1. How Heavy can Neutralino Dark Matter be?
Hajime Fukuda (Kavli IPMU)
Based on
with S. Shirai and F. Luo

2. Outline Introduction Coannihilation
Coannihilation through the brown muck

3. Introduction

4. TeV scale supersymmetry (SUSY)
Minimal SUSY SM (MSSM) at TeV scale has many motivations
Naturalness (?)
Coupling unification
Dark matter

5. Is MSSM getting unfavored?
MSSM parameter regions
easy to LHC
is getting unfavored
ATLAS Summary Plot

6. Is there a goal for SUSY search?
We can impose an upper bound for the lightest SUSY particle (LSP) mass If
R-parity is conserved, so that the LSP is DM
LSP abundance is given by thermal freeze-out
Once the Universe is hot enough and the LSP is in the thermal bath

7. Why does an upper bound exist?
WIMP Miracle
Ω ℎ 2 ∼ −26 c m 3 /s 〈𝜎𝑣〉
For too large LSP mass, 〈𝜎𝑣〉 is too small and Ω ℎ 2 is too large
It’s quite important to clarify the upper bound of 〈𝜎𝑣〉 to get the LSP mass upper bound

8. Coannihilation

9. Coannihilation LSP Candidates: 𝑏 , 𝑤 , ℎ
Color
Neutral
LSP Candidates: 𝑏 , 𝑤 , ℎ
If a colored sparticle “helps” LSP annihilation, effective 〈𝜎𝑣〉 is much enhanced ⇒ Coannihilation

10. Mass difference is less than about 𝑇 𝑓𝑟𝑒𝑒𝑧𝑒 ∼ 𝑚 𝐿𝑆𝑃 30
Mass spectrum
Mass
𝑞 or 𝑔
Mass difference is less than about 𝑇 𝑓𝑟𝑒𝑒𝑧𝑒 ∼ 𝑚 𝐿𝑆𝑃 30
LSP

11. How is LSP Annihilation Enhanced?
Amount
/d.o.f.
@ 𝑇∼ 𝑇 𝑓𝑟𝑒𝑒𝑧𝑒
𝑞 or 𝑔
LSP

12. How is LSP Annihilation Enhanced?
Amount
/d.o.f.
@ 𝑇∼ 𝑇 𝑓𝑟𝑒𝑒𝑧𝑒
𝑞 or 𝑔
LSP

13. How is LSP Annihilation Enhanced?
Amount
/d.o.f.
@ 𝑇∼ 𝑇 𝑓𝑟𝑒𝑒𝑧𝑒
Scattering with 𝑞 or 𝑔
𝑞 or 𝑔
LSP

14. Mass bound by pert. coannihilation
Bino LSP coannihilation
with gluino ⇒ 8 TeV
with squark ⇒ 2 TeV
Can we go beyond this? – Use of brown muck
Assume bino LSP and degenerated right handed squark
See e.g. Ellis, Luo, Olive 15
Ibarra et al. 15
(Non-perturbative effect of QCD)
Gross et al. 18
HF, Luo, Shirai 18

15. Coannihilation through the brown muck

16. Brown muck
Kang et al. 06
If the squark lives after the QCD PT, the quark/gluon cloud surrounds it (brown muck)
𝑅 ℎ𝑎𝑑 = Λ ℎ𝑎𝑑 −1

17. Brown muck collision 𝐸 𝑚𝑢𝑐𝑘 ∼𝑇→ 𝑣 𝑚𝑢𝑐𝑘 ∼ 𝑇/ 𝑀 𝑞 𝐹∼1/ 𝑅 ℎ𝑎𝑑 2
Kang et al. 06
𝐸 𝑚𝑢𝑐𝑘 ∼𝑇→ 𝑣 𝑚𝑢𝑐𝑘 ∼ 𝑇/ 𝑀 𝑞
𝐹∼1/ 𝑅 ℎ𝑎𝑑 2
Δ𝑡∼ 𝑅 ℎ𝑎𝑑 / 𝑣 𝑚𝑢𝑐𝑘
→Δ𝑝∼𝐹Δ𝑡∼ 𝒪(1)𝑝 𝑚𝑢𝑐𝑘
𝑣 𝑚𝑢𝑐𝑘

18. Brown muck collision Large annihilation?
Kang et al. 06
Brown mucks form a bound state with 𝜎∼𝜋 𝑅 ℎ𝑎𝑑 2
Thus, if the bound state decays soon, the effective DM annihilation cross section is 𝜎𝑣 𝑒𝑓𝑓 ∼𝜋 𝑅 ℎ𝑎𝑑 2 𝑣 𝑚𝑢𝑐𝑘
Large annihilation?

19. Bound state decay Bound state doesn’t decay immediately
Kang et al. 06
Bound state doesn’t decay immediately
Due to the small overwrap of the wavefunctions
𝑝 𝑞 ∼ 𝑀 𝑞 𝑇
𝑅∼ 𝑅 ℎ𝑎𝑑
→𝐿∼ 𝑝 𝑞 𝑅∼ 𝑀 𝑞 TeV

20. Fate of the bound state
Eventually, it deexcites into the ground state and annihilates efficiently
Tracking the deexcitation process is essential to estimate 𝜎𝑣 𝑒𝑓𝑓

21. Deexcitation & Destruction
During deexcitation, squarkonium can also be broken by squark decay/particle collision
In total, the effective annihilation cross section for the squark is
𝜎∼ Γ 𝑑𝑒𝑒𝑥𝑡 Γ 𝑑𝑒𝑒𝑥𝑡 + Γ 𝑑𝑒𝑠𝑡 𝜋 𝑅 ℎ𝑎𝑑 2

22. Deexcitation process Dipole emission Collision b/w pion/photon
Boltzmann supp. for pion

23. Destruction process
Decay (& collisional decay)
Collision

24. Annihilation efficiency
Γ 𝑑𝑒𝑒𝑥𝑡 Γ 𝑑𝑒𝑒𝑥𝑡 + Γ 𝑑𝑒𝑠𝑡

25. Chemical Equilibrium

26. Chemical Equilibrium
Difficult to maintain!

27. Chemical Equilibrium Boltzmann suppression for meson is large
Weak interaction is too weak

28. Chemical equilibrium: result

29. Result
For bino LSP

30. Detection
Direct detection is effective

31. Result

32. Result

33. Summary
Using QCD non-perturbative effect, the DM mass can be as heavy as 300 TeV
Since the squark and bino is highly degenerated, the direct detection is effective for light flavor squarks

35. Brown muck: flavor

36. Result

37. Difference b/w Strumia’s group
They didn’t consider the confinement effect
It seems that they simply extrapolate the perturbative treatment of the bound state
They didn’t consider chem. eq.

38. What if for other NLSP? Left-handed squark NLSP Gluino NLSP
d.o.f is larger
Up and down type squarks are degenerated
Gluino NLSP
Chem. eq. is hard to maintain
The squark must be light
No Larmor radiation

39. What if for other LSP? Wino LSP Higgsino LSP d.o.f is larger
Chem. eq. w/ gluino can be achieved by 𝒪(100 TeV) squark & gluino ?