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

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1 THE DREAM OF GRAND UNIFIED THEORIES AND THE HC atsis symposium, Zurich, 2013 Graham Ross

2 The Standard Model after HC 8 u Symmetries è Dynamics Gauge bosons Chiral Matter Higgs u i d i SU(3) SU(2) U(1) H + H 0, u ir, d ir, l i ν i W ±, Z, h 0, l ir, ν ir u Unanswered questions - Gauge and multiplet structure? - Charges? - 18(27) parameters? - Neutrino masses? - Baryogenesis? - Dark matter? - Strong CP problem? The Higgs Era

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

4 Grand Unification (String Unification) e.g. SO(10) SU (5) SU (3) SU (2) U (1) g g g g } d c d c SU (3) ( 5 ) } : d c e } (X,Y ) µ, M X GeV ν SU (2) e u Unanswered questions - Gauge and multiplet structure(?) - Charges - 23 parameters? - Neutrino masses - Baryogenesis - Dark matter? - Strong CP problem ( 10 ) : u c - u c u d u c u d u d e c (16) = (10) + (5) + ( 1) { <H> m ν < H >2 m ν R <H> m 2 l,q og 10 [Energy Scale (GeV)] ν ν R ν m ν R Smirnov

5 BUT

6 Doublet-Triplet splitting problem: Higgs doublet H + H 0 but no SU(5) colour triplet partner H H H _ H - H 0 }? The Standard Model as an EFT: H A µ, Ψ H m h 2 (Q 2 ) = m h 2 + δ m h 2 (Q 2 ) X µ δ m 2 h M 2 X ln Q2 2 + M X µ 2 = O(1015 GeV ) The hierarchy problem!

7 Doublet-Triplet splitting problem: Higgs doublet H + H 0 but no SU(5) colour triplet partner H H H _ H - H 0 }? The Standard Model as an EFT: H A µ, Ψ H m h 2 (Q 2 ) = m h 2 + δ m h 2 (Q 2 ) δ m 2 2 h M SUSY ln Q2 2 + M X µ 2 Solution Supersymmetric GUTs - M SUSY 1TeV X µ H X

8 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 ( 5 ) : d c d c dc e ν e } SU (3) } SU (2) ( 10 ) : u c - u c u d u c u d u d e c (16) = (10) + (5) + (1) M SUSY TeV Dimopoulos. Georgi Ibanez, GGR Dimopoulos, Raby, Wilczek

9 1 HC SUSY searches so far negative m g, q > GeV SP mass [GeV] g- ~ g ~ production, CMS Preliminary s = 8 TeV HCP 2013 Observed SUSY Observed -1 σ theory Expected m(gluino) - m(sp) = 2 m(top) g ~ t t χ -1 SUS lep (E T +H T ) 19.4 fb -1 SUS lep (n 6) 19.4 fb jets SUS lep (SS+b) 10.5 fb -1 SUS lep (3l+b) 19.5 fb gluino mass [GeV] [GeV] m % C limits. SUSY theory not included. 0-lepton, 7-10 jets [ int -1 = 20.3 fb ] ~ 0 g- ~ g production, ~ g tt, 1 ATAS-CONF lepton, 3 b-jets ATAS-CONF leptons, 4 jets ATAS-CONF tt 0 g ~ forbidden ATAS Preliminary s = 8 TeV -1 [ = 12.8 fb ] int -1 [ = 12.8 fb ] int -1 2-SS-leptons, 0-3 b-jets[ = 20.7 fb ] int ATAS-CONF Status: HCP 2013 Expected Observed Expected Observed Expected Observed Expected Observed m~ [GeV] g Significance? Fine tuning measure Δ (not optional in likelihood fit!) δ m 2 h a i m 2 i + b i M 2 i +..., a i,b i log M X q,l g,w,b m h Ghilencea, GGR Casas et al ( 2 δ m ) h i 2 m h 20 still room for SUSY! Δ δ m 2 h,i 2 m h (C)GNMSSM Kaminska, GGR, Schmidt- Hoberg

10 GUTs - Nucleon decay SU(5) SU (3) SU(2) U (1) ( 5 ) : d c d c dc e e } : X µ New lepto-quark gauge interactions p M X π 0 e + } u d c ( 10 ) : u c -u c u d u c u d u d e c u X µ τ M X 4, τ p e + π 0 > yrs, M X > GeV e +

11 SUSY GUTS Nucleon decay 1 Λ QQQ F τ p e + π 0 > yrs, M X > GeV τ p K + ν > yrs Λ > GeV, 10 9 M Planck Raby Murayama et al

12 SUSY GUTS Nucleon decay 1 Λ QQQ F τ p e + π 0 > yrs, M X > GeV τ p K + ν > yrs, Λ > GeV, 10 8 M Planck Recent developments: GUT SU(5), SO(10) µ-term small (Higgsino mass) Anomaly free (discrete) symmetry No D=5 Discrete R-symmetry Z 4 R... Split multiplets (Higgs) Higher dimension e.g.string unification ee et al Ratz et al Doublet Triplet splitting

13 Doublet-Triplet splitting from higher dimensions Compactification: K = K 0 / H freely acting discrete group Wilson line breaking: W : H G Massless states: embedding of H into gauge group G H H singlets W = P exp i T a A a m dx m γ Breit, Ovrut, Segre 2iπ /3 e.g. SU(5) : H = Z 3, H = Diag(α,α,α,1,1), α = e ( R R) : (1 5) H H 0 1 ( ) e, 3,5 ν e 1 d c d c d c α 2, Matter ( 3,5 + 10)

14 SUSY-GUT gauge coupling unification 2 sin θ W = ± I Ghilencea, GGR sin 2 θ W = (12) (Expt) α s = ± (sin 2 θ W ) c. f (7) (Expt)?

15 c.f. String Unification - Weakly Coupled Heterotic String HS 10 φ 4 ki 2 eff = d x ge ( R+ TrF...) 4 3 i + α' α' } 4 d xv } 1 α 10 α = 2 ' 1/ M string only scale Gross, Harvey,Martinec, Rohm G 4 3 = αα ' 10 ' αα 10 ' αstringα N, α = String G = N 64πV 16πV 4 1 g i 2 ( M Z ) = k i + b ln Mstring 2 i g string M Z + Δ i M string = g string.m Planck = GeV Kaplunovsky

16 String unification with gravity WCHS MU = M P E GeV?..close..but not close enough!..string threshold corrections, Δ i? I sin 2 θ W = (12) (Expt) GGR, D.Ghilencea MU = (2.5 ± 2) GeV α s = ± (sin 2 θ W ) c. f (7) (Expt)

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

18 Precision Unification possible String unification with gravity M P E + Wilson line breaking e.g. Z 3 : SU (5) SM M WCHS U = GeV, δ (α s ) = I sin 2 θ W = (12) (Expt) GGR, D.Ghilencea GGR M U = (2.5 ± 2) GeV α s = ± (sin 2 θ W ) c. f (7) (Expt)?

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

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

21 Outlook indirect signals Nucleon decay D=6 operators Operator renormalisation τ SuperK p e + π 0 > yrs Hadronic matrix element Giudice, Romanino c. f. M U = (2.5 ± 2) GeV

22 Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw Majorana mass violation: m ν < H >2 m ν R m l,q 2 m ν R Baryogenesis via eptogenesis ν R decay: Thermal leptogenesis m ν < 0.1eV, m ν R1 > GeV Buchmuller review

23 Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing Egede Beneke

24 e.g. epton FCNC: ( ) m Γ µ eγ ( 2 ) 12 = f l erh 1 + f ν ν R h 2 + m ν R ν R ν R ( 2 m ) ij 1 ( )( f ν f ) ν ij log m ν R 3m 2 2 8π A 0 M U Borzumati, Masiero

25 Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing HC, SUSY Higgs Sphicas Dark Matter SUSY WIMP, Axions f axion > 10 9 GeV Sarkar, Aprile

26 Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing HC, SUSY HC Higgs 14! Dark Matter SUSY WIMP, Axions Sphicas f axion > 10 9 GeV Sarkar, Aprile

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28 Unification in split SUSY Giudice, Romanino