THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, - PowerPoint PPT Presentation

THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, Zurich, 2013 Graham Ross

The Standard Model after LHC 8 u Symmetries è Dynamics Gauge SU (3) × SU (2) × U (1) bosons ⎛ ⎞ ⎛ ⎞ u i l i Chiral , l iR , ν iR ⎜ ⎟ ⎜ ⎟ , u iR , d iR , Matter ⎜ ⎟ ⎜ ⎟ ν i d i ⎝ ⎠ ⎝ ⎠ L L ⎛ ⎞ H + Higgs ⎟ → W L ± , Z L , h 0 ⎜ ⎝ ⎠ H 0 u Unanswered questions The Higgs Era - Gauge and multiplet structure? - Charges? - 18(27) parameters? - Neutrino masses? - Baryogenesis? - Dark matter? - Strong CP problem?

Grand Unification (String Unification) u Unanswered questions - Gauge and multiplet structure(?) - Charges e . g . SO (10) ⊃ SU (5) ⊃ SU (3) ⊗ SU (2) ⊗ U (1) - 18 (27) parameters? - Neutrino masses? - Baryogenesis? } d c - Dark matter? d c SU (3) ( ) - Strong CP problem? 5 : d c + = 3 Q Q − 0 ? L } e e SU (2) ν e = Q 1/3 Georgi Glashow 1974 c d { u c ¡ -­‑u c ¡ u ¡ d ¡ u c ¡u ¡ d ¡ LH states SU(2) doublets ( ) u ¡ d ¡ 10 : L e c ¡ c ≡ ν e , R ν e , L = + + (16 ) (10 ) (5 ) ( ) 1 L L L L

Grand Unification (String Unification) u Unanswered questions - Gauge and multiplet structure(?) 45 24 12 ¡ - Charges e . g . SO (10) ⊃ SU (5) ⊃ SU (3) ⊗ SU (2) ⊗ U (1) - 23 parameters? g 5 g 3 - Neutrino masses g 2 g 1 - Baryogenesis } d c - Dark matter? } ¡ d c SU (3) ( ) - Strong CP problem 5 : d c ( X , Y ) µ , M X  10 15 − 16 GeV } L e SU (2) ν e { <H> ¡ <H> ¡ u c ¡ -­‑u c ¡ u ¡ d ¡ u c ¡u ¡ d ¡ ν R ¡ ¡ ( ) u ¡ d ¡ 10 : ν ν L L L e c ¡ 2 m l , q ν L ∝ < H > 2 m  m m = + + (16 ) (10 ) (5 ) ( ) 1 ν R ν R 9 11 13 15 17 L L L L Log 10 [Energy Scale (GeV)] Smirnov

BUT…

Doublet-Triplet splitting problem : } ¡ ? H H ⎛ ⎞ H + …but no SU(5) colour triplet partner H ✔ ¡ Higgs doublet ⎜ ⎟ ⎝ H 0 ⎠ H -­‑ _ H 0 The Standard Model as an EFT: H A µ ✔ , Ψ ✔ H ✗ 2 + δ m h X µ 2 ( Q 2 ) = m h 2 ( Q 2 ) m h 2 ln Q 2 + M X ⎛ ⎞ 2 2 ∝ M X δ m h ⎟ = O (10 15 GeV ) ⎜ ⎝ µ 2 ⎠ The hierarchy problem !

Doublet-Triplet splitting problem : } ¡ ? H H ⎛ ⎞ H + …but no SU(5) colour triplet partner H ✔ ¡ Higgs doublet ⎜ ⎟ ⎝ H 0 ⎠ H -­‑ _ H 0 The Standard Model as an EFT: H A µ ✔ , Ψ ✔ H ✔ 2 + δ m h X µ 2 ( Q 2 ) = m h 2 ( Q 2 ) m h  H ln Q 2 + M X ⎛ ⎞ 2 2 ∝ M SUSY δ m h 2 ⎜ ⎟ µ 2 ⎝ ⎠  X Solution – Supersymmetric GUTs - M SUSY  1 TeV

• Grand Unification, String Unification e . g . SO (10) ⊃ ⊃ ⊗ ⊗ SU (5) SU (3) SU (2) U (1) g 5 g 3 g 2 g 1 gauge ¡coupling ¡ unifica3on ¡ } d c d c SU (3) ( ) 5 : dc L e } SU (2) ν e u c ¡ -­‑u c ¡ u ¡ d ¡ u c ¡u ¡ d ¡ ( ) u ¡ d ¡ 10 : L e c ¡ M SUSY  TeV (16) L = (10) L + (5) L + (1) L Dimopoulos. Georgi Ibanez, GGR Dimopoulos, Raby, Wilczek

SUSY@TeV ? ∼ ~ ~ ~ 0 → χ g - g production, g t t ~ ~ ~ � 0 g - g production, g t t , s = 8 TeV 1 � � Status: LHCP 2013 LSP mass [GeV] 1 [GeV] SUSY 95% CL limits. � not included. 800 CMS Preliminary -1 SUS-12-024 0-lep ( E +H ) 19.4 fb 1000 theory T T Expected -1 ≥ -1 0-lepton, 7 - 10 jets [L = 20.3 fb ] SUS-13-007 1-lep (n 6) 19.4 fb � int s = 8 TeV Observed jets ATLAS-CONF-2013-054 0 1 � � -1 Expected 700 SUS-12-017 2-lep (SS+b) 10.5 fb m LHCP 2013 [L = 12.8 fb -1 ] 0-lepton, � 3 b-jets int Observed -1 SUS-13-008 3-lep (3l+b) 19.5 fb ATLAS-CONF-2012-145 800 Expected -1 Observed [L = 12.8 fb ] 3-leptons, � 4 jets 600 ) σ p int Observed Observed -1 SUSY o ATLAS-CONF-2012-151 t theory ( LHC SUSY searches so far negative m Expected Expected -1 2 2-SS-leptons, 0 - 3 b-jets [L = 20.7 fb ] � = int Observed ) ATLAS-CONF-2013-007 P 500 S L ( 600 m - ) o n i 400 u l g ( m n e d 400 d 300 i b r o f 0 � �  > 1 − 1.5 GeV t 1 t � ~ m g 200 g  , q 200 100 ATLAS Preliminary 0 500 600 700 800 900 1000 1100 1200 1300 1400 1500 500 600 700 800 900 1000 1100 1200 1300 m [GeV] gluino mass [GeV] ~ g Significance? –Fine tuning measure Δ (not optional in likelihood fit!) Ghilencea, GGR Casas et al ⎛ ⎞ a i , b i ∝ log M 2  ∑ ∑  i  i 2 2 δ m h + + ..., a i m b i M X ⎜ ⎟ ⎝ ⎠ m h  , l   , B  , W  q g Δ ≈ δ m h , i ( ) i 2 δ m h 2 ≥ 20 still room for SUSY! 2 m h 2 m h (C)GNMSSM Kaminska, ¡GGR, ¡Schmidt-­‑Hoberg ¡

GUTs - Nucleon decay ⊃ ⊗ ⊗ SU (5) SU (3) SU (2) U (1) M d c ¡ X } ( ) d c ¡ X µ 5 : : New lepto-quark gauge interactions dc ¡ L e ¡ + → π 0 p e � e ¡ } ¡ u d c u c -u c u d u c u d ( ) X µ 10 : u d e + L e c u τ p → e + π 0 > 1 × 10 34 yrs, τ ∝ M X M X > 10 16 GeV 4 ,

SUSY GUTS – Nucleon decay 1 Λ QQQL F τ p → e + π 0 > 1 × 10 34 yrs, M X > 10 16 GeV τ p → K + ν > 3.3 × 10 33 yrs Λ > 10 27 GeV , 10 9 M Planck Raby Murayama et al

SUSY GUTS – Nucleon decay 1 Λ QQQL F τ p → e + π 0 > 1 × 10 34 yrs, M X > 10 16 GeV τ p → K + ν > 3.3 × 10 33 yrs , Λ > 10 27 GeV , 10 8 M Planck No D=5 ✔ ¡ Recent developments: Lee et al Discrete R-symmetry Z 4 R ... GUT SU(5), SO(10) ⇒ † Split multiplets (Higgs) µ-term small (Higgsino mass) † Higher dimension Anomaly free (discrete) symmetry e.g.string unification Ratz et al † Doublet – Triplet splitting

Doublet-Triplet splitting from higher dimensions Compactifi cation: K = K 0 / H freely acting discrete group Wilson line breaking: H ⊂ G W : ⎛ ⎞ embedding of H into gauge group G ∫ a dx m W = P exp − i T a A m ⎜ ⎟ ⎝ ⎠ γ H ⊗ H singlets Massless states: Breit, Ovrut, Segre α = e 2 i π /3 H = Z 3 , H = Diag ( α , α , α ,1,1), e . g . SU (5): ⎛ ⎞ d c ⎛ ⎞ ⎛ ⎞ H − ( ) : ( ) → ( ) ⎜ ⎟ e R ⊗ R (1 ⊗ 5) → ⊕ → 3,5 + 10 ⎜ ⎟ , 3,5 ⎜ ⎟ , Matter d c ⎜ ⎟ ν e 0 ⎝ ⎠ ⎝ ⎠ H ⎜ ⎟ ⎝ ⎠ d c 1 1 α 2

SUSY-GUT gauge coupling unification θ = ± 2 sin 0.2312 0.0002 W I Ghilencea, GGR sin 2 θ W = 0.23116(12) ( Expt ) c . f . 0.1184(7) ( Expt )? α s = 0.134 ± 0.01 − 4(sin 2 θ W − 0.23116)

c.f. String Unification - Weakly Coupled Heterotic String Gross, Harvey,Martinec, Rohm 4 k ∫ = − φ + + HS 10 2 L d x ge ( R i Tr F ...) eff i α α 4 3 ' ' } ¡ } ¡ ∫ 4 d x V α − 1 α = 2 ' 1/ M only scale 10 string α α α α α α 4 3 ' ' ' = α = = String G 10 , 10 G N String N π π 64 V 16 V 4 ⎛ ⎞ M string k i 1 2 ( M Z ) = + b i ln ⎟ + Δ i ⎜ 2 M Z g i g string ⎝ ⎠ M string = g string . M Planck = 3.6 × 10 17 GeV Kaplunovsky

String unification with gravity ¡ ¡ -60 10 E M P = × WCHS 17 M 3.6 10 GeV ? U ..close..but not close enough! Δ i ? ..string threshold corrections, I = ± 16 M (2.5 2).10 GeV U GGR, D.Ghilencea sin 2 θ W = 0.23116(12) ( Expt ) c . f . 0.1184(7) ( Expt ) α s = 0.134 ± 0.01 − 4(sin 2 θ W − 0.23116)

Δ i String threshold effects, : Wilson line breaking . GGR Raby . Ratz → ⊗ ⊗ S U (5 ) SU (3) SU (2) U ( 1) . X Y , 1 3,2,1 } ¡ σ = χ + + ρ 2 2 2 M ( ) ( n ) n = ± 1 σ n 2 R n = 0 3,2,1 β σ β − β σ X Y , SU (5 ) ( ) ( ) ¡ ¡ ( ) + ρ + − ρ = − ρ . 2 2 i log( m ) log( m ) i l og ( m ) π π 4 4 Reduction in X,Y boson contribution - equivalent to reduction in unification scale.

String unification with gravity Precision Unification possible -60 10 E M P + ¡Wilson ¡line ¡breaking ¡ Z 3 : SU (5) → SM e . g . WCHS = 6.10 16 GeV , M U δ ( α s ) = − 0.008 GGR I M U = (2.5 ± 2).10 16 GeV GGR, D.Ghilencea sin 2 θ W = 0.23116(12) ( Expt ) c . f . 0.1184(7) ( Expt )? α s = 0.126 ± 0.01 − 4(sin 2 θ W − 0.23116)

Summary ⇒ • Gauge, matter multiplets SU (5), SO (10), … GUT ⇒ Hierarchy problem SUSY GUT R ⊂ Lorentz symmetry D>4 ⇒ µ-term Z 4 ⇒ Doublet-triplet splitting Wilson line breaking • Precision gauge and gravity coupling unification possible α s = 0.126 ± 0.01 − 4(sin 2 θ W − 0.23116) M U = (2.5 ± 2).10 16 GeV • String compactification Family replication and masses GUT relations m b = m τ , Det [ M d ] = Det [ M l ] Family symmetries (?) 

Summary ⇒ • Gauge, matter multiplets SU (5), SO (10), … GUT ⇒ Hierarchy problem SUSY GUT R ⊂ Lorentz symmetry D>4 ⇒ µ-term Z 4 ⇒ Doublet-triplet splitting Wilson line breaking • Precision gauge and gravity coupling unification possible α s = 0.126 ± 0.01 − 4(sin 2 θ W − 0.23116) M U = (2.5 ± 2).10 16 GeV • String compactification Family replication and masses GUT relations m b = m τ , Det [ M d ] = Det [ M l ] Family symmetries (?)  Soft masses – radiative breaking Ibanez,GGR