arXiv subjects

F. J. Yndurain

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

At least 37 records · Page 2Linked to original sources

arXiv2004

Consistency checks of pion-pion scattering data and chiral dispersive calculations

We have evaluated forward dispersion relations for scattering amplitudes that follow from direct fits to several sets of pion-pion scattering experiments, together with the precise K decay results, and high to energy data. We find that some of the most commonly used experimental sets, as well as some recent theoretical analyses based on Roy equations, do not satisfy these constraints by several standard deviations. Finally, we provide a consistent pion-pion amplitude by improving a global fit to data with these dispersion relations.

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arXiv2004

Comments on some chiral-dispersive calculations of $ππ$ scattering

We consider the $ππ$ scattering amplitude obtained by Colangelo, Gasser and Leutwyler (CGL), using dispersion relations and chiral perturbation theory to two loops. We point out that the input used by CGL for energies above 1.42 GeV is incompatible with a number of experimental results. Moreover, the error they adscribe to the $δ_0^{(0)}$ phase at 0.8 GeV, an important part of their input, is much underestimated, and its central value is probably displaced. Then, we compare CGL results with direct fits to experimental $ππ$ data; the outcome of this test is mismatch of the CGL amplitude, for several quantities by as much as 4 standard deviations. We also evaluate forward dispersion relations with the CGL amplitudes. We find that these dispersion relations are fulfilled less and less well as the energy increases towards 0.8 GeV. Moreover, the size that the experimental results for $ππ$ scattering indicates for the two loop corrections in a chiral perturbation theory analysis is less than those required by CGL, which suggests that at least some of the CGL corrections are so large to cover biases in their $ππ$ amplitude and in the evaluation of the scalar form factor of the pion. We conclude on the necessity of repeating the analysis of CGL with correct high energy amplitudes and a more realistic input for the $δ_0^{(0)}$ phase at 0.8 GeV.

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arXiv2004

Scattering amplitudes at multi TeV energies

We show that a generalized Regge behaviour, $$Im F(s,t)\simeq Φ(t)(\log s/\hat{s})^{ν(t)}(s/\hat{s})^{α_P(t)},\quad{\rm for} |t|<|t_0|, s\to\infty$$ where $Φ(t)\simeq e^{bt}$, $α_P(t)\simeq α_P(0)+α'_P(0)t$, and $t_0$ is the first zero of $α_P(t)$, $α_P(t_0)=0$, implies that the corresponding cross section is bounded by $$σ_{\rm tot}(s)<({\rm Const.})\times\log s/\hat{s}.$$ This growth, however, is not sufficient to fit the experimental cross sections. If, instead of this, we assume saturation of the improved Froissart bound, i.e., a behaviour $$Im F(s,0)\simeq A(s/\hat{s})\log^2{{s}\over{s_1\log^{7/2} s/s_2}}, $$ a good fit is obtained to $ππ$, $πN$, $KN$ and $NN$ cross sections from c.m. kinetic energy $E_{\rm kin}\simeq1 $ GeV to 30 TeV (producing a cross section of $108\pm6$ mb at LHC energy). This suggests that the Regge-type behaviour only holds for values of the momentum transfer very near zero.

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arXiv2004

The quadratic scalar radius of the pion and the mixed $π-K$ radius

We consider the quadratic scalar radius of the pion, $ $, and the mixed $K-π$ scalar radius, $ $. With respect to the second, we point out that the more recent (post-1974) experimental results in $K_{l3}$ decays imply a value, $ =0.31\pm0.06 {\rm fm}^2$, which is about $2 σ$ above estimates based on chiral perturbation theory. On the other hand, we show that this value of $ $ suggests the existence of a low mass S$\tfrac{1}{2}$ $Kπ$ resonance. With respect to $ $, we contest the central value and accuracy of current evaluations, that give $ =0.61\pm0.04 {\rm fm}^2$. Based on experiment, we find a robust lower bound of $ \geq0.70\pm0.06 {\rm fm}^2$ and a reliable estimate, $ =0.75\pm0.07 {\rm fm}^2$, where the error bars are attainable. This implies, in particular, that the chiral result for $ $ is $1.4 σ$ away from experiment. We also comment on implications about the chiral parameter $\bar{l}_4$, very likely substantially larger (and with larger errors) than usually assumed.

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arXiv2004

Regge analysis of pion-pion (and pion-kaon) scattering for energy s^{1/2}>1.4 GeV

We perform a detailed Regge analysis of NN, pion-N and pion-pion scattering. From it, we find expressions that represent the pion-pion scattering amplitudes with an accuracy of a few percent, for exchange of isospin zero, and $\sim15%$ for exchange of isospin 1, and this for energies s^{1/2}> 1.4 GeV and for momentum transfers |t|^{1/2}< 0.4 GeV. These Regge formulas are perfectly compatible with the low energy (s^{1/2}< 1.4 GeV) scattering amplitudes deduced from pion-pion phase shift analyses as well as with higher energy (s^{1/2}>1.4 GeV) experimental pion-pion cross sections. They are also compatible with NN and pion-N experimental cross sections using factorization, a property that we check with great precision. This contrasts with results from phase shift analyses of the pion-pion scattering amplitude which bear little resemblance to reality in the region $1.4 1.7 GeV. As a byproduct of our analysis we present also a fit of $NN$, $πN$ and $KN$ cross sections valid from c.m. kinetic energy $E_{\rm kin}\simeq1$ GeV to multi TeV energies.

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arXiv2003

Low Energy Pion Physics

In these notes we present an introductory review on various topics about low energy pion physics (some kaon physics is discussed as well). Among these, we include the uses of analyticity and unitarity to describe partial wave amplitudes (for which we give accurate and economical parametrizations) and form factors; (forward) dispersion relations; and the use of the Froissart--Gribov representation to evaluate accurately the low energy parameters (scattering lengths and effective ranges) for higher ($l\geq1$) waves. Finally, we describe some pion physics in QCD and then pass on to study the nonlinear sigma model, and the chiral perturbation theory approach to low energy pion interactions.\hb \indent Most of the results presented here are well known, but we also give a set of state of the art, precise determinations of some scattering lengths as well as an independent calculation of three of the parameters $\bar{l}_2$, $\bar{l}_4$, $\bar{l}_6$ (to one loop), and one $\bar{f}_2$, to two loops, that appear in chiral perturbation theory. The S waves are discussed and compared with chiral perturbation theory expectations, and the same is done for larger $l$ scattering lengths and effective range parameters. Also new is the evaluation of some electromagnetic corrections.

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arXiv2003

On the precision of chiral-dispersive calculations of $ππ$ scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $ππ$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.

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arXiv2002

Basic Parameters and Some Precision Tests of the Standard Model

We present a review of the masses (except for neutrino masses) and interaction strengths in the standard model. Special emphasis is put on quantities that have been determined with significantly improved precision in the last few years. In particular, a number of determinations of $α_s$ and the electromagnetic coupling on the $Z$, $α_{\rm QED}(M_Z^2)$ are presented and their implications for the Higgs mass discussed; the best prediction that results for this last quantity being $$M_H=102^{+54}_{-36} GeV/c^2.$$ Besides this, we also discuss a few extra precision tests of the standard model: the electron magnetic moment and dipole moment, and the muon magnetic moment.

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arXiv2002

Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$

We perform a new calculation of the hadronic contributions, $a({\rm Hadronic})$ to the anomalous magnetic moment of the muon, $a_μ$. For the low energy contributions of order $α^2$ we carry over an analysis of the pion form factor $F_π(t)$ using recent data both on $e^+e^-\toπ^+π^-$ and $τ^+\to \barν_τπ^+π^0$. In this analysis we take into account that the phase of the form factor is equal to that of $ππ$ scattering. This allows us to profit fully from analyticity properties so we can use also experimental information on $F_π(t)$ at spacelike $t$. At higher energy we use QCD to supplement experimental data, including the recent measurements of $e^+e^-\to {\rm hadrons}$ both around 1 GeV and near the $\bar{c}c$ threshold. This yields a precise determination of the $O(α^2)$ and $O(α^2)+O(α^3)$ hadronic part of the photon vacuum polarization pieces, $$10^{11}\times a^{(2)}({\rm h.v.p.})=6 909\pm64;\quad 10^{11}\times a^{(2+3)}({\rm h.v.p.})=7 002\pm66$$ As byproducts we also get the masses and widths of the $ρ^0, ρ^+$, and very accurate values for the charge radius and second coefficient of the pion. Adding the remaining order $α^3$ hadronic contributions we find $$10^{11}\times a^{\rm theory}(\hbox{Hadronic})= 6 993\pm69\quad(e^+e^- + τ+ {\rm spacel.})$$ The figures given are obtained including $τ$ decay data. This is to be compared with the recent experimental value, $$10^{11}\times a^{\rm exp.}(\hbox{Hadronic})=7 174\pm150.$$

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arXiv2002

Calculation of $\barα_{\rm Q.E.D.}$ on the Z

We perform a new, detailed calculation of the hadronic contributions to the running electromagnetic coupling, $\barα$, defined on the Z particle (91 GeV). We find for the hadronic contribution, including radiative corrections, $$10^5\times \deltav_{\rm had.}α(M_Z^2)= 2740\pm12,$$ or, excluding the top quark contribution, $$10^5\times \deltav_{\rm had.}α^{(5)}(M_Z^2)= 2747\pm12.$$ Adding the pure QED corrections we get a value for the running electromagnetic coupling of $$\barα_{\rm Q.E.D.}(M_Z^2)= {{1}\over{128.965\pm0.017}}.$$

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arXiv2001

Restriction on SUSY Masses from $Z\to hadrons$

We remark that the precision of recent determinations of $α_s(M^2_Z)$ is such that one can get bounds on supersymmetric partner masses (squark and gluino) by requiring consistency of determinations of $α_s$ at "low" energies, where those particles do not contribute, and on the $Z$ peak. For approximately degenerate squarks and gluinos with mass $\widetilde{m}$, we find the bound $\widetilde{m}\geq 173$ GeV, at the $2σ$ level. At the $2.5σ$ level, $\widetilde{m}\geq 121$ GeV.

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arXiv2001

Improved Calculation of F2 in Electroproduction and xF3 in Neutrino Scattering to NNLO and Determination of alpha_s

We improve the existing calculations of deep inelastic scattering to next to next to leading order in the following manner. First, we use the recently calculated values of the anomalous dimensions for moments with index n=10,12 in ep scattering. Second, we use also recently calculated anomalous dimensions for n=1,3,...,13 for xF3 in neutrino N scattering, to extend the calculation to this process. Lastly, we use the determinantal constraints on the moments that follow from positivity of the structure functions to stabilize the fits. We find substantial improvement over previous results, getting the following numbers: Lambda(n_f=4, 3 loops)= 274 \pm 20 MeV, alpha_s^{3 loops}(M_Z^2)=0.1166 \pm 0.0013 and chi^2/dof= 92/(153-18) from ep and, from νN, Lambda(n_f=4, 3 loops)=255 \pm 72 MeV, alpha_s^{3 loops}(M_Z^2)=0.1153 \pm 0.0063 and chi^2/dof=0.335/(64-7). The errors take into account experimental errors and higher twist effects among other estimated theoretical errors. We can also extrapolate the fit, made originally for the range 3.5 < Q^2 < 230 GeV^2 to higher momenta, obtaining very good reproduction of experimental data up to Q^2=5000 GeV^2. From this, in particular, we can exclude supersymmetric partners (squarks or gluinos) for masses up to some 60 GeV. The fitted value of the coupling is now, including the data at high Q^2, alpha_s^{3 loops}(M_Z^2)=0.1163 \pm 0.0014.

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arXiv2001

Disagreement between standard model and experiment for muon g-2 ?

In a recent experimental paper reporting a precise measurement of the muon anomalous magnetic moment, Brown et al. claim disagreement of their result with evaluations based on the standard model. This claim is based on comparison with a single theoretical evaluation. It is pointed out that other equally legitimate theoretical evaluations exist in the literature, with which the new experimental figure is quite compatible. The claim of indications for new physics beyond the standard model does not appear justified. In this version we take into account corrections to one of the works quoted, we include a new discussion at the end, and also minor errors are corrected. The conclusions remain unchanged.

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arXiv2000

QCD Calculations of Heavy Quarkonium States

Recent results on the QCD analysis of bound states of heavy $\bar{q}q$ quarks are reviewed, paying attention to what can be derived from the theory with a reasonable degree of rigour. We report a calculation of $\bar{b}c$ bound states; a very precise evaluation of $b, c$ quark masses from quarkonium spectrum; the NNLO evaluation of $Υ\to e^+e^-$; and a discussion of power corrections. For the $b$ quark {\sl pole} mass we get, including $O(m_c^2/m_b^2)$ and $O(α_s^5\log α_s)$ corrections, $m_b=5.020\pm0.058 GeV$; and for the $\bar{MS}$ mass the result, correct to $O(α_s^3)$, $O(m_c^2/m_b^2)$, $\bar{m}_b(\bar{m}_b)=4.286\pm0.036 GeV$. For the decay $Υ\to e^+e^-$, higher corrections are too large to permit a reliable calculation, but we can predict a toponium width of $13\pm1 keV$.

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arXiv2000

The ground state of bottomium to two loops and higher

We consider the properties of the ground state of bottomium. The $Υ$ mass is evaluated to two loops, and including leading higher order [$O(α_s^5\logα_s)$] and $m_c^2/m_b^2$ corrections. This allows us to present updated values for the pole mass and $\bar{MS}$ mass of the $b$ quark: $m_b=5022\pm58$ MeV, for the pole mass, and $\bar{m}_b(\bar{m}_b)=4286\pm36$ MeV for the $\bar{MS}$ one. The value for the \msbar mass is accurate including and $O(α_s^3)$ corrections and leading orders in the ratio $m_c^2/m_b^2$. We then consider the wave function for the ground state of $\bar{b}b$, which is calculated to two loops in the nonrelativistic approximation. Taking into account the evaluation of the matching coefficients by Beneke and Signer one can calculate, in principle, the width for the decay $Υ\to e^+e^-$ to order $α_s^5$. Unfortunately, given the size of the corrections it is impossible to produce reliable numbers. The situation is slightly better for the ground state of toponium, where a decay width into $e^+e^-$ of 11 -- 14 keV is predicted.

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arXiv2000

Improved determination of b quark mass from spectroscopy

Using recently evaluated contributions (including a novel one calculated here), we present updated values for the pole mass and $\bar{MS}$ mass of the $b$ quark: $m_b=5022\pm58$ MeV, for the pole mass, and $\bar{m}_b(\bar{m}_b)=4286\pm36$ MeV for the $\bar{MS}$ one. These values are accurate including, respectively, $O(α_s^5\logα_s)$ and $O(α_s^3)$ corrections and, in both cases, leading orders in the ratio $m_c^2/m_b^2$.

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arXiv1999

Heavy Quarkonium

Bound states of heavy $\bar{q}q$ quarks are reviewed within the context of QCD. First of all, we consider the calculations which can be performed {\sl ab initio}, which includes $\bar{t}t$ with principal quantum number $n$ up to four, $\bar{b}b$ states with $n=1$ and (to a lesser extent) $\bar{b}b$ with $n=2$ and $\bar{c}c$ for $n=1$. Among the results, we report a very precise $O(α_s^4)$ evaluation of $b, c$ quark masses from quarkonium spectrum with a potential to two loops, a calculation of the decay $Υ\to e^+e^-$ and a prediction for the splitting $Υ- η_b$. We then consider how, with the help of reasonable assumptions, one can extend QCD calculations to other states of heavy quarks. Finally, a few words are said on the treatment of light quark bound states.

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arXiv1999

Calculation of Electroproduction to NNLO and Precision Determination of $α_s$

We use the known values of the two loop Wilson coefficients and the three loop anomalous dimension matrix $γ(n)$ to perform a next-to-next-to leading order (NNLO) calculation of $ep$ deep inelastic scattering. Because $γ(n)$ is only known for a few values of $n$, the method of average reconstruction has to be used, which leaves 102 effective experimental points, for 12 parameters: the QCD mass $Λ$, and 11 initial values for the moments of the structure functions. The data points spread in the range of momenta $2.5 GeV^2\leq Q^2\leq 230 GeV^2$. The chi/dof decreases substantially when going from LO to NLO, and also from NLO to NNLO (although only a little now) to $χ/dof=79.2/(102-12)$. The favoured value of $Λ$ is $$Λ(n_f=4,3 {\rm loop})=282.7\pm35.1 MeV,$$ corresponding to the value of the coupling at the Z mass of $$α^{(\rm 3 loop)}_s(M_Z^2)=0.1172\pm0.0024. $$ The calculation, which constitutes a very precise test of QCD, includes target mass corrections; the error takes into account experimental errors and higher twist effects among other estimated theoretical errors.

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