1 ±Expected 95% CL limit (
, EW prod. Obs.)-1ATLAS (8 TeV, 20.3 fbTheory (Phys. Lett. B721 (2013) 252)ALEPH (Phys. Lett. B533 (2002) 223)
ATLAS-1=13TeV, 36.1 fbs
> 0µ = 5, βtan production
±
1χ∼±
1χ∼,
0
1χ∼ ±
1χ∼
cτW ∼ 6 cm, mW < 460 GeV excluded
cτH ∼ 1 cm, mH < 152 GeV excluded for pure Higgsino
Higgsino mixed with gaugino : cτ ≪ O(cm)
mono-X search : recognize events with initial state radiationno bound on Higgsino @ LHC H. Baer, et al. [1401.1162]
5 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Invitation : indirect study using colliders
Today I introduce
Indirect search with ℓℓ/ℓν production @ 100TeV collider
qa
qb
�
�/ν
χ0, χ±
γ, Z,W
Features
Independent of EWIMP lifetime ⇒ Good for Higgsino
Clean events : 2 energetic leptons (+ jet)
⇒ Signal shape as a func. of lepton inv. mass is usable
to control systematic errors
to determine EWIMP mass and charges6 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Table of contents
1 Introduction
2 EWIMP effects on the processes
3 EWIMP detection and statistical method
4 Determination of EWIMP properties
5 Conclusion
7 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Table of contents
1 Introduction
2 EWIMP effects on the processes
3 EWIMP detection and statistical method
4 Determination of EWIMP properties
5 Conclusion
7 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Vacuum polarization effect from EWIMP
Assume all new physics except EWIMPs are decoupled
χ0, χ±
γ, Z,W γ, Z,W
finiteq
∝ i(q2gµν − qµqν)f
(q2
m2
)
f is a loop function
f(x) =
1
16π2
∫ 1
0dy y(1− y) ln(1− y(1− y)x− i0) (Fermion)
1
16π2
∫ 1
0dy (1− 2y)2 ln(1− y(1− y)x− i0) (Scalar)
EWIMP effects are parametrized by parameters C1 and C2
Leff = LSM + C1g′2Bµνf
(− ∂2
m2
)Bµν + C2g
2W aµνf
(−D2
m2
)W aµν
8 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Group theoretical factors C1, C2
SU(2)L n-plet with U(1)Y charge Y contributes
C1 =κ
8nY 2, C2 =
κ
96(n3 − n),
κ =
16 (Dirac fermion)
8 (Weyl or Majorana fermion)
2 (complex scalar)
1 (real scalar)
For popular EWIMPs
Higgsino Wino 5-fermion (Y = 0) 7-scalar (Y = 0)
C1 1 0 0 0
C2 1 2 10 7/29 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Neutral current (NC) / Charged current (CC)
Parton level scattering amplitude for qaqb → ℓℓ (NC) / ℓν (CC)
M =
qa
qb
�
�/ν
γ, Z,W
q︸ ︷︷ ︸MSM
+
qa
qb
�
�/ν
χ0, χ±
γ, Z,W
︸ ︷︷ ︸MEWIMP
+ · · ·
Differential cross section for fixed q2 ≡ s′
|M|2 = |MSM|2 + 2ℜ [MSMM∗EWIMP] + · · ·
dσab
d√s′
≡dσab
SM
d√s′
+dσab
EWIMP
d√s′
+ · · ·
Define the size of correction
δabσ (√s′) ≡
dσabEWIMP/d
√s′
dσabSM/d
√s′ 10 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Cross section correction from EWIMPs
Plot of δabσ with m = 1 TeV EWIMPs
1000 2000 3000 4000 5000 6000 7000√s′ [GeV]
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
δ σ[%
]
peak at√s′ = 2m
HiggsinoWino5-plet scalar
Peak structure at√s′ = 2m plays an important role
“threshold effect”
χ0, χ±
γ, Z,W γ, Z,W
11 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Event generation
√s = 100TeV, L = 30 ab−1 for SM, binned by collision energy
MadGraph5 aMC@NLO : hard process @ NLO
Pythia8 : parton shower (PS), hadronization
Delphes3 : detector simulation
pp → �+�− + PS pp → �+�−(NLO) + PS pp → �+�−j + PS
Delphes
Detector
Simul.
1000 2000 3000 4000 5000Invariant mass [GeV]
102
103
104
105
106
107
108
Nevents
e + e − invariant mass distribution (30ab−1)
EWIMP effect is included by rescaling
NSM+EWIMP =
NSM∑events
[1 + δabσ (
√s′)
]12 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Table of contents
1 Introduction
2 EWIMP effects on the processes
3 EWIMP detection and statistical method
4 Determination of EWIMP properties
5 Conclusion
12 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Statistical treatment (optimistic)
Consider number of events in i-th bin of collision energy
− x = {xi} : prediction for SM (Now use NSM)
− x = {xi} : experimental data (Now use NSM+EWIMP instead)
Compare signal (S) with statistical error (δB)
Si
δBi=
|xi − xi|√xi
≃ |xi − xi|√xi
Following test statistic tests validity of SM
q0 ≡∑i:bin
S2i
δB2i
q0 obeys a χ2 distribution within SM13 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Idea of fitting based analysis
Systematic errors may modify theoretical predictiondσSM
d√s′, xi
luminosity error
beam energy error
choice of renormalization scale
choice of factorization scale
choice of PDF
etc · · ·mchar
Cross section
dσSM
dmchar
dσSM
dmcharfsys(θ,mchar)
Idea of fitting based analysis
Absorb above errors into additional parameters θ
(Similar to “side band analysis”)
14 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Fitting systematic errors
− y = {yi} : prediction for SM
− y = {yi} : data with one of errors included
luminosity error (±5%)
beam energy error (±1%)
choice of renormalization scale (2Q,Q/2)
choice of factorization scale (2Q,Q/2)
choice of PDF
By introducing fitting function fsys,i(θ), fitting procedure is
yi(θ) ≡ yifsys,i(θ)
χ2 = minθ
∑i:bin
(yi − yi(θ))2
yi(θ)
χ2 checks if above systematic errors can be absorbed into θ
15 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Fitting based analysis
Consider five parameters function
fsys,i(θ) = eθ1(1 + θ2pi)p(θ3+θ4 ln pi+θ5 ln
2 pi)i
pi = 2√
s′i/√s
CDF collaboration ’08
Systematic errors are fitted well (χ2/d.o.f. < 1)
Define new theoretical prediction xi(θ)
xi(θ) ≡ xi fsys,i(θ) ; xi(0) = xi
Test statistic q0 that obeys χ2 distribution within SM
q0 ∼ minθ
∑i:bin
(xi − xi(θ))2
xi(θ)
16 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Detection reach
500 1000 1500 2000 2500 3000mass [GeV]
0
1
2
3
4
5
6
√ q 0Integrated luminosity 30ab−1
Higgsino (w/o fit)
Wino (w/o fit)
Higgsino (w/ fit)
Wino (w/ fit)
Higgsino Wino
5σ (w/ fit) 760 GeV 1.4 TeV
5σ (w/o fit) 1.7 TeV 2.5 TeV
It is important tounderstand
systematic errors
17 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Detection reach
500 1000 1500 2000 2500 3000mass [GeV]
0
1
2
3
4
5
6
√ q 0Integrated luminosity 30ab−1
Higgsino (w/o fit)
Wino (w/o fit)
Higgsino (w/ fit)
Wino (w/ fit)
Higgsino (Controlled)
Wino (Controlled)
Higgsino Wino
5σ (w/ fit) 760 GeV 1.4 TeV
5σ (contr.) 850 GeV 1.6 TeV
5σ (w/o fit) 1.7 TeV 2.5 TeV
It is important tounderstand
systematic errors
17 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Fit result of systematic errors and σ
Best fit values for ℓℓ (NC)
Sources of systematic errors θ1 θ2 θ3 θ4 θ5Luminosity: ±5% 0.07 0 0 0 0
Beam energy: ±1% negligible
Renormalization scale: 2Q,Q/2 0.6 0.9 0.4 0.08 0.006
Factorization scale: 2Q,Q/2 0.5 0.7 0.3 0.07 0.007
PDF choice 0.4 0.7 0.3 0.06 0.004
Each value: possible size of |θ| within SM due to errors
Let’s call them as “σ” · · · standard deviation of |θ|
Sources of systematic errors σ1 σ2 σ3 σ4 σ5Combined 0.9 1.3 0.5 0.1 0.01
18 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Profile likelihood (controlled) method
We assume θ are distributed according to Gaussian
distributions with standard deviations σ
Definition of test statistic q0
q0 ≡ minθ
∑i:bin
(xi − xi(θ))2
xi(θ)︸ ︷︷ ︸try to fit data
+
5∑α=1
θ2ασ2α︸ ︷︷ ︸
control size of θ
q0 obeys χ2(1) within SM Wilk ’38
19 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Detection reach
500 1000 1500 2000 2500 3000mass [GeV]
0
1
2
3
4
5
6
√ q 0Integrated luminosity 30ab−1
Higgsino (σ→0)
Wino (σ→0)
Higgsino (σ→∞)
Wino (σ→∞)
Higgsino (Controlled)
Wino (Controlled)
Better understanding of systematic errors will push up the
detection reach : temporally 850GeV at 5σ for Higgsino
20 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Comparison with other approaches
Higgsino production at√s = 100 TeV, L = 30 ab−1
disappearing track search
(for pure Higgsino cτH ∼ 1 cm)
0 500 1000 1500
Higgsino Mass m [GeV]
0
1
2
3
4
5
6
S/B
5
95%
20% bkg.
500% bkg.
14 TeV, 3 ab 1
27 TeV, 15 ab 1
100 TeV, 30 ab 1
indirect study
Probe mH < 850GeV (1.7TeV)
at 5σ (95% C.L.) level
mono-jet search
(for any cτH)
0 500 1000 1500 2000
Higgsino Mass m [GeV]
0
1
2
3
4
5
6
S/B
5
95%
1% syst.
2% syst.
14 TeV, 3 ab 1
27 TeV, 15 ab 1
100 TeV, 30 ab 1
T. Han+ ’18
Our method provides
− comparable reach for pure Higgsino
− better for short lifetime Higgsino
21 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Which bin contributes a lot?
Plot contribution to q0 from each bin
1000 2000 3000 4000 5000 6000 7000√s ′ [GeV]
0
1
2
3
4
5
6
7
contr
ibuti
on t
o q
0
absorbed into θ
peak still contributes
1TeV Higgsino (stat.)
1TeV Higgsino
1000 2000 3000 4000 5000 6000 7000√s′ [GeV]
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
δ σ[%
]
peak at√s′ = 2m
HiggsinoWino5-plet scalar
Peak structure at√s′ ∼ 2m is not absorbed into θ.
It is very important for detection.
22 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Table of contents
1 Introduction
2 EWIMP effects on the processes
3 EWIMP detection and statistical method
4 Determination of EWIMP properties
5 Conclusion
22 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Peak structure revisited
Leff = LSM + C1g′2Bµνf
(− ∂2
m2
)Bµν + C2g
2W aµνf
(−D2
m2
)W aµν
1000 2000 3000 4000 5000 6000 7000√s′ [GeV]
−1.5
−1.0
−0.5
0.0
0.5
1.0δ σ
[%]
peak height⇔ C1, C2
peak position⇔ m
peak at√s′ = 2m
ℓℓ (NC) depends on C1, C2
ℓν (CC) depends only on C2
We can extract m,C1, C2
23 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Determination of (m,C1, C2) for 1.1TeV Higgsino
2 0 2 4 6 8 10 12C1
1
0
1
2
3
4
C2
30
3Maj
2Maj
20 21/2 21
m= 1. 1TeV
NC
CC
Combined
Solid (Dotted) : 2σ (1σ)
nY : SU(2)L n-plet
with U(1)Y charge Y
− Only doublet is allowed
− m ∼ 1.1TeV±100GeV
2 0 2 4 6 8 10 12C1
900
1000
1100
1200
1300
1400
1500
m [
GeV
]
21
C2 = 1
NC
CC
Combined
1 0 1 2 3 4C2
900
1000
1100
1200
1300
1400
1500
m [
GeV
]
C1 = 1
NC
CC
Combined
24 / 25
Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion
Conclusion
I have introduced a way for probing EWIMPs with Precise
measurement at 100 TeV colliders
I also introduced fitting based analysis, where systematic errors
are absorbed into the fit function
All the errors we have considered are fitted well
Strong discovery potential for short lifetime Higgsino
850 GeV (1.7 TeV) at 5σ (95% C.L.)
The signal shape of the EWIMP effect can also be used to
determine the EWIMP properties (mass, charge)
Peak at√s′ = 2m is important for all the analysis
25 / 25
Backup slides
25 / 25
Higgsino phenomenology
Chargino neutralino mass difference H. Fukuda, et al. [1703.09675]
∆m+ = ∆mrad +∆mtree
∆mrad ≃ 1
2α2mZs
2W
(1− 3mZ
2πmχ±
)≃ 355MeV,
∆mtree ≃v2
8|µ|[|X|∆X + sin 2β ℜ(Y )] ∼ 1GeV
∣∣∣∣ µ
Mi
∣∣∣∣ ,with X,Y = µ∗(g21/M1 ± g22/M2), ∆X =
√1− sin2 θX sin2 2β
cτ ≃ 0.7 cm
[(∆m+
340MeV
)3√
1− m2π
∆m2+
]−1
26 / 25
Future prospects for Higgsino at indirect detection
B. Bhattacherjee, et al. [1405.4914] R. Krall, et al. [1705.04843]
Wino Dark Matter Mass (GeV)310
)-1
s3v
(cm
σ
-2610
-2510
-2410
-2310
-2210Combined
Fermi-LAT (15 yrs)+ GAMMA-400 (10 yrs)
) = 0.1All J
10 (logδ
100 200 500 1000 20001
510
50100
5001000
mχ [GeV]
<σv>
[10-26cm
3 /s]
Continuum Gamma Rays: χ0χ0→WW+ZZ
Winos
Higgsinos
HESS GC
Fermi Dwarfs
27 / 25
Studies of indirect search at collider
Applicable to Higgsino independent of life time
qa
qb
�
�/ν
χ0, χ±
γ, Z,W
1
2
3
4
5
6
7
8
9
10
200 400 600 800 1000 1200
n
Mass [GeV]
“Higgsino”Wino
5plet MDM
obsereved 36 fb−1
expeceted 3 ab−1
δmW (1σ) ILC250 (0.2%sys.)
S. Matsumoto, et al.
Previous analysis:
D. S. M. Alves, et al. [1410.6810] @ LHC, 100 TeV
C. Gross, et al. [1602.03877] @ LHC
M. Farina, et al. [1609.08157] @ LHC
K. Harigaya, et al. [1504.03402] @ lepton collider
S. Matsumoto, et al. [1711.05449] @ HL-LHC
Up to HL-LHC era
Only a part of allowed region probed
mW < 300 GeV ≪ 3 TeV
mH < 150 GeV ≪ 1 TeV
28 / 25
From parton-level to proton cross section
Proton cross section at√s = 100 TeV can be obtained using
dLab
dmℓℓ≡ 1
s
∫ 1
0dx1dx2 fa(x1)fb(x2)δ(
m2ℓℓ
s− x1x2)
fa(x) : parton distribution function (PDF) for a
dσ
dmℓℓ=
∑a,b
dLab
dmℓℓ
dσab
dmℓℓ
29 / 25
CC process and transverse mass
For ℓν (CC), neutrino is missing
We can use pT,miss and transverse mass mT instead:
m2T ≡ 2pT,ℓ pT,miss(1− cosϕT,ℓ,miss)
(mT ≃√s′ if pℓ,z, pν,z are small)
beam axis
transverse plane
pT,miss
pT,l
ΦT,l,miss
0.0 0.5 1.0 1.5 2.0Ratio mT/m`ν
0
500
1000
1500
2000
2500
3000
3500
4000
4500
# o
f events
peak atmT =m`ν
mT >m`ν :detector effect
mT distribution in unit of m`ν
30 / 25
δσ as function of mT
ℓν (CC) events are binned by mT
1000 2000 3000 4000 5000 6000 7000√s′ [GeV]
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
δ σ[%
]
peak at√s′ = 2m
HiggsinoWino5-plet scalar
1000 2000 3000 4000 5000 6000 7000mT [GeV]
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
∆N/N
[%]
peak structure remains
HiggsinoWino5-plet scalar
Peak structure exists as a function of mT
31 / 25
Event generation in detail
EWIMP effect can be included with δabσ (mℓℓ)
Number of events xi in i-th bin mminℓℓ < mℓℓ < mmax
ℓℓ
For SM, xi =∑
mminℓℓ <mobs
ℓℓ <mmaxℓℓ
1
For SM + EWIMP, xi =∑
mminℓℓ <mobs
ℓℓ <mmaxℓℓ
[1 + δabσ (mtrue
ℓℓ )]
Each event in SM data set has {mobsℓℓ ,mtrue
ℓℓ , a, b}
mobsℓℓ : observed mℓℓ from Delphes3 output
mtrueℓℓ : true mℓℓ from MadGraph5 aMC@NLO output
a, b : initial partons from MadGraph5 aMC@NLO output
∗ Detector effect causes mobsℓℓ = mtrue
ℓℓ
32 / 25
Statistical treatment in our analysis
xi(µ) ≡∑events
[1 + µ δabσ (mchar)
]; xi(θ, µ) ≡ xi(µ)fi(θ)
Definition of q0 in fitting based analysis Wilk ’38
q0 = −2 lnL(x; ˆθ, µ = 0)
L(x; θ, µ)∼ χ2(1)
L(x;θ, µ) ≡∏i
exp
[−(xi − xi(θ, µ))
2
2xi(θ, µ)
]∏α
exp
[− θ2α2σ2
α
]− ˆθ maximizes numerator L(x; ˆθ, µ = 0)
− {θ, µ} maximizes denominator L(x; θ, µ)
Within our analysis, x = xi(µ = 1) and
{θ, µ} = {0, 1} with L(x; θ, µ) = 1
33 / 25
Disappearing track search of Wino
0 1000 2000 3000 4000 5000 6000 7000
Wino Mass m [GeV]
0
1
2
3
4
5
6S
/B
5
95%
20% bkg.
500% bkg.
14 TeV, 3 ab 1
27 TeV, 15 ab 1
100 TeV, 30 ab 1
34 / 25
Other sources of systematic errors
Smooth correction seems to be well absorbed into θ : Then,
estimation error in detector effect
may also be absorbed : our method can be applied!!
higher order loop effect within SM
background process
in principle possible to take account of (future task)
Yet remaining sources:
pile-up effect
underlying event
negligible thanks to clean signal with two energetic leptons35 / 25
Comparison of several statistical treatments
500 1000 1500 2000 2500 3000mass [GeV]
0
1
2
3
4
5
6
√ q 0
Higgsino (Gaussian)
Higgsino (Top-hat)
Higgsino (6 params)
Wino (Gaussian)
Wino (Top-hat)
Wino (6 params)
36 / 25
Statistical treatment for properties determination
Consider SM+EWIMP and focus on (m,C1, C2) dependence
xi(m,C1, C2) ≡∑events
[1 + δabσ (m,C1, C2;
√s′)
]Assume x for 1.1TeV Higgsino as example:
xi = xi(m = 1.1TeV, C1 = 1, C2 = 1)Although still 3.5σ hint we try...
q(m,C1, C2) ≡ minθ
[∑i:bin
(xi − xi(θ,m,C1, C2))2
xi(θ,m,C1, C2)+
5∑α=1
θ2ασ2α
]
q tests validity of model (m,C1, C2)
37 / 25
Statistical treatment for spin determination
Next, compare with scalar EWIMP effect
xi(m,C1, C2) ≡∑events
[1 + δ(scalar)σ (m,C1, C2;
√s′)
]
1000 2000 3000 4000 5000 6000 7000√s′ [GeV]
−1.5
−1.0
−0.5
0.0
0.5
1.0
δ σ[%
]
shape of peak⇔ EWIMP spin
peak at√s′ = 2m
Higgsino5-plet scalar
Again assume 1.1TeV Higgsino as example:38 / 25
Determination of spin
2 0 2 4 6 8 10 12C1
750
800
850
900
950
1000
1050
1100
1150
1200
m [
GeV
]
C2 = 1. 2
NC
CC
Combined
0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0C2
750
800
850
900
950
1000
1050
1100
1150
1200
m [
GeV
]
C1 = 0
NC
CC
Combined
2 0 2 4 6 8 10 12C1
0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
C2
1. 1TeV Higgsino & 920GeV scalar
NC
CC
Combined
Solid (Dotted) : 2σ (1σ)
− Best fit:
(m,C1, C2) = (920GeV, 0, 1.2)
− Bosonic EWIMP possibility
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