![Page 1: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/1.jpg)
1
Bhaskar DuttaTexas A&M University
Particle Theory Models and Dark Matter: A Status Update
October 31, 2017
Texas Tech University, Lubbock
![Page 2: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/2.jpg)
2
QuestionsSome Outstanding Issues of High Energy Theory
1. Dark Matter content ( is 27%)
2. Electroweak Scale
3. Ordinary Matter (baryon) Content ( is 5%)
4. Rapid Expansion of the Early Universe
5. Neutrino Mass and interactions...
Need: Theory, Experiment and Observation
DMΩ
bΩ
![Page 3: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/3.jpg)
3
Questions
![Page 4: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/4.jpg)
4
Current Status
Collider Experiments: LHCDirect Detection Experiments: DAMA, CDMS, XENON 100,
CoGeNT, LUX etc.Indirect Detection Experiments: Fermi, AMS, PAMELACosmic Microwave Sky: Planck, WMAPNeutrino Experiments: T2K, Daya Bay, Double CHOOZ,
RENO etc. COHERENT
What have we learnt? What is the status of theory models? What do we expect in the near future?Are we closing in?
![Page 5: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/5.jpg)
5
What have we learnt so far? LHC, Direct and Indirect Detection Experiments, Planck Data
Status of Models with DM Dark Matter: Cosmological History Dark Matter, Ordinary Matter Contents
Expectations Future Direct and Indirect Detection results Dark Matter at the LHC
Concluding Insights
Presentation Outline
![Page 6: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/6.jpg)
6
Large Hadron Collider(LHC)
Proton-Proton Collision
![Page 7: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/7.jpg)
7
Higgs Boson has been found Mass (mh) 125 GeVCompletes Standard Model
3 families of quarks, leptons, Gauge Bosons (force carriers) : W±, Z, γ, g
LHC: Higgs
Higgs mechanism breaks the SM symmetry spontaneously and generates mass for quarks, leptons, W, Z and Higgs
Symmetry breaking scale(Electroweak scale): 246 GeV
Much lower than the Planck scale: 1.22 x 1019 GeV
Mz=91.18 GeV, Mw=80.22 GeV
![Page 8: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/8.jpg)
8
• Higgs mass increases rapidly with scale mh2= m0
2+k Λ2: divergence problem solution needs fine tuning (1 part in 1032)
• SM prediction: mh<850 GeV to satisfy the unitarity in W scattering
• Fine tuning problem solved in supersymmetry due to fermions ↔ bosons symmetry
• Higgs mass predicted in SUSY Model?Minimal Supersymmetry Standard Model (MSSM):
loop correction prediction: mh<135 GeV
•Measured mass (125 GeV) appears in the tight MSSM window
LHC: Higgs
+= β2222 CosMm Zh Mz=91.18 GeV
![Page 9: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/9.jpg)
9
LHC: Supersymmetry
Most models predict: 1-3 TeV (colored particle masses)So far: No colored particle up to 1.9 TeV
Non-colored SUSY particles: 100 GeV to 1-2 TeV(Major role in the DM content of the Universe)
Weak LHC bound for non-colored particles hole in searches!
Trouble in Models with very tight correlation between colored and non-colored particles , e.g., minimal SUGRA/CMSSM
LHC + Direct Detection + Indirect Detection quite constraining
![Page 10: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/10.jpg)
10
Direct Detection Experiments
Any parameter space left?
DM
DM
CDMS, DAMA, CoGeNT:Signal for Low mass DM
LUX: No signal for Low or High DM mass
arXiv:1608.07648
Status of New physics/SUSY in the direct detection experiments:
• Astrophysical and nuclear matrix element uncertainties• No signal: some particle physics models are ruled out
![Page 11: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/11.jpg)
Indirect Detection: Fermi
11
: smaller than the thermal valueoannv ><σ
>< vannσ
Thermal DM 27%
Gamma-rays constraints: Dwarf spheroidals, Galactic center
Experimental constraints:
Fermi Collaboration: arXiv:1503.02641
LargeCross-sectionis constrained
![Page 12: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/12.jpg)
12
From Planck
http://public.planck.fr/images/resultats/2014-matiere-noire/plot_constraints_planck2014.jpg
![Page 13: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/13.jpg)
Indirect Detection Excess of positrons has been found by both
AMS, PAMELA and Fermi
13
Dark Matter Mass: More than 100 GeVTheory Models predictions: The excess will fall off
Pulsar can produce this excess
Is this excess due toDM annihilation?
Need Larger Cross-section (larger than the thermal cross-section 3x 10-26 cm3/sec)
![Page 14: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/14.jpg)
14
Probing Dark Matter
SM
Dark Energy68%
Atoms5%
Dark Matter27% +
Collider experiments
Overlapping region
DM content (CMB) + overlapping region:
Cosmological history, particle physics models, astrophysics
![Page 15: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/15.jpg)
Summary
Direct Production at the collider: SUSY lurking around? More Higgs? New signal?
Direct Detection and LHC: Low/high mass DM particle?
Indirect Detection and LHC: DM thermal/non-thermal/multi-component?
15
![Page 16: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/16.jpg)
~ 0.0000001 seconds
Dark Matter: When?
16
Now
![Page 17: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/17.jpg)
Dark Matter: ThermalProduction of thermal non-relativistic DM:
particlesSMDMDM ⇔+
particlesSMDMDM ⇒+
Universe cools (T<mDM)
particlesSMDMDM ⇔+
Boltzmann equation
][3 2,
2eqDMDMeqDM
DM nnvHndt
dn−−=+ σ
∫
∫+−
+−
=
6
/)(2
31
3
6
/)(2
31
3
)2(
)2(21
21
π
πσ
σ TEE
TEE
eq epdpd
vepdpd
vvolnostppfdgn /.
)2(),(
3
3
≡= ∫ π
m/T
3* Tgn
snY
s
==Y
![Page 18: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/18.jpg)
Dark Matter: Thermal
Freeze-Out: Hubble expansion dominates over the interaction rate
18
v1~DM σρc
DMDM nm=Ω
20~ DM
fmT
Dark Matter content:
Assuming : 2
2
~vχ
χασmf
αχ~O(10-2) with mχ ~ O(100) GeVleads to the correct relic abundance
m/T
freeze out
scm3
26103v −×=σY becomes constant for T>Tf
Nc G
Hπ
ρ83 2
0=
Y
Y~10-11 for mχ~100 GeVto satisfy the DM content
![Page 19: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/19.jpg)
Thermal Dark Matter
DM particle + DM Particle SM particles
Annihilation Cross-section Rate:
19
>< vannσ
DM
DM
DM
DM
f: SM particles; h, H, A: various Higgs, : SUSY particleNote: All the particles in the diagram are colorless
v1~DM σ
Ω
DM Abundance:
f~
scm3
26103v −×=σWe need to satisfy thermal DM requirement
![Page 20: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/20.jpg)
20
Suitable DM Candidate: Weakly Interacting Massive Particle (WIMP)
Typical in Physics beyond the SM (LSP, LKP, …)
Most Common: Neutralino (SUSY Models)
Neutralino: Mixture of Wino, Higgsino and Bino
Neutralino can give rise to larger/smaller annihilation rate
Larger/Smaller Annihilation Non-thermal Models
Thermal Dark Matter
![Page 21: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/21.jpg)
Thermal Dark Matter
Dark Energy68%
Atoms5%
Dark Matter27%
v1~DM σ
Ω
20~ DM
fmT
Dark Matter content:
Weak scale physics :
2
2
~vχ
χασmf
αχ~O(10-2) with mχ ~ O(100) GeVleads to the correct relic abundance
freeze out
scm3
26103v −×=σ
Mp
Inflation
TeV
GeV
MeVBBN
~ WIMP freeze-out
![Page 22: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/22.jpg)
Non-standard thermal history at is generic in some explicit high Scale theories.
fTfTT >
Acharya, Kumar, Bobkov, Kane, Shao’08Acharya, Kane, Watson, Kumar’09Allahverdi, Cicoli, Dutta, Sinha,’13
Status of Thermal DMThermal equilibrium above is an assumption.
DM content will be different in non-standard thermal histories Barrow’82, Kamionkowski, Turner’90
DM will be a strong probe of the thermal history after it is discovered and a model is established.
![Page 23: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/23.jpg)
23
Non-Thermal DM
Decay of moduli/heavy field occurs at:
)MeV5(TeV100
~2/3
2/1
φmcTr
Tr ~ MeV : Not allowed by BBN
[Moduli : heavy scalar fields gravitationally coupled to matter]
>< vannσ : different from thermal average, is not 27% Non-thermal DM can be a solution
DM from the decay of heavy scalar field, e.g., Moduli decay
For Tr<Tf: Non-thermal dark matter
v1~DM σ
Ω
Decay of moduli produce both DM and ordinary matter
Moroi, Randall’99; Acharya, Kane, Watson’08,Randall; Kitano, Murayama, Ratz’08; Dutta, Leblond, Sinha’09; Allahverdi, Cicoli, Dutta, Sinha,’13Baer, Choi, Kim, Roszkowski’ 14 Mp
Inflatio
TeV
GeV
MeV
![Page 24: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/24.jpg)
24
Non-thermal DM
Non-thermal DM Production from moduli decay
Ordinary Matter and DM from moduli decay ⇒ Cladogenesis of DM and Ordinary Matter (Baryons) [Allaverdi, Dutta, Sinha’11]
Cladogenesis: is an evolutionary splitting event in a species in which each branch and its smaller branches forms a "clade", an evolutionary mechanism and a process of adaptive evolution that leads to the development of a greater variety of sister species.
![Page 25: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/25.jpg)
25
Mp
Inflation
TeV
GeV
MeVBBN
~ WIMP freeze-out
Mp
Inflation
TeV
GeV
MeVBBN
Non-thermal DM
Large multicomponent/non-thermal; Small Non-thermal
Probe directly at Indirect and Collider experiments
>< vannσ
DM content: summary
>< vannσ
![Page 26: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/26.jpg)
26
Future: Direct
Neutrino background seems to be a real problem!
![Page 27: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/27.jpg)
27
Neutrino background difficulties:
1. Measure the background very well in other experiments2. Measure the recoil spectrum to identify DM from neutrino
Future: Direct
1. Background is due to coherent scattering of solar and atmospheric neutrinos
Measure the coherent scattering: reactor (𝝂𝝂𝒆𝒆) and stopped pion sources (𝝂𝝂𝝁𝝁,𝝂𝝂𝝁𝝁, 𝝂𝝂𝒆𝒆)
Recent results: COHERENT (Science 03 Aug 2017)Future results: Miner, MINER+CONNIE : Texas A&M University
Determine the neutrino background carefully
2. Shape of the recoil spectra are different for different operators Identify neutrino from DM
Dent, Dutta, Newstead, Strigari, Walker, 2016
![Page 28: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/28.jpg)
28
Future: Indirect
DM+DM 𝑓𝑓 + 𝒇𝒇 𝟐𝟐𝑓𝑓 + 𝟐𝟐𝒇𝒇
b quark final states have the best constraints
Clark, Dutta, Strigari, arXiv:1709.07410
<σv>
cm
3 /s
MDM (GeV)
![Page 29: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/29.jpg)
29
Dark Matter at the LHC
Annihilation of lightest neutralinos (DM particles) quarks, leptons etc.At the LHC: proton + proton DM particles
DM Annihilation diagrams: mostly non-colored particlese.g., sleptons, staus, charginos, neutralinos, etc.
How do we produce these non-colored particles and the DM particle at the LHC? Can we measure the annihilation cross-section ?>< vannσ
![Page 30: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/30.jpg)
30
The signal : SM particles + DM particle(Missing energy)
Via Cascade decays at the LHC
(or l+l-, τ+τ−)DM
DMColored particles are produced and they decay finally into the weakly interacting stable particle
High PT jet
(or l+l-, τ+τ−)LHC is very complicated
![Page 31: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/31.jpg)
DM at the LHC
31
LHC has a blind spot for productions of non-colored particle
Special search strategy needed to extract the signal
The W boson (colorless) coming out of high energy protons can produce colorless particlesVector Boson Fusion(VBF)
New way of understanding DM or new physicssector at the LHC
Using a high ET jet + missing energy
Dutta, Gurrola, Kamon et al ’13,’14,’15,’16
![Page 32: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/32.jpg)
32
Cross Sections via VBFDM Via W at the LHCjjpp 0
10
1~~ χχ→
DM
![Page 33: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/33.jpg)
33
DM Content via VBF
Simultaneous fit of various observables:
How to check that LHC observations lead to correct dark matter content? Measure Ω at the LHC (Ω is 27%: Planck Measurement)
Dutta, Kamon etal, Phys.Rev.Lett. 111 (2013) 061801
![Page 34: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/34.jpg)
34
DM via jets +missing energy
CMS PAS EXO-16-048
Kunori et al
![Page 35: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/35.jpg)
35
Concluding InsightsModel ideas have constraints from LHC, Planck,
Neutrino data, direct and indirect detection constraints Higgs mass is within the supersymmetry model prediction
window Non-thermal Dark matter is well motivated Both Thermal and Non-thermal Dark matter have
allowed parameter spaceNon-thermal scenarios can allow us to understand the
Ordinary Matter-Dark Matter coincidence puzzleDetermination of the property of DM is crucial: LHC, direct and Indirect detections identify DM modelNeed to investigate colorless particles (suitable for DM
calculation), new force mediators at the LHC and in other experiments (e.g., Coherent neutrino scattering)
![Page 36: Particle Theory Models and Dark Matter: A Status Updatepeople.physics.tamu.edu/dutta/talks_2017/colloquiumTTU.pdf · Particle Theory Models and Dark Matter: A Status Update. October](https://reader035.vdocuments.us/reader035/viewer/2022063018/5fdcd354a877a370114b68c5/html5/thumbnails/36.jpg)
36
Concluding Insights