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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS Irene Hidalgo. IFT, Madrid Collaboration with: Pre-SUSY A. Casas6 July 2005 J.R. Espinosa

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Outline Hierarchy problem of SM. Fine-tuning: SUSY Little Higgs Conclusions.

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Hierarchy problem of SM SM as an effective theory valid up to a cut-off scale Λ SM Radiative corrections to the Higgs mass: No fine-tuning between tree-level and 1 loop contributions to m h Λ SM few TeV ( Big hierarchy problem ). E.g. m h =130 GeV Veltman

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Tension between these bounds in Λ SM and the experimental bounds on the effective scale of non-renormalizable operators (that parametrize new physics). Typically Little hierarchy problem LH 10 TeV ~ >

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Veltman´s condition (1-loop): Λ SM could be larger than expected if Veltman´s condition is fulfilled. At higher order this condition becomes cut-off dependent. Kolda & Murayama

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. FINE-TUNING Standard definition of the fine-tuning parameters:, with α i the independent parameters of the model. Barbieri & Giudice = 10 10% fine-tuning = 100 1% fine-tuning

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. SM: Λ SM as an indepedent parameter Veltman´s throat Contourplot of Δ Λ Other relevant parameters in the SM for the fine-tuninng: λ t and λ Kolda & Murayama

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Top mass: m t = 178 ± 4.3 GeV with But m h has not been measured: < 2.5 TeV SM aver

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. SUSY models SUSY: There are the same number of bosonic and fermionic degrees of freedom. The hierarchy problem is solved due to the cancellation of quadratic divergences of the Higgs mass. The Minimal Supersymmetric extension of the SM: the MSSM Higgs sector: 2 doublets, H 1 and H 2. Tree-level scalar potential: with

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Along the breaking direction in the H 1 0, H 2 0 space: where λ and m 2 are functions of the soft masses and the μ-parameter at the initial scale. Minimization:Fine-tuning: MSSM

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Contourplot of the fine-tuning in the MSSM

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. LOW SCALE SUSY with the SUSY breaking scale and M the messenger scale. - Gravity-mediated models: M~10 19 GeV - Low scale SUSY models: and M of similar order ~ TeV – Concrete example: where T is the singlet responsible for the breaking of SUSY and m = Λ S 2 / M ~

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Integrating the singlet T out: 2HDM μ = 0.3 M, m =0.5 M, e 1 = -2, α t = 1 ~

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Little Higgs Models Stabilization of Higgs mass by making the Higgs a pseudo-Goldstone boson resulting from a spontaneously broken approximate symmetry. Spectrum: New particles at 1 TeV than cancel quadratic divergences in m h. SML. H. H.E. cut-off m h ~ 200 GeV ~ 4 f ~ 10 TeV m ~ f~ 1 TeV

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. The Littlest Higgs is a non-linear σ model based on a global SU(5) symmetry which is spontaneously broken to SO(5) at the scale f ~ 1 TeV. An [SU(2)×U(1)] 2 subgroup of SU(5) is gauged, and is spontaneously broken to the diagonal SU(2)×U(1) subgroup. New states that cancel the quadratic divergences: – Heavy top T : – Extra gauge bosons W, B :, - Triplet : The Littlest Higgs Arkani-Hamed et al.

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Tree-level Lagrangian: Radiative corrections: The Littlest Higgs ( g 1, g 2, g 1 ´, g 2 ´) ( 1, 2 ) constrained by

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. The operators O 1 and O 2 already at tree-level: c and c unknown coefficients. The Littlest Higgs

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Electroweak symmetry breaking. At energies beneath m, integrating out the triplet: The Littlest Higgs with

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Parametrization of the amount of fine-tuning: Rough estimate: heavy top contribution t m h 2 = 2 with 2 t 2 t m h f 2 e.g. for f = 1 TeV, m h = 150 GeV t m h 2 / m h 2 33 Fine-tuning in the Littlest

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. But heavy top contribution is not all. Using the standard definition of fine-tuning parameters. Parameters in Littlest: c, c´, λ 1, λ 2, g 1, g 2, g´ 1, g´ 2. (Constraints between them) Two regions: A) λ λ b « λ a M 2 Φ /f 2 B) λ λ a « λ b M 2 Φ /f 2 Fine-tuning in the Littlest

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Fine-tuning in the Littlest Case A. f = 1TeV, g 1 2 = g 2 2 = 2 g 2 m h = 115 GeV m h = 250 GeV

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Fine-tuning in the Littlest Case A c small Implicit fine-tuning between c tree and c 1-loop c instead of c m h = 250 GeV tree total with c tree

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Fine-tuning in the Littlest Case B. f = 1TeV, g 1 2 = g 2 2 = 2 g 2 m h = 115 GeV total with c tree Fine-tuning larger than case A. Delicately tuned

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Extra symmetry: T-parity. Coupling h 2 Φ is forbidden, and also direct couplings of SM fields to new gauge bosons. Parameters : c, c´, λ 1, λ 2 Two cases: A) λ 1 < λ 2 B) λ 2 < λ 1 Littlest with T-parity Cheng & Low

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Differences from the Littlest: There is a quadratic divergence contribution to m h 2 due to U(1) Y Absence of the heavy B boson. Two regions (A and B heirs of the Littlest): Case A similar fine-tuning as Littlest. Case B is worse in terms of fine-tuning. [SU(2)] 2 x U(1) Y model m h 2 = c g´ 2 2 / 16 2 m h = 250 GeV Peskin et al. Case A

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Global [SU(3)×U(1)] 2 / [SU(2)×U(1)] 2 Two scales: f 1, f 2. Radiatively induced δm 2 <0 : Add tree-level mass μ 2 Parameters: f 1, f 2, μ 2, λ 1, λ 2. Fine-tuning in the Simplest f 1 = f 2 = 1 TeV

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Conclusions SM hierarchy problem Physics Beyond SM ~ few TeV. SUSY MSSM Logarithmic and finite contributions from sparticles Bounds on sparticles masses λ tree is small Low scale SUSY λ tree is larger No big effects of running MSSM ~5 % fine-tuned Improvement in the fine-tuning problem

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THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS. Little Higgs models. Rough estimate with the heavy top contribution : few % fine-tuned. Taking into account the standard definition of fine-tuning and all the parameters in the 3 studied models: More fine-tuned than the rough estimate due to implicit tunings between the parameters of the models to work properly and have the correct EW scale. Conclusions Minimum value of Δ accessible by varying the parameters

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