Title: Ignasi Rosell Universidad CEU Cardenal Herrera IFIC, CSICUniversitat de Valncia
1Ignasi RosellUniversidad CEU Cardenal
HerreraIFIC, CSIC-Universitat de València
- Current correlators and form factors in the
resonance region
QCD08, 8th July 2008
In collaboration with A. Pich (IFIC) J.J.
Sanz-Cillero (IFAE)
JHEP 07 (2008) 014 arXiv0803.1567 JHEP 01
(2007) 039 hep-ph/0610290 JHEP 08 (2004) 042
hep-ph/0407240
2OUTLINE
- Motivation
- A few words about Chiral Perturbation Theory
- Resonance Chiral Theory
- Form Factors and correlators
- The V-A correlator in RChT
- The chiral couplings and
- Summary
31. Motivation
Why quantum loops in the resonance region?
Improvement of the implementation of
non-perturbative QCD
Phenomenological problems in the
hadronic contributions
Physics in the resonance region
Distinguish New Physics effects from Standard
Model
Dyson-Schwinger resummation of subleading
contributions to describe the amplitudes near the
resonance peak
matching with ChPT
Theoretical prediction of the chiral LECs at
NLO control of µ dependence
Rosell, Sanz-Cillero and Pich 04, 07, 08
Portolés, Rosell and Ruiz-Femenía 05, 07
42. A few words about Chiral Perturbation Theory
- Asymptotic Freedom pQCD
- Confinement non p-QCD
running of as ( lt 0)
PROBLEM!!!
a SOLUTION Effective Field Theories
ChPT EFT of QCD at very low energies
- Massless limit ? chiral invariant
- Global symmetries ? spectrum
- CCWZ formalism ? build effective lagrangians
with SSB
representations multiplet much lighter
Weinberg 79 Gasser and Leutwyler 84 85
Bijnens, Colangelo and Ecker 99 00
5The ChPT Lagrangian
- By using CCWZ, the pGB (pion multiplet) can be
parameterized with - , one can
use only ChPT until scales with
. - Organization in terms of increasing powers of
momentum, - The precision in present phenomenological
applications makes necessary to include
corrections of NLO required LECs.
Callan et al. 69 Coleman et al.69
63. Resonance Chiral Theory
Many resonances and no mass gap
1st Problem
QCD at
No FORMAL EFT approach
2nd Problem
No natural expansion parameter
MODEL DEPENDENT cut in the tower of resonances
Tools
- Phenomenological lagrangians
- Large-NC QCD
- Short-distance properties of QCD
- WHY?
- Technical reasons
- Supported by phenomenology
- Heavier contributions suppressed by their masses
Ecker et al. 89 Cirigliano et al. 06
Weinberg 79
t Hooft 74 Witten 79
72009 ?
Matching
Resonance region
High energies
Very low energies
RChT
ChPT
QCD
predictions of LECs
reduction of the unknown couplings
2007
2008
84. Form factors and correlators
i) Two-point correlation functions of two QCD
currents in the chiral limit
sum of positive contributions corresponding to
the different intermediate states
ii) Associated spectral functions
- In the limit
- tends to a constant
- grows as
?
?
Brodsky-Lepage rules of the form factors
VANISHING FORM FACTORS AT LARGE ENERGIES AS A
REASONABLE ASSUMPTION
behaviour of
one-particle exchange
Floratos, Narison and De Rafael 79 Pascual
and De Rafael 82 Shifman, Vainshtein and
Zakharov 79 Jamin and Munz 95
vanishes as
9Very low energies
Resonance region
High energies
ChPT
QCD
RChT
reduction of the unknown couplings by using
short-distance constraints
predictions of LECs
Also resonances as asymptotic states
OPE
Form factors
105. The V-A correlator in RChT
tree-level
one-loop
i) Single resonance approximation
Resonance parameters in terms of F and MR
Weinberg sum rules
SS-PP sum rules
Well-behaved form factors
Relation between masses
Weinberg sum rules at NLO
11ii) Inclusion of heavier vector and axial
multiplets
Not surprising in the context of large-NC
Conflicts between short- distance constraints
Inclusion of additional resonance multiplets
Only considered at LO
Introduction of tiny corrections
Resonance parameters in terms of F and MR
Weinberg sum rules
SS-PP sum rules
Well-behaved form factors
Relation between masses
Weinberg sum rules at NLO
126. The chiral couplings and
ChPT at NLO in
i) The large-NC limit in RChT
Low-energy expansion LECs at LO
Short-distance behaviour
13dispersive calculation
ii) NLO corrections
Short-distance behaviour
Phenomenological values
Low-energy expansion LECs at NLO
i) SRA
ii) Inclusion of extra multiplets
Bijnens Talavera 97 Davier Girlanda 98
González-Alonso, Pich Prades 08
Masjuan Peris 08
147. Summary
- QCD at
- An effective procedure to incorporate the
mesonic states - Ingredients 1/NC expansion and short-distance
information
RChT
- Improvement of the physics in the resonance
region - Theoretical prediction of the LECs at NLO
2. Why?
NLO corrections
- Single resonance approximation
- Inclusion of V and A
3. What?
The V-A correlator
Conflict between short- distance constraints
4. How?
Dispersive calculation
Future
Result
- Vector form factor
- Scalar form factor
15- Comparison of the NLO prediction for
(gray band) compared to our LO estimate (red). - Comparison of the NLO prediction for
(gray band) compared to our LO estimate (red) - and the large-NC result from Pade approximants
(dotted).
Masjuan and Peris 08