Background & Motivation The Two Higgs Doublet Model Summary & Conclusions An Unusual Two-Higgs Doublet Model from Warped Space We-Fu Chang 1 John N. Ng 2 . Spray 2 Andrew P 1 National Tsing Hua University, Taiwan 2 TRIUMF, Canada 2010 Phenomenology Symposium Andy Spray An Unusual 2HDM from RS
Background & Motivation The Two Higgs Doublet Model Summary & Conclusions Outline The Elevator Talk Overview t ¯ t condensation in RS 1 Two Higgs Doublet Model 2 Move Q 3 L away from IR brane 3 Ease EWPO constraints. 4 Andy Spray An Unusual 2HDM from RS
Background & Motivation Randall-Sundrum Models and Z → b ¯ b The Two Higgs Doublet Model The Gap Equation and Composite Higgs Summary & Conclusions Randall Sundrum Models The Bare Essentials RS Models are 5D theories with a non-trivial warped geometry. d s 2 = e − k | y | d x µ d x µ − d y 2 . The SM states are the zero modes of 5D fields. The fermions and KK modes are localised in the XD. Andy Spray An Unusual 2HDM from RS
Background & Motivation Randall-Sundrum Models and Z → b ¯ b The Two Higgs Doublet Model The Gap Equation and Composite Higgs Summary & Conclusions Electroweak Constraints and Z → b ¯ b Low energy theory: integrate out KK modes. = ⇒ Large effective operators for t R , Q 3 L . Relevant LEP constraints: Solve these problems by: T -parameter; Gauging SU ( 2 ) R ; Z → b ¯ b . Adding a P LR symmetry. Can also ease constraints by moving Q 3 L away from IR brane. Andy Spray An Unusual 2HDM from RS
Background & Motivation Randall-Sundrum Models and Z → b ¯ b The Two Higgs Doublet Model The Gap Equation and Composite Higgs Summary & Conclusions Composite Higgses in RS KK gluon mediates strong top-sector interactions. ¯ t Φ . . . ∼ t Extra Higgs = ⇒ extra contribution to m top = ⇒ move Q 3 L away from IR brane. Earlier ideas: Using exotic fermions; or Using high (30 TeV) KK scale; and No fundamental Higgs. Andy Spray An Unusual 2HDM from RS
✁ � Background & Motivation Randall-Sundrum Models and Z → b ¯ b The Two Higgs Doublet Model The Gap Equation and Composite Higgs Summary & Conclusions The Gap Equation NJL Models Integrate out KK gluon: = ⇒ Generate mass term non-perturbatively: ✂☎✄✝✆ ✂☎✞✟✆ Rewrite NJL four-fermion term using auxillary scalar: � ¯ � 2 = M 2 g KK Φ 2 + g Φ¯ ΨΨ ΨΨ . M 2 KK Andy Spray An Unusual 2HDM from RS
☞ ✠ ☛ ✠ ☛ ✡ Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Physics Below the KK Scale RGEs Renormalisation of fields below KK gluon mass: Generates: Kinetic term for Φ ; 1 Sizeable kinetic mixing between H , Φ ; 2 Mass mixing between H , Φ ; 3 All possible quartic terms. 4 Model quite predictive: M KK , m 0 , µ , λ t , g t , λ 0 . Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Diagonalising the Kinetic Sector Need to: Remove kinetic mixing; 1 Bring kinetic terms to canonical normalisation. 2 Accomplish these goals with the field redefinition: H = ˆ H Φ = − λ t 1 ˆ ˆ H + √ ǫ Φ g t g t Leads to very simple Lagrangian: � � H † ˆ H † ˆ Φ † ˆ Φ † ˆ V (ˆ H , ˆ hh ˆ ˆ Φ + ˆ ΦΦ ˆ Φ) = M 2 H − M 2 + M 2 Φ H h Φ + 1 H ) 2 + 1 H † ˆ Φ † ˆ ǫ (ˆ 2 λ 0 (ˆ Φ) 2 . Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Matching to the Standard Model Low Energy Boundary Conditions In our model, both Higgses acquire a vev. = ⇒ CP , U ( 1 ) em are automatically conserved. Matching to SM: Match EWSB: v 2 ew = v 2 H + v 2 Φ . 1 Match top quark mass: m t = v cos β √ 2 ǫ . 2 This determines both vevs! Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions A Qualitative Analysis The Decoupling Limit Neglecting mass mixing, scalar potential has symmetry SU ( 2 ) Φ L × SU ( 2 ) Φ R × SU ( 2 ) HL × SU ( 2 ) HL . Vevs break this to SU ( 2 ) Φ D × SU ( 2 ) HD ; mass mixing to SU ( 2 ) V . ⇒ Implies degeneracy of H ± , A 0 ( SU ( 2 ) V triplet). = Model lives in decoupling limit: M 2 H ∼ M 2 KK ≫ v ew . = ⇒ Lighter scalar very SM-like; = ⇒ Small mixing among neutral scalars. Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Numerical Results I 2HDM Lagrangian Parameters 4.0 0.6 0.5 3.5 0.4 m 0 � TeV � g t 3.0 0.3 0.2 2.5 0.1 0.0 2.0 0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Λ 0 Λ t Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Numerical Results II Spectrum 450 4.0 400 3.5 350 3.0 m h � GeV � 300 2.5 m � M KK 250 2.0 200 1.5 150 1.0 0.5 100 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0 1 2 3 4 g t Λ 0 Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Numerical Results III RS Lagrangian Parameters 1.0 0 . 6 c 3 y 5 D = 1 . 5 R 0.5 0 . 4 0 . 2 c R 0.0 0 . 0 y 5 D = 2 . 0 � 0.5 − 0 . 2 0 . 30 0 . 35 � 1.0 c 3 � 1.0 � 0.5 0.0 0.5 1.0 L c L Andy Spray An Unusual 2HDM from RS
Background & Motivation Set-Up: Running from High to Low The Two Higgs Doublet Model Results Summary & Conclusions Future Directions Flavour-Changing Neutral Currents Or, How I Learnt to Stop Worrying and Love My Model Won’t this model lead to tree-level FCNCs? Yes. Yukawa sector: √ √ 2 M d 2 M u v sin β Q iL u jR � ij ij v sin β Q Li d jR ˆ ˆ L Y = − H − H � � � ˆ + 1 H � ˆ Φ − + h . c . √ ǫ Q 3 L t R tan β Suppression factors: Light Higgs: sin ( α − β ) ≈ 10 − 3 ; Heavy Higgs: M − 1 KK ; Small Mixing Angles: Q 3 L , t R mostly top. Andy Spray An Unusual 2HDM from RS
Background & Motivation The Two Higgs Doublet Model Summary & Conclusions Summary & Conclusions Time For Tea! Formation of a composite scalar doublet 1 is quasi-generic in RS models. The resultant 2HDM eases some of the constraints. 2 Flavour-changing top decays expected; 3 other FCNCs probably small. Andy Spray An Unusual 2HDM from RS
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