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Lecture 8 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA A A A A A A A

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Overview Final lecture today! Can cover the following topics today: Sfermion, chargino and neutralino masses Fine Tuning What this really means, how we may quantify it. How LHC squark, gluino and Higgs searches affect this Changing universality assumptions Relaxing some constraints Using different breaking scheme inspired constraints Non-minimal Supersymmetry Extend the chiral superfield content Extend the gauge structure Can give overview of all or focus on one or two?

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MSSM Chiral Superfield Content Left handed quark chiral superfields Note: left handed fermions are described by chiral superfields, right handed fermions by anti-chiral superfields. Superpotential is a function of chiral superfields only so we include right handed fermions by taking the conjugate, which transforms as a left handed superfield! Conjugate of right handed quark superfields

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MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.

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EWSB conditions For successful EWSB: With:

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Higgs Masses Goldstone bosons CP-even Higgs bosons Charged Higgs boson CP-odd Higgs boson

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Sfermion masses Softmass: Flavour diagonal postulate F-terms D-terms

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Sfermion masses Home exercise: find all the mistakes on the previous slide, then write in matrix form below and diagonalise.

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Chargino and Neutralino masses Soft masses: Superpotential: Kahler potential: VEVs (Home exercise) Hints:

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Chargino and Neutralino masses

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parameter space volume restricted by, Parameter space point, Tuning: `` Compare dimensionless variations in: ALL parameters vs ALL observables Our Approach PA & D.J.Millier PRD 76, (2007)

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parameter space volume restricted by, Parameter space point, Tuning: `` Compare dimensionless variations in: parameters vs observables Our Approach PA & D.J.Millier PRD 76, (2007) Probability of random point from lying in : But remember any parameter space point is incredibly unlikely if all equally likely (flat prior)! Fine tuning is when a special qualitative feature ( ) is far less likely that other typical case ( )

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Any G << F parameter space volume restricted by, Parameter space point, Tuning: `` Compare dimensionless variations in: parameters vs observables Our Approach PA & D.J.Millier PRD 76, (2007) Probability of random point from lying in : But what if : large for all points (or all values of O) Global sensitivity (Anderson & Castano 1995)

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Any G << F parameter space volume restricted by, Parameter space point, Tuning: `` Compare dimensionless variations in: parameters vs observables Our Approach PA & D.J.Millier PRD 76, (2007) Probability of random point from lying in : But what if : large for all points (or all values of O) Rescale to our expectation for

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Regardless of measure details, fine tuning is increased when searches increase mass limits on squarks and gluinos: Search pushes up. Larger cancellation required!

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What about the Higgs? Heavy stops Large soft masses and large one loop corrections A relatively heavy Higgs requires heavy stops Break cMSSM link between stop masses and light squarks and evade fine tuning LEP bound Tuning? Tentative LHC Higgs signal

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Fine Tuning Summary Most important consideration at the LHC (by far) is what do we seec Higgs? Beyond the standard model (BSM) signal? If BSM signal is observed initially all efforts on understanding new physics. Eventually will know if new physics solves Hierachy Problem Residual tuning may also be a hint about highscale physics If no SUSY signal? Where does that leave us? Subjective question, depends on tuning measure, but also prejudice Conventional wisdom: no observation ) SUSY is fine tuned! Motivation for low energy SUSY weakened (doesnt remove fine tuning). No BSM signal at all Hierarchy Problem motivated BSM models have tuning too. Nature is fine tuned? SM true up to Planck scale? Or we need some great new idea

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Beyond the CMSSM (Relaxing high scale constraints) Non-universal Higgs MSSM (NUHM) Motivated since Higgs bosons do not fit into the same SU(5) or SO(10) GUT multiplets: 10 5*5* *5* Color triplets +

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Beyond the CMSSM (Relaxing high scale constraints) Non-universal Higgs MSSM (NUHM) Impact: Higgs masses not linked to other scalar masses so strongly easier to fit EWSB constraints and other observables Motivated since Higgs bosons do not fit into the same SU(5) or SO(10) GUT multiplets: Very mild modification to the CMSSM

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Beyond the CMSSM (Relaxing high scale constraints) Non-universal Gaugino masses For universal gauginos we have a (one loop) relation: Testable predictions for gaugino universality! Breaks ratio get different gaugino mass patterns: One can also ignore the universality more parameters to consider the model with less prejudice, e.g. pMSSM

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In gauge mediated symmetry breaking the SUSY breaking is transmitted from the hidden sector via SM gauge interactions of heavy messenger fields. Chiral Messenger fields couple to Hidden sector SUSY breaking in messenger spectrum SM Gauge interactions couple them to visible sector Loops from gauge interactions with virtual messengers flavour diagonal soft masses. Non-universal soft gaugino masses since they depend on gauge interactions! Soft mass relations imposed at messenger scale Gauge Mediation More details and a more general definition given in Steve Abels lectures Loop diagram:

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Minimal Gauge Mediated SUSY Breaking (mGMSB) Messenger fields form Complete SU(5) representations From EWSB as in CMSSM Number of SU(5) multiplets Messenger scale

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Beyond the MSSM Non-minimal Supersymmetry The fundamental motivations for Supersymmetry are: - The hierarchy problem (fine tuning) - Gauge Coupling Unification - Dark matter None of these require Supersymmetry to be realised in a minimal form. MSSM is not the only model we can consider!

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The MSSM superpotential is written down before EWSB or SUSY breaking: The problem What mass should we use? The natural choices would be 0 or M Planck (or M GUT ) ) it should know nothing about the EW scale. Phenomenological Constraints ) ¹ ¼ TeV ( ¹ -parameter has the dimension of mass! The superpotential contains a mass scale! ) Scale of origin Forbidden by symmetry )

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Solve the -problem by introducing an extra singlet [Another way is to use the Giudice-Masiero mechanism, which I wont talk about here.] Introduce a new iso-singlet neutral colorless chiral superfield, coupling together the usual two Higgs doublet superfields. If S gains a vacuum expectation value we generate an effective -term, automatically of oder the electroweak scale with We must also modify the supersymmetry breaking terms to reflect the new structure

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Yukawa terms effective term So our superpotential so far is But this too has a problem – it has an extra U(1) Peccei-Quinn symmetry Lagrangian invariant under the (global) transformation: This extra U(1) is broken with electroweak symmetry breaking (by the effective -term) massless axion!

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Yukawa terms effective term PQ breaking term NMSSM Chiral Superfield Content massless axion!

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The superpotential of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is Yukawa terms effective term PQ breaking term We also need new soft supersymmetry breaking terms in the Lagrangian: [Dine, Fischler and Srednicki] [Ellis, Gunion, Haber, Roszkowski, Zwirner] Modified Higgs sector: 3 CP-even Higgs, 2 CP-odd Higgs (new real and imagnary scalar S) Neutralino sector: 5 neutralinos (new fermion component of S)

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Parameters: The MSSM limit is ! 0, ! 0, keeping / and fixed. and are forced to be reasonably small due to renormalisation group running. Top left entry of CP-odd mass matrix. Becomes MSSM M A in MSSM limit. minimisation conditions Finally:

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Supersymmetric Models Minimal Supersymmetric Standard Model (MSSM) Next to Minimal Supersymmetric Standard Model (NMSSM) [Dine, Fischler and Srednicki] [Ellis, Gunion, Haber, Roszkowski, Zwirner] Decouple the axion PQSNMSSM Alternative solution to Peccei–Quinn symmetry : Linear S term nMSSM Eat the axionZ 0 models (e.g. USSM, E 6 SSM) In the latter we 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 masless axion to become massive vector boson!

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Supersymmetric Models Minimal Supersymmetric Standard Model (MSSM) Next to Minimal Supersymmetric Standard Model (NMSSM) Other variants: nmMSSM, PQSNMSSM. U(1) extended Supersymmetric Standard Model (USSM) Exceptional Supersymmetric Standard Model (E 6 SSM) [Dine, Fischler and Srednicki] [Ellis, Gunion, Haber, Roszkowski, Zwirner] [S.F. King, S. Moretti, R. Nevzrov, Phys.Rev. D73 (2006) ]

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Yukawa terms effective term USSM Chiral Superfield Content Problem: to avoid gauge anomalies

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Yukawa terms effective term USSM Chiral Superfield Content Problem: to avoid gauge anomalies Charges not specified in the definition of the USSM

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U(1) extended Supersymmetric Standard Model (USSM) Yukawa terms effective term Modified Higgs sector: 3 CP-even Higgs, 2 CP-odd Higgs (new real and imagnary scalar S) Modified Neutralino sector: 6 neutralinos: (new singlino + Zprimino ) Modified Gauge sector, new Z 0

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Disclaimer: I work on the E 6 SSM Final part included for vanity

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For anomaly cancelation, one can use complete E 6 matter multiplets New U(1) 0 from E 6 E 6 inspired models 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

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All the SM matter fields are contained in one 27-plet of E 6 per generation , 1 5 *, 2 5 *, - 3 5, - 2 1, U(1) N charge SU(5) reps. 1, 5 + singlets right handed neutrino 3 generations of Higgs exotic quarks Exceptional Supersymmetric Standard Model (E 6 SSM) [ Phys.Rev. D73 (2006) , Phys.Lett. B634 (2006) S.F.King, S.Moretti & R. Nevzorov ]

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E 6 SSM Chiral Superfield Content Note: In its usual form there are also two extra SU(2) doublets included for single step gauge coupling unification, but these are negleected here for simplicity.

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SUSY Theory space Gauge group (vector superfields) Chiral superfields Minimal superfields Complete E6 multiplets E 6 SSM MSSM NMSSM USSM

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Thank you for listening End of Supersymmetry Lecture course

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Sfermion masses

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