The SUSY Twin Higgs Diego Redigolo Higgs Hunting, Paris August - PowerPoint PPT Presentation

The SUSY Twin Higgs Diego Redigolo Higgs Hunting, Paris August 31st based on to appear with A. Katz, A. Mariotti, S. Pokorski and R. Ziegler

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS EXACT SYMMETRIES Lesson:

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson:

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson: Twin Higgs easier= /accidental symmetry enforced by a Z 2 4d description is the easier implementation exchanging two copies of the SM 0506256 Chacko, Goh and Harnik (less easy ways have been explored 0609152 Burdman, Chacko, Goh and Harnik 1411.7393 Craig, Knapen, Longhi 1601.07181 Craig, Knapen, Longhi,Strassler 1601.07181 Cohen, Craig, Lou, Pinner

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson:

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson: 2 challenges (in the original Twin already)

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson: 2 challenges (in the original Twin already) Z 2 Breaking introduces some degree of model dependence: EXPLORING THE PARAMETER SPACE of the Twin Higgs

Neutral Naturalness is by now a well established paradigm to circumvent the null results at LHC keeping the fine tuning ~10 % General COLORED TOP-PARTNERS ACCIDENTAL SYMMETRIES Lesson: 2 challenges (in the original Twin already) Z 2 Breaking introduces some degree of model dependence: EXPLORING THE PARAMETER SPACE of the Twin Higgs UV COMPLETIONS of Twin Higgs constructions: FINE TUNING vs LHC searches: How long to exclude 10% FT @ LHC?

A fresh look to the Twin Higgs

Twin Higgs: Setup Double SM gauge fields, Higgs and tops G A G SM G B → × SM SM H, Q 3 , U 3 → H A , Q 3 A , U 3 A H B , Q 3 B , U 3 B + } } visible sector “dark” sector: neutral under SM! Natural Z 2 exchange symmetry: H A H B ← → . . . Z 2 involves the full SM 0509242 Barbieri, Hall & Gregoire the rest of the spectrum Minimal ( “fraternal” ) Twin Higgs 1501.05310 Craig, Katz, Strassler & Sundrum A ff ect a lot of phenomenology both cosmological and at collider but we leave it unspecified in our discussion…

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B f 2 > 0 λ > 0 U (4) spontaneously broken

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B f 2 > 0 λ > 0 U (4) spontaneously broken 7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B f 2 > 0 κ > 0 Z 2 unbroken λ > 0 (see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken) U (4) spontaneously broken 7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B f 2 > 0 κ > 0 Z 2 unbroken λ > 0 (see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken) U (4) spontaneously broken SM Higgs is a PGB m h ⌧ m H as long as κ ⌧ λ 7 GB - 6 eaten = SM Higgs is a GB

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B f 2 > 0 κ > 0 Z 2 unbroken λ > 0 (see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken) U (4) spontaneously broken SM Higgs is a PGB m h ⌧ m H as long as κ ⌧ λ 7 GB - 6 eaten = h = h A c θ + h B s θ SM Higgs is a GB maximal Z 2 preserved mixing √ s θ = 1 / 2 > 0 . 45 excluded!

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B µ 2 ˜ soft breaking f 2 > 0 κ > 0 Z 2 unbroken λ > 0 ρ hard breaking (see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken) U (4) spontaneously broken SM Higgs is a PGB m h ⌧ m H as long as κ ⌧ λ 7 GB - 6 eaten = h = h A c θ + h B s θ SM Higgs is a GB maximal Z 2 preserved mixing √ s θ = 1 / 2 > 0 . 45 excluded!

Linear sigma model λ ( | H A | 2 + | H B | 2 − f 2 ) 2 + κ ( | H A | 4 + | H B | 4 ) + ˜ µ 2 | H A | 2 + ρ | H A | 4 { { { V U 4 V / U 4 ,/ V / Z 2 U 4 ,Z 2 respects U (4) even under H A ↔ H B µ 2 ˜ soft breaking f 2 > 0 κ > 0 Z 2 unbroken λ > 0 ρ hard breaking (see 1510.06069 Beauchesne, Earl, Grégoire for spontaneously broken) U (4) spontaneously broken s θ ≈ v/f > 0 . 45 SM Higgs is a PGB m h ⌧ m H as long as κ ⌧ λ 7 GB - 6 eaten = f > 2 . 3 v ≈ 400 GeV h = h A c θ + h B s θ SM Higgs is a GB viable! maximal Z 2 preserved mixing √ s θ = 1 / 2 > 0 . 45 excluded!

0.20 f ê v > 2.3 k< 0 0.15 m h = 130 GeV k THE TWIN HIGGS on a plane… m h = 125 GeV 0.05 0.10 m h = 120 GeV µ 2 κ ρ f { { , ˜ 4 parameters: , , 0.05 r 0.1 0 - 2 constraints: EWSB+ HIGGS soft Z 2 - breaking 0.00 0.15 - 0.05 2 dimensional par. space 0.2 f/v > 2 . 3 with the constraint 0.25 - 0.10 - 0.10 - 0.05 0.00 0.05 0.10 0.15 0.20 é 2 ê f 2 m

0.20 f ê v > 2.3 k< 0 0.15 m h = 130 GeV k THE TWIN HIGGS on a plane… m h = 125 GeV 0.05 0.10 m h = 120 GeV µ 2 κ ρ f { { , ˜ 4 parameters: , , 0.05 r 0.1 0 - 2 constraints: EWSB+ HIGGS soft Z 2 - breaking 0.00 0.15 - 0.05 2 dimensional par. space 0.2 f/v > 2 . 3 with the constraint 0.25 - 0.10 - 0.10 - 0.05 0.00 0.05 0.10 0.15 0.20 é 2 ê f 2 m Hard breaking o ff er new possibilities:

0.20 f ê v > 2.3 k< 0 0.15 m h = 130 GeV k THE TWIN HIGGS on a plane… m h = 125 GeV 0.05 0.10 m h = 120 GeV µ 2 κ ρ f { { , ˜ 4 parameters: , , 0.05 r 0.1 0 - 2 constraints: EWSB+ HIGGS soft Z 2 - breaking 0.00 0.15 - 0.05 2 dimensional par. space 0.2 f/v > 2 . 3 with the constraint 0.25 - 0.10 - 0.10 - 0.05 0.00 0.05 0.10 0.15 0.20 é 2 ê f 2 m Hard breaking o ff er new possibilities: µ 2 ≈ 2 κ f 2 µ 2 /f 2 f/v > 2 . 3 soft - breaking: tuning to get ρ ⌧ ˜ ˜

0.20 f ê v > 2.3 k< 0 0.15 m h = 130 GeV k THE TWIN HIGGS on a plane… m h = 125 GeV 0.05 0.10 m h = 120 GeV µ 2 κ ρ f { { , ˜ 4 parameters: , , 0.05 r 0.1 0 - 2 constraints: EWSB+ HIGGS soft Z 2 - breaking 0.00 0.15 - 0.05 2 dimensional par. space 0.2 f/v > 2 . 3 with the constraint 0.25 - 0.10 - 0.10 - 0.05 0.00 0.05 0.10 0.15 0.20 é 2 ê f 2 m Hard breaking o ff er new possibilities: µ 2 ≈ 2 κ f 2 µ 2 /f 2 f/v > 2 . 3 soft - breaking: tuning to get ρ ⌧ ˜ ˜ µ 2 /f 2 ⌧ ρ κ ⌧ ρ to get m h tuning hard - breaking: ˜

soft m 2 h ≈ 8 κ v 2 v/f ≈ 1 − f 2 ∆ soft 2 v 2 low fine - tuning favours small f Extra positive κ 0 to get m h = 125 GeV

soft hard 8 v 2 κ m 2 h ≈ 8 κ v 2 m 2 h | hard ≈ F ( Λ ρ , f ) v/f ≈ 1 − f 2 1 − f 2 ✓ ◆ ∆ soft ∆ | hard F ( Λ ρ , f ) v/f ≈ 2 v 2 2 v 2 the gain in fine - tuning is larger at large f low fine - tuning favours small f the gain in fine - tuning correspond to an Extra positive κ 0 to get m h = 125 GeV enhancement of the Higgs mass

soft hard 8 v 2 κ m 2 h ≈ 8 κ v 2 m 2 h | hard ≈ F ( Λ ρ , f ) v/f ≈ 1 − f 2 1 − f 2 ✓ ◆ ∆ soft ∆ | hard F ( Λ ρ , f ) v/f ≈ 2 v 2 2 v 2 the gain in fine - tuning is larger at large f low fine - tuning favours small f the gain in fine - tuning correspond to an Extra positive κ 0 to get m h = 125 GeV enhancement of the Higgs mass 5 0.7 0.6 4 0.5 0.4 0.3 3 e L r @ TeV D F ( Λ ρ , f ) 0.2 2 0.1 1 0 F H L r , f L - 1 e=+ 1 e=- 1 - 2 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 f ê v