Borut Bajc Vector like matter and grand unification Borut Bajc J. Stefan Institute, Ljubljana, Slovenia Kaladi Babu, BB and Zurab Tavartkiladze, to appear What is ν ?, GGI Firenze, 2012 1
Borut Bajc Outline • The minimal susy SU(5) • Mass constraint: problem and known solutions • RGEs and proton decay: problems and known solutions • New solution with vectorlike matter: the idea • New solution with vectorlike matter: details • Few thoughts on neutrino masses • Conclusions What is ν ?, GGI Firenze, 2012 2
Borut Bajc The minimal susy SU(5) It is made of • 3 generations of matter in ¯ 5 i + 10 i • Higgses in 24 H and 5 H + ¯ 5 H • gauge superfield in 24 V What is ν ?, GGI Firenze, 2012 3
Borut Bajc Mass constraint: the problem and known solutions In minimal renormalizable susy SU(5) most general Yukawas W SU (5) = Y ij 10 10 i 10 j 5 H + Y ij 5 ¯ 5 i 10 j ¯ 5 H Y i, j = 1 , . . . 3 (generation indices) MSSM Yukawas parametrized by = Y ij j H u + Y ij j H d + Y ij W MSSM U Q i u c D Q i d c E Le c H d Y What is ν ?, GGI Firenze, 2012 4
Borut Bajc Easy to derive in our GUT that M T M U = ( ∝ Y 10 ) U M T BAD → M D = ( ∝ Y 5 ) E 3 rd generation ( m b = m τ at GUT scale) OK 1 st and 2 nd generation bad even after RGE’s from GUT scale to EW scale What is ν ?, GGI Firenze, 2012 5
Borut Bajc Well known solutions: • add non-renormalizable (1 /M P lanck ) terms: 1 Y ij (¯ 5 i ) α (10 j ) αβ (24 H ) γ β (¯ 5 H ) γ M P lanck α, β, γ = 1 , . . . 5 (SU(5) indices) • extra Higgses: 45 H + 45 H In both cases accidental SU(4) of Yukawa terms after � ¯ 5 H � � = 0 broken What is ν ?, GGI Firenze, 2012 6
Borut Bajc RGEs and proton decay: the problem and known solutions From RGE’s and known exp values of α i ( M Z ): � 5 / 2 � m 3 M T ≈ 10 15 GeV m 8 m 3 , 8 . . . masses of weak triplet and color octet in 24 H . In minimal renormalizable susy SU(5): m 3 = m 8 → M T ≈ 10 15 GeV Color triplet T too light, mediates too fast proton decay! � ¯ W T = Y ij T + Y ij Q i Q j + u c i e c u c i d c � � � j + Q i L j T 10 j 5 What is ν ?, GGI Firenze, 2012 7
Borut Bajc Well known solutions: • extra Higgs terms suppressed by 1 /M P lanck : If 24 4 H /M P lanck >> λ 24 3 H → m 3 = 4 m 8 and M T ≈ 10 16 − 17 GeV Not enough yet, but much better. • extra Yukawa terms suppressed by 1 /M P lanck : 1 (10 i 10 j 24 H 5 H + 10 i ¯ 5 j 24 H ¯ 5 H + . . . ) M P lanck → Yukawas in front of T � = Yukawas in front of H • sfermion mixing can help, even make vanish the amplitude! What is ν ?, GGI Firenze, 2012 8
Borut Bajc New solution with vectorlike matter: the idea We look for solutions to both problems assuming renormalizable susy SU(5). Just add an extra vectorlike matter multiplet 5 4 + ¯ 5 4 with M T 4 /M D 4 ≈ 10 − 2 • will give M D � = M T E • RGE solution will change into � 5 / 2 � M D 4 � m 3 � M T ≈ 10 15 GeV m 8 M T 4 In other words, it will be T 4 that will save unification, not T anymore. But T 4 does not mediate proton decay and thus can be lighter! What is ν ?, GGI Firenze, 2012 9
Borut Bajc New solution with vectorlike matter: details First, correction to masses ¯ 5 a ( µ a + η a 24 H ) 5 4 a = 1 , . . . 4 m 0 i δ ij M i 10 j � � ¯ ¯ W Y = 5 i 5 4 0 M 4 5 4 Find unitary matrix U such that M i 0 = U � M 2 i + M 2 M 4 4 What is ν ?, GGI Firenze, 2012 10
Borut Bajc Λ − Λ .x U = . . . . . . with x i x j √ √ x i = M i /M 4 Λ ij = δ ij − 1 + x 2 + 1) 1 + x 2 ( Then � � � � ¯ ¯ ¯ ¯ → U 5 i 5 4 5 i 5 4 so that What is ν ?, GGI Firenze, 2012 11
Borut Bajc Λ m 0 0 10 j � � ¯ ¯ W Y → 5 i 5 4 O ( m 0 ) M 5 4 Since M a = µ a + η a � 24 H � breaks SU(5) we get d c Λ d m 0 d + e Λ e m 0 e c so that M D = Λ d m 0 M E = m 0 Λ e and one can successfully fit the masses What is ν ?, GGI Firenze, 2012 12
Borut Bajc Second, p-decay On top of the previous possible increase of T mass, other changes: T � V CKM V † e c � uPM diag V CKM d + u c M diag U U v u ¯ T � CKM P † u c � νM diag V d − eM diag V V † CKM u + d c M diag V † + E E D v d P . . . diagonal phase matrix (already in the minimal model) V . . . arbitrary unitary matrix (new) One can further play with V to suppress some dangerous decay modes! What is ν ?, GGI Firenze, 2012 13
Borut Bajc Two reasons why p-decay slow here: • M T can be larger that in the minimal SU(5) → M T 4 /M D 4 ≈ 10 − 2 νK + • freedom in V to cancel for example p → ¯ What is ν ?, GGI Firenze, 2012 14
Borut Bajc Few thoughts on neutrino masses • one can always add SU(5) singlets ν R ’s, but obviously no prediction • we have now terms η i ¯ 5 i 24 H 5 4 . Integrating heavy singlets S and weak triplets T in 24 H gives the Weinberg operator η i η j 5 i 5 4 5 4 ¯ ¯ 5 j M S,T But 1. only rank 1 2. masses M S,T too large 3. � 5 4 � = 0 here What is ν ?, GGI Firenze, 2012 15
Borut Bajc • This brings us to the possibility of R-parity violation What we have here is in general M i µ i 5 4 � � ¯ ¯ ¯ 5 i 5 4 5 H M 4 µ 4 5 H M H µ H this mass matrix is different for doublets and triplets What is ν ?, GGI Firenze, 2012 16
Borut Bajc 1. for doublets: � � � � ∝ M i M 4 M H µ i µ 4 µ H → 4 light weak doublets, 1 heavy weak doublet 2. for triplets: no particular relation so that → 3 light weak doublets, 2 heavy weak doublet but with mixing between heavy color tripelt ¯ T and MSSM d c i small enough (otherwise too large tree-level d = 4 p-decay): < M EW U Hi ∼ M GUT Fine-tuning obviously needed What is ν ?, GGI Firenze, 2012 17
Borut Bajc • all this becomes harder and more constrained in SO(10): 1. ν R ∈ 16 already, M ν Dirac ≈ M EW 2. give Majorana mass to ν R Work in progress. What is ν ?, GGI Firenze, 2012 18
Borut Bajc Conclusions • The renormalizable supersymmetric minimal SU(5) hard to reconcile with observations because of 1. mass equality between charged leptons and down quarks 2. light color triplet from unification → too fast proton decay • we suggest to add extra heavy vectorlike 5 4 + ¯ 5 4 : 1. mixing with light down quarks and charged leptons change their light mass matrix 2. these extra color triplets can help unification, thus allowing color triplets that mediate proton decay to be heavier • unexpected bonus: an extra arbitrary unitary matrix V in the Yukawas with color triplets further helps in suppressing p-decay • ν masses can be obtained in a predictive fashion maybe only through R-parity breking couplings. Work still in progress. What is ν ?, GGI Firenze, 2012 19
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