Fermion Masses and Unification Steve King University of Southampton

Lecture 2 Unification

Simple Group Quarks and Leptons unified into representations of Most popular Groups are: Quarks, Leptons Quarks, Leptons, right-handed neutrino Quarks, Leptons, exotics, SM singlet,

Simple Group Single coupling constant Applies to all three examples spontaneously broken: If no additional (non-SM singlet) fermions are added: Couplings assumed to ‘run’ to measured SM couplings At GUT energy.

GUTs

Each family fits nicely into the SU(5) multiplets N.B in minimal SU(5) neutrino masses are zero. Right-handed neutrinos may be added to give neutrino masses but they are not predicted. SU(5) GUT Georgi and Glashow With the hypercharge embedding

Gauge Sector of SU(5)

Summary of Matter and Gauge Sector of SU(5)

Candidate Higgs reps of SU(5) are contained in matter bilinears constructed from 5 * and 10 Minimal suitable Higgs reps for fermion masses consist of 5 H + 5 * H Higgs Sector of SU(5)

The smallest Higgs rep which contains a singlet under the SM subgroup is the 24 Higgs rep and is a candidate to break SU(5) The Higgs superpotential involving the minimal Higgs sector of SU(5) consisting of the 24 H plus 5 H plus 5 H * With some tuning (see later) one can achieve light Higgs doublets which can develop weak scale vevs

The Yukawa superpotential for one family with Higgs H=5, H * =5 * goodbad c.f. good SUSY relations at M GUT : m b ¼ m , m s ¼ m  /3, m d ¼ 3m e

Pati-Salam Partial Unification

The Yukawa superpotential for one family at the GUT scale Could work for the third family, but certainly not for all three families at the GUT scale is bad at the GUT scale is almost good

Georgi-Jarlskog Textures Gives good SUSY relations at M GUT : m b ¼ m , m s ¼ m  /3, m d ¼ 3m e Gives GJ factor of -3 for the lepton

Summary of Pati-Salam -- Predicts RH neutrinos with lepton number as the “fourth colour” -- Allows the possibility of restoring parity if LR symmetry is imposed -- (Quark-lepton) unification of 16 family into two LR symmetric reps -- B-L as a gauge symmetry -- Quantization of electric charge  Q e = -Q p -- Pati-Salam can be unified into SO(10)

SO(10) GUT Georgi; Fritzsch and Minkowski The 16 of SO(10) contains a single quark and lepton family and also predicts a single right-handed neutrino per family. The SU(5) reps are unified into SO(10): The two Higgs doublets are contained in a 10 of SO(10)

Neutrino masses in SO(10) Dirac mass Heavy Majorana mass SO(10) contains all the ingredients for the see-saw mechanism and tends to predict a hierarchical pattern of neutrino masses

Like ‘matter’ particles, Leads to new (triplet) particles D. All give new particles:, Problems: Spoil Unification of MSSM gauge couplings Cause rapid proton decay Higgs must be embedded into representations of e.g. 1 2

Say representation of To produce SM Yukawa terms one generally uses terms Gives following SM interactions: But also gives ‘dangerous’ terms involving with SM particles: And quarks and leptons representation of Proton decay

D-exchange generates superfield operators  In terms of scalar and fermion components some examples of dangerous operators are shown below

Minimal SU(5) is ruled out by proton decay -- but it gives unacceptable fermion masses anyway

Two possible types of solutions: a Give large GUT scale masses to b Allow TeV scale masses to but suppress interactions Doublet-Triplet splitting Yukawa suppression is required a ‘Solves’ Proton Decay and Unification problems b ‘Solves’ Proton Decay problem but leaves Unification problem

Nontrivial to give huge masses to but not e.g. most simple mass term would be in Minimal superpotential contains: Fine tuning to within 1 part in Superpotential: GUTEW scale

Pair up H with a G representation that contains (colour) triplets Take superpotential to contain: Under : Nothing for Higgs h u, h d to couple to Problems: Large rank representations ‘Missing – partner’ mechanism’ but not (weak) doublets (at least after G is broken). Proton decay via triplet Higgsino from And in direction gives mass couplings to effective term.  problem for Higgs mass 50 contains (3,1) but not (1,2)

The  problem (light Higgs mass) is intimately related to the doublet-triplet splitting problem (heavy triplet mass) One approach is to allow both light Higgs doublets and triplets Requirements: generate TeV scale mass terms for the light Higgs doublets and triplets, suppress proton decay due to triplet exchange while allowing triplets to decay in less that 0.1 s to avoid problems with nucleosynthesis The Exceptional Supersymmetric Standard Model (ESSM) is an example of a model with extra low energy exotic matter forming complete 27’s of E 6 plus the two Higgs doublets of the MSSM: [5 * +10+ (5+5 * )+1+1]xthree families +(H,H’) Quarks, leptons Triplets,Higgs, singlets 27 Non-Higgs

E 6 ! SU(5)£U(1) N M GUT TeV U(1) N broken, Z’ and triplets get mass,  term generated Incomplete multiplets (required for unification) Right handed neutrino masses M String E 8 £ E 8 ! E 6 Quarks, leptons Triplets and Higgs Singlets and RH s H’,H’-bar MWMW SU(2) L £ U(1) Y broken Right handed neutrinos are neutral under: ESSM= MSSM+3(5+5 * )+Singlets ! SM £ U(1) N

Family Universal Anomaly Free Charges: Most general E 6 allowed couplings from 27 3 : Allows p and D,D * decay FCNC’s due to extra Higgs

Rapid proton decay + FCNCs  extra symmetry required: Introduce a Z 2 under which third family Higgs and singlet are even all else odd  forbids W 1 and W 2 and only allows Yukawa couplings involving third family Higgs and singlet Forbids proton decay and FCNCs, but also forbids D,D* decay so Z 2 must be broken! Yukawa couplings g<10 -8 will suppress p decay sufficiently Yukawa couplings g> 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

Unification in the MSSM Blow-up of GUT region M SUSY =250 GeV 2 loop,  3 (M Z )=0.118

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

MESSM= 3x27’s (no H,H’) M GUT TeV U(1) X broken, Z’ and triplets get mass,  term generated Right handed neutrino masses M Planck Quarks, leptons Triplets and Higgs Singlet MWMW SU(2) L £ U(1) Y broken E 6 ! SU(4) PS £ SU(2) L £ SU(2) R SU(4) PS £ SU(2) L £ SU(2) R £ U(1)  ! SM £ U(1) X x three families £ U(1) 

Planck Scale Unification with 3x27’s Low energy (below M GUT ) three complete families of 27’s of E 6 High energy (above M GUT » GeV) this is embedded into a left-right symmetric Pati-Salam model and additional heavy Higgs are added. M Planck