Papers by Juan Josè Sanz-Cillero
The IVth International Conference on Quarks and Nuclear Physics, 2007
This talk presents a systematic procedure for the computation of the SS-PP correlator beyond the ... more 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 L r 8 (µ) at the one-loop level, i.e., up to next-to-leading order in 1/NC .
Nuclear Physics B - Proceedings Supplements, 2010
The SU(3) octet S S − PP correlator and the difference of the singlet and octet scalar correlator... more The SU(3) octet S S − PP correlator and the difference of the singlet and octet scalar correlators are computed within Resonance Chiral Theory. The calculation is carried on up to the one-loop level, i.e., up to next-to-leading order in the 1/N C expansion. Using the resonance expressions as interpolators between long and short distances, we demand the correlators to follow the high-energy power behavior prescribed by the operator product expansion and extract predictions for the low-energy constants. By adding more and more complicated operators to the hadronic action, our description is progressively improved, producing for the SS-PP correlator the chiral coupling estimates L 8 (µ) = (1.0 ± 0.4) · 10 −3 and C 38 (µ) = (8 ± 5) · 10 −6 for µ = 770 MeV. Some first results for the S 1 S 1 − S 8 S 8 correlator are shown, like, for instance, the positivity of the spectral function for two-meson cuts, the high-energy constraints for each separate scalar form-factor and preliminary expressions for the L 6 (µ) low-energy constant.
Nuclear Physics B - Proceedings Supplements, 2007
The semileptonic B → Xuℓν decays allow a pretty clean determination of the CKM matrix element |V ... more The semileptonic B → Xuℓν decays allow a pretty clean determination of the CKM matrix element |V ub |. Nevertheless, the presence of weak annihilation effects near the end-point of the q 2 spectrum introduces uncertainties in the inclusive calculation, requiring the use of non-perturbative techniques like heavy meson chiral perturbation theory and large NC limit.
Nuclear Physics B, 2006
The relation between the quark-gluon description of QCD and the hadronic picture is studied up to... more The relation between the quark-gluon description of QCD and the hadronic picture is studied up to order α s . The analysis of the spin-1 correlators is developed within the large N C 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 α s running in the correlators, to fix the ρ(770) and a 1 (1260) couplings, and to produce a prediction for the values of the condensates. The Operator Product Expansion is improved by the large N C 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.
Physics Letters B, 2009
The use of the equations of motion and meson field redefinitions allows the simplification of the... more The use of the equations of motion and meson field redefinitions allows the simplification of the subleading operators required in the one-loop resonance chiral theory calculation of the ππvector form-factor. The study of the renormalization group equations of the relevant parameters shows the existence of an infrared fixed point for all the couplings. It is important to remark that this result does not rely on the high-energy form-factor constraints, which are often considered in other works. The possibility of developing a perturbative 1/N C expansion in the slow running region around the fixed point is shown here.
Physics Letters B, 2007
The structure of the two-point QCD Green-functions is studied in this note in the limit of large ... more 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.
Physical Review D, 2004
The Lattice results for the pion and kaon decay constants are analysed within the Resonance Chira... more The Lattice results for the pion and kaon decay constants are analysed within the Resonance Chiral Theory framework in the large N C 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 M S = 1049 ± 25 MeV and the Chiral Perturbation Theory parameters at leading order in 1/N C .
Arxiv preprint arXiv:1002.3512, 2010
The use of Padé approximants for the description of QCD matrix elements is discussed in this talk... more The use of Padé approximants for the description of QCD matrix elements is discussed in this talk. We will see how they prove to be an extremely useful tool, specially in the case of resonant amplitudes. It will allow the inclusion of high-energy Euclidian data to improve the determination of low-energy properties, such as the quadratic vector radius. This does not mean that the rational approximations can be arbitrarily employed for the extraction of any desired hadronic parameter. A discussion about the validity, limitations and possible issues of the Padé analysis is carried on along the paper. Finally, based on the de Montessus de Ballore's theorem, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed here and illustrated with the example of the ρ(770).
The European Physical Journal C, 2013
Based on the mathematically well defined Padé Theory, a theoretically safe new procedure for the ... more Based on the mathematically well defined Padé Theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the Second Riemann Sheet of an amplitude to search for the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation.
Physics Letters B, 2008
We present a critical analysis of Padé-based methods for the unitarization of low energy amplitud... more We present a critical analysis of Padé-based methods for the unitarization of low energy amplitudes. We show that the use of certain Padé Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect results for the mass and width of the sigma. Alternative sequences of Padés are studied and we find that the diagonal sequences (i.e., [N/N ]) have much better convergence properties.
The Dalitz plot distribution of the eta' -> eta pi pi decays is analyzed in the frameworks... more The Dalitz plot distribution of the eta' -> eta pi pi decays is analyzed in the frameworks of Large-Nc Chiral Perturbation Theory and Resonance Chiral Theory. The size of the eta' branching ratios is thus satisfactorily understood. However, unitarity effects and, more exactly, the impact of pi-pi loops need to be incorporated in order to achieve an appropriate description of
Physical Review D, 2008
Padé Approximants can be used to go beyond Vector Meson Dominance in a systematic approximation. ... more Padé Approximants can be used to go beyond Vector Meson Dominance in a systematic approximation. We illustrate this fact with the case of the pion vector form factor and extract values for the first two coefficients of its Taylor expansion. Padé Approximants are shown to be a useful and simple tool for incorporating high-energy information, allowing an improved determination of these Taylor coefficients.
Journal of High Energy Physics, 2011
The hadronic decays η ′ → ηππ are studied in the frameworks of large-N C Chiral Perturbation Theo... more The hadronic decays η ′ → ηππ are studied in the frameworks of large-N C Chiral Perturbation Theory, at lowest and next-to-leading orders, and Resonance Chiral Theory in the leading 1/N C approximation. Higher order effects such as ππ final state interactions are taken into account through a detailed unitarization procedure. The inclusion of finite-width effects in the case of RChT is also discussed. The Dalitz plot distribution and the differential branching ratio are computed in both approaches. The predicted Dalitz plot parameters obtained from the different treatments are compared with the most recent measured values. We find that the η ′ → ηππ branching ratios are easily understood, while the Dalitz plot parameters require the inclusion of ππ loops in order to achieve a reasonable agreement. Our final predictions agree with the experimental measurements. We hope our results to be of relevance for present and future experimental analyses of these decays.
Physical Review D, 2014
In this work, we present a precise and model-independent method to extract resonance pole paramet... more In this work, we present a precise and model-independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Padé approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-and twice-subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the f0 at √ s = (453 ± 15) − i(297 ± 15) MeV, the ρ(770) at √ s = (761.4 ± 1.2) − i(71.8 ± 1.0) MeV, and the pole of the f2(1270), located at √ s = (1267.3 ± 1.7) − i(95.0 ± 2.3) MeV. The couplings of the resonances to two pions are also determined with high precision, obtaining respectively, 3.8±0.4 GeV, 5.92±0.15 and 4.41±0.23 GeV −1 . Special attention is dedicated to the systematic treatment of the theoretical and statistical uncertainties, together with their comparison with previous determinations.
We present a dispersive method which allows to investigate the low-energy couplings of chiral per... more 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/NC 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
The hadronic decays eta' -> eta pi pi are studied in the frameworks of large-Nc Chiral Per... more The hadronic decays eta' -> eta pi pi are studied in the frameworks of large-Nc Chiral Perturbation Theory, at lowest and next-to-leading orders, and Resonance Chiral Theory in the leading 1/Nc approximation. Higher order effects such as pi-pi final state interactions are taken into account through a detailed unitarization procedure. The inclusion of finite-width effects in the case of RChT is also discussed. The Dalitz plot distribution and the differential branching ratio are computed in both approaches. The predicted Dalitz plot parameters obtained from the different treatments are compared with the most recent measured values. We find that the eta' -> eta pi pi branching ratios are easily understood, while the Dalitz plot parameters require the inclusion of pi-pi loops in order to achieve a reasonable agreement. Our final predictions agree with the experimental measurements. We hope our results to be of relevance for present and future experimental analyses of thes...
Journal of High Energy Physics, 2011
Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor ... more Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p 4 ) and O(p 6 ) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At µ 0 = 0.77 GeV, we obtain L 9 (µ 0 ) = (7.9 ± 0.4) · 10 −3 and C 88 (µ 0 ) − C 90 (µ 0 ) = (−4.6 ± 0.4) · 10 −5 .
Physical Review D, 2010
We study the octet SS − P P correlator within resonance chiral theory up to the oneloop level, i.... more We study the octet SS − P P correlator within resonance chiral theory up to the oneloop level, i.e., up to next-to-leading order in the 1/N C expansion. We will require that our correlator follows the power behaviour prescribed by the operator product expansion at high euclidian momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high-energy behaviour 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 8 (µ) SU (3) = (1.0±0.4)·10 −3 and C 38 (µ) SU (3) = (8±5)·10 −6 for µ = 770 MeV. The effect of alternative renormalization schemes is also discussed in the article.
Journal of High Energy Physics, 2007
Using 1/N C expansion and dispersion theory techniques, without relying on any explicit resonance... more Using 1/N C expansion and dispersion theory techniques, without relying on any explicit resonance lagrangian, we generalize the KSRF relation by including the scalar meson effects, at leading order of chiral expansion. Two sum rules for the low energy constants L 2 , L 3 and a new relation between resonance couplings are also derived. A rather detailed examination to the new relation is also given. We also discussed the N c properties of partial wave amplitudes and the broad σ resonance.
Journal of High Energy Physics, 2008
Using the resonance chiral theory Lagrangian, we perform a calculation of the vector and axial-ve... more 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/N C expansion. We have analyzed these correlators within the singleresonance 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) ≡ Π V V (t) − Π AA (t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L 10 and C 87 at NLO, keeping full control of their renormalization scale dependence. At µ 0 = 0.77 GeV, we obtain L r 10 (µ 0 ) = (−4.4±0.9)·10 −3 and C r 87
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Papers by Juan Josè Sanz-Cillero