How Heavy can Neutralino Dark Matter be? Hajime Fukuda (Kavli IPMU) Based on 1812.02066 with S. Shirai and F. Luo

Outline Introduction Coannihilation Coannihilation through the brown muck

Introduction

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

Is MSSM getting unfavored? MSSM parameter regions easy to see @ LHC is getting unfavored ATLAS Summary Plot

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

Why does an upper bound exist? WIMP Miracle Ω ℎ 2 ∼0.1 10 −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

Coannihilation

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

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

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

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

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

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

Coannihilation through the brown muck

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

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

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?

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∼10 𝑀 𝑞 TeV

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

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

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

Destruction process Decay (& collisional decay) Collision

Annihilation efficiency Γ 𝑑𝑒𝑒𝑥𝑡 Γ 𝑑𝑒𝑒𝑥𝑡 + Γ 𝑑𝑒𝑠𝑡

Chemical Equilibrium

Chemical Equilibrium Difficult to maintain!

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

Chemical equilibrium: result

Result For bino LSP

Detection Direct detection is effective

Result

Result

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

Brown muck: flavor

Result

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.

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

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 ?