Matter Models Matt Gonderinger UW Madison NPAC Pheno, 2010.05.11 - PowerPoint PPT Presentation

Vacuum Stability of Singlet Dark Matter Models Matt Gonderinger UW Madison – NPAC Pheno, 2010.05.11 MG, Y. Li, H. Patel and M. J. Ramsey-Musolf, JHEP 1001 (2010) 053 [0910.3167]

Outline  Motivation for scalar singlets  The real scalar singlet potential & parameters  Explanation of vacuum stability analysis  Constraining scalar singlet dark matter Vacuum stability analysis restricts mass , self-interaction , and new physics scale in a real scalar singlet model of dark matter M. Gonderinger, Pheno 2010

Why study scalar singlets?  Dark matter candidate if stable  Mixing with the Higgs  Play a role in electroweak phase transition  Arise in MSSM extensions  They are simple! M. Gonderinger, Pheno 2010

Real Scalar Singlet 𝑊 = 𝑛 2 𝐼 † 𝐼 + 𝜇 2 6 𝐼 † 𝐼 +𝑏 2 𝑇 2 𝐼 † 𝐼 + 𝑐 2 2 𝑇 2 + 𝑐 4 4 𝑇 4  ℤ 2 symmetry  Minimum at ℎ = 𝑤 = 246 𝐻𝑓𝑊, 𝑇 = 0  ⇒ the singlet is a stable dark matter candidate M. Gonderinger, Pheno 2010

Parameters 2 = 𝜇𝑤 2 /3 (no mixing between the Higgs and  𝑛 ℎ singlet) 2 = 𝑐 2 + 𝑏 2 𝑤 2 (small 𝑛 𝑇 and moderate 𝑏 2 ⇒ 𝑐 2 < 0 )  𝑛 𝑇  𝑏 2 determines both direct detection cross section and relic density 1 ∼ 1 2 Ω 𝑇 ∼ 𝜏 𝑒𝑒 ∼ 𝑏 2 2 𝜏 𝑏𝑜𝑜 𝑏 2 M. Gonderinger, Pheno 2010

Diagrams ∼ 𝑏 2 𝑤 M. Gonderinger, Pheno 2010

Vacuum Stability  RG-improved one-loop effective potential is a function of the two fields, ℎ and 𝑇  Require that ℎ = 𝑤, 𝑇 = 0 be the global minimum below new physics scale Λ  Choose parameters to avoid:  Second minimum along ℎ axis due to running of 𝜇  Deeper minimum along 𝑇 axis when 𝑐 2 < 0  Runaway direction caused by negative 𝑏 2 M. Gonderinger, Pheno 2010

Cartoons 𝑏 2 > 0 𝑇 𝑊 𝑊 𝑇 ℎ 𝑊 ≤ 𝑊 𝐹𝑋 𝛾 𝜇 ∼ 4𝜇 2 − 36𝑧 𝑢 4 𝑐 2 < 0 ℎ 2 + ⋯ +12𝑏 2 M. Gonderinger, Pheno 2010

Dark Matter CDMS Vacuum stability excluded region excluded (not most recent results) Λ = 1 𝑈𝑓𝑊 Super-CDMS WMAP sensitivity region M. Gonderinger, Pheno 2010

More Dark Matter Λ = 10 9 𝐻𝑓𝑊 Λ = 1 𝑈𝑓𝑊 M. Gonderinger, Pheno 2010

Even More Dark Matter Λ = 1 𝑈𝑓𝑊 Λ = 10 9 𝐻𝑓𝑊 M. Gonderinger, Pheno 2010

OMG Dark Matter XENON100? He et al., [1004.3464] M. Gonderinger, Pheno 2010

Hope  Can the real scalar singlet be a very light (𝑛 𝑇 < 10 𝐻𝑓𝑊) dark matter particle?  Possibly, but vacuum stability requires…  a low new physics scale Λ ( 𝑏 2 is small)  a large self-interaction 𝑐 4 ( 𝑐 2 is negative)  A more thorough analysis is necessary for this small 𝑛 𝑇 region (including most recent experimental limits) M. Gonderinger, Pheno 2010

Summary Direct detection + relic density Constrain mass, self- interaction, new physics scale Vacuum stability analysis M. Gonderinger, Pheno 2010

For the Future  Vacuum stability is a generally interesting analysis  Complex scalar singlet?  Finite temperature electroweak phase transition?  Metastable vacuum and tunneling?  Non-zero singlet vev?  Higgs phenomenology? M. Gonderinger, Pheno 2010