arXiv subjects

J. J. Sanz-Cillero

Publications and source records attributed to J. J. Sanz-Cillero.

50 records · Page 3Linked to original sources

arXiv2007

Can a resonance theory be a renormalizable theory?

In this talk we make an exhaustive analysis of the possible chiral invariant operators that may described the resonance decay S->pi pi. These provide at the same time the only available chiral invariant structures for the loop ultraviolet divergences in this amplitude. Independently of the order in perturbation theory, we find just one single-trace term (four if multi-trace operators are allowed), whose renormalization renders the matrix element finite.

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arXiv2007

Renormalizable Sectors in Resonance Chiral Theory: S -> pi pi Decay Amplitude

We develop a resonance chiral theory without any a priori limitation on the number of derivatives in the hadronic operators. Through an exhaustive analysis of the resonance lagrangian and by means of field redefinitions, we find that the number of independent operator contributing to the S -> pi pi decay amplitude is finite: there is only one single-trace operator (the cd term) and three multi-trace terms. The deep implication of this fact is that the ultraviolet divergences that appear in this amplitude at the loop level can only appear through these chiral invariant structures. Hence, a renormalization of these couplings renders the amplitude finite.

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arXiv2007

On the structure of two-point Green-functions at next-to-leading order in 1/Nc

The structure of the two-point QCD Green-functions is studied in this note in the limit of large number of colours. Their general form at next-to-leading order in 1/Nc is derived keeping the infinite resonance summation and without relying on a particular realization of the hadronic action. It is found that the contributions from chiral operators without resonance fields of order p^4 or higher are irrelevant for the computation of the correlators and, hence, they can be dropped at the beginning of the calculation. The possibility of a more general cancelation of these local terms at the level of the generating functional is discussed.

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arXiv2007

1/NC Expansion of QCD Amplitudes

This talk comments the main features of a hadronic description of QCD in the limit of large number of colours. We derive a quantum field theory for mesons based on chiral symmetry and a perturbative expansion in 1/NC. Some large-NC and next-to-leading order results are reviewed.

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arXiv2007

Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)

We present a dispersive method which allows to investigate the low-energy couplings of chiral perturbation theory at the next-to-leading order (NLO) in the 1/N(C) expansion, keeping full control of their renormalization scale dependence. Using the resonance chiral theory Lagrangian, we perform a NLO calculation of the scalar and pseudoscalar two-point functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference Pi(t)=Pi_S(t)-Pi_P(t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L_8 and C_38. At mu_0=0.77 GeV, we obtain L_8(mu_0)^{SU(3)} = (0.6+-0.4)10^{-3} and C_{38}(mu_0)^{SU(3)}=(2+-6)10^{-6}.

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arXiv2006

Resonance Form-Factors: L8 Determination at Next-to-Leading Order in 1/NC

This talk presents a systematic procedure for the computation of the SS-PP correlator beyond the large--NC limit. The present calculation is carried on within a perturbative 1/NC framework . By constraining the meson form-factors at leading order in 1/NC, one obtains a one-loop spectral function well behaved at short distances. The Weinberg sum-rules get modified, gaining an extra contribution suppressed by 1/NC. This leads to a prediction for the low energy chiral perturbation theory coupling L8^r(mu) at the one-loop level, i.e., up to next-to-leading order in 1/NC.

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arXiv2006

Effective Theory Description of Weak Annihilation in B-> Xu l nu Decays

The semileptonic B-> Xu l nu decays allow a pretty clean determination of the CKM matrix element |Vub|. Nevertheless, the presence of weak-annihilation effects near the end-point of the q2 spectrum introduces uncertainties in the inclusive calculation, requiring the use of non-perturbative techniques like heavy meson chiral perturbation theory and large NC limit.

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arXiv2006

Spin-1 Correlators at Large NC: Matching OPE and Resonance Theory up to O(alpha_s)

The relation between the quark-gluon description of QCD and the hadronic picture is studied up to order alpha_s. The analysis of the spin-1 correlators is developed within the large NC framework. Both representations are shown to be equivalent in the euclidean domain, where the Operator Product Expansion is valid. By considering different models for the hadronic spectrum at high energies, one is able to recover the alpha_s running in the correlators, to fix the rho(770) and a1(1260) couplings, and to produce a prediction for the values of the condensates. The Operator Product Expansion is improved by the large NC resonance theory, extending its range of validity. Dispersion relations are employed in order to study the minkowskian region and some convenient sum rules, specially sensitive to the resonance structure of QCD, are worked out. A first experimental estimate of these sum rules allows a cross-check of former determinations of the QCD parameters and helps to discern and to discard some of the considered hadronical models. Finally, the truncated resonance theory and the Minimal Hadronical Approximation arise as a natural approach to the full resonance theory, not as a model.

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arXiv2006

V+A and V-A Correlators at Large NC: From OPE to Resonance Theory

The spin-1 correlators are analysed in this talk through a large NC resonance theory. The matching to perturbative QCD and the first terms in the OPE constrains the hadronic parameters. A further sum-rule analysis shows the wider range of validity of the resonance description, which can help to discern the proper structure of the QCD mass spectrum.

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arXiv2005

QCD Correlators at Large NC

This talk explores the spin--1 correlators up to O(alpha_s) through a large NC resonance theory. The phenomenological analyses of this kind must take these corrections into account since they produce a larger impact than the first OPE condensates. It is also necessary to separate low and high energy regimes; fixing the parameters of the lightest multiplets through perturbative QCD arguments is unfair and introduces errors in the determination of the condensates and resonance parameters. This separation of regimes improves our understanding of the Minimal Hadronical Approximation. The study at O(alpha_s) already allows discerning between different hadronical models, where the Regge-like mass spectrum shows the best agreement to phenomenology.

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arXiv2004

Pion and Kaon Decay Constants: Lattice vs. Resonance Chiral Theory

The Lattice results for the pion and kaon decay constants are analysed within the Resonance Chiral Theory framework in the large NC limit. The approximately linear behaviour of the observable at large light-quark mass is explained through the interaction with the lightest multiplet of scalar resonances. The analysis of the Lattice results allows to obtain the resonance mass MS=1049 +- 25 MeV and the Chiral Perturbation Theory parameters at leading order in 1/NC.

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arXiv2004

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

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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arXiv2003

Rho Meson Properties

We study the mass, width and couplings of the lightest vector multiplet. Effective field theories based on chiral symmetry and a 1/N_C counting are adopted in order to describe the vector form factor associated to the two-pseudoscalar 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_rho{pole}= 764.1 +- 2.7 (^{+4.0}_{-2.5}) MeV and the chiral coupling L9^r(mu0)= (7.04 +- 0.05 (^{+0.19}_{-0.27}))* 10^{-3}, at mu0=770 MeV. We show how the running affects the resonance parameters and that mu is really unphysical, so saturation occurs at any scale.

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arXiv2002

Rho Meson Properties in the Chiral Theory Framework

We study the mass, width and couplings of the lightest resonance multiplet with I(J^{PC})=1(1^{--}) quantum numbers. Effective field theories based on chiral symmetry are employed in order to describe the form factor associated with the two-pseudoscalar matrix element of the QCD vector current. The bare poles of the intermediate resonances are regularized through a Dyson-Schwinger-like summation. We explore the role of the resonance width in physical observables and make a coupled-channel analysis of final-state interactions. This provides many interesting properties, as the pole mass M_rho{pole}= 764.1 +- 2.7 +4.0-2.5 MeV. At energies E~1 GeV, a second 1(1^{--}) resonance multiplet is considered in order to describe the data in a more consistent way. From the phenomenologically extracted resonance couplings, we obtain the chiral coupling L_9^r(mu0)= (7.04 +- 0.05 +0.19-0.27)* 10^{-3}, at mu0=770$ MeV, and show how the running with the scale mu affects the resonance parameters. A 1/N_C counting is adopted in this work and the consistency of the large--N_C expansion is tested. Finally, we make an estimation of the contribution from diagrams with resonances in crossed channels.

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