Exceptional Supersymmetry at the Large Hadron Collider
E 6 SSM model and motivation Contents Why go beyond the Standard Model? Why consider non-minimal SUSY? Exceptional SUSY Structure, particle content etc Grand Unification Radiative electroweak symmetry breaking LHC and the ce 6 SSM Z physics Squark and Gluino searches Higgs limits/signal Exotic quarks?
Standard Model Standard Model (SM) of particle physics Beautiful description of Electromagnetic, Weak and Strong forces Tested to incredible precision, e.g. the anomalous magnetic moment of the electron, a e (Exp) = 11596521810 7 10 13 a e (SM) = 11596521827:8(0:772)(0:011)(0:026) 10 13 Electroweak (EW) symmetry is broken by the Higgs Mechanism. Predicts the (still!) undiscovered Higgs boson. The Higgs boson is sought at the Large Hadron collider.
MSSM Chiral Superfield Content
Hierarchy Problem Motivation Huge Fine tuning! SUSY: Quadratic divergences cancel Gauge Coupling Unification Dark-Matter / R-parity R-Parity: SM particles even SUSY partners odd One More Reason Stable LSP Dark Matter candidate Ideas for new physics for experimentalists/ phenomenologists to work with!
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well Hierarchy Problem No Gauge Coupling Unification in SM Dark matter Ad hoc shape for Higgs potential. *though there is an enormous body of experimental evidence to support it.
Why consider non-minimal Supersymmetry?
The problem and singlet extensions The MSSM superpotential contains a mass scale, ¹ apriori this is not connected to SUSY breaking or EWSB TeV scale soft SUSY breaking masses are generated ) EWSB naturally driven by radiative correc tions. Why should ¹ be related to this scale? Add - SM-gauge singlet, is allowed Requires ¹ ¼ 0.1-1 TeV with If ¹ not generated or forbidden, and radiative corrections ) s = O(TeV ) Problem solved!
So our superpotential so far is Yukawa terms effective -term But this has a (global) Peccei-Quinn symmetry massless axion!
massless axion! NMSSM Chiral Superfield Content [Dine, Fischler and Srednicki] [Ellis, Gunion, Haber, Roszkowski, Zwirner] PQ breaking
Supersymmetric Models Minimal Supersymmetric Standard Model (MSSM) Next to Minimal Supersymmetric Standard Model (NMSSM) [Dine, Fischler and Srednicki] [Ellis, Gunion, Haber, Roszkowski, Zwirner] Alternative solution to Peccei Quinn symmetry : Eat the axion Extend the gauge group of the SM with an extra gauged U(1) 0! When U(1) 0 is broken as S gets a vev, Z 0 eats the massless axion to become massive vector boson!
USSM Chiral Superfield Content [M. Cvetic, D.A. Demir, J.R. Espinosa, L. Everett, P. Langacker ] Problem: to avoid gauge anomalies etc Charges not specified in the definition of the USSM
E 6 SSM Chiral Superfield Content Complete E6 multiplets of matter anomalies are automatically cancelled!
LHC Higgs and MSSM Current LHC limits place Higgs mass in range Tentative signal at At tree level MSSM Upper bound: Consequence of quartic coupling fixed in terms of gauge couplings (compare with free parameter in SM) Radiative corrections significantly raise this Including radiative corrections
In the E 6 SSM already there is a new contribution already at tree level, e.g. Two Loop Upper Bounds on the Light Higgs ESSM NMSSM MSSM
Exceptional New Physics just beyond the Standard Model E 8 E 0 8 Heterotic String Theory Grand Unified Theory, e.g. SU(5), SO(10), E 6 ) Desert Supersymmetry, e.g. MSSM Electroweak physics E 6 SSM
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential. *though there is an enormous body of experimental evidence to support it.
Exceptional Supersymmetric Standard Model [Phys.Rev. D73 (2006) 035009, Phys.Lett. B634 (2006) 278-284 S.F.King, S.Moretti & R. Nevzorov] E 6 inspired model with an extra gauged U(1) symmetry Inspired by: Solves the ¹-problem! Matter from 3 complete generations of E 6 ) automatic cancellation of gauge anomalies In the E 6 SSM ) right-handed neutrino is a gauge singlet ) super heavy right-handed neutrinos, generates lepton/baryon asymmetry of the universe [JHEP 0812, 042 (2008), S.F.King, R. Luo, R.Nevorov & D.J. Miller]
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential. *though there is an enormous body of experimental evidence to support it.
Does the E 6 SSM also solve the problems that motivated SUSY?
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential. The cancellation of quadratic divergences takes place in any softly broken SUSY model!
Gauge Coupling Unification Running modified at TeV scale! ) TeV scale new physics Minimal Supersymmetric Standard Model SU(N) gauge theory Gauginos b N = 11 3 N 2 3 N 1 3 n f 1 6 n s d 1 i d(log Q) = b i 2¼ Number of fermions U(1) gauge b 1 = 1 3 Pi Y i 2 (matter particles in Number of fundamental scalars representation )
GUT matter multiplets 27 16 10 + 5 * + 1 10 5 + 5 * Color triplets 1 1 SM singlets
Gauge Coupling Unification Running modified at TeV scale! ) TeV scale new physics Minimal Supersymmetric Standard Model d 1 i d(log Q) = b i 2¼ Complete GUT multiplets give equal b i Single step unification )incomplete multiplets Higgs SU(5) matter multiplet. SU(N) gauge theory Gauginos b N = 11 3 N 2 3 N 1 3 n f 1 6 n s Number of fermions U(1) gauge b 1 = 1 3 Pi Y i 2 (matter particles in Number of fundamental scalars representation )
If only complete E6 multiplets at low energies No gauge coupling unification! Unless... E 6 SSM (usually) augmented by relics from and 27 0 27 0 Called survival Higgs and Alternative version: only complete E6 multiplets ) 2 step unification without relics [see R.Howl, S.F. King PLB 652, 331, JHEP 0801:030]
Gauge Coupling Unification Excepional Supersymmetric Standard Model SU(N) gauge theory Gauginos b N = 11 3 N 2 3 N 1 3 n f 1 6 n s Number of fermions New exotic matter! Evolution changed dramatically! Strong gauge coupling beta vanishes at one loop! 2-loop and threshold effects important! Higgs 2 E_6 27plets ) relics of and, ( and ). 27 0 U(1) gauge b 1 = 1 3 Number of scalars 27 0 ( for 2 step unification without relics see R.Howl, S.F. King PLB 652, 331, JHEP 0801:030) Pi Y 2 i (matter particles in fundamental representation )
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential.
Baryon and Lepton number violating interactions ) Proton decay Solution: Impose R-parity. Dark Matter and R-parity All SM particles + Higgs bosons: All SUSY particles: Lightest Supersymetric Particle (LSP) Stable, neutral, non-baryonic matter ) Dark Matter Candidate Dark matter inferred from rotation curves and gravitational lensing Physics beyond the SM is required! Two independent phenomenological problems, same solution!
E 6 SSM Dark Matter and FCNC Z 2 B or Z 2 L symmetries To evade rapid proton decay. Like R-parity but is odd while is even. Z B 2 ) leptoquarks ; Z L 2 ) diquarks. Z 2 H symmetry (approximate) To evade large Flavour Changing Neutral Currents. H 1,3, H 2,3 and S 3 (superfields) : even, all others : odd. Exotic quarks and inert Higgs decay, violate Z 2 H ) Z 2 H only approximate! For top down constructions see: King and Howl, PLB 687, 355 (2010), Braam, Knochel and Reuter, JHEP 106, 013 (2010) In E_6SSM Relic density can be achieved entirely from the inert sector, or from a bino like neutralino with massless singlinos. [SF King, JP Hall, JHEP 0908:088 (2009), JHEP 1106 (2011) 006 ]
Beyond the Standard Model The SM has not been fully verified* The SM Higgs boson has not been found yet. SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential. *though there is an enormous body of experimental evidence to support it.
Radiative ElectroWeak Symmetry Breaking SM Higgs Potential If ) EWSB Imposed MSSM Higgs Potential V H = m 2 1jH d j 2 + m 2 2jH u j 2 + b(² H d Hū + h.c.) + 1 8 (g2 + g 02 ) jh d j 2 jh u j 2 2 1 + 2 g2 jh dh u j 2 where m 2 1 = j¹ 2 j + m 2 H d m 2 2 = j¹ 2 j + m 2 H i
E 6 SSM Electro-weak Symmetry Breaking ¹ problem solved! Higgs Potential V = 2jSj 2 (jh d j 2 + jh u j 2 ) + 2j(H d H u )j 2 + g2 2 ³H yd 8 ¾ ah d + Hu¾ y a H u 2 + g0 2 jhd j 2 jh u j 2 2 g 0 2 ³ + 1 ~Q1 jh d j 2 + Q 8 2 ~ 2 jh u j 2 + Q ~ S jsj 2 2 + m 2 SjSj 2 + m 2 1jH d j 2 + m 2 2jH u j 2 + A S(H u H d ) + h:c: + V ;
The Constrained E 6 SSM [PA, S.F.King, D.J.Miller, S.Moretti, R.Nevzorov, PRD 80, 035009 (2009), PLB 681, 448] At M X ¼ 10 15 GeV Parameters: Universal Gaugino Mass Universal trilinear soft mass Universal scalar mass Simulaneously solve: GUT scale universality + low scale EWSB b.c. with E6SSM spectrum generator Use EWSB Replace soft parameters with Free Parameters: Connect GUT and EW scales via RGEs : Gauge and Yukawa couplings (2 loop). Soft breaking gaugino and trilinear masses (2 loop). Soft scalar masses (1 loop).
(Pre LHC) allowed regions in the m 0 - M ½ plane Fix, 1 2 = 0.1, vary 3 and (inert Higgs)
(Pre LHC) allowed regions in the m 0 - M ½ plane As previous, but now allowing s to vary too Note: since m 0, M 1/2 are derived, some possible regions are sparsely populated 35
SM is incomplete Neglects gravitation, very weak at low energies (large distances) Expect New Physics at Planck Energy (mass) Neutrinos have mass Baryon/lepton asymmetry Expect New Physics at the TeV scale as well No Gauge Coupling Unification in SM Dark matter Beyond the Standard Model If it ain t broke, why fix it? The SM has not been fully verified* The SM Higgs boson has not been found yet. Hierarchy Problem / Naturalness Ad hoc shape for Higgs potential. EWSB *though there is an enormous body of experimental evidence to support it.
What do the LHC results tell us? Squark and gluino searches Z searches Higgs searches/signal
Representative Scenarios (test cases)
ce 6 SSM BMC Large drives electroweak symmetry breaking With a universal exotic coupling at the GUT scale ) exotic quarks are always heavy ( ) Break [PA, S.F.King, D.J.Miller, S.Moretti, R.Nevzorov, PLB 681, 448] universality and exotic quarks can be light
BM4 (high with light spectra and light exotic scalar) [PA, S.F.King, D.J.Miller, S.Moretti, R.Nevzorov, PRD 80, 035009 (2009)] Large mixing gives light exotic scalar Also features light Inert Higgs bosons, due to large and negative D-term contributions (/ s 2 )
Z physics at the LHC
Partial Widths Assuming negligible fermion masses
Partial Widths Decoupled Singlinos can be very light! (10,30 GeV here)
Partial Widths
BMC - 7 TeV [PA, S.F.King, D.J.Miller, S.Moretti, R.Nevzorov PRD 84, 055006]
BM4-14 TeV [PA, S.F.King, D.J.Miller, S.Moretti, R.Nevzorov PRD 84, 055006]
Latest ATLAS Z 0 limits E 6 SSM has the couplings. But BEWARE limit assumes no light exotics! [ATLAS-CONF-2012-007.]
Z-prime mass limit (accounting for exotics) From: Accomando, Belyaev, Fedeli, King, Shepherd-Themistocleous, PRD 83, 075012, 2011. Using the narrow width approximation: Related to parton luminosities Depends on the model, but not mass spectrum Depends on mass spectrum Depends on the model, but not mass spectrum Depends on mass spectrum Usual Z 0 mass limits assume no new particles are light enough to affect this. We can rescale c u and c d using results for BMC
Z-prime mass limit (accounting for exotics) For our benchmarks: BMC: BM4: Without exotics: Depends on the model, but not mass spectrum Depends on mass spectrum Depends on the model, but not mass spectrum Depends on mass spectrum
Impose Z limits from LHC Fix, 1 2 = 0.1, vary 3 and (inert Higgs)
Atlas and CMS SUSY searches
All the exotics could be heavy and challenging to detect. Gluino always lighter squarks and sleptons! Result of the RGE evolution Decay: ~g! ¹q~q! q¹q + E Miss T ) Appreciable enhancement of: ¹q q ~Â 0 1 pp! q¹qq¹q + E Miss T + X g g ~g ~q g ~g ~q ¹q q ~Â 0 1
SUSY Search typically look for jets + missing E T (And 0+ leptons) R-parity conserving signal
Fix (Pre LHC) Experimentally allowed regions in the m 0 - M ½ plane, 1 2 = 0.1, vary 3 and (inert Higgs)
Higgs Limits
LHC Higgs and MSSM Current LHC limits place Higgs mass in range Tentative signal at At tree level MSSM Upper bound: Consequence of quartic coupling fixed in terms of gauge couplings (compare with free parameter in SM) Radiative corrections significantly raise this Including radiative corrections
In the E 6 SSM already there is a new contribution already at tree level, e.g. Two Loop Upper Bounds on the Light Higgs ESSM NMSSM MSSM
So s = 5 TeV is highly constrained already! LHC could kill it even without Z searches What more can it do?
Conclusions None of the fundamental SUSY motivations imply minimality Should consider non-minimal SUSY as well E 6 SSM is a well-motivated realisation of a highly non-minimal SUSY model with an extended gauge sector and full E6 matter multiplets. Inspired by E6 GUTs, solves the -problem, gives exciting exotic phenomenology with a Z and exotic diquarks/leptoquarks. Can accommodate a heavier Higgs much more easily than the minimal model! LHC searches for Z, jets (+ leptons)+ MET and Higgs provide complimentary (though often overlapping) information. We have a SM-like light Higgs that fits tentative LHC signal / is allowed by 95% CL restrictions in much of the parameter space. Z, jets (+ leptons)+ MET searches have put constraints on the mass scale, more precise studies needed on detail for the latter.