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Effective Operators in the MSSM Guillaume Drieu La Rochelle, LAPTH

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A powerful but insufficient Standard Model Arbitrariness of the parameters Running of the coupling constants Quadratic loop divergences Naturalness issue The SUSY solution Supersymmetric Free of quadratic divergences Unification of the coupling constants Minimal Most natural extension No Unification Hierarchy RPP Lyon 25/01/101/15MSSM with effective operators Guillaume Drieu La Rochelle

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Betrayed by the experiments An elusive Higgs Radiative Corrections, but … The fine-tuning issue High High stop mass for Radiative Corrections Collider search Narrow more and more the susy scenario Far from complete Mechanism for the susy breaking The mu problem The little hierarchy problem RPP Lyon 25/01/102/15MSSM with effective operators Guillaume Drieu La Rochelle ?!

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o Why? Include high energy physics contribution without the explicit knowing of that high energy theory. o How? Global theory at low energy Low energy lagrangian + Effective Operators EFT How-To 1.Choose a scale high/low energy. 2.Choose a field theory for low energy physics (renormalizable). 3.Add some effective operators. (M,v,f) scales of effective theory 4.Infer the value of c k : -from measurements -knowing of the underlying theory. EFT How-To 1.Choose a scale high/low energy. 2.Choose a field theory for low energy physics (renormalizable). 3.Add some effective operators. (M,v,f) scales of effective theory 4.Infer the value of c k : -from measurements -knowing of the underlying theory. Compatible with symmetries of the low-energy theory RPP Lyon 25/01/103/15MSSM with effective operators Guillaume Drieu La Rochelle

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Rescuing the MSSM : New physics at the TeV scale Done in many Beyond the MSSM models NMSSM, phenomenological MSSM, etc.. Model independant approach Include all effective operators allowed by the symmetries Equivalent to taking a specific BMSSM model & integrating out heavy particles Infer the consequences of high energy physics Which corrections to expect Each effective operator acts on several observables Correlations Gauge Susy... See later RPP Lyon 25/01/104/15MSSM with effective operators Guillaume Drieu La Rochelle

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Constraints Recap : The MSSM has only dimension up to 4 operators. Susy/Gauge Invariance Focus on the Higgs sector (possible extension to other sectors) Effective Operators +... Standard Effectif +... See Antoniadis et al. arxiv/0910.1100 Dimension 5 Dimension 6 Superfield formulation RPP Lyon 25/01/105/15MSSM with effective operators Guillaume Drieu La Rochelle Kähler PotentialSuperpotential

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Dimension 6Dimension 5 Strong action on masses Action on standard couplings Higgs/Neutralinos masses High versus Low RPP Lyon 25/01/106/15MSSM with effective operators Guillaume Drieu La Rochelle

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Constraints Susy/Gauge Invariance Superfield formulation Focus on the Higgs sector Spurions Example Spurion formulation SpurionStandard Operator Superpotential term Scalar higgs mixing RPP Lyon 25/01/107/15MSSM with effective operators Guillaume Drieu La Rochelle

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Scalar Higgs potential D and F terms Scalar Higgs – Gauge bosons interactions Standard fermions masses and couplings Higgsinos masses Higgsinos gauginos mixing Standard MSSMEffective Operators An automatic code : LanHEP Mathematica An automatic code : LanHEP Mathematica... RPP Lyon 25/01/108/15MSSM with effective operators Guillaume Drieu La Rochelle

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Theory Data Renormalisation/Reparametrisation Input Set In the effective expansion : parameter In the loop expansion The two effects add up at order 1 Consider only the expansion Effects Standard coupling changes Higgs & Neutralinos masses Correlations Sum rules modified Constraints LEP,... Predictions Dark matter searches Collider experiments The effect of each operator propagates to all the Higgs sector ! RPP Lyon 25/01/109/15MSSM with effective operators Guillaume Drieu La Rochelle

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Coupling between Z and standard fermions Forward Backward asymmetries Constraints quite loose RPP Lyon 25/01/1010/15MSSM with effective operators Guillaume Drieu La Rochelle

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Correction to the light Higgs mass (from Antoniadis et al.) Main OperatorsEffects Neutralino massA few GeV Light Higgs mass10-20 GeV Operators appearing : RPP Lyon 25/01/1011/15MSSM with effective operators Guillaume Drieu La Rochelle others

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Sensitive Operators : Most sensitive are : Higgs and neutralinos correlation for RPP Lyon 25/01/1012/15MSSM with effective operators Guillaume Drieu La Rochelle = 10 = 5 = 3 Light Higgs mass (GeV) Lightest neutralino mass (GeV) PRELIMINARY

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Similar results : Mass sum rules get modified Corrections depend on the physical input Corrections to different observables are correlated Can we include one in the other? Use effective couplings to account for loops Check whether a loop induces the same correlations than an effective operator Fasten one-loop calculations RPP Lyon 25/01/1013/15MSSM with effective operators Guillaume Drieu La Rochelle

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Higgs phenomenology Effects on Dark Matter and colliders experiments Join effective operators with one loop calculations Infer what kind of physics leads to what kind of operators RPP Lyon 25/01/1015/15MSSM with effective operators Guillaume Drieu La Rochelle

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