(Composite) Twin Higgs Andrea Tesi University of Chicago Thanks to - PowerPoint PPT Presentation

Gearing up for LHC13 – GGI, Firenze – 24 September 2015 (Composite) Twin Higgs Andrea Tesi University of Chicago

Thanks to Matthew Low LianTao Wang (UChicago / IAS) (UChicago)

Thanks to Dario Buttazzo Filippo Sala (TUM Munich) (Paris, Saclay)

What Next?

Look for new states! Early stages of the LHC Run-II crucial for direct searches 8 TeV/14 TeV 2.0 1.5 m NEW � m OLD gg 1.0 m OLD � 1TeV 0.5 0.0 0 20 40 60 80 100 L � fb � 1 � Slower improvements after 20-30/fb

Many motivated “benchmarks” A long wish list, especially colored particles � Stops � Gluinos � Top partners ... ...

What if LHC14 finds nothing?

The usual story If new symmetries stabilize the weak scale h ≃ C g 2 δm 2 16 π 2 M 2 SM NP + · · ·

The usual story If new symmetries stabilize the weak scale h ≃ C g 2 δm 2 16 π 2 M 2 SM NP + · · · LHC8 measured a lot of tuning 1 Any model? 0.1 1 0.01 � NMSSM 0.001 LHC8 LHC14 MSSM 10 � 4 0.5 1.0 1.5 2.0 2.5 3.0 M NP � TeV � The “problem” is that M NP is “colored”

Twin Higgs mechanism

The basic idea The cancellation of the quadratic divergence can be achieved without colored particles Chacko, Goh, Harnik

The basic idea The cancellation of the quadratic divergence can be achieved without colored particles Chacko, Goh, Harnik The actual realization � Mirror copy of SM � Assume a SO(8)/SO(7) accidental symmetry H 2 H ′ 2 � λ ( H 2 + H ′ 2 − f 2 ) 2 SM SM’ � 7GBs - 3W - 3W’ = one physical pGB, h √ � A radial mode m σ ∼ λf Chacko, Goh, Harnik � Gauge and Yukawas break global symmetry

Cancellation of quadratic corrections Thanks to Z 2 , accidental SO(8)-invariance at O ( g 2 SM ) V ⊃ C g 2 32 π 2 Λ 2 ( H 2 + H ′ 2 ) SM

Cancellation of quadratic corrections Thanks to Z 2 , accidental SO(8)-invariance at O ( g 2 SM ) V ⊃ C g 2 32 π 2 Λ 2 ( H 2 + H ′ 2 ) SM Higher corrections in g SM break SO(8) SM ) ⊃ C ′ g 4 Λ 2 Λ 2 32 π 2 ( H 4 log SM | H | 2 + H ′ 4 log SM V O ( g 4 SM | H ′ | 2 ) g 2 g 2

Putting all together V ( H, H ′ ) = λ ( H 2 + H ′ 2 − f 2 ) 2 + δ ( H 4 + H ′ 4 ) The model is ruled out

Putting all together V ( H, H ′ ) = λ ( H 2 + H ′ 2 − f 2 ) 2 + δ ( H 4 + H ′ 4 ) The model is ruled out We need a Z 2 breaking term V ( H, H ′ ) = λ ( H 2 + H ′ 2 − f 2 ) 2 + δ ( H 4 + H ′ 4 ) + m 2 ( H 2 − H ′ 2 ) � H � = v ≪ � H ′ � ∼ f

Putting all together V ( H, H ′ ) = λ ( H 2 + H ′ 2 − f 2 ) 2 + δ ( H 4 + H ′ 4 ) The model is ruled out We need a Z 2 breaking term V ( H, H ′ ) = λ ( H 2 + H ′ 2 − f 2 ) 2 + δ ( H 4 + H ′ 4 ) + m 2 ( H 2 − H ′ 2 ) � H � = v ≪ � H ′ � ∼ f Now the model is phenomenologically viable � Higgs coupling deviations measured by v 2 /f 2 � Mirror sector is heavier by a factor f/v

The low energy spectrum needed “UV” embedding (to protect from higher order corrections) √ mirror top, y t f mirror Higgs, λf f ≃ 7 − 800 GeV mirror vectors, gf Higgs All the light new states are total singlets: difficult to produce and detect. Twin mechanism makes the naturalness-partners invisible. h/h ∗ pair production ∼ v

The size of λ distinguishes between two scenarios λ

The size of λ distinguishes between two scenarios λ If λ ∼ O (1) radial mode close to f look for the singlet! w/ Dario Buttazzo and Filippo Sala see also [Craig, Katz, Strassler, Sundrum]

The size of λ distinguishes between two scenarios λ If λ ∼ O (16 π 2 ) If λ ∼ O (1) radial mode close to f radial mode decoupled look for the singlet! Composite Twin Higgs w/ Dario Buttazzo and Filippo Sala w/ Matthew Low and LianTao Wang see also [Craig, Katz, Strassler, Sundrum] [Geller, Telem; Barbieri, Greco, Rattazzi, Wulzer]

The size of λ distinguishes between two scenarios λ If λ ∼ O (16 π 2 ) If λ ∼ O (1) radial mode close to f radial mode decoupled look for the singlet! Composite Twin Higgs w/ Dario Buttazzo and Filippo Sala w/ Matthew Low and LianTao Wang see also [Craig, Katz, Strassler, Sundrum] [Geller, Telem; Barbieri, Greco, Rattazzi, Wulzer]

Look for the twin Higgs! 1200 �Μ � Μ SM BR Σ� inv. � 3 � 7 Σ � SM sin 2 γ ≃ v 2 f 2 + O (1 /m 2 σ ) 0.05 1000 Higgs couplings & Direct Searches f � GeV � 800 σ h 0.1 cos γ sin γ 0.15 600 0.23 400 500 1000 1500 2000 m Σ � GeV � If Twin Higgs is weakly coupled, the twin Higgs (singlet) could be visible

The size of λ distinguishes between two scenarios λ If λ ∼ O (16 π 2 ) If λ ∼ O (1) radial mode close to f radial mode decoupled look for the singlet! Composite Twin Higgs w/ Dario Buttazzo and Filippo Sala w/ Matthew Low and LianTao Wang see also [Craig, Katz, Strassler, Sundrum] [Geller, Telem; Barbieri, Greco, Rattazzi, Wulzer]

Composite (Twin) Higgs

Composite Higgs A µ g Higgs (and W/Z goldstones) are part of the strong sector G/H m ρ = g ρ f The external fields are the SM quarks and ψ (transverse) gauge bosons ψ 1-loop potential breaks EWSB. The scale of the potential is set by the mass of the resonances: both vectors and fermions m ∗ = g ∗ f SO(5)/SO(4) minimal case Agashe, Contino, Pomarol

Crucial role of fermions Gauge sector does not break EW, other contributions needed Assume linear mixing of SM fields to composite fermions y L f ¯ q L Ψ q + y R f ¯ u R Ψ u + h.c. Kaplan ’90 � Ψ are colored, m ψ ∼ g ψ f � SM Yukawas are y ∼ y L y R g ψ ... ... Partial compositeness The SM quarks are a combination of elementary and composite fields

Higgs Potential U = exp( ih/fT 4 ) y L f ¯ q L U Ψ q + y R f ¯ u R U Ψ u + L comp (Ψ , U, m ψ , g ψ ) , � � N c a ( yf ) 2 m 2 ψ F 1 ( h/f ) + b ( yf ) 4 F 2 ( h/f ) V ( h ) ≃ 16 π 2 Giudice, Grojean, Pomarol, Rattazzi � F 1 , 2 trigonometric function � a, b O(1) coefficients Focussing on top sector y t ∼ y 2 f m ψ � N c a y t f F 1 + b ( y t f 16 π 2 m 4 ) 2 F 2 � V ≃ Ψ m Ψ m Ψ V ( h ) highly sensitive to m ψ

Higgs mass and tuning h ≃ b N c y 2 t v 2 m 2 ∆ ≃ m 2 = f 2 m 2 m 2 Ψ Ψ Ψ f 2 , 2 π 2 m 2 v 2 y 2 t f 2 t � Light top partners for the Higgs mass [Contino, Da Rold, Pomarol; Matsedonsky, Panico, Wulzer; Pomarol, Riva; Marzocca, Serone, Shu; Redi, T;...] � Tuning grows with m 2 Ψ

Higgs mass and tuning h ≃ b N c y 2 t v 2 m 2 ∆ ≃ m 2 = f 2 m 2 m 2 Ψ Ψ Ψ f 2 , 2 π 2 m 2 v 2 y 2 t f 2 t � Light top partners for the Higgs mass [Contino, Da Rold, Pomarol; Matsedonsky, Panico, Wulzer; Pomarol, Riva; Marzocca, Serone, Shu; Redi, T;...] � Tuning grows with m 2 Ψ Within minimal models tuning always larger than f 2 /v 2 if top partners are not found

A real problem? Not now, but we will know soon taken from A. Wulzer’s talk at Neutral Naturalness workshop

Can we have heavy top partners and small tuning? Panico, Redi, T, Wulzer tuning g ψ ≃ g ρ g ψ ≃ g ρ anomalously ad hoc tuning light partners MCHM 5 , 10 , 4 14 L + composite t R , . . . g ψ ≃ 1 5 L + 5 R , 14 L + 14 R , . . . 14 L + composite t R , . . . top partners mass

Composite Twin Higgs

Natural embedding in the Composite Higgs see also Geller, Telem; Barbieri, Greco, Rattazzi, Wulzer In the gauge sector � g · SO (4) SO (8) /SO (7) 0 � A µ = g ′ · SO (4) ′ m ∗ = g ∗ f 0 Z 2 � � Σ = 0 , 0 , 0 , s h , 0 , 0 , 0 , c h SM ′ SM Z 2 � Inside SO(8) gauge two copies of SM � Add mirror QCD Three “sectors” elementary fields — ele. mirror fields — composite resonances ( Z 2 )

Effect of the mirror top L ) i Σ i u 1 q L i / u R i / q 8 L = ¯ Dq L + ¯ Du R + y t f (¯ R + (mirror) L ) i = 2 ( ib L , b L , it L , − t L , 0 , 0 , 0 , 0) i 1 � q L in 8 of SO(8), ( q 8 √ � Top and mirror top mass m t = y t fs h m t ′ = y t fc h √ 2 , √ 2

Effect of the mirror top L ) i Σ i u 1 q L i / u R i / q 8 L = ¯ Dq L + ¯ Du R + y t f (¯ R + (mirror) L ) i = 2 ( ib L , b L , it L , − t L , 0 , 0 , 0 , 0) i 1 � q L in 8 of SO(8), ( q 8 √ � Top and mirror top mass m t = y t fs h m t ′ = y t fc h √ 2 , √ 2 The potential is not sensitive to quadratic “divergences” � 2Λ 2 V = N c y 4 t f 4 2Λ 2 − N c y 2 t f 2 Λ 2 � � � �� c 4 + s 4 ( s 2 h + c 2 h log h log h ) 64 π 2 y 2 t f 2 c 2 y 2 t f 2 s 2 16 π 2 h h Need a breaking of Z 2 to have f > v

Z 2 breaking and minimal tuning Let us suppose that exists a model with Z 2 -breaking � 2Λ 2 N c y 4 t f 4 2Λ 2 + N c y 4 t f 4 � � � �� c 4 + s 4 32 π 2 b s 2 h log h log y 2 t f 2 c 2 y 2 t f 2 s 2 h 64 π 2 h h

Z 2 breaking and minimal tuning Let us suppose that exists a model with Z 2 -breaking � 2Λ 2 N c y 4 t f 4 2Λ 2 + N c y 4 t f 4 � � � �� c 4 + s 4 32 π 2 b s 2 h log h log y 2 t f 2 c 2 y 2 t f 2 s 2 h 64 π 2 h h Then we have � Minimal tuning f 2 /v 2 (for b ∼ O (1) ) � Higgs mass in the right ballpark m 2 t m 2 Λ 2 h ≃ N c � � � � m 2 t ′ log + · · · π 2 f 2 m t ′ m t