Presentation on theme: "THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS"— Presentation transcript:
1 THE FINE-TUNING PROBLEM IN SUSY AND LITTLE HIGGS Irene Hidalgo.IFT, MadridCollaboration with: Pre-SUSYA. Casas July 2005J.R. Espinosa
2 Outline Hierarchy problem of SM. Fine-tuning: Conclusions. SUSY Little HiggsConclusions.
3 Hierarchy problem of SM SM as an effective theory valid up to a cut-off scale ΛSM → Radiative corrections to the Higgs mass:No fine-tuning between tree-level and 1 loop contributions to mh → ΛSM≤ few TeV ( “Big” hierarchy problem ) .E.g. mh =130 GeVVeltman
4 Tension between these bounds in ΛSM and the experimental bounds on the effective scale of non-renormalizable operators (that parametrize new physics).Typically“Little” hierarchy problemLH10 TeV~>
5 Veltman´s condition (1-loop): Kolda & MurayamaVeltman´s condition (1-loop):ΛSM could be larger than expected if Veltman´s condition is fulfilled.At higher order this condition becomes cut-off dependent.
6 FINE-TUNING = 100 1% fine-tuning Barbieri & GiudiceStandard definition of the fine-tuning parameters:,with αi the independent parameters of the model. = 10% fine-tuning = 100 1% fine-tuning
7 SM: ΛSM as an indepedent parameter Veltman´s throat Contourplot of ΔΛ Kolda & MurayamaSM: ΛSM as an indepedent parameter Veltman´s throatContourplot of ΔΛOther relevant parameters in the SM for the fine-tuninng: λ t and λ
8 < 2.5 TeV Top mass: mt = 178 ± 4.3 GeV with But mh has not been measured: < 2.5 TeVSMaver
9 SUSY modelsSUSY: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 MSSMHiggs sector: 2 doublets, H1 and H2 .Tree-level scalar potential:with
10 Along the breaking direction in the H10, H20 space: where λ and m2 are functions of the soft masses and the μ-parameter at the initial scale.Minimization: Fine-tuning:MSSM
12 LOW SCALE SUSYwith the SUSY breaking scale and M the messenger scale.- Gravity-mediated models: M~1019 GeV- Low scale SUSY models: and M of similar order ~ TeVConcrete example:where T is the singlet responsible for the breaking of SUSY and m = ΛS2 / M~
13 ~ Integrating the singlet T out: 2HDM μ = 0.3 M , m =0.5 M , e1 = -2, αt = 1~
14 Little Higgs Models mh ~ 200 GeV SM L. H. H.E. cut-off m ~ f~ 1 TeV 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 mh.SML. H.H.E. cut-offmh ~ 200 GeVm ~ f~ 1 TeV ~ 4 f ~ 10 TeV
15 The Littlest HiggsArkani-Hamed et al.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 :
16 The Littlest Higgs Tree-level Lagrangian: Radiative corrections: (g1, g2 , g1´, g2´)(1, 2)constrained by
17 The Littlest Higgs The operators O 1 and O2 already at tree-level: c and c’ unknown coefficients.
18 The Littlest Higgs Electroweak symmetry breaking. At energies beneath m , integrating out the triplet:with
19 Fine-tuning in the Littlest Parametrization of the amount of fine-tuning:Rough estimate: heavy top contributiont mh2 = 2with 2 t2t mh2 f 2e.g. for f = 1 TeV, mh = 150 GeVt mh2 / mh2 33
20 Fine-tuning in the Littlest But heavy top contribution is not all.Using the standard definition of fine-tuning parameters.Parameters in Littlest: c, c´ , λ1 , λ2 , g1 , g2 , g´1 , g´2 . (Constraints between them)Two regions:A) λ ≈ λb « λa ≈ M2Φ/f2B) λ ≈ λa « λb ≈ M2Φ/f2
21 Fine-tuning in the Littlest Case A. f = 1TeV , g’12= g’22= 2 g’2mh = 250 GeVmh = 115 GeV
22 Fine-tuning in the Littlest Case A → c small → Implicit fine-tuning between ctree and c1-loop c instead of ctree total with c total with cmh = 250 GeVtree
23 Fine-tuning in the Littlest mh = 115 GeVCase B. f = 1TeV , g’12= g’22= 2 g’2Fine-tuning larger than case A. total with cDelicately tunedtree
24 Littlest with T-parity Cheng & LowExtra symmetry: T-parity.Coupling h2Φ is forbidden, and also direct couplings of SM fields to new gauge bosons.Parameters : c, c´ , λ1 , λ2Two cases:A) λ1 < λ2B) λ2 < λ1
25 mh2 = c g´2 2 / 162 [SU(2)]2 x U(1)Y model mh = 250 GeV Case A Peskin et al.Differences from the Littlest:There is a quadratic divergence contribution to mh2 due to U(1)YAbsence 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.Case A mh2 = c g´2 2 / 162mh = 250 GeV
26 Fine-tuning in the Simplest f1 = f2 = 1 TeVGlobal [SU(3)×U(1)]2 / [SU(2)×U(1)]2Two scales: f1 , f2 .Radiatively induced δm2<0 :Add tree-level mass μ2Parameters: f1 , f2 , μ2, λ 1 , λ 2 .
27 Conclusions → MSSM ~5 % fine-tuned SM → hierarchy problem → Physics Beyond SM ~ few TeV.SUSYMSSMLogarithmic and finite contributions from sparticlesBounds on sparticles massesλtree is smallLow scale SUSYλtree is largerNo big effects of running→ MSSM ~5 % fine-tuned→ Improvement in the fine-tuning problem
28 Conclusions Minimum value of Δ accessible by varying the parameters “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 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.Minimum value of Δ accessibleby varying the parameters
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