QuarkLepton Symmetry In 5 D Kristian Mc Donald

Quark-Lepton Symmetry In 5 D Kristian Mc. Donald University of Melbourne, Australia

Overview • QL symmetry is useful if you like split fermions • Quartification is less arbitrary in 5 D

Quark-Lepton Symmetry • SM is QL asymmetric • Add leptons: E = ( e, e’’) • Extend gauge group • Can define QL symmetry:

QL Symmetry In 5 D • In 5 D inherently extra dimensional techniques become available – Orbifold Compactification • Provides an alternative means to break gauge symmetries • Introduces an additional energy scale, 1/R • Mass of some gauge fields is governed by 1/R rather than a scalar VEV • Different collider phenomenology • Fermions: bulk or brane ?

Split Fermions • Introduce a singlet scalar field with a kink VEV solution. • Fermions get localised at one of the scalar kinks. L= x 5 f<0 f>0

QL Split Fermion Model • Let be odd under QL symmetry: • Thus f. L= -f. Q , fe= -fu , f = -fd and if f. Q , fu , fd >0 d Q L u e

Two scalar kinks: ‹ 2 › L= (f 1+g 2) ‹ 1 › f ‹ 1›+g ‹ 2› =20 20 ffff= == 20 20 g= =-4. 5 -5 g -4 0 -3 ggg === -1 -2 • Suppress proton decay and obtain flavour but requires 36 new parameters in SM.

QL Split Fermion Model • QL symmetry implies mu=me etc. unless quark and lepton profiles are different. • Choose 2 to be even under QL: g. Q , gu , gd >0, g. L=g. Q , ge=gu , g =gd d d u Q Q u LL e e

Grand Unification • Can we unify with leptonic colour? • Can’t use: But:

Quartification In 4 D Break: Unification requires intermediate symmetry breaking scales Can unify via a number of routes both with and without

HIGGS CONTENT • Want to have • 4 ways to go in successive stages • Eight Higgs multiplets, four gain VEVs • Intra-multiplet hierarchy

Unification achieved but… • Complicated Higgs sector: – – Large Higgs potential- lots of parameters Intra-multiplet hierarchy Arbitrary masses 7 light Higgs doublets • If we remove Higgs sector these problems disappear. How? • Place theory on an orbifold

ORBIFOLD BREAKING • Gauge fields in bulk • Under vector components have parities:

BRANE BREAKING • Scalar fields localised on brane • Define • Boundary condition • In the limit • (+, +) fields • Zero mode of (+, +)R, l are shifted up by Mc. • Higgs fields have decoupled

SU(3)q SU(2)L SU(2)l U(1)Y

GAUGE COUPLING UNIFICATION • Mc~ 4 x 1014 Ge. V, MGUT~ 4 x 1016 Ge. V Only occurs for

CONCLUSIONS • 5 D QL symmetry is useful if you like split fermions – Suppress p-decay – Address flavor • Quartification allows for QL symmetric GUT – In 4 D: multiple symmetry breaking routes, with and without remnant lepton color symmetry – Complicated Higgs sector – In 5 D: unique route which demands – Higgsless limit

Acknowledgements • Alison Demaria • Andrew Coulthurst • Ray Volkas and • Bruce Mc. Kellar from the University of Melbourne.