Chiral lagrangians for massive spin-1 fields

We complete the recalculation of the available two-loop expressions for the reaction γγ → ππ in the framework of chiral perturbation theory. Here, we present the results for charged pions. The cross section and the values of the dipole polarizabilities agree very well with the earlier calculation, provided the same set of low-energy constants (LECs) is used. With updated values for the LECs at order p 4 , we find for the dipole polarizabilities (α 1 − β 1 ) π ± = (5.7 ± 1.0) × 10 −4 fm 3 , which is in conflict with the experimental result recently reported by the MAMI Collaboration.

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“…In Ref. [16], a large N C framework and the ENJL model were used to pin down these constants, with the result [17]. Finally, we note that in Ref.…”

Section: The Effective Lagrangian and Its Low-energy Constantsmentioning

confidence: 98%

Revisiting at low energies

2006

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“…The short-distance properties of the underlying QCD dynamics impose strong constraints on the couplings of the hadronic effective theory [9,11]. The infinite sums of meson exchanges contributing to any given Green function should obey the right QCD behaviour G(t) ∼ t ω at large momenta.…”

Section: Introductionmentioning

confidence: 99%

“…The most drastic and simplest scheme is the so-called Single Resonance Approximation, which only considers the contributions from the lightest meson with any given quantum numbers [8,9,13,14]. The short-distance QCD constraints determine in this case all hadronic parameters in terms of the pion decay constant F π and the two masses of the vector and scalar multiplets, M V and M S [11].…”

Section: Introductionmentioning

confidence: 99%

“…The resonance contributions to some O(p 6 ) χPT couplings have been already analyzed in this way, by studying an appropriate set of three-point functions [16][17][18]. The N C → ∞ limit of the resonance chiral theory (RχT) has been investigated in many works [8,9,11,[13][14][15][16][17][18] and a very successful leading order phenomenology already exists [11]. However, we are still lacking a systematic procedure to incorporate next-to-leading contributions in the 1/N C counting.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Rosell

Sanz-Cillero

Pich

2004

J. High Energy Phys.

172

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We present a calculation of the Vector Form Factor at the next-to-leading order in the 1/N C expansion, within the framework of Resonance Chiral Theory. The calculation is performed in the chiral limit, and with two dynamical quark flavours. The ultraviolet behaviour of quantum loops involving virtual resonance propagators is analyzed, together with the kind of counterterms needed in the renormalization procedure. Using the lowest-order equations of motion, we show that only a few combinations of local couplings appear in the final result. The low-energy limit of our calculation reproduces the standard Chiral Perturbation Theory formula, allowing us to determine the resonance contribution to the chiral low-energy couplings, at the next-to-leading order in 1/N C , keeping a full control of their renormalization scale dependence.

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“…Moreover, the EFTs based on chiral symmetry have been very successful [2,3,4,5]. We have focused our attention on the study of the vector resonances through the pion vector form-factor (VFF).…”

Section: Introductionmentioning

confidence: 99%

Rho Meson Properties

Sanz-Cillero¹,

Pich

2004

Nuclear Physics B - Proceedings Supplements

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We study the mass, width and couplings of the lightest vector multiplet. Effective field theories based on chiral symmetry and a 1/NC counting are adopted in order to describe the vector form factor associated to the twopseudoscalar matrix element of the QCD vector current. The bare poles of the intermediate s-channel resonances are regularized through a Dyson-Schwinger-like summation. This procedure provides many interesting properties, as the pole mass M pole ρ = 764.1 ± 2.7 +4.0 −2.5 MeV and the chiral coupling L r 9 (µ0) = (7.04 ± 0.05 +0.19 −0.27 ) · 10 −3 , at µ0 = 770 MeV. We show how the running affects the resonance parameters and that µ is really unphysical, so saturation occurs at any scale. This talk is mainly based on Ref. [1].

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Chiral lagrangians for massive spin-1 fields

Cited by 902 publications

References 17 publications

Revisiting at low energies

Revisiting at low energies

Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Rho Meson Properties

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