Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSIC–Universitat de València
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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 progressRelated works:JHEP 07 (2008) 014 [arXiv:0803.1567]JHEP 01 (2007) 039 [hep-ph/0610290]JHEP 08 (2004) 042 [hep-ph/0407240]
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2/15
OUTLINE
1) Motivation
2) The framework:ChPT and RChT
3) Towards a determination of thechiral LECs
4) Why revisiting the Vector Form Factor?
5) The Vector Form Factor within RChT
6) The chiral couplings L9 and (C88– C90)
7) Phenomenology
8) Summary
Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell
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1. Motivation
i) The amplitude:
ii) The framework:
Chiral Perturbation Theory (ChPT) up toO(p6) *
Resonance Chiral Theory (RChT)
i) 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 3/15
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2. The framework: ChPT and RChT
ChiralPerturbationTheory * ResonanceChiralTheory **
* Weinberg ’79* Gasser &Leutwyler ‘84 ‘85* Bijnens et al. ‘99 ‘00** Ecker et al. ’89** Cirigliano et al. ’06*** Knecht& de Rafael ‘97
•EffectiveFieldTheory (EFT) ofQCD at very-lowenergies.
•Key-point: LQCD ischiralinvariantin themasslesslimit.
•Organization in termsofincreasingpowersofmomentumormasses.
•GeV.
•Thenumberofcouplingsincreasesveryfast: 10 at NLO and 90 at NNLO.
• QCD at GeV.
• No natural expansionparameterandmanyresonanceswithclosemasses: a formal EFT approachisnotpossible.
•Mainfeatures:
•Chiralinvariant.•1/NC expansion.•Requirementof a good short-distancebehavior.
•Modeldependence: truncationofthetowerofresonances***.
Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell 4/15
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2. The framework: ChPT and RChT
3 couplings !!!
9 couplingsand 3 masses !!!
ChiralPerturbationTheory * ResonanceChiralTheory **
* 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 5/15
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• 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.
3. Towards a determination of the chiral LECs
Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell 6/15
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ChPT QCDRChT
predictions of LECs
reduction of the unknown couplings
Resonance saturation
Very low energies Resonance region High energies
20072008
2004 and this work2011 ?
Revisitingthe Vector Form Factor at NLO in 1/NC, I. Rosell 7/15
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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 usingEquationsofMotion(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 8/15
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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 9/15
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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 massesShort-distancebehaviour
* Portolés, IR & Ruiz-Femenia ’07* IR, Ruiz-Femenía& Sanz-Cillero ‘09
3 couplings (F,GV,FA) and3 masses (MV,MA,MS)
Consideringconstraintsfromother observables it can be reducedto 1 coupling (F) and 3 masses (MV,MA,MS).
** Ecker et al. ’89*** Guo et al. ‘07**** Pich, IR & Sanz-Cillero ‘08
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6. The chiral couplings L9 and (C88–C90)
i) The LO estimation
ii) The NLO estimation
RChT at LO in 1/NC
ChPT at NLO in 1/NC
ChPT at LO 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 11/15
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7. Phenomenology
Preliminary
i) Input ii) Ouput (high- andlow- energycontributions)
iv) Literature
* Gasser &Leutwyler ’85** Bijnens& Talavera ’02*** Sanz-Cillero & Pich ’03**** Gonzalez-Alonso et al. ’09***** Kaiser ‘05
iii) Ouput (final number)
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8. Summary
2. Where?
NLO corrections3. Why?
1. What?
4. How?
The Vector Form Factor
Dispersive/diagrammatical calculation
RChTa) QCD at intermediate energies
b) An effective procedure to incorporate the mesonic states
c) Ingredients: 1/NC expansion and short-distance information
a) Improvement of thePhysics in the resonance regionb) Theoretical prediction of the LECs at NLO
a) Again?
TheestimationoftheLECs as a majorproblemofChPT ThemostimportantcontributionstotheLECs come
fromthelightestresonances Therenormalization-scaledependenceissizable
Cutswith up tooneresonancefield Well-behavedat highenergies NO free NLO couplings
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Thedeterminationof L9 at NLO step by step
i) Well-behavedspectralfunctionchannel by channel
ii) Well-behaved full Vector Form Factor
11couplingsand3masses 3couplingsand3masses
iii) MatchingbetweenChPTandRChT
iv) Literature
•Gasser &Leutwyler ’85
Preliminary
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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 15/15