The spontaneous Z 2 breaking Twin Higgs Hugues Beauchesne, Kevin Earl , Thomas Gr´ egoire arXiv: 1510.06069 Carleton University June 16, 2016 2016 CAP Congress 1
Outline 1. The Higgs mass, the hierarchy problem, and the pursuit of naturalness 2. Beyond the Standard Model (BSM) solutions including neutral naturalness 3. The original Twin Higgs 4. The spontaneous Z 2 breaking Twin Higgs 5. Conclusion 2
The Higgs mass, the hierarchy problem, and the pursuit of naturalness The Higgs mass The Standard Model (SM) Lagrangian contains a Higgs mass term L SM ⊃ − 1 2 m 2 h h 2 and also some Higgs couplings tt + g 2 µ − 1 L SM ⊃ − y t 4 h 2 W µ + W − 4 λ h 4 . h ¯ √ 2 W ν W µ h h t h t h h h h 3
The Higgs mass, the hierarchy problem, and the pursuit of naturalness We can use these couplings to draw the following diagrams W h t h h h h h h each of which contribute to the mass of the Higgs boson � Λ d 4 k δ m 2 k 2 ∼ Λ 2 . h ∼ The Higgs mass is quadratically sensitive to the cutoff Λ! 4
The Higgs mass, the hierarchy problem, and the pursuit of naturalness The hierarchy problem Imagine a world where the SM is all that there is up to the scale where quantum gravity becomes important. In that case we have that Λ ≈ M P ≈ 10 18 GeV. This leads to a tuning of one part in the M 2 ≈ (10 18 ) 2 (10 2 ) 2 = 10 32 . P m 2 h Are we to believe this? Is Nature this tuned? 5
The Higgs mass, the hierarchy problem, and the pursuit of naturalness The pursuit of naturalness Field Symmetry as m → 0 Implications Ψ → e i αγ 5 Ψ Spin 1/2 δ m ∝ m − m ¯ ΨΨ (chiral symmetry) natural A µ → A µ − 1 Spin 1 e ∂ µ α δ m ∝ m 1 2 m 2 A µ A µ (gauge invariance) natural Spin 0 δ m ∝ Λ None − 1 2 m 2 φ 2 unnatural “Perhaps this is the reason why there seem to be no elementary scalar fields in Nature.” - An Introduction to Quantum Field Theory, Peskin and Schroeder 6
Beyond the Standard Model (BSM) solutions including neutral naturalness The most well known solution: Supersymmetry Supersymmetry is a symmetry linking bosons to fermions capable of solving the hierarchy problem. Every SM particle has a partner particle. Most importantly, quadratic contributions to scalar masses cancel between supersymmetric partner particles. ˜ t t h h h h However, natural Supersymmetry appears to be on thin ice. 7
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