THE DREAM OF GRAND UNIFIED THEORIES AND THE HC atsis symposium, Zurich, 2013 Graham Ross
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
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
Grand Unification (String Unification) 45 24 12 e.g. SO(10) SU (5) SU (3) SU (2) U (1) g g g g } 5 3 2 1 d c d c SU (3) ( 5 ) } : d c e } (X,Y ) µ, M X 10 15 16 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 9 11 13 15 17 og 10 [Energy Scale (GeV)] ν ν R ν m ν R Smirnov
BUT
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!
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
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
1 SUSY@TeV? HC SUSY searches so far negative m g, q > 1 1.5 GeV SP mass [GeV] 800 700 600 500 400 300 200 100 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-12-024 0-lep (E T +H T ) 19.4 fb -1 SUS-13-007 1-lep (n 6) 19.4 fb jets 0 500 600 700 800 900 1000 1100 1200 1300 1400 1500 0 1-1 SUS-12-017 2-lep (SS+b) 10.5 fb -1 SUS-13-008 3-lep (3l+b) 19.5 fb gluino mass [GeV] [GeV] m 0 1000 95% C limits. SUSY theory not included. 0-lepton, 7-10 jets [ int -1 = 20.3 fb ] 600 400 200 ~ 0 g- ~ g production, ~ g tt, 1 ATAS-CONF-2013-054 0-lepton, 3 b-jets ATAS-CONF-2012-145 800 3-leptons, 4 jets ATAS-CONF-2012-151 1 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-2013-007 Status: HCP 2013 Expected Observed Expected Observed Expected Observed Expected Observed 500 600 700 800 900 1000 1100 1200 1300 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
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 > 1 10 34 yrs, M X > 10 16 GeV e +
SUSY GUTS Nucleon decay 1 Λ QQQ F τ p e + π 0 > 1 10 34 yrs, M X > 10 16 GeV τ p K + ν > 3.3 1033 yrs Λ > 10 27 GeV, 10 9 M Planck Raby Murayama et al
SUSY GUTS Nucleon decay 1 Λ QQQ F τ p e + π 0 > 1 10 34 yrs, M X > 10 16 GeV τ p K + ν > 3.3 1033 yrs, Λ > 10 27 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
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)
SUSY-GUT gauge coupling unification 2 sin θ W = 0.2312 ± 0.0002 I Ghilencea, GGR sin 2 θ W = 0.23116(12) (Expt) α s = 0.134 ± 0.01 4(sin 2 θ W 0.23116) c. f. 0.1184(7) (Expt)?
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 = 3.6 1017 GeV Kaplunovsky
String unification with gravity 10-60 WCHS MU = M P E 17 3.6 10 GeV?..close..but not close enough!..string threshold corrections, Δ i? I sin 2 θ W = 0.23116(12) (Expt) GGR, D.Ghilencea MU = (2.5 ± 2).10 16 GeV α s = 0.134 ± 0.01 4(sin 2 θ W 0.23116) c. f. 0.1184(7) (Expt)
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 2 2 2 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.
Precision Unification possible String unification with gravity 10-60 M P E + Wilson line breaking e.g. Z 3 : SU (5) SM M WCHS U = 6.10 16 GeV, δ (α s ) = 0.008 I sin 2 θ W = 0.23116(12) (Expt) GGR, D.Ghilencea GGR M U = (2.5 ± 2).10 16 GeV α s = 0.126 ± 0.01 4(sin 2 θ W 0.23116) c. f. 0.1184(7) (Expt)?
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 = 0.126 ± 0.01 4(sin 2 θ W 0.23116) M U = (2.5 ± 2).10 16 GeV Family replication and masses String compactification GUT relations m b = m τ, Det[M d ] = Det[M l ] Family symmetries (?)
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 = 0.126 ± 0.01 4(sin 2 θ W 0.23116) M U = (2.5 ± 2).10 16 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
Outlook indirect signals Nucleon decay D=6 operators Operator renormalisation τ SuperK p e + π 0 > 1 10 34 yrs Hadronic matrix element Giudice, Romanino c. f. M U = (2.5 ± 2).10 16 GeV
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 > 4 10 8 GeV Buchmuller review
Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing Egede Beneke
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 2 0 + A 0 M U Borzumati, Masiero
Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing SUSY @ HC, SUSY Higgs Sphicas Dark Matter SUSY WIMP, Axions f axion > 10 9 GeV Sarkar, Aprile
Outlook indirect signals Nucleon decay D=6 operators Neutrino masses see-saw FCNC q, l,ν mixing SUSY @ HC, SUSY HC Higgs 14! Dark Matter SUSY WIMP, Axions Sphicas f axion > 10 9 GeV Sarkar, Aprile
Unification in split SUSY Giudice, Romanino