Juan Jose Sanz-Cillero

Form-factors and current correlators: chiral couplings L10r(μ) and C87r(μ) at NLO in 1/NC

Using the resonance chiral theory Lagrangian, we perform a calculation of the vector and axial-vector two-point functions at the next-to-leading order (NLO) in the 1/NC expansion. We have analyzed these correlators within the single-resonance approximation and have also investigated the corrections induced by a second multiplet of vector and axial-vector resonance states. Imposing the correct QCD short-distance constraints, one determines the difference of the two correlators Π(t) ≡ ΠVV(t)−ΠAA(t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L10 and C87 at NLO, keeping full control of their renormalization scale dependence. At μ0 = 0.77 GeV, we obtain L10r(μ0) = (−4.4±0.9) 10−3 and C87r(μ0) = (3.1±1.1) 10−5.

Some remarks on the Padé unitarization of low-energy amplitudes

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the (weakly coupled) Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method does not recover the correct values for the mass and width of the sigma. Alternative sequences of Pades are studied and we find that the diagonal sequences (i.e., [N/N]) have much better convergence properties.

Renormalization group equations in resonance chiral theory

Abstract The use of the equations of motion and meson field redefinitions allows the development of a simplified resonance chiral theory Lagrangian: terms including resonance fields and a large number of derivatives can be reduced into corresponding O ( p 2 ) resonance operators, containing the lowest possible number of derivatives. This is shown by means of the explicit computation of the pion vector form-factor up to next-to-leading order in 1 / N C . The study of the renormalization group equations for the corresponding couplings demonstrates the existence of an infrared fixed point in the resonance theory. The possibility of developing a perturbative 1 / N C expansion in the slow running region around the fixed point is shown here.

One loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson

The work of F. K. G. is supported in part by the NSFC and DFG through funds provided to the SinoGerman CRC 110 “Symmetries and the Emergence of Structure in QCD” (NSFC Grant No. 11261130311) and NSFC (Grant No. 11165005). The work of J. J. S. C. is supported by ERDF funds from the European Commission [Grants No. FPA2010-17747, No. FPA2013-44773-P, No. SEV-2012-0249, and No. CSD2007-00042]. The research of P. R. F. was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe”

Refined analysis on the X (3872) resonance

This work is supported in part by National Nature Science Foundations of China under Contracts No. 10925522 and No. 11021092, and ERDF funds from the European Commission [FPA2010-17747, FPA2013- 44773-P, SEV-2012-0249, CSD2007-00042] and the Comunidad de Madrid [HEPHACOS S2009/ESP-1473]

High energy constraints in the octet SS − P P correlator and resonance saturation at NLO in 1= N C

We study the octet SS-PP correlator within resonance chiral theory up to the one-loop level, i.e., up to next-to-leading order in the 1/N{sub C} expansion. We require that our correlator follows the power behavior prescribed by the operator product expansion at high Euclidean momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high energy behavior will be demanded for the whole correlator, not for individual absorptive channels. The amplitude is progressively improved by considering more and more complicated operators in the hadronic Lagrangian. Matching the resonance chiral theory result with chiral perturbation theory at low energies produces the estimates L{sub 8}({mu}){sup SU(3)}=(1.0{+-}0.4)x10{sup -3} and C{sub 38}({mu}){sup SU(3)}=(8{+-}5)x10{sup -6} for {mu}=770 MeV. The effect of alternative renormalization schemes is also discussed in the article.

pi pi-scattering lengths at O(p**6) revisited

This article completes a former work where part of the O(p^6) low-energy constants entering in the pi pi scattering were estimated. Some resonance contributions were missed in former calculations and slight differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p^6) couplings. We also perform a reanalysis of the hadronic inputs used for the estimation (resonance masses, widths...). Their reliability was checked together with the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the a^I_J is negligible after combining them with the other uncertainties. Based on this consistency, we conclude that the previous scattering length determinations seem to be rather solid and reliable, with the cO(p^6) low-energy constants quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p^6) couplings is properly increased.

Resonance saturation of the chiral couplings at next-to-leading order in 1 / N C

The precision obtainable in phenomenological applications of chiral perturbation theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-N{sub C} resonance Lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/N{sub C} expansion within the framework of resonance chiral theory. We find that, by imposing QCD short-distance constraints, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of resonance chiral theory. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance Lagrangian. Going beyond leading order in the 1/N{sub C} counting allows us to keep full control of the renormalization scale dependence of the LEC estimates.

ππ-scattering lengths at O(p6) revisited

This article completes a former work where part of the O(p^6) low-energy constants entering in the pi pi scattering were estimated. Some resonance contributions were missed in former calculations and slight differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p^6) couplings. We also perform a reanalysis of the hadronic inputs used for the estimation (resonance masses, widths...). Their reliability was checked together with the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the a^I_J is negligible after combining them with the other uncertainties. Based on this consistency, we conclude that the previous scattering length determinations seem to be rather solid and reliable, with the cO(p^6) low-energy constants quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p^6) couplings is properly increased.

π π -scattering lengths at O ( p 6 ) revisited

This article completes a former work where part of the O(p^6) low-energy constants entering in the pi pi scattering were estimated. Some resonance contributions were missed in former calculations and slight differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p^6) couplings. We also perform a reanalysis of the hadronic inputs used for the estimation (resonance masses, widths...). Their reliability was checked together with the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the a^I_J is negligible after combining them with the other uncertainties. Based on this consistency, we conclude that the previous scattering length determinations seem to be rather solid and reliable, with the cO(p^6) low-energy constants quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p^6) couplings is properly increased.