M inimal N eutral N aturalness M odel Ling - Xiao Xu ( 徐凌霄 ) Peking University hep-ph/1810.01882 with Jiang - Hao Y u and Shou - hua Zhu KEK-PH 2018 Winter @ Tsukuba, Japan 5 December, 2018
Origin of EWSB • Landau Ginzburg Potential with its origin unexplained V ( H ) = − μ 2 H † H + λ ( H † H ) 2 • Other Possibilities? 1
Origin of EWSB • Landau Ginzburg Potential with its origin unexplained V ( H ) = − μ 2 H † H + λ ( H † H ) 2 • Other Possibilities? • Pseudo Nambu - Goldstone Higgs ( coset G/H ) m h ∼ a y t f 4 π ∼ 3 M T • Naturalness problem solved 4 π • Radiative Higgs potential π → π + c Shift Symmetry • EWSB explained 1
Explaining EWSB misalignment: 2
Explaining EWSB misalignment: β ≪ γ ( No EWSB f 2 ∼ 1 ) v 2 | Σ | = f EWSB direction 2
Explaining EWSB misalignment: β ≪ γ ( No EWSB f 2 ∼ 1 ) v 2 | Σ | = f β = γ ( f 2 = 0.5 ) v 2 EWSB direction 2
Explaining EWSB misalignment: β ≪ γ ( No EWSB f 2 ∼ 1 ) v 2 | Σ | = f β = γ ( f 2 = 0.5 ) v 2 EWSB direction γ ≪ β ( f 2 ∼ 0.1 ) v 2 as required by Higgs data 2
Explaining EWSB misalignment: β ≪ γ ( No EWSB f 2 ∼ 1 ) v 2 | Σ | = f β = γ ( f 2 = 0.5 ) v 2 EWSB direction γ ≪ β ( f 2 ∼ 0.1 ) v 2 as required by Higgs data Can small misalignment angle be realized naturally? even only considering fermion contribution? 2
Neutral Naturalness Era m h ∼ a y t f 4 π ∼ 3 M T sub - TeV top partner 4 π Colorless top partners are highly motivated! 3
Neutral Naturalness Era m h ∼ a y t f 4 π ∼ 3 M T sub - TeV top partner 4 π Colorless top partners are highly motivated! • Neutral Naturalness Models ( apology if I miss your work ) Twin Higgs: Chacko, Goh, Harnik, 0506256 Quirky Little Higgs: Cai, Cheng, Terning, 0812.0843 Orbifold Higgs: Craig, Knapen, Longhi, 1410.6808 Composite Twin Higgs: Geller, Telem, 1411.2974; Barbieri, Greco, Rattazzi, Wulzer, 1501.07803; Low, Tesi, Wang 1501.07890 Neutral Naturalness in SO(6)/SO(5) (trigonometric parity within coset): Serra, Torre, 1709.05399; Csaki, Ma, Shu, 1709.08636; Dillon, 1806.10702 … 3
Twin Higgs as a benchmark of neutral naturalness: N eff v , ˜ ˜ γ • Mirror copy of the SM • Coset: SU(4)/SU(3) or SO(8)/SO(7) • Additional Z2 - breaking sources needed for vacuum misalignment 4
Twin Higgs as a benchmark of neutral naturalness: N eff v , ˜ ˜ γ • Mirror copy of the SM • Coset: SU(4)/SU(3) or SO(8)/SO(7) • Additional Z2 - breaking sources needed for vacuum misalignment Our construction with minimal spectrum and coset: • V ector - like top partners: one doublet and one singlet 4
Twin Higgs as a benchmark of neutral naturalness: N eff v , ˜ ˜ γ • Mirror copy of the SM • Coset: SU(4)/SU(3) or SO(8)/SO(7) • Additional Z2 - breaking sources needed for vacuum misalignment Our construction with minimal spectrum and coset: • V ector - like top partners: one doublet and one singlet • Minimal coset SO(5)/SO(4), without compositeness at low energies Agashe, Contino, Pomarol, 0412089 4
Twin Higgs as a benchmark of neutral naturalness: N eff v , ˜ ˜ γ • Mirror copy of the SM • Coset: SU(4)/SU(3) or SO(8)/SO(7) • Additional Z2 - breaking sources needed for vacuum misalignment Our construction with minimal spectrum and coset: • V ector - like top partners: one doublet and one singlet • Minimal coset SO(5)/SO(4), without compositeness at low energies Agashe, Contino, Pomarol, 0412089 • Natural vacuum misalignment even with only fermions 4
Fermion Embeddings 5
Fermion Embeddings 5
• Quadratic divergence cancellation from symmetry perspective 6
• Quadratic divergence cancellation from symmetry perspective • Logarithmic divergent Higgs Potential from Y ukawa terms EWSB is triggered! 6
• Quadratic divergence cancellation from symmetry perspective • Logarithmic divergent Higgs Potential from Y ukawa terms EWSB is triggered! • So far, vacuum is not correctly misaligned 6
V acuum Misalignment • Logarithmic divergent Higgs Potential including the mass term 7
V acuum Misalignment • Logarithmic divergent Higgs Potential including the mass term • Total logarithmic divergent Higgs potential 7
V acuum Misalignment • Logarithmic divergent Higgs Potential including the mass term • Total logarithmic divergent Higgs potential • Further including the finite part will not change the result 7
Spectrum of Minimal Setup global symmetry singlet and doublet breaking scale f T and t vacuum misalignment t, W , Z EW scale v PNGB Higgs 8
Composite/Holographic Extension Composite top strong dynamics Composite T and t Composite W and Z partial compositeness partial compositeness global symmetry singlet and doublet breaking scale f T and t vacuum misalignment t, W , Z EW scale v PNGB Higgs 8
Two - site Construction composite states 9
Two - site Construction composite states collective breaking: explicit breaking SO ( 5 ) 2 9
Holographic Setup for SM Top • Fermions living in the bulk 10
Holographic Setup for SM Top • Fermions living in the bulk • Zero modes as the low energy building blocks 10
Holographic Setup for SM Top • Fermions living in the bulk • Zero modes as the low energy building blocks • Breaking SO ( 5 ) on the IR brane 10 • Otherwise Higgs is an exact Goldstone boson
Holographic Setup for Neutral Tops • Fermions living in the bulk • Zero modes as the low energy building blocks • UV brane construction • Breaking SO ( 5 ) on the IR brane 11
Phenomenology • Only two free parameters at low energies 12
Phenomenology • Only two free parameters at low energies • Rich Phenomenology to be done in the future dark hadron spectra, heavy composites phenomenology, dark matter candidate, collider signatures and cosmological implications… 12
Concluding Remarks • W e present a neutral naturalness model with the Higgs boson identified as a PNGB of SO(5)/SO(4) • V acuum misalignment naturally obtained with only fermions • UV realization in the holographic/composite Higgs framework • Finite Higgs potential in holographic/composite framework still many to explore in the future ! Thank you! 13
Backup Slides
Symmetry Breaking in 5D Strong Dynamics ( bulk+IR ) A M ≡ ( A μ , A 5 ) UV bulk IR ( H0 ) ( G ) ( H1 ) G: SO(5) realistic model: H1: SO(4) H0: SU(2) U(1) × 1
Boundary Conditions G: SO(5) H1: SO(4) A μ H0: SU(2) U(1) × The boundary condition ( +,+ ) reflects the fact that W , Z are massless before EWSB 5D perspective: the Goldstone matrix corresponds to the Wilson line of A5 along the fifth dimension 2
Strong Dynamics at Low Energies • Information of heavy particles encoded in form factors • Identical to the spectrum of the minimal setup • Explicitly check: Higgs is an exact Goldstone if all the mixings vanish 3
Higgs Potential in Composite Models t R s h s h pole top top Π t L t R Π t L t R × t L top top ∑ M ( i ) KK i 4 The contribution of the whole tower of Kaluza - Klein states has been resummed
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