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

Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València. Revisiting the vector form factor at NLO in 1/N C. QCD10 , 29th June 2010. In collaboration with: A. Pich (IFIC) J.J. Sanz-Cillero (IFAE). Work in progress Related works:

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

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  1. Ignasi RosellUniversidad CEU Cardenal HerreraIFIC, CSIC–Universitat de València Revisiting the vector form factor at NLO in 1/NC QCD10, 29th June 2010 In collaboration with: A. Pich (IFIC) J.J. Sanz-Cillero (IFAE) Work in progress Related works: JHEP 07 (2008) 014 [arXiv:0803.1567] JHEP 01 (2007) 039 [hep-ph/0610290] JHEP 08 (2004) 042 [hep-ph/0407240]

  2. OUTLINE • Motivation • The framework:ChPT and RChT • Towards a determination of thechiral LECs • Why revisiting the Vector Form Factor? • The Vector Form Factor within RChT • The chiral couplings L9 and (C88– C90) • Phenomenology • Summary Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  3. 1. Motivation • The amplitude: • The framework: • Chiral Perturbation Theory (ChPT) up toO(p6) * • Resonance Chiral Theory (RChT) • Main aims: Physics in the resonance region and estimation of related LECs (L9) in theresonanceregion up toO(NC0) ** at therhomesonpeak up to O(1/NC) *** in theresonanceregion up to O(1/NC) **** Correct framework to incorporate the resonance states within an effective lagrangian formalism. Needto be improved * Gasser &Leutwyler ’84 * Bijnens et al. ’98 ’02 ** Ecker et al. ‘89 *** Guerrero & Pich ’97 **** IR, Sanz-Cillero & Pich ‘04 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  4. 2. The framework: ChPT and RChT ChiralPerturbationTheory * ResonanceChiralTheory ** • QCD at GeV. • No natural expansionparameterandmanyresonanceswithclosemasses: a formal EFT approachisnotpossible. • Mainfeatures: • Chiralinvariant. • 1/NC expansion. • Requirementof a good short- • distancebehavior. • Modeldependence: truncationofthetowerofresonances***. • EffectiveFieldTheory (EFT) ofQCD at very-lowenergies. • Key-point: LQCD ischiralinvariantin themasslesslimit. • Organization in termsofincreasingpowersofmomentumormasses. • GeV. • Thenumberofcouplingsincreasesveryfast: 10 at NLO and 90 at NNLO. * Weinberg ’79 * Gasser &Leutwyler ‘84 ‘85 * Bijnens et al. ‘99 ‘00 ** Ecker et al. ’89 ** Cirigliano et al. ’06 *** Knecht& de Rafael ‘97 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  5. 2. The framework: ChPT and RChT ChiralPerturbationTheory * ResonanceChiralTheory ** 3 couplings !!! 9 couplingsand 3 masses !!! * Weinberg ’79 * Gasser &Leutwyler ‘84 ‘85 * Bijnens et al. ‘99 ‘00 ** Ecker et al. ’89 ** Cirigliano et al. ‘06 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  6. 3. Towards a determination of the chiral LECs • OneofthemajorproblemsofChiralPerturbationTheoryistheestimationofthelow-energyconstants (LECs). • ThemostimportantcontributionstotheLECs come fromthephysicsoflow-lyingresonances. • ResonanceChiralTheoryis a correctframeworktoincorporatetheresonancestateswithinaneffectivelagrangianformalism, ruled by the1/NC expansion. • At leading-order(LO) in 1/NC resonancesaturationworksproperly. • Large-NC estimates are unableto control therenormalization-scaledependenceoftheLECs, which may produce sizablevariations. Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  7. Resonance saturation 2004 and this work 2011 ? Resonance region High energies Very low energies RChT ChPT QCD predictions of LECs reduction of the unknown couplings 2008 2007 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  8. 4. Why revisiting the Vector Form Factor? I.R., Sanz-Cillero & Pich ‘04 Thiswork • Ourfirstapproachto NLO calculationsin ResonanceChiralTheory • DeterminationofLECskeeping a full control oftherenormalizationscaledependenceμ • Single ResonanceApproximation • Twoflavoursin thechirallimit • Operators up tooneresonancefield • LO operatorswithup toO(p2) chiralstructures • Diagrammaticalcalculation • Removeof NLO operators by using • EquationsofMotion(fieldredefinitions) • Bad-behaved at highenergies • Free NLO couplings • No ourfirstapproachto NLO calculationsin ResonanceChiralTheory • DeterminationofLECskeeping a full control oftherenormalizationscaledependenceμ • Single ResonanceApproximation • Threeflavoursin thechirallimit • Cutswith up tooneresonancefield • LO operatorswithup toO(p2) chiralstructures • Dispersive/diagrammaticalcalculation • Removeofsubtractionconstantsby absorptionintothetree-level NLO contributions • Well-behaved at highenergies • NO free NLO couplings Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  9. 5. The Vector Form Factor within Resonance Chiral Theory ChPT at NLO in 1/NC i) Thelarge-NC limit in RChT (treelevel) Short-distancebehaviour No couplingsand 1 mass !!! Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  10. ii) NLO corrections in RChT (one-looplevel) • Single ResonanceApproximation • Operatorswith up toO(p2) chiralstructures • No needof * • Cutswith up tooneresonancefield • Dispersive/diagrammaticalcalculation • Absorptionofsubtractionconstantsinto • 9 couplingsand 3 masses Short-distancebehaviour 3 couplings (F,GV,FA) and 3 masses (MV,MA,MS) • Consideringconstraintsfromother observables it can be reducedto 1 coupling (F) and 3 masses (MV,MA,MS). * Portolés, IR & Ruiz-Femenia ’07 * IR, Ruiz-Femenía& Sanz-Cillero ‘09 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell ** Ecker et al. ’89 *** Guo et al. ‘07 **** Pich, IR & Sanz-Cillero ‘08

  11. 6. The chiral couplings L9 and (C88–C90) i) The LO estimation ChPT at LO in 1/NC RChT at LO in 1/NC ii) The NLO estimation ChPT at NLO in 1/NC RChT at NLO in 1/NC * Ecker et al. ’89 ** Cirigliano et al. ‘06 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  12. 7. Phenomenology i) Input ii) Ouput (high- andlow- energycontributions) Preliminary iv) Literature iii) Ouput (final number) * Gasser &Leutwyler ’85 ** Bijnens& Talavera ’02 *** Sanz-Cillero & Pich ’03 **** Gonzalez-Alonso et al. ’09 ***** Kaiser ‘05 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  13. 8. Summary 1. What? The Vector Form Factor • QCD at intermediate energies • An effective procedure to incorporate the mesonic states • Ingredients: 1/NC expansion and short-distance information 2. Where? RChT • Improvement of thePhysics in the resonance region • Theoretical prediction of the LECs at NLO • Again? • TheestimationoftheLECs as a majorproblemofChPT • ThemostimportantcontributionstotheLECs come fromthelightestresonances • Therenormalization-scaledependenceissizable 3. Why? NLO corrections • Cutswith up tooneresonancefield • Well-behavedat highenergies • NO free NLO couplings 4. How? Dispersive/diagrammatical calculation Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  14. Thedeterminationof L9 at NLO step by step i) Well-behavedspectralfunctionchannel by channel 11couplingsand3masses 3couplingsand3masses ii) Well-behaved full Vector Form Factor iii) MatchingbetweenChPTandRChT Preliminary iv) Literature • Gasser &Leutwyler ’85 Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

  15. Nextsteps • Detaileduncertaintyestimate • Estimationof(C88– C90) at NLO • Analysisof experimental data (Physics in theresonanceregion) Futurework • ScalarForm Factor • Pionscattering Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell

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