Phase Transi+ons in Twin Higgs Models Kohei Fujikura (TITECH) Collaborators: Kohei Kamada (IBS), Yuichiro Nakai (Rutgers.U), Masahide Yamaguchi (TITECH). 1
Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transitions in Twin Higgs Models (Cosmological impact) 2
Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transi8ons in Twin Higgs Models (Cosmological impact) 3
Standard Model is incomplete SM describes phenomenology around the electroweak scale However, there are problems… Dynamics of Electroweak Symmetry Breaking V ( H ) SM Higgs Potential: V ( φ ) = m 2 | H | 2 + λ SM | H | 4 v SM √ 2 m 2 R = m 2 bare + δ m 2 H O ( M 2 pl ) O ( M 2 pl ) Why??? 4
Naturalness of the Higgs mass Higgs self-coupling SU (2) W Top quark δ m 2 + + h = − 3 y 2 + 9 g 2 + λ 4 π 2 Λ 2 t 32 π 2 Λ 2 2 4 π 2 Λ 2 Λ : cut − o ff scale The measure of Fine-Tuning: ∆ ≡ ( m R h ) 2 δ m 2 h h ) 2 = ( m bare ) 2 + δ m 2 ( m R For example, ∆ < 10 − 2 h h 15625 = 98715625 - 98700000 ∼ 10 2 GeV ∼ 10 19 GeV Unnatural Cancella5on! Λ ? M SM M pl (1% tuning is needed) Large Hierarchy Problem 5
<latexit sha1_base64="zoN48/HKI0LsJYQkjEs6IuzMB8Q=">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</latexit> <latexit sha1_base64="zoN48/HKI0LsJYQkjEs6IuzMB8Q=">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</latexit> <latexit sha1_base64="zoN48/HKI0LsJYQkjEs6IuzMB8Q=">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</latexit> SUPERSYMMETRY SUSY provides an excellent solu9on to Hierarchy Problem Top Stop H + H δ m 2 = Λ 2 − Λ 2 ✓ Λ 2 ' 3 y 2 ◆ 8 π 2 m 2 t stop log m 2 stop Quadra9c divergence is cancelled by Top partner (Stop). (SUSY protects quadra9c divergence mass correc9ons.) SoF SUSY-breaking mass is important for fine-tuning. Scalartop is a colored state � Strong Bounds LiNle Hierarchy Problem! Soft Mass must be Heavy M soft >> O (1)TeV ∆ < 0 . 01 6
Hierarchy Problem Large Hierarchy Problem ∼ 10 2 GeV 10 19 GeV ∼ TeV Little Hierarchy Problem How to solve? SUSY and Composite Higgs provide solu<on δ m 2 + + h = − 3 y 2 + 9 g 2 + λ 4 π 2 Λ 2 4 π 2 Λ 2 t 32 π 2 Λ 2 2 Problem is quadra<c-divergence sensi<ve Λ : cut − o ff scale 7
Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transitions in Twin Higgs Models (Cosmological impact) 8
Electron mass is natural L QED = − 1 4 F µ ν F µ ν + ¯ σ µ D µ e L + ¯ e R σ µ D µ e R − m e (¯ e L ¯ e L e R + ¯ e R e L ) , U (1) V × U (1) A invariant U (1) V invariant D µ ≡ ∂ µ − ieA µ Naive dimensional analysis δ m e ∼ Λ A µ ∆ m e ∼ 10 − 19 , ( Λ ∼ M pl ) ✓ Λ ◆ 3 α e e However, δ m e = m e 2 π log m e Charge e R e L U (1) V Natural !! +1 +1 Why log sensi4vity? U (1) A +1 − 1 m e is the only parameter which breaks the U (1) A symmetry. When we take m e → 0 limit, U (1) A symmetry is restored. δ m e → 0 , ( m e → 0) δ m e ∝ m e 9
U(1) Toy Model (Symmetry Protection) ◆ 2 | φ | 2 − f 2 ✓ V ( | φ | ) = λ 2 1 2( f + σ ( x )) e i a ( x ) φ ( x ) = f √ √ σ ( x ) :Massive Mode m σ = 2 λ f a ( x ) : Massless Goldstone Mode L ( σ , a ) = − 1 2 ∂ µ a ( x ) ∂ µ a ( x ) + L σ ( σ ) NG Boson has shi=-symmetry: a ( x ) → a ( x ) + const Add explicit breaking source: L U (1) breaking = − ρ f 3 ( φ + φ ∗ ) p NG Boson acquires mass: m a = 2 ρ f δ m 2 a ∝ m 2 ρ → 0 U(1) symmetry is restored a 10
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