Download
ignasi rosell universidad ceu cardenal herrera ific csic universitat de val ncia n.
Skip this Video
Loading SlideShow in 5 Seconds..
Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València PowerPoint Presentation
Download Presentation
Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València

Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València

128 Vues Download Presentation
Télécharger la présentation

Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Viability of strongly-coupledmodelswithintheElectroweakPrecision Observables Ignasi RosellUniversidad CEU Cardenal HerreraIFIC, CSIC–Universitat de València CD12, 6 - 10 August 2012 Viabilityof HiggslessmodelswithintheElectroweakPrecision Observables In collaboration with: A. Pich (IFIC, Valencia, Spain) J.J. Sanz-Cillero (INFN, Bari, Italy) Accepted in JHEP[arXiv:1206.3454 [hep-ph]] Related works: JHEP 07 (2008) 014 [arXiv:0803.1567]

  2. OUTLINE • Motivation • Oblique Electroweak Observables • TheEffectiveLagrangian • TheCalculation of S • High-energyConstraints • Phenomenology • Summary Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  3. 1. Motivation i) The Standard Model(SM) providesanextremelysuccesfuldescription of theelectroweakand stronginteractions. ii) A keyfeatureisthe particular mechanismadoptedto break theelectroweak gauge symmetrytotheelectroweaksubgroup,SU(2)L x U(1)Y  U(1)QED, so thattheW and Z bosonsbecomemassive. TheHiggsHunting iii) TheLHC has justdiscovered a new particlearound125 GeV*. iv) Whatifthis new particleisnot a Higgsboson? Or a notstandardone? Or a scalarresonance? Weshould look foralternativemechanisms of massgeneration. HiggslessElectroweak Models vi) Strongly-coupledmodels: usuallythey do containresonances. Manypossibilities in themarket:Technicolour, WalkingTechnicolour, ConformalTechnicolour, Extra Dimensions… Oblique Electroweak Observables** v) Theyshouldfulfilledtheexistingphenomenologicaltests. * CMS and ATLAS Collaborations. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell ** Peskin and Takeuchi’92.

  4. Why am I talkingabout EWSB at Chiral Dynamics 2012? i) In thelimitwherethe U(1)Ycoupling g’ isneglected, theLagrangianisinvariantunder global SU(2)L x SU(2)Rtransformations. TheElectroweakSymmetryBreaking(EWSB) turnsoutto be SU(2)L x SU(2)R SU(2)L+R(custodial symmetry). ii) Absolutely similar totheChiralSymmetryBreaking(ChSB) occuring in QCD. So thesame pion Lagrangian describes theGoldstonebosondynamicsassociatedwiththe EWSB, beingreplacedfπbyv=1/√(2GF)=246 GeV.Sameprocedure as in ChiralPerturbationTheory (ChPT)*. iii) We can introduce theresonancefieldsneeded in strongly-coupledHiggslessmodels in a similar way as in ChPT: ResonanceChiralTheory(RChT)**. • Note theimplications of a naïverescalingfrom QCD toEW: iv) Actually, theestimation of the S parameter in strongly-coupled EW modelsisequivalenttothedetermination of L10 in ChPT***. * Weinberg ’79 * Gasser & Leutwyler ‘84 ‘85 * Bijnens et al. ‘99 ‘00 **Eckeret al. ’89 ** Cirigliano et al. ’06 Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell *** Pich, IR, Sanz-Cillero ’08.

  5. 2. Oblique Electroweak Observables • Universal obliquecorrectionsviatheEW bosonself-energies(transverse in theLandau gauge) • S parameter:new physics in thedifferencebetweenthe Z self-energies at Q2=MZ2 and Q2=0. • WefollowtheusefuldispersiverepresentationintroducedbyPeskin and Takeuchi*. • Theconvergence of the integral needs a vanishingat short distances. • S parameterisdefinedfor a referencevaluefortheSM Higgsmass. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell * Peskin and Takeuchi’92.

  6. 3. TheEffectiveLagrangian Letusconsider a low-energyeffectivetheorycontainingtheSM gauge bosonscoupledtotheelectroweakGoldstonesand thelightestvector and axial-vector resonances: Wehavesevenresonanceparameters: FV, GV, FA, κ, σ, MV and MA. Thehigh-energyconstraintsare fundamental. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  7. 4. TheCalculation of S i) At leading-order (LO)* Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell * Peskin and Takeuchi’92.

  8. ii) At next-to-leadingorder (NLO)** • Once-subtracteddispersiverelation • Contributionsfromππ, Vπ and Aπ cuts, sincehighercuts are supposedto be suppressed. • FRr and MRrare renormalizedcouplingswhich define theresonancepoles at theone-looplevel. * Barbieri et al.’08 * Cata and Kamenik ‘08 * Orgogozo and Rynchov ‘08 Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  9. 5. High-energyConstraints • Wehavesevenresonanceparameters: FV, GV, FA, κ, σ, MV and MA. • Thenumber of unknowncouplings can be reducedbyusingshort-distanceinformation. • In contrastwiththeQCD case, we ignore theunderlyingdynamicaltheory. i) Weinberg Sum Rules (WSR)* i.i) LO i.ii) Imaginary NLO i.iii) Real NLO: fixing of FV,Ar orlowerbounds** 1or 2 constraints 3 or 4 constraints ConstraintsonFVr and FAr • * Weinberg’67 • * Bernard et al.’75. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell ** Pichet al.’08

  10. ii) Additional short-distanceconstraints ii.i) WLWL WLWLscattering* 3 additional constraints! ii.ii) Vector Form Factor** ii.iii) Axial Form Factor*** • Wehave up to9 (7) constraintswith2 (1) WSR and 7 resonanceparameters: wecannotconsideralltheconstraints at thesame time, someapproximately. • As a check of consistencyweconsiderdifferentcombination of constraints. • * Baggeret al.’94 • * Barbieri et al.’08 Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell • ** Ecker et al.’89 • *** Pich et al.’08

  11. 6. Phenomenology S = 0.04 ± 0.10 * (MH=0.120 TeV) i) LO results i.i) 1st and 2nd WSRs i.ii) Only1st WSR At LO MV > 1.5 TeV at 3σ Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell • * Gfitter • * LEP EWWG • * Zfitter

  12. ii) NLO results: 1st and 2nd WSRs • 1st and 2nd WSRs at LO and at NLO: • 6 constraints • MV theonly free parameter • 8 solutions. • Only2approximately compatible withVFF, AFF and scatteringconstraints(green). • If, alternatively, weconsiderthe1st and the2nd WSR only at NLO withthe VFF and AFF constraints (6 constraints), a heavierresultisfound: MV > 2.4 TeV at 3σ. At NLO withthe 1st and 2nd WSRs MV > 1.8 TeV at 3σ Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  13. iii) NLO results: only 1st WSR • 1st WSR at NLO + VFF and AFF constraints: • 5 constraints • MV and MA theonly free parameters are. • Withoutthe 2nd WSR we can only derive lowerboundson S. • Imposingthat Fv2 – FA2 > 0 wehavefoundonly2solutions. • One of them (red) isclearlydisfavoured: • Sharplyviolation of the 2nd WSR at LO and at NLO • Large NLO correction • Big splittingbetween MV and MA. At NLO withonlythe 1st WSR MV > 1.8 TeV at 3σ • Withoutthe 2nd WSR itispossibletheanalysiswithonlythe ππ cut. Thesameresultisfound: MV > 1.8 TeV at 3σ. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  14. 7. Summary 1. What? One-loopcalculation of theoblique S parameterwithinHiggslessmodels of EWSB • Weshould look foralternativewaysof massgeneration: strongly-coupledhiggslessmodels. • Theyshouldfulfilledtheexistingphenomenologicaltests. Whatifthis new particlearound125 GeVisnot a Higgsbosson? 2. Why? • EWSB: SU(2)L x SU(2)R SU(2)L+R: similar toChSB in QCD:ChPT. • Strongly-coupledHiggslessmodels: similar toresonancesin QCD: RChT. • General Lagrangianwith at mosttwoderivatives and short-distanceinformation. Effective approach 3. Where? 4. How? Dispersiverepresentation of Peskin and Takeuchi’92. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  15. Improvementsoverprevious NLO calculation: • Dispersivecalculation: no cut-offs. • A more general Lagrangian. • Short-distanceinformation as a crucial ingredient. • Wehaveconsidereddifferentpossibilites: • LO • NLOwiththe1st and 2nd WSR • NLOwithonlythe1st WSR • Similar results: • At LO MV > 1.5 TeVat 3σ. • At NLO MV > 1.8 TeV at 3σ. • In thesereasonablestronglycoupledmodelsthe S parameterrequires a highresonancemassscale, beyondthe 1 TeV. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell

  16. 8*. Futurework Preliminaryresultsgo in thisdirection! • Consideration of thisnew scalarwith a massaround125 GeV in ourcalculation: • Higgsboson? Whichone? • Ascalarresonance of strongly-coupledmodels? A new Sπ or Hπ cut!, butonly at NLO. • Oblique T parameter Absenceof a knowndispersiverepresentation. Viability of HiggslessmodelswithintheElectroweakPrecision Observables, I. Rosell