35 years of GUTs - where do we stand?

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1 MPI Heidelberg, November years of GUTs - where do we stand? Michal Malinský Royal Institute of Technology, Stockholm in collaboration with Stefano Bertolini and Luca di Luzio SISSA/ISAS Trieste based on Phys.Rev.D80:015013,2009 and arxiv:0912.xxxx[hep-ph]

2 Outline Grand Unified Theories - a brief intro Simplest Grand unified models and their status Minimal non-susy SO(10) No-go? No, go! Quantum resuscitation of the cadaver Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

3 Grand Unified Theories - a brief intro Convergence of the running gauge couplings at very high energies 60 1 [eq, eq] = α i = g2 i 4π t G M G GeV t = 1 2π ln µ M Z If not an accident the gauge interactions unify and a new dynamics pops up there Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

4 Grand Unified Theories - a brief intro Neutrino masses in the SM: L = ν =(1, 2, 1 2 ) - d = 5 Weinberg operator: L eff c Λ LHLH Neutrino oscillation parameters: m 2 2 m 2 1 m 2 = (8.0±0.3) 10 5 ev 2 m 2 3 m 2 2 m 2 A = (2.5±0.3) 10 3 ev 2 Λ ( )GeV New physics scale governing neutrino masses (seesaw) Remarkably close to the unification scale! O.K., let s take the gauge unification idea seriously... Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

5 Grand Unified Theories - a brief intro Consequences: GUT-scale predictions for one of the gauge couplings, e.g.: sin 2 θ W = 3 8 Quarks and leptons share the GUT multiplets - Yukawas spanned over the GUT multiplets insight into flavour - gauge transitions violate B and L exotic processes d = 6 proton decay: f 1 Qu c Qe c f1 2, u c Qd c f1 3 f1 4 L QQQL, M 2 G M 2 G M 2 G M 2 G u c u c d c e c vector-induced scalar-induced current SK limit: τ(p + π 0 e + ) years M G GeV Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

6 Grand Unified Theories - a brief intro Minimality is an invaluable guiding principle - overall predictivity - in particular for flavour (not dictated by symmetry but by Higgs structure) Minimal GUT gauge group: - rank 4 or higher - must have complex representations - correct multiplet patterns } SU(5) unique rank = 4 option Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

7 Minimal SU(5) model Gauge fields: 24 G =(8, 1, 0) (1, 3, 0) (1, 1, 0) (3, 2, 5 6 ) (3, 2, ) G µ A µ B µ Matter fields: 5 10 F =(1, 1, +1) (3, 2, ) (3, 1, 2 F =(1, 2, 1 2 ) (3, 1, ) 3 ) L Higgs fields: 5 H =(1, 2, 1 2 ) (3, 1, ) 24 H = (1, 1, 0)... H d c c e c (X µ,y µ ) Q SU(5)-breaking SM singlet u c Proton decay: X, Y c 10 F /D 10 F + 5 F /D 5 F Y 5 5 F 10 F 5 H + Y F 10 F 5 H Flavour structure: M M d = Ml T u = Mu T b-tau unification (?) Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

8 Minimal SU(5) model Gauge coupling unification in minimal SU(5) GUT: Y SU(5) t = 1 2π ln µ M Z no unification? Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

9 Minimal SUSY SU(5) GUT Gauge coupling unification in minimal SUSY SU(5) GUT: Y SU(5) 60 α gauginos + higgsinos + squarks and sleptons t = 1 2π ln µ M Z supersymmetric GUTs! - Good also for hierarchies Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

10 Minimal SUSY SU(5) GUT SUSY SU(5) : simpler than non-susy (up to an extra Higgs doublet) - d=5 proton decay operators in SUSY: d L s L d c L s L d c L ũ c ũ 2,3 ũ c 2,3 O L w ± O R h ± c l ẽ c u L ν u c L ν u c L ẽ c W L c L M c ˆQ ˆQ ˆQˆL W R c R M c û c û c ˆdcê c c L, c R Y u Y d,y u Y d Γ(p + K 0 e + ) α2 G (4π) 4 m 5 p M 2 c M 2 SUSY V CKM Y u Y d V CKM 2 - yields at best years; - perhaps viable with non-renormalizable operators invoked (?) Bajc, Fileviez-Perez, Senjanovic, 2002 Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

11 Interlude Both SUSY as well as non-susy minimal SU(5) very sick... - the only rank = 4 option though! How about rank = 5? - admits adding one more Cartan to the four SM ones - a very natural candidate: B - L - left-right symmetric models à la SU(3) c SU(2) L SU(2) R U(1) B L SU(3) c SU(2) L U(1) Y - SU(2)R requires RH neutrino, seesaw natural - rank = 5 admits more than a single breaking step like e.g. SU(4) C SU(2) L SU(2) R SU(3) c SU(2) L U(1) R U(1) B L - these emerge as subgroups of SO(10) Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

12 SO(10) basics Anomaly-free 16 F =(3, 2, ) (1, 2, 1 2 ) ( 3, 1, ) ( 3, 1, 2 3 ) (1, 1, +1) (1, 1, 0) 10 H =(1, 2, 1 2 ) (1, 2, ) ( 3, 1, ) (3, 1, 1 3 ) - N.B. doublets in pairs Strongly correlated Yukawa s: a chance to understand some aspects of flavour 16 F 16 F 10 H Dirac masses for everybody driven by a single coupling! RH neutrinos automate, renormalizable type I+II seesaw natural 126 H (1, 2, 1 2 ) (1, 2, ) (1, 1, 0) (1, 3, +1) F 16 F 126 H LH and RH Majorana neutrino masses, extra Dirac contributions SO(10) SSB: 126 H breaks large portion of the GUT symmetry, but not SU(5) Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

13 SO(10) basics SO(10) breaking chains (omitting the SU(5) options) : minimal non-susy option: 45 minimal SUSY option: 210 Chang, Mohapatra, Gipson, Marshak, Parida 1985 Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

14 SO(10) basics N.B. in SUSY the extra freedom in running is not very pronounced Example: SO(10) SU(3) c SU(2) L SU(2) R U(1) B L SM 60 α often like this hardly any more apart SUSY likes desert Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

15 Minimal SUSY SO(10) GUT Structure Matter: 3 16 F T.E. Clark, T.K. Kuo, N. Nakagawa 1982 C.S. Aulakh, Rabindra N. Mohapatra 1983 C.S.Aulakh, B.Bajc, A.Melfo, G.Senjanovic and F.Vissani 2004 Higgses: 10 H 126 H 126 H 210 H - D-flatness, realistic breaking pattern Proton decay - in a better shape than in SU(5) - many triplets around Neutrino challenge: High B - L scale Low B - L scale neutrinos too light thresholds hints: C.Aulakh, 2005 complete analysis: S.Bertolini, MM, T. Schwetz 2006 Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

16 Minimal non-susy SO(10) I won t be concerned about naturalness as long as predictivity is at stakes. Unlike minimal SU(5), minimal SO(10) can live and is simpler without SUSY - smaller representations, minimal model 45 H 16 H 10 H or 45 H 126 H 10 H - only d=6 or higher proton decay Typical multi-stage breaking pattern B L 2 R B L R non-susy doesn t like desert SO(10) - a more realistic example: SO(10) 3 c 2 L 2 R 1 B L 3 c 2 L 1 R 1 B L... n 2 n U factor SO(10) SU(2) R - gap between GUT and intermediate SSB Chang, Mohapatra, Gipson, Marshak, Parida 1985 recent reassessment: Bertolini, MM, Di Luzio 2009 n 1 Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

17 Minimal non-susy SO(10) (the variant) The gap from the minimal non-susy SO(10) perspective: The minimal Higgs sector dynamics does not support it!!! 45 H 45 = ω Y ω R ω R ω Y ω Y ω Y ω Y ω R ω R τ 2 triggers the following chains: SO(10) SU(3) c SU(2) L SU(2) R U(1) B L SU(3) c SU(2) L U(1) R U(1) B L SM SO(10) SU(4) C SU(2) L U(1) R U(1) B L SU(3) c SU(2) L U(1) R U(1) B L SM ω R = ±ω Y SO(10) SU(5) U(1) SM - this one we know is not realistic though! tachyons in the scalar spectrum unless 1 2 ω Y /ω R 2 m 2 (8,1,0) = 2a 2 (ω R ω Y )(ω R +2ω Y ) m 2 (1,3,0) = 2a 2 (ω Y ω R )(ω Y +2ω R ) Only the (flipped) SU(5) vacuum allowed! Yasue, Ma & co., Buccella & co. back in 1980 s Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

18 Status of the Minimal non-susy SO(10) This textbook result implies no-go also for the Minimal non-susy SO(10) Is that really a no-go? Second Weinberg s law of progress in particle physics : Never trust arguments based on the lowest order of perturbation theory. S.Weinberg (an essay from 1983) No-go? No! Go! Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

19 Resuscitating the Minimal non-susy SO(10) There is something peculiar about the tachyons : a 2 m 2 (8,1,0) = 2a 2 (ω R ω Y )(ω R +2ω Y ) a 2 m 2 (1,3,0) = 2a 2 (ω Y ω R )(ω Y +2ω R ) PGB s of an enhanced global symmetry of the scalar potential, but quite interesting... V = 1 2 m λ(16 16) m2 45Tr(45 2 )+a 1 [Tr(45 2 )] 2 + α16 16Tr(45 2 ) +a 2 Tr(45 4 )+β τ individual rotations of 16 and 45 preserved individual rotations of 16 and 45 broken explicitly How come that β and τ do not enter the PGB masses when turned on??? - the τ - term obviously does not have enough legs - the β - term is accidentally zero (resembles the SM gauge mass term) IRRELEVANT AT THE QUANTUM LEVEL! S.Bertolini, MM, L.Di Luzio, arxiv:0912.xxxx[hep-ph] Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

20 Resuscitating the Minimal non-susy SO(10) We have performed a one-loop analysis of the minimal SO(10) vacuum - Coleman-Weinberg effective potential minimization: m 2 (1,3,0) = m 2 (8,1,0) = 1 4π 2 τ 2 + β 2 (2ω 2 R ω R ω Y +2ω 2 Y )+g 4 16ω 2 R + ω Y ω R + 19ω 2 Y 1 4π 2 τ 2 + β 2 (ω 2 R ω R ω Y +3ω 2 Y )+g 4 13ω 2 R + ω Y ω R + 22ω 2 Y - radiative corrections to PGB masses non-trivial & large φ + logs, + logs, τ χ χ τ φ - compete with the tree-level parts for a 2 O(10 1 )β, τ NO TACHYONS even in the ω R ω Y or ω Y ω R regimes! φ φ β φ χ χ φ β φ φ THE GAP IS SUPPORTED AT THE QUANTUM LEVEL!!! φ φ g 2 g 2 - unexpected bonus : the gap shrinks a bit S.Bertolini, MM, L.Di Luzio, arxiv:0912.xxxx[hep-ph] Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

21 Conclusions Grand unifications are beatiful but the minimal (predictive) models tend to fail: Minimal SU(5) killed by unification constraints Minimal SUSY SU(5) killed by proton decay Minimal SUSY SO(10) killed by flavour + unification constraints Minimal non-susy SO(10) cursed 25 years ago for technical reasons The first quantum level analysis of its vacuum brings it back to life! True love s kiss to the Sleeping Beauty... just 75 years too early?! Michal Malinský (KTH Stockholm) 35 years of Grand Unification - where do we stand? MPI Heidelberg, Nov /21

22 Thank you for your kind attention!