Status of Composite Twin Higgs Riccardo Torre EPFL Lausanne based - PowerPoint PPT Presentation

A First Glance Beyond the Energy Frontier Trieste - 06 Sep 2016 Status of Composite Twin Higgs Riccardo Torre EPFL Lausanne based on papers to appear in collaboration with R. Contino, D. Greco, R. Mahbubani, R. Rattazzi and with J. Serra

Riccardo Torre Status of Composite Twin Higgs

The Naturalness Problem Riccardo Torre Status of Composite Twin Higgs

Naturalness in the SM SM effective theory U V C o m p l e t i o n Approximate CFT Λ UV m h,W,Z Just fixed by NDA 1. All deformations are either irrelevant, marginal or very close to marginal (e.g. QCD) 2. Relevant deformations are forbidden by symmetries ∆ L rel SM = c Λ 2 UV H † H (e.g. fermion masses forbidden by chiral symmetry) 3. The relevant deformations are tuned to be small m 2 h = c Λ 2 UV + δ m 2 h In order to make sense of the level of cancellation we should go to a model where the Higgs mass is calculable Naturalness is about symmetries and NDA Riccardo Torre Status of Composite Twin Higgs 1

Naturalness in the SM SM effective theory U V C o m p l e t i o n Approximate CFT Λ UV m h,W,Z Examples Supersymmetry Strong dynamics • IR scale dynamically generated • Enhanced symmetry in the UV • In the UV Higgs mass term is irrelevant • Supersymmetry broken softly New degrees of freedom expected at TeV scale Riccardo Torre Status of Composite Twin Higgs 2

Naturalness in the SM Viewing the SM as a low energy effective theory we assume the scales to be physical (eg masses of heavy particles) Λ e.g. numerically States “related” to the top quark are expected to be rather light If they are coloured this already implies some tuning (main player LHC!) Riccardo Torre Status of Composite Twin Higgs 3

Soft, supersoft, hypersoft Charged Naturalness Soft models Supersoft models • e.g. MSSM with low scale mediation and • e.g. MSSM with large scale mediation composite models • already constrained at LEP and Tevatron • probed at the LHC • higher tuning • moderate tuning Neutral Naturalness Hypersoft models t ∼ 4 ⇡ 2 × m 2 × g 2 Λ 2 h ∗ 3 y 2 g 2 ✏ t t SM • mass of coloured objects pushed up • evades LHC, testable at FCC • lower tuning Riccardo Torre Status of Composite Twin Higgs 4

The Twin Higgs Mechanism Riccardo Torre Status of Composite Twin Higgs

The Twin Higgs Mechanism Chacko, Goh, Harnik, hep-ph/0506256 Z 2 Barbieri, Gregoire, Hall, hep-ph/0509242 
 Chacko, Nomura, Papucci, Perez, hep-ph/0510273 f Chacko, Goh, Harnik, hep-ph/0512088 SM SM Chang, Hall, Weiner, hep-ph/0604076 …… Accidental SO (8) SO (8) → SO (4) × ^ SO (4) ˆ H | 2 ) + λ ∗ λ h H ( | H | 2 + | e 2 ( | H | 2 + | e H | 2 ) 2 + 4 ( | H | 4 + | e V ( H ) = − m 2 H | 4 ) ˆ SO(8) broken explicitly by and SM couplings λ h ˆ Treating as a perturbation one has λ h H i 2 = m 2 7 Goldstone, 6 eaten and h ˜ H ˆ ⌘ f 2 SO (8) /SO (7) λ h = 0 exactly massless Higgs 2 λ ∗ SO (8) → SO (4) × ^ h ∼ ˆ ˆ λ h ∼ ˆ m 2 λ h f 2 / 2 ∼ ( λ h / 2 λ ∗ ) m 2 λ h ⌧ λ ∗ SO (4) λ h H m 2 ∼ λ h / λ ∗ The physical Higgs mass is suppressed with respect to by a factor H Riccardo Torre Status of Composite Twin Higgs 5

The Twin Higgs Mechanism h ∼ ˆ m 2 λ h f 2 / 2 ∼ ( λ h / 2 λ ∗ ) m 2 λ h ∼ ˆ λ h H + + ˜ δ m 2 H ∼ m 2 t H t ∗ λ h ∼ 3 y 4 ✓ ◆ + ln m ∗ + ln m ∗ δ ˆ t ˜ t t 4 π 2 m t m ˜ t Already saturates the SM value Assuming is dominated by Yukawa induced RG λ h ∗ ' 3 y 2 8 π 2 ⇥ y 2 h & λ h ∗ ⇥ ln m ∗ hypersoft t t δ m 2 ⇥ m 2 ⇥ m 2 2 λ ∗ λ ∗ m t The maximal boost is obtained for the maximal λ ∗ d log µ = N + 8 d λ ∗ 16 π 2 λ 2 λ ∗ . λ max ∼ 16 π 2 / ( N + 8) ∼ 10 ∗ Then scale of coloured particles becomes s r r � ∗ 1 1 m ∗ ∼ 2 × ✏ TeV 10 × × ln m ∗ /m t Riccardo Torre Status of Composite Twin Higgs 6

The Twin Higgs Mechanism One can do even better protecting from large corrections H H & 3 y 2 + + ˜ δ m 2 4 π 2 m 2 t t H t ∗ λ h ∼ 3 y 4 ✓ ◆ + ln m ∗ + ln m ∗ δ ˆ t ˜ t t 4 π 2 m t m ˜ t Already saturates the SM value ✓ 3 y 2 ◆ 2 × 3 y 2 × y 2 h & λ h ∗ × ln m ∗ super-hypersoft t t t δ m 2 4 π 2 × m 2 × m 2 ∗ ∼ 4 π 2 2 λ ∗ 2 λ ∗ m t Then scale of coloured particles becomes s λ ∗ r For maximal 10% tuning is r � ∗ 1 1 m ∗ ∼ 8 × ✏ TeV enough to push the new coloured 10 × × ln m ∗ /m t states to ~10TeV, out of LHC reach Even for a more reasonable Main prediction: radial mode in λ ∗ ∼ 1 resonances up by a factor ~3 LHC reach Chang, Hall, Weiner, hep-ph/0604076 Buttazzo, Sala, Tesi, 1505.05488 [hep-ph] Craig, Howe, 1312.1341 [hep-ph] Riccardo Torre Status of Composite Twin Higgs 7

Z 2 breaking X Z 2 In the Z 2 symmetric case the potential has possible minima p p p h H i = h ˜ h H i = 0 , h ˜ h ˜ H i = m H / H i = m H / H i = 0 , h H i = m H / 2 λ ∗ 2 λ ∗ λ ∗ 0 6 = h H i ⌧ h ˜ In order to achieve one needs to explicitly break the Z 2 symmetry H i For instance a small Z 2 (soft) breaking mass term is sufficient m 2 ⇣ H | 2 ⌘ | H | 2 − | ˜ This can be realized in many ways, examples are: Barbieri, Greco, Rattazzi, Wulzer, 1501.07803 [hep-ph] 1. Twin hypercharge is not gauged Low, Tesi, Wang, 1501.07890 [hep-ph] 2. Only some fermions are twin (fraternal) Craig, Katz, Strassler, Sundrum, 1501.05310 [hep-ph] 3. All twin EW group is not gauged (Javi) Serra, RT, to appear 4. Hard breaking (relaxing tuning) ξ Katz, Mariotti, Pokorski, Redigolo, Ziegler Riccardo Torre Status of Composite Twin Higgs 8

Twin Higgs realisations Riccardo Torre Status of Composite Twin Higgs

Essential ingredients Strong Sector G → H G × SU (3) c × ^ → H × SU (3) c × ^ f ≡ m ∗ /g ∗ SU (3) c × Z ext SU (3) c × Z ext 2 2 G ⊃ H 1 × f H 1 × Z int × H 2 ⊃ H H ⊃ G EW y t ∼ y L y R /g ∗ 2 m ∗ Z 2 = Z ext × Z int y L , ˜ ˜ 2 2 y R , . . . Z 2 g, y L , y R , . . . Elementary sector m e t ∼ e y t f G SM × ˜ gauged G ⊂ G m f W ∼ e gf g, ˜ ˜ t, . . . γ , W, Z, g, h, t, b, . . . Z 2 m t,W,h • Twin symmetry needed at least for the states most relevant for the Higgs potential and in particular the top • If we want at least a twin copy of then SU (2) L rank G ≥ 3 • If some of the twin symmetries are not gauged this induces additional contributions to the Higgs potential which may be used to generate a viable potential • Twin color should be gauged to avoid large Z 2 breaking RG effects on the top sector Riccardo Torre Status of Composite Twin Higgs 9

Examples: Composite Twin Higgs Barbieri, Greco, Rattazzi, Wulzer, 1501.07803 [hep-ph] Low, Tesi, Wang, 1501.07890 [hep-ph] Strong Sector G × SU (3) c × ^ → H × SU (3) c × ^ SU (3) c × Z ext SU (3) c × Z ext 2 2 G ⊃ H 1 × f H 1 × Z int × H 2 ⊃ H H ⊃ G EW 2 Z 2 = Z ext × Z int y L , ˜ ˜ 2 2 y R , . . . Z 2 g, y L , y R , . . . Group structure Elementary sector G SM × ˜ G / H ∼ S 7 gauged G ⊂ G g, ˜ ˜ t, . . . γ , W, Z, g, h, t, b, . . . Global symmetry Z 2 G = SO (8) × U (1) X × ] U (1) X Field content H = SO (7) × U (1) X × ] U (1) X H 1 = SO (4) = SU (2) L × SU (2) R γ , W, Z, g, h, ψ SM SM fields H 1 = ^ SO (4) = ^ SU (2) L × ^ f SU (2) R g, e h, e W, e f Z, e ψ SM Neutral under the SM H 2 = I Twin symmetry explicitly broken by not gauging the Gauge symmetry twin hypercharge L , e T a T a L , T 3 R ( Y = T 3 R + X, Q = T 3 L + Y ) No twin photon Riccardo Torre Status of Composite Twin Higgs 10

Examples: Fraternal Twin Higgs Craig, Katz, Strassler, Sundrum, 1501.05310 [hep-ph] Strong Sector G × SU (3) c × ^ → H × SU (3) c × ^ SU (3) c × Z ext SU (3) c × Z ext 2 2 G ⊃ H 1 × f H 1 × Z int × H 2 ⊃ H H ⊃ G EW 2 Z 2 = Z ext × Z int y L , ˜ ˜ 2 2 y R , . . . Z 2 g, y L , y R , . . . Group structure Elementary sector G SM × ˜ G / H ∼ S 7 gauged G ⊂ G g, ˜ ˜ t, . . . γ , W, Z, g, h, t, b, . . . Global symmetry Z 2 G = SU (4) Field content H = SU (3) H 1 = SU (2) L γ , W, Z, g, h, ψ SM SM fields H 1 = ^ f SU (2) L g, e t R , e W, e f b R , e q L , e Z, e h, e L τ , e Neutral under the SM τ R H 2 = U (1) Y Twin symmetry explicitly broken by not gauging the twin hypercharge (small), and by QCD induced RG Gauge symmetry on the top Yukawa (large) L , e T a T a L , Y ( Q = T 3 L + Y ) No twin photon and no other twin fermions Riccardo Torre Status of Composite Twin Higgs 11