studying gauginos in supersymmetric model
TRANSCRIPT
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Studying Gauginos in Supersymmetric Model
at Future 100 TeV pp Collider
Takeo Moroi (Tokyo)
Asai, Chigusa, Kaji, TM, Saito, Sawada, Tanaka, Terashi & Uno
arXiv:1901.10389 [hep-ph]
YUCHE 2019 @ Yonsei University (2019.02.26)
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1. Introduction
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SUSY particles may be quite heavy (even if they exist)
) [GeV]g~m(
1000 1200 1400 1600 1800 2000 2200
) [G
eV
]0 1χ∼
m(
500
1000
1500
2000
2500
3000
35000 lep. [1712.02332]
0
1χ∼q q→g~
3 b-jets [1711.01901]≥0
1χ∼b b→g~
2 lep. SS [1711.01901, 1706.03731]≥ 3 b-jets +≥0
1χ∼t t→g~
0 lep. + 1 lep. [1712.02332, 1708.08232]0
1χ∼Wq q→g~
2 lep. SS ≥ 7-11 jets + 1 lep. + ≥0
1χ∼WZq q→g~
[1708.02794, 1708.08232, 1706.03731]
3 lep. [1805.11381, 1706.03731]≥2 lep. OS SF + ν∼/l~
via 0
1χ∼)νν(ll/q q→g~
[SUSY-2016-30]τ 1 ≥ν∼/τ∼ via 0
1χ∼)νν/ντ/ττ(q q→g~
[1802.03158]γ 1 ≥0
1χ∼ via G
~/Z)γ(q q→g~
ATLAS Preliminary
-1=13 TeV, 36.1 fbs
All limits at 95% CL
July 2018
)0
1χ∼
)<m(g~m(
800 1000 1200 1400 1600 1800 2000 2200
[GeV]g~m
0
200
400
600
800
1000
1200
1400
1600
[G
eV
]10χ∼
m
CMS
10χ∼q q→g~,g~g~→pp July 2018
(13 TeV)-135.9 fb
Expected
Observed
)miss
T1704.07781 (H
)T21705.04650 (M
)T
α1802.02110 (
Do we have a chance to study SUSY particles at colliders?
⇒ Future circular colliders (FCCs) with ECM ∼ 100 TeV maybe an option
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Today, I would like to discuss:
• FCC studies of pure gravity mediation model of SUSYbreaking based on anomaly mediation
• In particular, measurements of gaugino masses
Outline
1. Introduction
2. Model
3. Gauginos at FCCs
4. Gaugino Mass Determinations
5. Summary
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2. Model
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Mass spectrum of our interest
• Sfermion and Higgsino masses are of O(100) TeV
⇒ Heavy stops are good for mh ≃ 125 GeV
⇒ SUSY CP / flavor problems are relaxed
• Gaugino masses are loop suppressed, and are of O(1) TeV
⇒ Wino can be dark matter
⇒ Gauginos are primary targets of collider experiments
Such a mass spectrum is phenomenologically viable
⇒ What is the underlying theory?
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Anomaly mediation + pure gravity mediation[Giudice, Luty, Murayama & Rattazzi; Randall & Sundrum; Ibe, TM & Yanagida;
Ibe & Yanagida; Arkani-Hamed et al.]
MSSM
Higgsinos
Sfermions
Gauginos
D = 6 Kahler interaction
Anomaly mediation
Giudice-MasieroSUSY breaking sector
(No singlet)
• The most general supergravity Lagrangian with Planck-suppressed interactions
• No singlet in SUSY breaking sector
• Scalar masses are of the order of the gravitino mass m3/2
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Gaugino masses in the PGM model
M1 ≃g21
16π2
(11m3/2 + L
)
M2 ≃g22
16π2
(m3/2 + L
)
M3 ≃g23
16π2
(−3m3/2
)
L ≡ µ sin 2βm2
A
µ2 −m2A
lnµ2
m2A
• Wino (gaugino for SU(2)L) is likely to be the LSP
•∣∣∣∣∣∣10g
21
3g23mg̃ −
g21g22mW̃
∣∣∣∣∣∣<∼mB̃<∼
10g213g23
mg̃ +g21g22mW̃
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Motivation 1: Wino LSP as dark matter
0
0.1
0.2
0.3
1 2 3Wino Mass (TeV)
Non−perturbativePertu
rbativ
e
Ω (
Win
o)
[Hisano, Matsumoto, Nagai, Saito & Senami] [Moroi, Nagai, Takimoto]
• Thermally produced Wino can be DM, if mW̃ ≃ 2.9 TeV
⇒ Can we test such a Wino at colliders?
• Non-thermal production of Wino DM is also possible
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Motivation 2: Heavy stops are good for mh ≃ 125 GeV
m2h ≃ m2
Z cos2 2β +3m4
t
2π2v2
log m2t̃
m2t
+A2
t
m2t̃
1− A2t
12m2t̃
[Okada, Yamaguchi & Yanagida; Ellis, Ridolfi & Zwirner; Haber & Hempfling]
[TeV] S
M10
2103
10
[G
eV
]h
m
105
110
115
120
125
130
135
= 10βtan
= 5βtan
= 4βtan
= 3βtan
= 2.5βtan
⇒ The stop masses of O(10− 1000) TeV are suggested
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Motivation 3: Cosmological gravitino problemWino Mass = 500 GeV Wino Mass = 1 TeV
He4
DD
He4He (ITG)4He (ITG)4
He / D3
ΩLSP
M2 = 1.0 TeV
M1 = 1.4 TeV
M3 = 3.0 TeV
M2 = 0.5 TeV
M1 = 0.9 TeV
M3 = 2.0 TeV
[Kawasaki, Kohri, TM, Takaesu]
⇒ With m3/2>∼ 10 TeV, the reheating temperature as high as
TR>∼ 109 GeV is possible
⇒ Simple thermal leptogenesis may work[Buchmuller, Di Bari & Plumacher; Giudice, Notari, Raidal, Riotto & Strumia]
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Summary of Motivations
• Higgs mass of mh ≃ 125 GeV is easily realized
• Wino can be the LSP, which is a viable candidate of DM
• Cosmological gravitino problem is easily avoided
• Gauge coupling unification is OK
• SUSY CP / flavor problems may be avoided
Hierarchy between the SUSY scale and the EW scale is sizable
⇒ It’s better than the hierarchy between Planck scale andthe EW scale
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3. Gauginos at FCCs
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Let us consider
• How and how well we can determine gaugino masses
• Possibility to test the scenario
Sample points for MC studies (mW̃ < mB̃ < mg̃)
Point 1 Point 2
m3/2 [TeV] 250 302L [TeV] 800 756
mB̃ [TeV] 3.7 4.1mW̃ [TeV] 2.9 2.9mg̃ [TeV] 6.0 7.0
σ(pp → g̃g̃) [fb] 7.9 2.7
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Gluino decay
g̃ → q̄qB̃, q̄qW̃
q~
g~
q
q
B~ q
~
g~
q
q
W~
Assumptions:
• Br(g̃ → qq̄W̃ ) = Br(g̃ → qq̄B̃) = 0.5
• Gluino decays into all the generations universally
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Bino decay
B̃ → W∓W̃±, hW̃ 0
B~
W~
B~
h
W~
W
0
In the sample point of our choice:
• B̃ → W̃±W∓ dominates
• B̃ → ff̄W̃± is negligible
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Charged Wino decay: W̃± → W̃ 0π±
• ∆mW̃ ≃ 165 MeV
• cτW̃±→W̃ 0π± ≃ 5.8 cmW~
π
W~ 0
Charged Wino may be identified as short high-pT track
• W̃±-tracks can be reconstructed by inner pixel detector
• Requiring W̃±-like tracks, SM background can be reduced
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Long-lived W̃± at FCC-hh: case with pp → W̃±W̃±,0j
• Inner pixel detector has several layers at LT<∼ 10− 15 cm
[Saito, Sawada, Terashi & Asai 1901.02987]
2000− 1500− 1000− 500− 0 500 1000 1500 2000
z [mm]
0
50
100
150
200
250
300
350
400
450
500
Ra
diu
s [m
m]
2−10
1−10
1
10
210
310
410
510
610
Nu
mb
er
of ch
arg
ino
de
ca
ys
-1 = 100 TeV, 30 absFCC-hh,
Alternative layout (#3)
0 1 2 3 4 5
Chargino mass [TeV]
Higgsino
Wino
-1=100 TeV, 30 abs discovery, FCC-hh, σ5
-1=14 TeV, 3 absExpected exclusion, HL-LHC (ATLAS),
-1=14 TeV, 3 abs discovery, HL-LHC (ATLAS), σ5
-1=13 TeV, 36.1 fbsObserved exclusion, ATLAS,
Disappearing Track
• FCC-hh may cover the Wino mass up to 4− 5 TeV
• Sensitivity depends on the detector layout
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The events of our interest: gluino pair production
• Multi-jets
• Charged Wino track(s), identified by the pixel detector
Beam pipe (IP)
Inner pixex detector
Outer tracker
ECAL
HCAL
Charged Wino
Jet
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Expectation for the pixel detector
• 4th or 5th layer at LT ∼ 10− 15 cm
• Timing information is available: δt ∼ O(10 ps)
Timing information can be converted to the Wino velocity
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
δ β
/ β
β
δt = 50psec
δt = 40psec
δt = 30psec
δt = 20psec
δt = 10psec
⇒ δβ
β∼ (a few− 10) %× β(true)
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4. Gaugino Mass Determinations
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Flow-chart of our MC study
MadGraph5 for gluino pair production
ROOT
PYTHIA (decay and hadronization)
Delphes (detector simulation)
Analysis Code
Cuts
Invariant masses
Hemisphere analysis...
Wino velocity smearing
Wino info.
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Requirements on signal events:
• Two W̃±-tracks with LT > 10 cm and |η| < 1.5
• p(miss)T > 1 TeV
p(miss)T : Missing pT evaluated only from jets
We assume:
• Charged Wino can be identified if LT > 10 cm
• Velocity resolution of W̃± is 6 %
• There is no error in the charged Wino direction
Wino track can also be used to eliminate SM backgrounds
⇒ Fake track rate ∼ O(10−5) per track
⇒ SM backgrounds are negligible
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Measurement 1: Wino mass
• Wino velocity may be determined with timing information
• Momenta of Winos can be estimated using MET infor-mation (if two Wino tracks are observed)
⇔ Momentum is assumed to be carried away by jets andWinos
We determine Wino momenta by solving:
c1n⃗W̃1,T+ c2n⃗W̃2,T
= −p⃗miss ≡ −∑i:jets
p⃗i,T
p⃗W̃1= c1n⃗W̃1
p⃗W̃2= c2n⃗W̃2
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Wino mass in terms of observables:
m(rec)
W̃=
1
βW̃±γW̃±|p⃗W̃±| ≡
√1− β2
W̃±
βW̃±|p⃗W̃±|
We use the events with:
• W̃± with LT > 10 cm and β(obs) < 0.8 for reconstruction
• 2nd W̃± track for background reduction
• No isolated lepton
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Reconstructed Wino mass
histmwno1
Entries 250
Mean 2952
Std Dev 920.8
Mwno(Gauss) 54.8± 2911
σ 54.8± 695.8
A 2.2± 23.2
C 0.2527± 0.7339
0 2000 4000 6000
Wino Mass (GeV)
0
5
10
15
20
25
30-1#
/ 2
00
Ge
V / 1
0 a
bhistmwno1
Entries 250
Mean 2952
Std Dev 920.8
Mwno(Gauss) 54.8± 2911
σ 54.8± 695.8
A 2.2± 23.2
C 0.2527± 0.7339
Sample Point 1 histmwno1
Entries 103
Mean 3104
Std Dev 1056
Mwno(Gauss) 101.9± 3119
σ 105.3± 752.6
A 1.259± 7.987
C 0.2033± 0.4189
0 2000 4000 6000
Wino Mass (GeV)
0
2
4
6
8
10
-1#
/ 2
00
Ge
V / 1
0 a
b
histmwno1
Entries 103
Mean 3104
Std Dev 1056
Mwno(Gauss) 101.9± 3119
σ 105.3± 752.6
A 1.259± 7.987
C 0.2033± 0.4189
Sample Point 2
• True value: 2900 GeV
• Fit: Gaussian + constant
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Reconstructed Wino mass: pp → W̃+W̃−j
• True Wino mass: 2900 GeV
• βW̃± < 0.8
• p(miss)T > 1 TeV
0 2000 4000 6000
Wino Mass (GeV)
0
1
2
3
4
5
-1#
/ 2
00
Ge
V / 3
0 a
b
Wino Mass (10cm & 10cm)
histmwno1
Entries 32
Mean 2769
Std Dev 658.1
Mwno(Gauss) 113.8± 2775
σ 80.5± 643.8
A 0.859± 3.966
C 02− 2.787e±10 − 6.106e
Wino Mass (10cm & 10cm)
⇒ δm(obs)
W̃≃ 130 GeV (with L = 30 ab−1)
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Measurement 2: Bino mass
B~
W~
W : fat jet
: short high p trackT
• Wino momentum is known (if LT is long enough)
• W -jet may be identified as a fat jet
⇒ We use jets with mj ∼ mW
Reconstructed Bino mass (assuming mW̃ is known)
m(rec)
B̃=
√(mW̃uW̃± + pW )2 with uW̃± = (γW̃±, βW̃±γW̃±n⃗W̃±)
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Jet mass distribution (for Point 1)
40 60 80 100 120 140 160 180 200Jet Mass (GeV)
0
2000
4000
6000
8000
10000
-1#
/ 2 G
eV /
10 a
b
We require:
• W̃± with LT > 10 cm and β(obs) < 0.9 for reconstruction
• Jet with 70 GeV < mj < 90 GeV
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Reconstructed Bino mass (using true Wino mass)
histmbno1
Entries 581
Mean 4232
Std Dev 706.3
Mbno(Gauss) 9.3± 3628
σ 10.80± 70.38
A 2.90± 19.26
C 0.217± 3.917
3000 4000 5000 6000
Bino Mass (GeV)
0
5
10
15
20
25
30
-1#
/ 3
0 G
eV
/ 1
0 a
bhistmbno1
Entries 581
Mean 4232
Std Dev 706.3
Mbno(Gauss) 9.3± 3628
σ 10.80± 70.38
A 2.90± 19.26
C 0.217± 3.917
Sample Point 1 histmbno1
Entries 264
Mean 4353
Std Dev 701.9
Mbno(Gauss) 11.3± 4060
σ 10.80± 62.51
A 2.08± 10.51
C 0.137± 1.621
3000 4000 5000 6000
Bino Mass (GeV)
0
2
4
6
8
10
12
-1#
/ 3
0 G
eV
/ 1
0 a
b
histmbno1
Entries 264
Mean 4353
Std Dev 701.9
Mbno(Gauss) 11.3± 4060
σ 10.80± 62.51
A 2.08± 10.51
C 0.137± 1.621
Sample Point 2
• True value: 3660 GeV (Pt.1) / 4060 GeV (Pt.2)
• Fit: Gaussian + constant
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Measurement 3: Gluino mass (with hemisphere analysis)
pp
j
j j
j
j
jj
W~
W~
Hemisphere 1
Hemisphere 2
Reconstructed gluino mass
m(rec)g̃ =
√P 2Hemisphere with PHemisphere ≡ PW̃± +
∑j∈H
pj
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Hemisphere analysis with two observed Wino tracks
• Two charged Winos are assigned to different hemispheres:
W̃±A ∈ HA (A = 1, 2)
• For each high pT jet:ji ∈ H1: if d(pH1
, pji) < d(pH2, pji)
ji ∈ H2: if d(pH2, pji) < d(pH1
, pji)
Momentum of A-th hemisphere HA
pHA= pW̃±
A+
∑ji∈HA
pji
Distance function[See De Roeck (Editor), CMS Physics TDR]
d(pH , pj) =(EH − |pH | cos θHj)EH
(EH + Ej)2
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We study the invariant mass of hemispheres containing W̃±
• Two long enough W̃± tracks
• No isolated lepton
• We use jets with |η| < 2
Hemisphere analysis with two charged Winos
• Momenta of Winos are determined using missing momen-tum information
• Each hemisphere contains one W̃± (and jets)
• Invariant mass of the hemisphere is regarded as (recon-structed) gluino mass
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Reconstructed gluino mass (with true Wino mass):
histmgno1
Entries 756
Mean 6242
Std Dev 1782
Mgno(Gauss) 54.7± 5932
σ 49.3± 1224
A 2.17± 42.24
C 0.277± 1.687
5000 10000
Gluino Mass (GeV)
0
10
20
30
40
50
60
-1#
/ 2
00
Ge
V / 1
0 a
bhistmgno1
Entries 756
Mean 6242
Std Dev 1782
Mgno(Gauss) 54.7± 5932
σ 49.3± 1224
A 2.17± 42.24
C 0.277± 1.687
Sample Point 1 histmgno1
Entries 348
Mean 6883
Std Dev 1918
Mgno(Gauss) 100.0± 6631
σ 85.7± 1511
A 1.15± 15.54
C 0.2231± 0.7323
5000 10000
Gluino Mass (GeV)
0
5
10
15
20
25
-1#
/ 2
00
Ge
V / 1
0 a
b
histmgno1
Entries 348
Mean 6883
Std Dev 1918
Mgno(Gauss) 100.0± 6631
σ 85.7± 1511
A 1.15± 15.54
C 0.2231± 0.7323
Sample Point 2
• True value: 6000 GeV (Pt.1) / 7000 GeV (Pt.2)
• Fit: Gaussian + constant
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5. Summary
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Gaugino mass determinations may be possible
Sample Point 1 (with L = 10 ab−1):
δmB̃ δmW̃ δmg̃
δm(stat)
X̃8GeV 61GeV 59GeV
Due to δmW̃ 61GeV − 61GeV
Total 62GeV 61GeV 85GeV
⇒ Test of the model∣∣∣∣∣∣10g21
3g23mg̃ −
g21g22mW̃
∣∣∣∣∣∣<∼mB̃<∼
10g213g23
mg̃ +g21g22mW̃
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Information about the mechanism of SUSY breaking
Sample Point 1
Sample Point 1
⇒ Determination of m3/2, |L|, · · ·⇒ Impact on cosmology
FCC-hh can have significant impact on BSM studies
• Discovery
• Measurements