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Fermion Masses and Unification

Fermion Masses and Unification. Steve King University of Southampton. Lecture III Family Symmetry and Unification I. Doublet-triplet splitting Introduction to family symmetry Froggatt-Nielsen mechanism Gauged U(1) family symmetry and unification

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Fermion Masses and Unification

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  1. Fermion Masses and Unification Steve King University of Southampton

  2. Lecture III Family Symmetry and Unification I Doublet-triplet splitting Introduction to family symmetry Froggatt-Nielsen mechanism Gauged U(1) family symmetry and unification SO(3) or A4 family symmetry and unification

  3. a a b Doublet-triplet splitting or light triplets? Two possible types of solutions: Give large GUT scale masses to Doublet-Triplet splitting Allow TeV scale masses to but suppress interactions b Yukawa suppression is required (discussion session?) ‘Solves’ Proton Decay and Unification problems ‘Solves’ Proton Decay problem but leaves Unification problem

  4. GUT EW scale Doublet-Triplet Splitting Problem Nontrivial to give huge masses to but not e.g. most simple mass term would be in Minimal superpotential contains: Need to fine tune  =  m to within 1 part in 1014 to achieve » TeV light Higgs

  5. Missing Partner Mechanism Pair up H with a G representation (e.g. 50 of SU(5) ) that contains (colour) triplets but not (weak) doublets Suppose superpotential contains: Under : 50 contains (3,1) but not (1,2) Then in direction gives mass couplings to Nothing for Higgs hu , hd to couple to Problems: Large rank representations problem for Higgs mass…

  6. Introduction to Family Symmetry We would like to account for the hierarchies embodied in the textures SUSY GUTs can describe but not explain such hierarchies To understand such hierarchies we shall introduce a family symmetry that distinguishes the three families It must be spontaneously broken since we do not observe massless gauge bosons which mediate family transitions The Higgs which break family symmetry are called flavons  The flavon VEVs introduce an expansion parameter  = < >/M where M is a high energy mass scale. Idea is to use  to explain the textures.

  7. What is a suitable family symmetry? In SM the largest family symmetry possible is the symmetry of the kinetic terms In SO(10) ,  = 16, so the family largest symmetry is U(3) Candidate continuous symmetries are U(1), SU(2), SU(3) or SO(3) … N.B. If family symmetries are gauged and broken at high energies then no direct low energy signatures

  8. Candidate Family Symmetries (incomplete) Nothing

  9. Simplest example is U(1) family symmetry spontaneously broken by a flavon vev For D-flatness we use a pair of flavons with opposite U(1) charges U(1) Family Symmetry Example: U(1) charges as Q (3 )=0, Q (2 )=1, Q (1 )=3, Q(H)=0, Q( )=-1,Q()=1 Then at tree level the only allowed Yukawa coupling is H 33! The other Yukawa couplings are generated from higher order operators which respect U(1) family symmetry due to flavon  insertions: When the flavon gets its VEV it generates small effective Yukawa couplings in terms of the expansion parameter

  10. Froggatt-Nielsen Mechanism What is the origin of the higher order operators? Froggat and Nielsen took their inspiration from the see-saw mechanism Where  are heavy fermion messengers c.f. heavy RH neutrinos

  11. There may be Higgs messengers or fermion messengers Fermion messengers may be SU(2)L doublets or singlets

  12. Ibanez, Ross; Kane, SFK, Peddie, Velasco-Sevilla Gauged U(1) Family Symmetry Problem: anomaly cancellation of SU(3)C2U(1), SU(2)L2U(1) and U(1)Y2U(1) anomalies implies that U(1) is linear combination of Y and B-L (only anomaly free U(1)’s available) but these symmetries are family independent Solution: use Green-Schwartz anomaly cancellation mechanism by which anomalies cancel if they appear in the ratio:

  13. Suppose we restrict the sums of charges to satisfy Then A1, A2, A3 anomalies are cancelled a’ la GS for any values of x,y,z,u,v But we still need to satisfy the A1’=0 anomaly cancellation condition.

  14. The simplest example is for u=0 and v=0 which is automatic in SU(5)GUT since10=(Q,Uc,Ec) and 5*=(L,Dc)  qi=ui=ei and di=li so only two independent ei, li. In this case it turns out that A1’=0 so all anomalies are cancelled. Assuming for a large top Yukawa we then have: SO(10) further implies qi=ui=ei=di=li

  15. F=(Q,L) and Fc=(Uc,Dc,Ec,Nc)  In this case it turns out that A1’=0. PS implies x+u=y and x=x+2u=y+v. So all anomalies are cancelled with u=v=0, x=y. Also h=(hu, hd)  The only anomaly cancellation constraint on the charges is x=y which implies Note that Yf is invariant under the transformations This means that in practice it is trivial to satisfy for any choices of charges

  16. Shortcomings of U(1) Family Symmetry A Problem with U(1) Models is that it is impossible to obtain For example consider Pati-Salam where there are effectively no constraints on the charges from anomaly cancellation There is no choice of li and ei that can give the desired texture e.g. previous example l1=e1=3, l2=e2=1, l3=e3=hf=0 gave: The desired texture can be achieved with non-Abelian family symmetry. There is also an independent motivation for non-Abelian symmetry from neutrino physics…

  17. Andre de Gouvea Lepton mixing is large Valle et al e.g. Tri-bimaximal Harrison, Perkins, Scott

  18. Large Lepton Mixing From the See-Saw Heavy Majorana Dirac Light Majorana Each element has three contributions, one from each RH neutrino. If the right-handed neutrino of mass X dominates and A1=0 then we have approximately only (2,3) elements with m1,2¿ m3 and tan 23¼ A2/A3

  19. Diagonal RH nu basis columns See-saw Sequential dominance Dominant m3 Subdominant m2 Decoupled m1 Tri-bimaximal Constrained SD Sequential dominance can account for large neutrino mixing

  20. Large lepton mixing motivates non-Abelian family symmetry Need with CSD 2$ 3 symmetry (from maximal atmospheric mixing) 1$ 2 $ 3 symmetry (from tri-maximal solar mixing) Suitable non-Abelian family symmetries must span all three families e.g. SFK, Ross; Velasco-Sevilla; Varzelias SFK, Malinsky

  21. SO(3) family symmetry Suppose that left handed leptons are triplets under SO(3) family symmetry and right handed leptons are singlets To break the family symmetry introduce three flavons 3, 23, 123 Real vacuum alignment (a,b,c,e,f,h real)

  22. If each flavon is associated with a particular right-handed neutrino then the following Yukawa matrix results But this is not sufficient to account for tri-bimaximal neutrino mixing

  23. For tri-bimaximal neutrino mixing we need This requires a delicate vacuum alignment of flavon vevs – see next lecture

  24. Extra Slides

  25. The  problem • MSSM solves “technical hierarchy problem” (loops) • But no reason why » msoft the “ problem”. • In the NMSSM =0 but S Hu Hd  <S> Hu Hd where <S>» • S3 term required to avoid a massless axion due to global U(1) PQ symmetry • S3 breaks PQ to Z3 resulting in cosmo domain walls (or tadpoles if broken) • One solution is to forbid S3 and gauge U(1) PQ symmetry so that the dangerous axion is eaten to form a massive Z’ gauge boson  U(1)’ model • Anomaly cancellation in low energy gauged U(1)’ models implies either extra low energy exotic matter or family-nonuniversal U(1)’ charges • For example can have an E6 model with three complete 27’s at the TeV scale with a U(1)’ broken by singlets which solve the  problem • This is an example of a model where Higgs triplets are not split from doublets

  26. MString E8£ E8! E6 MGUT E6! SU(5)£U(1)N Right handed neutrino masses Quarks, leptons Triplets and Higgs Singlets and RH s H’,H’-bar Incomplete multiplets (required for unification) TeV U(1)N broken, Z’ and triplets get mass,  term generated MW SU(2)L£ U(1)Y broken E6SSM= MSSM+3(5+5*)+Singlets Right handed neutrinos are neutral under: ! SM £ U(1)N

  27. Most general E6 allowed couplings from 273: FCNC’s due to extra Higgs Allows p and D,D* decay SFK, Moretti, Nevzorov Family Universal Anomaly Free Charges: term Triplet mass terms

  28. Rapid proton decay + FCNCs extra symmetry required: • Introduce a Z2under which third family Higgs and singlet are even all else odd  forbids W1 and W2 and only allows Yukawa couplings involving third family Higgs and singlet • Forbids proton decay and FCNCs, but also forbids D,D* decay so Z2must be broken! • Yukawa couplings g<10-8 will suppress p decay sufficiently • Yukawa couplings g>10-12 will allow D,D* decay with lifetime <0.1 s (nucleosynthesis) • This works because D decay amplitude involves single g while p decay involves two g’s

  29. Blow-up of GUT region Unification in the MSSM 2 loop, 3(MZ)=0.118 MSUSY=250 GeV

  30. Blow-up of GUT region Unification with MSSM+3(5+5*) 2 loop, 3(MZ)=0.118 1.5 TeV 250 GeV

  31. SUSY with 3x27’s at TeV scale MPlanck E6! SU(4)PS£ SU(2)L£ SU(2)R £ U(1) MGUT SU(4)PS£ SU(2)L£ SU(2)R£ U(1)! SM £ U(1)X x three families Right handed neutrino masses Quarks, leptons Triplets and Higgs Singlet TeV U(1)X broken, Z’ and triplets get mass,  term generated MW SU(2)L£ U(1)Y broken

  32. Howl, SFK Planck Scale Unification with 3x27’s MPlanck MPlanck Low energy (below MGUT) three complete families of 27’s of E6 High energy (above MGUT»1016 GeV) this is embedded into a left-right symmetric Pati-Salam model and additional heavy Higgs are added.

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