Concluding Remarks

Concluding Remarks March 17, 2012 @ GUT2012 Taichiro Kugo, YITP

Higgs seems to be 125GeV This is a very interesting value, allowing SUSY, but with a small tension to the naïve realization • NMSSM(JEKim), Extra vector-like quarks (Iwamoto) • Difference with 100GeV suggested by the radiative corrections already implies the existence of new matters beyond standard model. • No direct evidence for superparticles: but Analysis may have been missing signals (Hagiwara) At the end of 1972, all experiments did not find Neutral Current Maskawa summarized ``Weinberg-Salam model is a very beautiful theory, but Nature did not adopt it, unfortunately” • May allow some mixture of SUSY and composite Higgs (Kitano)

We all believe in GUTs • The existence of GUT is bound to be correct. Anomaly cancellation or Tr Q = 0 between quarks and leptons. Also supported by tiny neutrino masses and gauge coupling unifications

Here I would like to discuss only How to understand problems of • Generations, i.e., chiral generations No promising ideas: enlarging GUT group – horizontal symmetry, Hodge numbers of CY manifold, orbifolds, …. • Dark energy or vacuum condensates

Generations: • Survival Hypothesis (Georgi) Quarks and Leptons are light (compared with Planck scale), because they are chiral (complex representation) with respect to the SM group SU(3)×SU(2)×U(1) This beautifully explains why they exist, but it also pose a difficulty in naïve trials of Bigger GUT groups Higher dimensions to include generations Higher N SUSY vector-like (non-chiral )

Simple Groups do not work (naively) • SU(n), SO(4k+2), E6 allow complex rprs. But SU(n) with n>5, SO(4k+2) with k>2 have only real (vector-like) reprs wrt the subgroup SU(5) or SO(10). • E7 and E8have only real rprs. • Needs: orbifolding, or Kawamura mechanism complex structure for extra dimensions, CY Or simply, direct product horizontal symmetry (Mohapatra,Maekawa) other ideas? Quasi-NG-fermion

Quasi-NG-fermions • If spontaneous breaking of a global symmetry: G → H, then Nambu-Goldstone bosons appear for broken generators G/H at around ＭＰｌａｎcｋ • If ∃SUSY, NG bosons are accompanied by massless spin ½ fermions, called Quasi-NG-fermions (Buchmüller-Peccei-Yanagida’87，Ong’83 ) • Kugo-Yanagida’84 three generations from E7/SU(5)×SU(3)×U(1)

Exceptional Groups: En Maximal: a priori Raison d'être superstring, … E8 248 ↓ E7 133 ↓ E6 78 ↓ E5 = SO(10) 45 ↓ E4 = SU(5) 24　→　 E3 = SU(3)×SU(2) N=8 SUGRA E7(7)

Suppose ∃E8 or E7 →E4 ×U(１)n E8 →E4 ×U(１)４ E7 → E4 ×U(１)3 E5 = SO(10) , E4 = SU(5)

Exceptional Groups: En E8 248 　　　　　⊃E7 ↓248-(133+1) = 56 +1 + h.c. → NG chiral multiplet 56 of E7 but any reprs of E7 are real 56 = 27+1+27*+1* → 0 generations E7 133 ↓ 133-(78+1) = 27 + h.c. →

Sequential Symmetry Breaking: En E7 133 ⊃E6 ↓ 133-(78+1) = 27 + h.c. → E627 E6 78 ⊃E5 ↓ 78-(45+1) = 16 +h.c. → E516 E5 = SO(10) 45 ⊃E4 ↓ 45-(24+1) = 10 +h.c. →E410 E4 = SU(5) 24

Appearing NG chiral multiplets E7 ⊃E5 ↓ → E627 = 16 + 10 + 1 = (10+5*+1)+(5+5*)+1 E6 ⊃E4 ↓ → E516 = 10+5*+1 E5 = SO(10) ⊃E4 ↓ → E410 = 10 E4 = SU(5)

Appearing NG chiral multiplets E7 ⊃E5 ↓ → E6 27 = 16 + 10 + 1 = (10+5*+1)+(5+5*)+1 E6 ⊃E4 ↓ → E5 16 = 10+5*+1 E5 = SO(10) ⊃E4 ↓ → E4 10 = 10 E4 = SU(5) Three generations 3×(10+5*) + 5 + singlets !

Yet another big problem • Dark matter 23% • Dark energy 73% Despite the brilliant SM, which describes only 5% matters in our Universe! • Higgs condensates ~ 1062 % QCD chiral condensates~ 1050 %, …. Dark energy will pose a totally different problems.

Cosmological constant Λ, or vacuum energy • Present value Λ0 ≈ 10−29gr/cm³ ≈ (2.5×10−12 GeV)4 ≈ 10−44 ×〈〉4QCD chiral condensate ≈ 10−56 ×〈Higgs〉4 ≈ 10−120 ×(ＭＰｌａｎcｋ)4 Reduced Planck scale ＭＰｌａｎcｋ= 1018 GeV

Particle Physicists: static view • Why is it so tiny? huge zero-point vacuum energies of fields • Global SUSY guarantees Λ= 0 But it is (spontaneously) broken at MSUSY ≈ 1 TeV so that we expect Λ= (MSUSY )4 ≈ 1060 × Λ0 • Moreover, SUGRA (local SUSY) does not guarantees Λ= 0, but requires fine tuning of 10−120 order

Remarks • Condensation energy for Spontaneous Sym Breaking ⊃Vacuum energy boson field: zero-point oscillation energy fermion: Dirac’s negative energy sea • Quantum gravity is irrelevant since it is low energy problem, totally classical gravity • Classical gravity field at microscopic (≈ 1fm) level may ≠macroscopic gravity field we feel everyday • Field theory (e.g., QCD) is correct

Cosmologists: historical view • In the order going back history, 1. QCD chiral sym breaking: -ΛQCD ≈ -（200 MeV)4 2. Electroweak symmetry breaking: -ΛEW ≈ -（200 GeV)4 3. GUT symmetry breaking: -ΛGUT ≈ -（10−2ＭＰｌａｎcｋ)4 So that the initial cosmological constant should be Λinitial = Λ0 + ΛQCD + ΛEW + ΛGUT + ? where Λ0 ≪ ΛQCD ≪ ΛEW ≪ ΛGUT

Cosmologists: historical view • There must be huge cosmological constant at the beginning of our universe: Λinitial = Λ0 + ΛQCD + ΛEW + ΛGUT + ? nearly 10120-8 times larger than Λ0 . • Explain this initial value • Or, why is Λ0 so tiny at present? • Possibility of observing this thermal history

Conclusion • We still have many big problems whose beautiful solutions we can believe to exist and can discover! • Let us hope that we will soon get important clues from LHC and astrophysical observations.

Thank you all for coming to this workshop Let us thank also true organizers, Takeshi Fukuyama Hiroaki Sugiyama International organizers

Concluding Remarks