arXiv subjects

F. J. Yndurain

Publications and source records attributed to F. J. Yndurain.

At least 19 recordsLinked 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.

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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.

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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

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

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

Methods and Models for Hadron Physics

A round table held during the Hadron07 Conference focusing on experimental observations of new hadronic states, on theoretical perspectives for their description, and on the role of hadronic spectroscopy in furthering our knowledge of the fundamental theory of strong interactions.

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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 $δ_0^{(0)}(m^2_K)-δ_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.

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arXiv2007

Elements of Group Theory

\noindent 1. Generalities\hfil\break 2. Lie groups and Lie algebras\hfil\break 3. The unitary groups\hfil\break 4. Representations of the SU(n) groups (and of their algebras)\hfil\break 5. The tensor method for unitary groups, and\hb the permutation group\hfil\break 6. Relativistic invariance. The Lorentz group\hfil\break 7. General representation of relativistic states

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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, $$M_σ=484\pm17 \mev,\quad\gammav_σ/2= 255\pm10 {\rm MeV}.$$

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arXiv2007

Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering

We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell. We find, with current data, that both the pion-pion and pion-nucleon sum rules are satisfied to better than six percent, and we give detailed estimates of the experimental and extrapolation errors in the closure discrepancies.

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arXiv2006

The Olsson sum rule and the rho Regge pole

We consider the Olsson sum rule, i.e., the forward dispersion relation for pion-pion scattering with exchange of isospin unity at threshold. We show that, if using the S0, S2 and P wave expressions of Colangelo, Gasser and Leutwyler, then either the sum rule is not satisfied or, if adjusting the residue of the rho exchange Regge amplitude to have the sum rule satisfied (as recently proposed by Caprini, Colangelo and Leutwyler) then the subsequent high energy amplitude is in disagreement with experimental pi-pi cross sections.

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arXiv2006

Forward dispersion relations and Roy equations in pi-pi scattering

We review results of an analysis of pipi interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the K anti-K threshold using more data for phase shifts and including the S0 wave inelasticity from pipi -> K anti-K. In addition, we have improved the fit to the f2(1270) resonance and used a more flexible P wave parametrization above the K anti-K threshold and included an estimation of the D2 wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. We have checked that the pipi scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.

hep-ph↗

arXiv2006

The pion-pion scattering amplitude. II: Improved analysis above $\bar{K}K$ threshold

We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$ GeV, the energy-dependent phase shift analysis of $ππ$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $ππ\to\bar{K}K$. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\geq1.42$ GeV, which we also carry out. We show that this more realistic input produces $ππ$ scattering amplitudes that satisfy better forward dispersion relations, particularly for $π^0π^0$ scattering.

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arXiv2005

Some comments on calculations of the scalar radius of the pion and the chiral constant $\bar{l}_4$

The pion scalar radius is given by $ =(6/π)\int_{4M^2_π}^\infty{\rm d}t δ_S(t)/t^2$, with $δ_S$ the phase of the scalar form factor. Below $\bar{K}K$ threshold, $δ_S=δ_0$, $δ_0$ being the isoscalar, S-wave $ππ$ phase shift. Between $\bar{K}K$ threshold and $t^{1/2}\sim 1.5 {\rm GeV}$ I argued, in two previous letters, that one can approximate $δ_S\simδ_0$, because inelasticity is small, compared with the errors. This gives $ =0.75\pm0.07 {\rm fm}^2$ and the value $\bar{l}_4=5.4\pm0.5$ for the one-loop chiral perturbation theory constant, compared with the values given by Leutwyler and collaborators, $ =0.61\pm0.04 {\rm fm}^2$ and $\bar{l}_4=4.4\pm0.3$. At high energy, $t^{1/2}>1.5 {\rm GeV}$, I remarked that the value of $δ_S$ that follows from perturbative QCD agrees with my interpolation and disagrees with that of Leutwyler and collaborators. In a recent article, Caprini, Colangelo and Leutwyler claim that my estimate of the asymptotic phase $δ_S$ is incorrect as it neglects higher twist contributions. Here I remark that, when correctly calculated, higher twist contributions are likely negligible. I also show that chiral perturbation theory gives $\bar{l}_4=6.60\pm0.43$, compatible with my estimate but widely off the value $\bar{l}_4=4.4\pm0.3$ of Leutwyler and collaborators.

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arXiv2005

Chiral-dispersive calculations of pion-pion scattering confront experiment

In a series of papers we have applied several sum rules and forward dispersion relations, to pion-pion scattering. We have found that some widely used data sets fail to satisfy these constraints, and we have provided an amplitude that describes data consistently with the dispersive tests. Furthermore, we noted that the input and precision claimed in a Roy equation analysis by Colangelo, Gasser and Leutwyler, lead to several mismatches with some sum rules. Subsequently, Caprini, Colangelo, Gasser and Leutwyler claimed that our Regge parametrization was incorrect. We collect here the answers to their various claims, and try to clarify the points of agreement and disagreement, showing experimental evidence that substantiates our results, and that, in addition, their representation fails to satisfy all three forward dispersion relations up to sqrt{s}<=800 MeV by several standard deviations.

hep-ph↗

arXiv2005

The hadronic contributions to the anomalous magnetic moment of the muon

We present a new, completely revised calculation of the muon anomalous magnetic moment, $a_μ=(g_μ-2)/2$, comparing it with the more recent experimental determination of this quantity; this furnishes an important test of theories of strong, weak and electromagnetic interactions. These theoretical and experimental determinations give the very precise numbers, $$10^{11}\times a_μ=\cases{116 591 806\pm50\pm10 ({\rm rad.})\pm30 (\ell\times\ell)\quad\hbox{[Th., no $τ$]}\cr 116 591 889\pm49\pm10 ({\rm rad.})\pm30 (\ell\times\ell)\quad\hbox{[Theory, $τ$]}\cr 116 592 080\pm60\quad\hbox{[Experiment]}.\cr}$$ In the theoretical evaluations, the first quantity does not, and the second one does, use information from $τ$ decay. The first errors for the theoretical evaluations include statistical plus systematic errors; the other ones are the estimated errors due to incomplete treatment of radiative corrections and the estimated error in the light-by-light scattering contribution. We thus have a significant mismatch between theory and experiment. We also use part of the theoretical calculations to give a precise evaluation of the electromagnetic coupling on the $Z$, $\barα_{\rm Q.E.D.}(M^2_{Z})$, of the masses and widths of the (charged and neutral) rho resonances, of the scattering length and effective range for the P wave in $ππ$ scattering, and of the quadratic radius and second coefficient of the pion form factor.

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arXiv2005

The scalar radius of the pion

The pion scalar radius is given by $ =(6/π)\int_{4M^2_π}^\infty{\rm d}s δ_S(s)/s^2$, with $δ_S$ the phase of the scalar form factor. Below $\bar{K}K$ threshold, $δ_S=δ_π$, $δ_π$ being the isoscalar, S-wave $ππ$ phase shift. At high energy, $s>2 {\rm GeV}^2$, $δ_S$ is given by perturbative QCD. In between I argued, in a previous letter, that one can interpolate $δ_S\simδ_π$, because inelasticity is small, compared with the errors. This gives $ =0.75\pm0.07 {\rm fm}^2$. Recently, Ananthanarayan, Caprini, Colangelo, Gasser and Leutwyler (ACCGL) have claimed that this is incorrect and one should have instead $δ_S\simeqδ_π-π$; then $ =0.61\pm0.04 {\rm fm}^2$. Here I show that the ACCGL phase $δ_S$ is pathological in that it is discontinuous for small inelasticity, does not coincide with what perturbative QCD suggests at high energy, and only occurs because these authors take a value for $δ_π(4m^2_K)$ different from what experiment indicates. If one uses the value for $δ_π(4m^2_K)$ favoured by experiment, the ensuing phase $δ_S$ is continuous, agrees with perturbative QCD expectations, and satisfies $δ_S\simeqδ_π$, thus confirming the correctness of my previous estimate, $ =0.75\pm0.07 {\rm fm}^2$.

hep-ph↗

arXiv2005

The pion-pion scattering amplitude

We obtain reliable $ππ$ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy ($s^{1/2}\leq1.42 {\rm GeV}$) phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin~0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behaviour as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing $ππ$ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as $s - t - u$ crossing sum rules and other consistency conditions. The improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating $K$ decays. In this respect, we find $[a_0^{(0)}-a_0^{(2)}]^2=(0.077\pm0.008) M^{-1}_π$ and $δ_0^{(0)}(m^2_K)-δ_0^{(2)}(m^2_K)=52.9\pm1.6^{\rm o}$.

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