The Minimal Exceptional Supersymmetric Standard Model Richard Howl

The Minimal Exceptional Supersymmetric Standard Model Richard Howl University of Southampton UK BSM 2007

1 / 12 MESSM = Minimal Exceptional Supersymmetric Standard Model An SUSY Grand Unified Theory based on the Like the , MESSM attempts to solve the - problem of the MSSM But without theoretical difficulties caused by incomplete that are introduced in the multiplets for gauge coupling unification

2 / 12 MSSM superpotential contains which gives mass to the Higgsinos Important for determining the Higgs scalar potential and the pattern of Electro-weak Symmetry Breaking (EWSB) From phenomenology we require SUSY breaking (or EW) scale is a free parameter, term is SUSY invariant, can be present before SUSY is broken why SUSY breaking (not e. g. )? A popular solution is to introduce a SM singlet and a superpotential term: (dynamically produced) However, this term creates a global (PQ) symmetry which will produce a Goldstone boson when gets its VEV One way to avoid this Goldstone boson is to embed the global Inside a local The would-be Goldstone boson gets ‘eaten’ The bilinear - term is forbidden by this local symmetry

3 / 12 Gauge coupling unification for MSSM suggests can embed it within some Supersymmetric Grand Unified Theory If assume GUT exists and wish to solve the - problem with a and , then both of these must be derived from the Grand Unified Theory VEV could then be determined from a radiative mechanism from GUT However: SUSY GUTs colour triplet particles: when we embed , into complete GUT multiplets Can cause rapid proton decay and can destroy gauge coupling unification Most popular solution is to give large (GUT scale) mass to via a doublet-triplet splitting mechanism don’t participate in low energy theory and proton decay suppressed

4 / 12 Problem: Since and come from the same representations: To generate the term, we generally also get a With a large effective VEV from mass term, could generally acquire a large (one-loop tadpole diagrams) destroying EWSB Whereas if have small masses (EW scale) then they can affect the RGEs to help drive the soft square mass of Also, light term large and negative could be used to cancel any anomalies for the Suggests should try to keep (to solve – problem) ‘light’

5 / 12 generally interact with quarks and leptons in GUTs via these terms: 1 2 Induce proton decay via d = 6 operators suppressed by Therefore if are light we must suppress proton decay by making Yukawa constants sufficiently small Must only suppress terms inducesince proton decay andwould not However, we cannot the have all that‘small’ then the terms allow the triplets to decay become stable that particles. e. g. apply a discrete symmetry on the leptons or leptons From standard Big Bang cosmological arguments wethe should be and abletriplets to observe ‘heavy’ stable in hadrons today 1 strong Then or 2 interacting are allowed but the otherparticles is forbidden Strong on such stable particles proton limits decay put sufficiently suppressed and with mass are nobetween longer stable 1 Ge. V to 10 Te. V Another possibility could be applythat a family symmetry and / or Must try to suppress thetoterms induce proton decay butgenerate not 1 orthe 2 terms via higher dimensional operators that allow the triplets to decay more work needed

6 / 12 Proton decay now suppressed but keeping (2 – loop) light spoils the unification of the MSSM:

6 / 12 Proton decay now suppressed but keeping light spoils the unification of the MSSM: (2 – loop) The Black line indicates mass of The green lines show their effect on the RGEs

6 / 12 Proton decay now suppressed but keeping light spoils the unification of the MSSM: (2 – loop) (No Unification) The Black line indicates mass of The green lines show their effect on the RGEs

6 / 12 Proton decay now suppressed but keeping light spoils the unification of the MSSM: (2 – loop) A possible solution is to add two additional EW doublets to light spectrum have added two complete multiplets ( ) to the MSSM

6 / 12 Proton decay now suppressed but keeping light spoils the unification of the MSSM: (2 – loop) (higher unification coupling constant than for MSSM. ) However these new particles could introduce theoretical problems: A possible solution is to add two additional EW doublets to light spectrum e. g. How to keep the two extra doublets light but rest of GUT multiplet heavy. have added two complete multiplets ( ) to the MSSM Essentially a D-T (mass) splitting problem

7 / 12 An example of a SUSY GUT that requires two additional EW doublets for gauge coupling unification is the is essentially an SUSY GUT that breaks to and places the quarks, leptons, from and All 3 generations of , into 3 generations of a are both used to solve the are ‘light’ to help - problem of the MSSM solve the - problem and to cancel gauge anomalies contains like MSSM + complete reps. ( )+ spoil unification

7 / 12 e. g. example In are put into generations a An of amatter SUSY and GUTHiggs that requires two 3 additional EWofdoublets for All 3 generations of areis‘light’ gauge coupling unification the is essentially an SUSY GUT that breaks to and places the quarks, leptons, from and All 3 generations of , into 3 generations of a are both used to solve the are ‘light’ to help - problem of the MSSM solve the - problem and to cancel gauge anomalies contains like MSSM + complete reps. ( )+ spoil unification

7 / 12 e. g. In matter and Higgs are put into 3 generations of a All 3 generations of like MSSM + are ‘light’ + two extra doublets complete reps. ( )+ spoil unification

7 / 12 e. g. In matter and Higgs are put into 3 generations of a All 3 generations of are ‘light’ + two extra doublets like MSSM + complete reps. ( ) Problems: No explanation for why are light but rest of their complete representations are at GUT scale The extra doublets are given mass via a ‘ Why does a D-T splitting problem - term’ : SUSY breaking scale (and not e. g. Introduced another - problem to theory ! )?

8 / 12 A way of avoiding these new doublet particles could be to use an intermediate symmetry to ‘repair’ the unification instead non-simple group Grand Unified Group gauge couplings no longer need to unify but instead turn into gauge couplings (at the symmetry breaking scale) which do unify e. g. in and we could use a left-right symmetric Pati-Salam: At the P-S symmetry breaking scale the SM gauge couplings must satisfy: (When GUT normalized and with P-S symmetry breaking scale determined from running gauge couplings with energy until they satisfy the above equation. )

9 / 12 e. g. with quarks, leptons, All 3 generations of ‘light’. in a fundamental

9 / 12 e. g. with quarks, leptons, All 3 generations of in a fundamental ‘light’. Can now obtain unification if: Unification occurs at Planck scale using standard RGEs. Effect of quantum gravity on RGEs is unknown could spoil unification However, unification at Planck scale is suggestive of a unification of the gauge fields with from gravity. Use Higgs multiplets to break P-S symmetry. assumed quantum gravity does not spoil this unification but instead Assumed havewith mass order fields. of the P-S breaking scale. could unify gravity theofgauge

10 / 12 If assume Planck scale unification then can use an intermediate symmetry rather than two EW doublets for gauge coupling unification. avoiding theoretical difficulties they introduce. The MESSM is based on the but uses a Pati-Salam symmetry for gauge coupling unification instead of the EW doublets no need for a D-T splitting mechanism or the extra To break P-S to SM we use Higgs bosons from with VEVs in : from term and are used to solve - problem of MSSM are singlets of the SM Can generate conventional see-saw mechanisms. direction

11 / 12 Pati-Salam symmetry broken at symmetry assumed to be broken at the Planck mass scale

12 / 12 The MESSM attempts to solve the a SM singlet particle To help solve the all 3 generations of - problem of the MSSM using and a local group from an GUT - problem and to cancel anomalies, light. (including the colour triplets) To ‘repair’ the gauge coupling unification an intermediate Pati-Salam symmetry is used. The P-S symmetry is broken at the GUT scale The symmetry is assumed to be broken at the Planck mass scale. The Higgs bosons used to break P-S come from have the same (GUT scale) mass No multiplet (mass) splitting. which can