arXiv subjects

J. R. Pelaez

Publications and source records attributed to J. R. Pelaez.

At least 55 records · Page 3Linked to original sources

arXiv2009

Once subtracted Roy-like dispersion relations and a precise analysis of $ππ$ scattering data

We report our progress on the data analysis of $ππ$ scattering data in terms of Forward Dispersion Relations (FDR), as well as Roy equations (RE) and their once-subtracted counterpart, GKPY equations. The first part of the analysis consists of independent fits to the different $ππ$ channels. The GKPY equations provide a more stringent consistency check for the parametrizations of the S0-wave data in the region from 400 to 1100 MeV, In the second part we present our preliminary analysis where the fits are constrained to satisfy all dispersion relations within errors, including the new GKPY Eqs., thus providing a very precise and model independent description of data using just analyticity, causality and crossing.

hep-ph↗

arXiv2009

Light scalar mesons: comments on their behavior in the 1/Nc expansion near Nc=3 versus the Nc --> infinity limit

We briefly review how light meson resonances are described within one and two-loop Unitarized Chiral Perturbation Theory amplitudes and how, close to Nc=3, light vectors follow the Nc behavior of $q\bar q$ mesons whereas light scalars do not. This supports the hypothesis that the lightest scalar is not predominantly a $q\bar q$ meson, although a subdominant $q\bar q$ component is suggested around 1 GeV at somewhat larger Nc. In contrast, when Nc is very far from 3, like in the Nc --> infinity limit, we explain again in detail why unitarization is not, a priori, reliable nor robust and why this limit should not be used to drag any conclusions about the dominant nature of physical light scalar mesons.

hep-ph↗

arXiv2009

Once and twice subtracted dispersion relations in the analysis of pi pi amplitudes

Once and twice subtracted crossing symmetric dispersion relations applied to $ππ\to ππ$ scattering data are analyzed and compared. Both sets of dispersion relations can be used to test the $ππ$ amplitudes in low partial waves up to about 1 GeV. We show how once subtracted dispersion relations can provide stronger constraints for $ππ$ amplitudes than twice subtracted ones in the 400 to 1100 MeV range, given the same experimental input.

hep-ph↗

arXiv2009

Sigma pole position and errors of a once and twice subtracted dispersive analysis of pi-pi scattering data

We show how the new precise data on kaon decays together with forward dispersion relations, sum rules and once- and twice-subtracted Roy's equations allow for a precise determination of the sigma meson pole position. We present a comparison and a study of the different sources of uncertainties when using either once- or twice-subtracted Roy's equations to analyze the data. Finally we present a preliminary determination of the sigma pole from the constrained dispersive data analysis.

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arXiv2008

Nature of the axial-vector mesons from their Nc behavior within the chiral unitary approach

By describing within the chiral unitary approach the s-wave interaction of the vector meson nonet with the octet of pseudoscalar Goldstone Bosons, we find that the main component of the axial vector mesons b_1(1235), h_1(1170), h_1(1380), a_1(1260), f_1(1285) and the two states associated to the K_1(1270) does not follow the QCD dependence on the number of colors for ordinary qqbar mesons.

hep-ph↗

arXiv2008

In memory of Paco Yndurain: A precise determination of pion-pion scattering from experiment and dispersion relations

This talk is dedicated to the memory of Paco Yndurain, the original speaker in the conference. After a short account of his scientific career, we briefly review our ongoing collaboration to determine precisely the $ππ$ scattering amplitude including the most recent data by means of Forward Dispersion Relations and Roy Equations. A remarkable improvement in precision over the intermediate energy region is obtained by using once-subtracted Roy Equations in addition to the standard twice-subtracted ones.

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arXiv2008

Precise dispersive data analysis of the f0(600) pole

We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the sigma region. We also improve the matching between the parametrizations at low and intermediate energy of the S0 wave, and show that the effect of this on the sigma pole position is negligible.

hep-ph↗

arXiv2008

New dispersion relations in the description of $ππ$ scattering amplitudes

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $ππ$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $ππ$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $ππ$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.

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arXiv2008

Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory

We use the one-loop Chiral Perturbation Theory pion-pion scattering amplitude and dispersion theory in the form of the inverse amplitude method, to study the quark mass dependence of the two lightest resonances of the strong interactions, the f_0(600) (sigma) and the rho-meson. As main results we find that the rho-pion-pion coupling constant is almost quark mass independent and that the rho mass shows a smooth quark mass dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.

hep-ph↗

arXiv2008

Precise analysis of pion-pion scattering data from Roy equations and forward dispersion relations

We review our recent analysis of pion-pion scattering data in terms of Roy equations and Forward Dispersion Relations, and present some preliminary results in terms of a new set of once-subtracted coupled equations for partial waves. The first analysis consists of independent fits to the different pion-pion channels that satisfies rather well the dispersive representation. In the second analysis we constrain the fit with the dispersion relations. The latter provides a very precise and model independent description of data using just analyticity, causality and crossing.

hep-ph↗

arXiv2008

Precise determination of the sigma pole location from a dispersive analysis

We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the sigma resonance region. For practical applications, these results are shown to be very well approximated by a very simple conformal expansion.

hep-ph↗

arXiv2008

$η\to π^0 γγ$ decay within a chiral unitary approach revisited

In view of the recent experimental developments on the experimental side in the $η\to π^0 γγ$ decay, and the fact that the Particle Data Group in the on line edition of 2007 reports sizable changes of the radiative decay widths of vector mesons used as input in the theoretical calculations of \cite{eta}, a reevaluation of the decay width of the $η$ in this channel has been done, reducing its uncertainty by almost a factor of two. The new input of the PDG is used and invariant mass distributions and total widths are compared with the most recent results from AGS, MAMI and preliminary ones of KLOE. The agreement of the theory with the AGS and MAMI data is very good, both for the total rates as well as for the invariant mass distributions of the two photons.

hep-ph↗

arXiv2008

The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $ππ$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 σ$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_π$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_π$ and $δ_0^{(0)}(m^2_K)-δ_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.

hep-ph↗

arXiv2007

Chiral Extrapolation of light resonances from Unitarized Chiral Perturbation Theory

Both scalar and vector light resonances can be generated from the unitarization of one-loop chiral perturbation theory. This amounts to using in a dispersion relation the chiral expansion, which incorporates the correct QCD quark mass dependence. We can thus predict the quark mass dependence of the poles associated to those light resonances. Our results compare well with some recent lattice results for the rho(770) mass and can be used as a benchmark for future lattice results on the rho(770) or the f0(600) also known as the sigma.

hep-ph↗

arXiv2007

The Inverse Amplitude Method and Adler Zeros

The Inverse Amplitude Method is a powerful unitarization technique to enlarge the energy applicability region of Effective Lagrangians. It has been widely used to describe resonances from Chiral Perturbation Theory as well as for the Strongly Interacting Symmetry Breaking Sector. In this work we show how it can be slightly modified to account also for the sub-threshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

hep-ph↗

arXiv2007

The effect of isospin violation on scalar meson production

We investigate the isospin-violating mixing of the light scalar mesons a0(980) and f0(980) within the unitarized chiral approach. Isospin-violating effects are considered to leading order in the quark mass difference and electromagnetism. In this approach both resonances are generated through meson-meson dynamics. Our results provide a description of the mixing phenomenon within a framework consistent with chiral symmetry and unitarity, where these resonances are not predominantly quark-antiquark states. We discuss in detail the reactions J/Psi to phi S, where S denotes a suitable pair of pseudo--scalar mesons in the scalar channel, namely pi0 eta, K+K-, and K0 \bar K^0. In this work predictions for the cross section in the kaon channels are given for the first time with isospin violating effects included.

hep-ph↗

arXiv2007

Experimental status of the $ππ$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length

The experimental results obtained in the last few years on kaon decays (K$\to2π$ and, above all, Ke4 decays) allow a reliable, model independent determination of low energy $ππ$ scattering in the S0 wave. Using them and, eventually, other sets of data, it is possible to give a precise parametrization of the S0 wave as well as to find the scattering length and effective range parameter. One can also perform an extrapolation to the pole of the "$σ$ resonance" [$f_0(600)$]. We obtain the results $$a_0^{(0)}=0.233\pm0.013 M^{-1}_π,\quad b_0^{(0)}=0.285\pm0.012 M^{-3}_π$$ and, for the $σ$ pole, $$M_σ=484\pm17 \mev,\quad\gammav_σ/2= 255\pm10 {\rm MeV}.$$

hep-ph↗

arXiv2006

Dispersive chiral approach to Meson-meson dynamics: Spectroscopy results for light scalars and precision studies

Dispersive approaches provide model independent description of meson-meson scattering. We first review here the use of dispersion relations to obtain a model independent unitarization of Chiral Perturbation Theory amplitudes, that establish the existence of light scalar mesons and whose leading 1/N_c behavior suggest they ahve a non q-qbar dominant component. We also review the forward dispersion relation checks on conflicting experimental data and the resulting very precise pion-pion scattering scattering amplitudes.

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