arXiv subjects

R. Garcia-Martin

Publications and source records attributed to R. Garcia-Martin.

12 recordsLinked to original sources

arXiv2012

Precise determination of the f0(500) and f0(980) parameters in dispersive analysis of the pipi data

We review the use of new and precise dispersive equations, which also implement crossing symmetry, in order to shed further light on the long-standing puzzle in the parameters of the f0(500), as well as the f0(980). This puzzle is finally being settled thanks to several analyses carried out during the last years. In this talk we show how our very recent dispersive data analysis allowed for a precise and model independent determination of the amplitudes for the S,P,D and F waves. In particular, we show how the analytic continuation of once subtracted dispersion relations for the S0 wave to the complex energy plane leads to very precise results for the f0(500) pole: sqrt(s)_pole = 457^(+14)_(-13) - i 279^(+11)_(-7) MeV and for the f0(980) pole: sqrt(s)_pole = 996+/-7 - i 25^(+10)_(-6) MeV. We also comment on how these results have been already used for other practical applications, including a refit of a previous model to the pipi S-wave amplitudes below 1000 MeV, which improves its consistency with the poles found with the dispersive approach.

hep-ph↗

arXiv2011

Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis

We use our latest dispersive analysis of pion-pion scattering data and the very recent Kl4 experimental results to obtain the mass, width and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model independent way by means of once and twice subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f0(600) pole at (457^{+14}_{-13})-i(279^{+11}_{-7}) MeV and that of the f0(980) at (996\pm7)-i(25^{+10}_{-6}) MeV, whereas their respective couplings to two pions are 3.59^{+0.11}_{-0.13} GeV and 2.3\pm0.2 GeV.

hep-ph↗

arXiv2010

MO analysis of the high statistics Belle results on $γγ\to π^+π^-,π^0π^0$ with chiral constraints

We reconsider Muskhelishvili-Omnès (MO) dispersive representations of photon-photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the low-energy $ππ$ scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the left-hand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to $\simeq1.3$ GeV are included. The tensor contributions to the left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum rule result on the $p^6$ chiral coupling $c_{34}$. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further $p^6$ couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the $f_0(980)$ region is discussed.

hep-ph↗

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

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.

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.

hep-ph↗

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.

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↗

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↗