Two Higgs Doublets from Fourth Generation Condensation Gustavo - PowerPoint PPT Presentation

Two Higgs Doublets from Fourth Generation Condensation Gustavo Burdman University of S˜ ao Paulo With Carlos Haluch, , arxiv:1109.xxxx

Outline Introduction and Motivation Is a Fourth Generation still allowed ? What is it good for ? Two Higgs Doublet Model from Fermion Condensation Effective Theory Scalar Spectrum Phenomenology Conclusions

Is a Fourth Generation Still Viable ? Higgs must either be: SM ATLAS Preliminary CLs Limits σ / σ th 4 Generation Model ◮ Light Observed 95% CL Limit on ∫ 10 Expected -1 Ldt = 1.0-2.3 fb m h < 120 GeV ± σ 1 s = 7 TeV ± σ 2 ◮ Heavy 1 m h > 600 GeV -1 10 -2 10 200 300 400 500 600 m [GeV] H Heavy quarks must be m t ′ > 450 GeV, m b ′ > 400 GeV

Possible Ways Out ◮ Dynamical explanation for m h > 600 GeV ◮ Fermion Condensation with low cutoff → Heavy Higgs/No Higgs ◮ One Higgs doublet always m h > 700 GeV ◮ More complicated scalar sector ◮ Fermion condensation → Two-Higgs doublets at low energy ◮ (Mostly) heavy scalar spectrum with different σ × BR

Why a Fourth Generation ? Heavy Chiral Fermions: strongly coupled to EWSB sector ◮ Top quark: m t ≃ v ⇒ y t ∼ 1 ◮ If Heavy Fourth Generation ⇒ y 4 > 1 Higgs sector is strongly coupled ◮ Natural to assume composite Higgs sector

Why a Fourth Generation ? Other motivation: ( Holdom, Hou, Hurth, Mangano, Sultanasoy, Unel ’09 ) ◮ New CP violation source for baryon asymmetry ◮ New sources of CPV in meson decays ◮ · · ·

Electroweak Symmetry Breaking Composite EWSB Sector: ◮ Technicolor: Asymptotically free, unbroken gauge interaction ⇒ � ¯ F L F R � � = 0 ⇒ EWSB F ’s are confined fermions, just as quarks in QCD. ◮ Alternative: gauge interaction spontaneously broken at Λ ∼ 1 TeV ⇒ F ’s un-confined heavy fermions with EW quantum #’s ( E.g. Bardeen,Hill, Lindner ’90, Hill ’91 )

EWSB from Fourth Generation Condensation Ingredients: ◮ A Chiral Fourth Generation: Q 4 , U 4 R , D 4 R , L 4 , E 4 R , N 4 R ◮ New strong interaction at the O (1) TeV scale: ◮ E.g. Broken gauge symmetry M ∼ TeV ◮ Strongly coupled to 4th gen. ⇒ � ¯ F 4 F 4 � � = 0 ⇒ m 4 ≃ (500 − 600) GeV ◮ Other fermion masses: higher dimensional operators like x ij Λ 2 ¯ L f j R ¯ f i U R U L

Models of Fourth Generation Condensation All ingredients present in AdS 5 ( GB, Da Rold ’07, GB, Da Rold, Matheus ’09 ) Extra dimensional theories in compact AdS 5 dual to strongly coupled theories in 4D: ◮ Naturally results in strongly coupled heavy fermions ◮ Higher-dimensional operators among light fermions suppressed by large UV scale Λ ◮ Build gauge theory in AdS 5 with one extra chiral generation and no Higgs . ◮ Minimal model: Only up-type 4G quark condenses > 700 GeV ⇒ Only 1 Higgs doublet, m h ∼

Models of Fourth Generation Condensation ◮ More general and more natural: both up and down type quarks condense ◮ More natural: interaction must be nearly isospin invariant to avoid T parameter constraints ◮ More general: would need to fine tune interaction to avoid one condensation ◮ ⇒ Two Higgs doublets at low energy

A Two Higgs Doublet from Fermion Condensation ( Luty ’90, Luty, Hill, Paschos ’90, GB, Haluch ’11 ) New fermions � U i � Q i = U i , D i , D i L with i gauge index of new interaction. New Strong Interaction: ◮ Want un-confined fermions ⇒ spontaneosly broken at scale M ◮ Massive bosons strongly coupled to Q i , U i and D i ◮ E.g. If G a color-octect ⇒ i = (1 − 3) is color index, Q i , U i and D i can be fourth-generation quarks

Electroweak Symmetry Breaking New strong interactions ⇒ four-fermion operators L 4f = g L g u UQ + g L g d QU ¯ ¯ QD ¯ ¯ DQ M 2 M 2 G G with g L , g u , g d gauge couplings. If 8 π 2 ⇒ � ¯ g L g u > QU � � = 0 N c 8 π 2 ⇒ � ¯ g L g d > QD � � = 0 N c One doublet condensing ⇒ SU (2) L × U (1) Y → U (1) EM

EWSB and Low Energy Scalar Spectrum Four-fermion interactions ← → Yukawa interactions Y U ( ¯ Q ˜ Φ U U + h . c . ) + Y D ( ¯ L eff . = Q Φ D D + h . c . ) G Φ † G Φ † − M 2 U Φ U − M 2 D Φ D with ˜ Y 2 Y 2 Φ U = − i σ 2 Φ ∗ U = g L g u , D = g L g d , U with hypercharges h U = − 1 / 2, h d = 1 / 2.

EWSB and Low Energy Scalar Spectrum At µ < M G : ◮ Scalars develop kinetic terms L kin . = Z Φ U ( µ )( D µ Φ U ) † D µ Φ U + Z Φ D ( µ )( D µ Φ D ) † D µ Φ D with the compositness BCs Z Φ U ( M G ) , Z Φ D ( M G ) = 0. ◮ They get VEVs if four-fermion couplings super-critical: � QU � � = 0 ↔ � Φ U � � = 0 � QD � � = 0 ↔ � Φ D � � = 0 ◮ Effective Two-Higgs doublet spectrum at low energy

Low Energy Scalar Spectrum At µ < M G all couplings get renormalized and some generated. E.g. : Y U Y D Y U → , Y D → � � Z Φ U Z Φ D G − g L g u N g µ 2 M 2 M 2 G − µ 2 � � = U 8 π 2 G − g L g d N g µ 2 M 2 M 2 G − µ 2 � � = D 8 π 2 We ca see that m 2 U < 0 and m 2 D < 0 for super-critical couplings ⇒ V (Φ U , Φ D ) with � Φ U � = v U , � Φ D � = v D

Φ U − Φ D Mixing and Peccei-Quinn Symmetry Theory is invariant under Q → e − i θ Q U → e i θ U D → e i θ D Φ U → e 2 i θ Φ U Φ D → e − 2 i θ Φ D , UD (Φ † forbids mixing term µ 2 U Φ D + h . c . ) in V (Φ U , Φ D ). This results in M A = 0

Instantons Induce M A Fermionic equivalent of mixing term U c ˜ L mix = G UD ( ¯ QD ¯ ( ˜ Q + h . c . ) , Q = − i σ 2 Q ) But this is generated by ’t Hooft fermion determinant ( Hill ’95 ) � ¯ k � L inst . = det Q L Q R M 2 G with k ∼ O (1). ⇒ Instantons of new strong interactions responsible for M A

Scalar Spectrum Scalar potential generated by fermion loops U | Φ U | 2 + µ 2 D | Φ D | 2 + µ 2 µ 2 UD (Φ U † Φ D + h . c . ) V (Φ U , Φ D ) = + λ 1 2 | Φ U | 4 + λ 2 2 | Φ D | 4 + λ 3 | Φ U | 2 | Φ D | 2 + λ 4 | Φ U † Φ D | 2 Couplings Y U , Y D , λ i , µ U , µ D , µ UD run down by using RGEs ⇒ scalar spectrum

Running to Low Energies Solutions for λ 1 ( µ ) for M G = 2 , 3 , 4 TeV 25 20 15 Λ � Μ � 10 5 0 0.0 0.5 1.0 1.5 Μ � TeV �

Scalar Spectrum √ � Im [Φ 0 D ] cos β − Im [Φ 0 � = 2 U ] sin β A √ � − Re [Φ 0 U ] sin γ + Re [Φ 0 � = 2 D ] cos γ h √ � Re [Φ 0 U ] cos γ + Re [Φ 0 � = 2 D ] sin γ H Φ ± D cos β − Φ ± H ± = U sin β tan β = v U / v D ≃ 1. The CP-even mixing is UD + ( λ 3 + λ 4 ) v 2 sin 2 β/ 2 tan 2 γ = µ 2 UD + λ 4 v 2 cos 2 β/ 2 µ 2

Scalar Masses E.g.: Pseudo-scalar mass λ 1 λ 2 cos 2 β sin 2 β UD = k v 2 µ 2 1 − kv 2 ( λ 1 cos 2 β cot β + λ 2 sin 2 β tan β ) / (2 M 2 2 M 2 � � G ) G and the pseudo-scalar mass is A = − 2 µ 2 M 2 UD sin 2 β

Scalar Masses For k = (0 . 1 − 1) M G = 2 TeV M G = 3 TeV M G = 4 TeV M A (26-118) GeV (15-59) GeV (10-39) GeV M h (548-580) GeV (459-467) GeV (422-425) GeV M H (651-732) GeV (530-537) GeV (482-585) GeV M H ± (603-719) GeV (495-512) GeV (453-459) GeV ◮ Heavy ( h , H , H ± ) ≃ (400 − 700) GeV depending on ( k , M G ) ◮ Light A ≃ (10 − 120) GeV

Phenomenology ◮ Usual h , H decay channels suppressed in favor of AA , A , Z ◮ If condensing fermions carry color (4G quarks) → σ prod . ( gg → ( h , H , A )) ≃ (6 − 7) SM values ◮ If new fermion colorless, no enhancement of σ prod . . But scalar spectrum still same.

Electroweak Precision Constraints Constraints in the S-T plot (68% and 95% C.L. contours Parameter space of scalar sector ( k , M G ) + fourth generation � � 2 to 4 TeV 0.4 0.3 0.2 0.1 T 0.0 � 0.1 � 0.2 � 0.2 � 0.1 0.0 0.1 0.2 0.3 0.4 S

Flavor ◮ Dynamics at the high scale introduce higher dimensional operators such as x ij Λ 2 ¯ L f j R ¯ f i U R U L ◮ Can always accommodate Φ U only couples to up-type quarks, Φ D only to down-type quarks and charged leptons ◮ PQ symmetry softly broken ⇒ mixing does not induce FCNCs at tree level ◮ Loop effects: H ± too heavy to give important effects in b → s γ , etc.

Summary/Outlook ◮ 4th Generation still not excluded by Higgs searches ◮ Composite 2HDM with light A and heavy ( h , H , H ± ) is a natural consequence of fermion condensation ◮ If new fermions carry color: ◮ We will see them soon ( m t ′ > 450 GeV) ◮ σ ( h , H , A ) larger than in standard 2HDM ◮ But preferred decay channels are ( h , H ) → ( A , A ) , ( A , Z ) ◮ If new fermions colorless, unusual scalar spectrum still hint of fermion condensation