One or more Higgs bosons? Beyond the SM after the first run of the - PowerPoint PPT Presentation

One or more Higgs bosons? Beyond the SM after the first run of the LHC GGI, July 9-12, 2013 Riccardo Barbieri SNS and INFN, Pisa B, Buttazzo, Kannike, Sala, Tesi 2013 1

Conclusion (no lack of ? marks) 1. The discovery of the Higgs boson: Is it the coronation of the Standard Model OR a first step towards unexplored territory? 2. Natural or unnatural theories? before accepting a shift of paradigm, useful to be patient and careful (but courageous as well) 3. One or more Higgs bosons? could be the lightest new particle(s) around 4. What about the flavour puzzle? m � s, V CKM ⇔ λ Y ukawa : a great embarrassment, ij unlikely to be solved without much needed key data 21/21

A quantitative measure (!?) of naturalness δ m 2 h ≈ aM 2 NP < ∆ m 2 h model dependent a measure of fine tuning (which exist in nature) hard to achieve fine tuning (some NMSSM gets to 0.2-0.3) an indicative MSSM ≈ LHC now ≈ LHC14 (?) 4/21

NMSSM ∆ f = λ H u H d Fayet 1975 Two independent reasons to consider it: 1. Add an extra contribution to m 2 hh = m 2 Z c 2 2 β + ∆ 2 t + λ 2 v 2 s 2 2 β thus allowing for lighter stops 2. Alleviates fine tuning in v for and moderate tan β λ ≈ 1 dv 2 dv 2 | MSSM ≈ 4 | NMSSM ≈ 1 versus dm 2 g 2 dm 2 λ 2 H u H u B, Hall, Nomura, Rychkov 2007 green points have better than 5% “combined” fine-tuning and in the scale Λ mess = 20 TeV invariant NMSSM m ˜ t 1 < 1 . 2 TeV m ˜ g < 3 TeV Gherghetta et al 2012 5/21

The pro’ s for just one Higgs boson 1. simplicity How about the 12 (18) matter and the 12 (3) vector states? 2. electromagnetism always preserved From 2 to 3 phases only 3. flavour No big reason to be proud of the λ ij 4. a single tuning, in case None is better, which often demands more Higgs bosons Can some extra Higgs bosons be the lightest new particles around?

Two ways to attack the problem ⇒ By direct search pp → h � = LHC + X decay products (perhaps itself in the decay products of...) ⇒ By precision measurements of the couplings of the 125 GeV (quasi-standard) Higgs boson (the NMSSM example) h 3 λ SH u H d H = s β H d − c β H u h 2 S h LHC h = c β H d + s β H u has SM properties

Purpose Outline an overall strategy See the impact of the ‘s µ ( h LHC ) Look at connection with the EWPT

How to deal with the plethora of parameters of the general NMSSM? (without scatter plots or benchmark points) tan 2 α = tan 2 β m 2 A − m 2 Z m 2 A + m 2 (up to rad. corr.) MSSM Z m 2 H + = m 2 A + m 2 m 2 A = m 2 h 3 + m 2 h 1 − m 2 W Z u , S ) T = R 12 σ ( h 3 , h 1 , h 2 ) T general ( H 0 d , H 0 α R 23 γ R 13 h 1 ≡ h LHC NMSSM M 2 = R diag( m 2 (with CP ≃ OK) h 2 ) R T h 3 , m 2 h 1 , m 2 � � m 2 Z c 2 β + m 2 A s 2 2 v 2 λ 2 − m 2 A − m 2 � � c β s β vM 1 Z β M 2 = � 2 v 2 λ 2 − m 2 A − m 2 � m 2 A c 2 β + m 2 Z s 2 β + ∆ 2 t /s 2 c β s β vM 2 � � Z β M 2 vM 1 vM 2 3 m 2 A = m 2 H + − m 2 W + λ 2 v 2 ⇒ α , γ , σ = α , γ , σ ( m 2 i , m 2 H + ; tan β , λ , ∆ t ) 7 /21

An orientation table S-”decoupled” (similarities with the MSSM ) h 3 < h LHC < h 2 ( ≈ S ) H h 3 h LHC h h LHC < h 3 < h 2 ( ≈ S ) H-”decoupled” h 2 < h LHC < h 3 ( ≈ H ) S h LHC h 2 h LHC < h 2 < h 3 ( ≈ H ) h with comments on full triple mixing (no “invisible” decays) (CP-odd not considered)

The signal strengths of h LHC From a theorist’ s informal combination of ATLAS&CMS data Giardino, Kannike, Masina, Raidal, Strumia 2013 projected errors after at LHC14 300 fb − 1 now

⇒ H S-decoupled NMSSM at variable λ h 3 h LHC h knowing m h LHC m h 3 , m H + , α = m h 3 , m H + , α (tan β , λ , ∆ t ) µA t ( t > � 1) almost irrelevant ∆ t ≤ 75 GeV < m 2 ˜ h 3 < h LHC ( < h 2 ( ≈ S )) h LHC < h 3 ( < h 2 ( ≈ S )) λ m H + orange = excluded by - measurements h LHC blue = unphysical

m 2 hh = m 2 Z c 2 2 β + ∆ 2 t ∆ t - isolines θ t = 45 0 D-term included

A projection from the measurements of the signal strengths of h LHC LHC14 at with ATLAS/CMS projected errors 300 fb − 1 NMSSM at variable S-decoupled λ h 3 < h LHC ( < h 2 ( ≈ S )) h LHC < h 3 ( < h 2 ( ≈ S )) h 3 → t ¯ t

µA t MSSM at variable and ∆ t t > < 1 < m 2 ˜ h 3 < h LHC h LHC < h 3 ∆ t m H + orange = excluded by - measurements region still allowed h LHC ∆ t only for largish red = excluded by direct searches ) ) L E P ( H C ( L h 3 < h LHC h LHC < h 3

A projection from the measurements of the signal strengths of h LHC MSSM h 3 < h LHC h LHC < h 2 / 3 The sensitivity region extends up to about 1 TeV for m h 2

Summary so far S-”decoupled” (similarities with the MSSM ) h 3 < h LHC < h 2 ( ≈ S ) µ ( h LHC ) � s h LHC < h 3 < h 2 ( ≈ S ) Any restriction from the EWPT on the figures above? No, because for δ = α − β + π / 2 → 0 H does not contribute at one loop to S or T (no breaking of ) SU (2) × U (1) and the signal strengths of strongly constrain δ h LHC

S NMSSM: H-decoupled h LHC h 2 h γ = γ ( m h 2 ; tan β , λ , ∆ t ) sin 2 γ < 0 . 15 after 300 fb − 1 sin 2 γ < 0 . 22 at 95% CL now λ = 0 . 1 , ∆ t = 85 GeV λ = 0 . 8 , ∆ t � 75 GeV Regions allowed at low λ sin 2 γ only for largish ∆ t

h 3 H = s β H d − c β H u h LHC Fully mixed case and the signal γγ S h 2 h = c β H d + s β H u isolines of normalized to SM µ ( h 2 → γγ ) λ = 0 . 8 , ∆ t � 75 GeV λ = 0 . 1 , ∆ t = 85 GeV magenta = excluded by LEP in ⇾ hadrons h 2 σ 2 = 0 . 001 , m h 3 = 500 GeV

H-decoupled h LHC < h 2 ( < h 3 ( ≈ H )) almost irrelevant ∆ t ≤ 75 GeV λ = 0 . 8 λ = 1 . 4 sin 2 γ “excluded” by -signal strenghts h LHC projection on sin 2 γ No big improvement

h 2 S NMSSM: Direct search at LHC14 h LHC h λ = 0 . 8 σ ( gg → h 2 ) BR ( h 2 → h 1 h 1 ) any other BR determined in this plane

NMSSM: H-decoupled h LHC < h 2 ( < h 3 ( ≈ H )) λ ( h 3 LHC ) significant deviations from 1 of possible λ ( h 3 SM ) λ = 0 . 8 λ = 1 . 4 but, at the proper time, the game might/should be over

How about the EWPT in the H-decoupled case? As in the S-decoupled case, not competitive with the measurements of the signal strengths ⇒ Heavy : h 2 m 2 m 2 3 α α h 2 h 2 ∆ ˆ ∆ ˆ s 2 s 2 S = + γ log , T = − γ log m 2 m 2 48 π s 2 16 π c 2 w w h LHC h LHC γ = m 2 hh − m 2 h LHC s 2 m 2 h 2 − m 2 B, Bellazzini, Rychkov, Varagnolo 2007 h LHC ⇒ m h 2 → m h LHC No effect on S and T since any mixing can be rotated away

An orientation/summary table S-”decoupled” (similarities with the MSSM ) h 3 < h LHC < h 2 ( ≈ S ) µ ( h LHC ) � s h LHC < h 3 < h 2 ( ≈ S ) H-”decoupled” h 2 < h LHC < h 3 ( ≈ H ) h 2 → γγ (?) λ h 3 LHC h LHC < h 2 < h 3 ( ≈ H ) h 2 → h LHC h LHC The triple mixing could help in the H-decoupled case with µ ( h 2 → γγ )

The (many) reactions to the FT problem 0. Ignore it and view the SM in isolation (untenable) 1. Cure it by symmetries: SUSY, Higgs as PGB 2. A new strong interaction nearby 3. A new strong interaction not so nearby: quasi-CFT 4. Saturate the UV nearby: extra-dimensions around the corner 5. Warp space-time: RS 6. Accept it: the multiverse, the vacua of string theory 10 120 Anything else? CERN June 2011

Last but not least Many thanks for the successful workshop (as usual) to: Stefania, Daniele Annalisa Emilian Mauro Yasunori James Fabio

NMSSM: H-decoupled h 2 < h LHC ( < h 3 ( ≈ H )) λ ( h 3 LHC ) significant deviations from 1 of possible λ ( h 3 SM ) ) (and even larger for h LHC < h 2 ( < h 3 ( ≈ H )) 15

F u,d + ¯ F u,d = 5 + ¯ 5 M u ≈ M d ≈ m u ≈ m d ≈ 1000 TeV