An improved description of four-pion production in electron-positron annihilation and in tau lepton decays is presented. The model amplitude is fitted to recent data from BaBar which cover a wide energy range and which were obtained exploiting the radiative return. Predicting tau decay distributions from e+e- data and comparing these predictions with ALEPH and CLEO results, the validity of isospin symmetry is confirmed within the present experimental errors. A good description of two- and three-pion sub-distributions is obtained. Special emphasis is put on the predictions for omega pi (-> pi+pi-pi0) in e+e- annihilation and in tau decay. The model amplitude is implemented in the Monte Carlo generator PHOKHARA.
We show that in the presence of sufficiently strong tau neutrino annihilations into majorons, the primordial nucleosynthesis constraints can not rule out tau neutrino masses in the MeV range.
tau -> (3 pions) nu_tau decays are analysed within the framework of the resonance effective theory of QCD. We work out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, in particular the local a_1(1260)-rho(770)-Goldstone interactions. The new coupling constants are constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values…
The role of the a_1(1420) resonance in the three-pion decays of the tau lepton is investigated using a phenomenological model. For all data before 2008, roughly equal fit quality is achieved when the basic a_1(1260) resonance is supplemented with either a_1(1640) or a_1(1420). However, two recent and more precise data sets require resonances with masses that are not very far from that of a_1(1420). This suggests that the axial-vector resonance that accompanies the a_1(1260) in the three-pion decays of the tauon is a_1(1420), not a_1(1640), as believed up to now. More data are needed to demonst…
We show that in the presence of sufficiently strong $ν_τ$ annihilations to majorons, primordial nucleosynthesis constraints can not rule out any values of the $ν_τ$ mass up the present laboratory limit.
The calculational precision of $\ee\to\tautau$ and $\ee\to\mumu$ production cross-sections in electron-positron annihilations at \roots = 10.58 \gev are studied for the \kk Monte Carlo simulation program. We determine $σ(\ee\to\tautau) = (0.919 \pm 0.003) \nb$ and $σ(\ee\to\mumu) = (1.147 \pm 0.005) \nb$, where the error represents the precision of the calculation.
A way to explain the puzzling difference between the pion form factor as measured in e+ e- annihilations and in tau decays is discussed. We show that isospin symmetry breaking, beside the already identified effects, produces also a full mixing between the rho0, omega and phi mesons which generates an isospin 0 component inside the rho0 meson. This effect, not accounted for in current treatments of the problem, seems able to account for the apparent mismatch between e+ e- and tau data below the phi mass.
The total cross-sections measured at LEP for e+e- annihilation into tau+tau-, c\bar{c} and b\bar{b} at 2E ~ 200 GeV are used to derive the upper limits 3*10^{-17}, 5*10^{-17}, 2*10^{-17} e*cm for the electric dipole moments and 4*10^{-17}, 7*10^{-17}, 2.5*10^{-17} e*cm for the weak dipole moments of the tau-lepton, c-, and b-quarks, respectively. Some of the existing limits on these moments are improved and for the b-quark the improvement is rather significant.
The predictions of an isospin model are compared with the branching ratios of the 5 and 6 pion decays of the tau lepton. In both cases, the isospin model suggests that the tau favours decays in which there is an omega resonance. Recent measurements of such tau decays confirm this hypothesis. If the decay of the tau to 7 pions also proceeds through an intermediate omega, then the isospin model predicts that the branching ratio of the tau to seven charged pions should be small when compared with other 7 pion decays. New limits on this mode appear to support this argument.
In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decreas…
The mSUGRA model predicts the polarization of the tau coming from the stau to bino decay in the co-annihilation region to be +1. This can be exploited to extract this soft tau signal at LHC and also to measure the tiny mass differences between the stau and the bino LSP. Moreover this strategy will be applicable for a wider class of bino LSP models, where the lighter stau has a right component at least of similar size as the left.
Accumulation and annihilation of weakly interacting massive particles (WIMPs) in the earth and the sun may be observed by the resulting neutrino signal. We demonstrate that, for certain parts of the SUSY parameter space, present and future neutrino telescopes can expect a higher rate of events due to tau-neutrinos than of events due to muon-neutrinos. We show how $ν_τ\leftrightarrowν_μ$ oscillations, and in the case of the sun also scattering, absorption and regeneration, modify the signal expectation. We find that most currently proposed neutralino models predict equal or increased muon fluxe…
A parametrization of the Bose-Einstein correlation function of pairs of identical pions produced in hadronic e+e- annihilation is proposed within the framework of a model (the tau-model) in which space-time and momentum space are very strongly correlated. Using information from the Bose-Einstein correlations as well as from single-pion spectra,it is then possible to reconstruct the space-time evolution of pion production.
We study the prospects for the measurement of the stau - lightest neutralino mass difference (dM) and the gluino mass (Mg) in the supersymmetric co-annihilation region at the LHC using tau leptons. Recent WMAP measurements of the amount of cold dark matter and previous accelerator experiments indicate that the coannihilation region of mSUGRA is characterized by a small dM (5-15 GeV). Focusing on taus from N2 -> tau stau -> tau tau N1 decays in gluino and squark production, we consider inclusive 3 tau+jet+missing Et production, with two taus above a high Et threshold and a third tau above a low…
We assume that nucleon antinucleon annihilation is a fast process leading to a classical coherent pion pulse. We develop the quantum description of such pion waves based on the method of coherent states. We study the consequences of such a description for averages of charge types and moments of distributions of pion momenta with iso-spin and four-momentum conservation taken into account. We briefly discuss the applicability of our method to annihilation at rest, where we find agreement with experiment, and suggest other avenues for its use.
We analyse tau -> (3 pions) nu_tau decays within the framework of the resonance chiral theory of QCD. We have worked out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, and the new coupling constants that arise have been constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values for the mass and on-shell width of the a_1(…
We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and annihilation channels are considered including the relevant experiments with lepton-proton scattering.
Based on the S-matrix approach, we introduce a modified formula for the $π^{\pm}$ electromagnetic form factor which describes very well the experimental data in the energy region $2m_π \leq \sqrt{s} \leq 1.1$ GeV. Using the CVC hypothesis we predict $B(\tpp) = (24.75 \pm 0.38)\% $, in excellent agreement with recent experiments.
Process of muon (pion) pair production with small invariant mass in the electron-positron high-energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Dell-Yan picture for differential cross section is valid in the charge-even experimental set-up. Radiative corrections both for electron block and for final state block are taken into account.
The recent measurement of the tau -> Ks pion nu_tau spectrum by the Belle Collaboration provides the frame to set forth a theoretical description of the decay, which is based on the contributing vector F_+(s) and scalar F_0(s) form factors. We show that a good representation of data is obtained through the use of form factors calculated within resonance chiral theory and constrained by dispersion relations and short-distance QCD. Hence we obtain a determination of K*(892) parameters and the low-energy parameterization of F_+(s).
Tau decays into hadrons foresee the study of the hadronization of vector and axial-vector QCD currents, yielding relevant information on the dynamics of the resonances entering into the processes. We analyse tau -> (3 pion) nu_tau decays within the framework of the Resonance Chiral Theory, comparing this theoretical scheme with the experimental data, namely ALEPH spectral function and branching ratio. Hence we get values for the mass and on-shell width of the a_1(1260) resonance, and provide the structure functions that have been measured by OPAL and CLEO-II.
We study the prospects of detecting the signal in the stau neutralino co-annihilation region at the LHC using tau leptons. The co-annihilation signal is characterized by the stau and neutralino mass difference (dM) to be 5-15 GeV to be consistent with the WMAP measurement of the cold dark matter relic density as well as all other experimental bounds within the minimal supergravity model. Focusing on tau's from neutralino_2 --> tau stau --> tau tau neutralino_1 decays in gluino and squark production, we consider inclusive MET+jet+3tau production, with two tau's above a high E_T threshold and a …
The pion multiplicity distribution is widely believed to reflect the statistical aspects of $\bar{p}p$ annihilation at rest. We try to reproduce it in a grand canonical picture with explicit conservation of electric charge, isospin, total angular momentum, and the parity quantum numbers $P$, $C$, and $G$ via the projection operator formalism. Bose statistics is found to be non-negligible, particularly in fixing the interaction volume. The calculated pion multiplicity distribution for $\left\langle n_π \right\rangle = 5$ turns out to depend strongly on the conservation of the angular momentum a…
We show that in a supernova core the annihilation process nu_e nu_e-bar -> nu_{mu,tau} nu_{mu,tau}-bar is always more important than the traditional reaction e^+ e^- -> nu_{mu,tau} nu_{mu,tau}-bar as a source for muon and tau neutrino pairs. We study the impact of the new process by means of a Monte Carlo transport code with a static stellar background model and by means of a self-consistent hydrodynamical simulation with Boltzmann neutrino transport. Nucleon bremsstrahlung NN -> NN nu_{mu,tau} nu_{mu,tau}-bar is also included as another important source term. Taking into account nu_e nu_e-bar…
We evaluate the cross section for anti-p p -> l+ l- pi0 in the forward direction and for large lepton pair invariant mass. In this kinematical region, the leading-twist amplitude factorises into a short-distance matrix element, long-distance dominated antiproton Distribution Amplitudes and proton to pion Transition Distribution Amplitudes (TDA). Using a modelling inspired from the chiral limit for these TDAs, we obtain a first estimate of this cross section, thus demonstrating that this process can be measured at GSI-FAIR.
The process of the muon (pion) pair production with small invariant mass in the electron--positron high--energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Drell--Yan picture for differential cross section is valid in the charge--even experimental set--up. Radiative corrections both for electron block and for final state block are taken into account.
The Monte Carlo event generator PHOKHARA, which simulates hadron and muon production at electron-positron colliders through radiative return, has been extended to final states with three pions. A model for the form factor based on generalized vector dominance has been employed, which is consistent with presently available experimental observations.
Forward-backward (charge) asymmetry in the processes of $e^+e^-$ annihilation into a pair of charged pseudoscalar mesons is recalculated in the one-loop approximation. The exact dependence on the meson masses is taken into account. Results known in the literature are partially corrected. The bulk of the charge asymmetry appears due to double-photon exchange in $s$ channel. Experimental studies of the asymmetry can be used to verify the point-like approximation used in calculation of radiative corrections due to emission of photons by pions or kaons.
Quark model intrinsic wave functions of highly energetic pions in the reaction \bar pp->π^-π^+ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology and the annihilated quark-antiquark pairs are in 3P_0 and 3S_1 states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.
We calculate the processes e+ e- -> 4 pions and tau -> nu_tau + 4 pions to O(p^4) in the low-energy expansion of the standard model. The chiral amplitudes of O(p^4) can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of omega, a_1 and double rho exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios BR(rho -> 4 pions) are in good agreement with available data.
We discuss pion pair production in two-photon collisions in two different kinematical regimes. When both photons are real and at moderately large center-of-mass energy s we elaborate on partonic transverse momentum and Sudakov corrections within the hard scattering approach. We also point out the difference between our approach and that of other authors. When one of the photons is highly virtual the produced pion pair can be described in terms of a two-pion distribution amplitude, for which we derive the perturbative limit at large s.
The photon pair production by pion annihilation in a hot and dense medium at the chiral phase transition is investigated within a chiral quark model. As a direct consequence of this transition the $σ$ meson appears as a bound state in the domain of temperatures and chemical potentials where the condition $M_σ(T,μ) \approx 2 M_π(T,μ)$ is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process $2 π\to 2 γ$ compared with the vacuum case. The calculation of the photon pair production rate as function of the invariant mass shows a strong enhance…
The processes of muons (tau) and charged pions pairs production at electron-positron annihilation with first order radiative corrections are considered. The calculation results are presented assuming the energies of final particles (cms implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation. Some analytical calculations are illustrated numerically. The pions were assumed to be point-like objects and scalar QED was applied for calculation. The QED radiative cor…
A potential way to distinguish tau-neutrinos from antineutrinos, below the tau-production threshold, but above the pion production one, is presented. It is based on the different behavior of the neutral current pion production off the nucleon, depending on whether it is induced by neutrinos or antineutrinos. This procedure for distinguishing tau-neutrinos from antineutrinos neither relies on any nuclear model, nor it is affected by any nuclear effect (distortion of the outgoing nucleon waves, etc...). We show that neutrino-antineutrino asymmetries occur both in the totally integrated cross sec…
We compute branching ratios and invariant mass distributions of the tau decays into four pions. The hadronic matrix elements are obtained by starting from the structure of the hadronic current in chiral limit and then implementing low-lying resonances in the different channels. Reasonable agreement with experiment is obtained both for the $τ\to ν_τ + (4 π) $ decay rates and the $e^+e^- \to (4 π) $ cross sections. Furthermore we supply an interface to use our matrix elements within the Tauola Monte-Carlo program.
Vacuum polarization integrals involve the vector spectral functions which can be experimentally determined from two sources: (i) e+e- annihilation cross sections and (ii) hadronic tau decays. Recently results with comparable precision have become available from CMD-2 on one side, and ALEPH, CLEO and OPAL on the other. The comparison of the respective spectral functions involves a correction from isospin-breaking effects, which is evaluated. After the correction it is found that the dominant pi+pi- spectral functions do not agree within experimental and theoretical uncertainties. Some disagreem…
The main aim of this paper is a new determination of transverse momentum dependence of unpolarized fragmentation function (TMD FFs) in single inclusive hadron production in electron-positron annihilation (SIA) process. Motivated by the need for a reliable and consistent determination of TMD FFs, we use the most recent TMD production cross sections of charged pions ($π^\pm$), kaons ($K^\pm$) and protons/antiprotons ($p/\bar{p}$) measured in inclusive $e^+e^-$ collisions by Belle Collaboration. These datasets are the first transverse momentum dependence of identified light charged hadron measure…
In frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study multi-pion production in antiproton nucleon collisions. The main interest of this reaction is related to the possibility to study the properties of the presumable $\bar N N$ atom and of its resonances. For the case of formation of a scalar or pseudoscalar resonant state, with $I^G(J^{P})=1^-(0^{\pm}),~0^+(0^-)$ numerical results are obtained. The differential cross section in an experimental set-up where the pions invariant mass is measured, is given with explicit dependence on the lepton pair and pions …
Recent experimental data on tau decays are used to reconstruct the difference in hadronic spectral densities with vector and axial-vector quantum numbers. The saturation of Das-Mathur-Okubo and Weinberg sum rules is studied. Two methods of improving convergence and decreasing errors are applied, and good agreement with the predictions of current algebra and chiral perturbation theory is observed. The resulting value of the pion polarisability is (2.64 +/- 0.36) 10^-4 fm^3.
We study inelastic meson-meson scattering that is governed by quark-antiquark annihilation and creation involving a quark and an antiquark annihilating into a gluon, and subsequently the gluon creating another quark-antiquark pair. The resultant hadronic reactions include for I=1: pion + pion to rho + rho, kaon + antikaon to kaon* + antikaon*, kaon + antikaon* to kaon* + antikaon*, kaon* + antikaon to kaon* + antikaon*, as well as pion + pion to kaon + antikaon, pion + rho to kaon + antikaon*, pion + rho to kaon* + antikaon, and kaon + antikaon to rho + rho. In each reaction, one or two Feynma…
Antiproton--proton annihilation into light mesons is revisited in the few GeV energy domain, in view of a global description of the existing data. An effective meson model is developed, with mesonic and baryonic degrees od freedom in $s$, $t$, and $u$ channels. Regge factors are added to reproduce the proper energy behavior and the forward and backward peaked behavior. A comparison with existing data and predictions for angular distributions and energy dependence are done for charged and neutral pion pair production.
We revise the pion-pion and quark-quark annihilation mechanisms of dilepton production during relativistic heavy-ion collisions. We focus on the modifications caused by the specific features of intramedium pion states rather than by medium modification of the rho-meson spectral density. The main ingredient emerging in our approach is a form-factor of the multi-pion (multi-quark) system. Replacing the usual delta-function the form-factor plays the role of distribution which, in some sense, "connects" the 4-momenta of the annihilating and outgoing particles. The difference between the c.m.s. vel…
We study a model-independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to sqrt(s) ~ 1.2 GeV and allows a model-independent determination of the mass of the rho(770) resonance, M(rho) = (775.1 +- 0.5) MeV. We analyse the experimental data on tau(-) -> pion(-) pion(0) neutrino(tau), in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two-pion contribution to the anomalous magnetic moment of the muon, a_muon, an…
We present a geometric interpretation of the so-called annihilation range in reactions of the type $\bar pp \to$ {\em two light mesons} based upon Lorentz effects in the highly relativistic final states ($γ=E_{\mathrm{cm}}/2mc^2\simeq 6.8-8.0$). Lorentz-boosted meson wave functions, within the framework of the constituent quark model, result in a richer angular dependence of the annihilation amplitudes and thus in higher partial wave contributions ($J>1$) than usually obtained. This approach sheds some light on what could be a "{\em short}" annihilation range and how it is influenced by the an…
The two-pion contribution to hadronic vacuum polarization can be extracted from tau decay data when isospin violating and radiative corrections are taken into account. When the dominant corrections are applied to the photon-inclusive decay of the tau into two pions, one obtains a shift (-12.0 +/- 2.6).10^{-10} for the anomalous magnetic moment of the muon. The shift appears to be too small to reconcile the determinations of hadronic vacuum polarization from existing tau and e+ e- data. The reliability of electromagnetic corrections in the photon-inclusive tau decay is examined.
We consider the production of $B^* \bar B^*$ meson pairs in $e^+e^-$ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two $P$-wave with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy $E \approx 15 ÷20$\,MeV above the threshold. We find that the $P-F$ mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy…
We evaluate the model-dependent piece of O(alpha) long-distance radiative corrections to tau^- \to π^- π^0ν_τ decays by using a meson dominance model. We find that these corrections to the di-pion invariant mass spectrum are smaller than in previous calculations based on chiral perturbation theory. The corresponding correction to the photon inclusive rate is tiny (-0.15%) but it can be of relevance when new measurements reach better precision.
We study the effect of rho^0-gamma mixing in e^+e^- to pi^+pi^- and its relevance for the comparison of the square modulus of the pion from-factor |F^(e)_pi|^2, as measured in e^+e^- annihilation experiments, and |F^(tau)_pi|^2 the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the tau-decay spectra. After correcting the tau data for the missing rho-gamma mixing contribution, besides the other known isospin symmetry violating corrections, the pi pi I=1 part of the hadronic vacuum polarization contribution to the muon g-2 are full…
Present experimental datas have shown a 3.8$σ$ level discrepancy with the standard model in $\overline{B}\to D^{(*)}τ\barν_τ$. Some new physics models have been considered to explain this discrepancy possibly with new source of the CP violation. In this paper, we construct CP violating observables by using multi-pion decays in $B\to Dτν_τ$, and estimate sensitivity of these observables to generic CP violating operators. We also discuss possibilities of CP violation in leptoquark models and in 2HDM of type-III.
We study the fluxes of neutrinos from annihilations of dark matter particles in the Sun and the Earth. We give the spectra of all neutrino flavors for the main known annihilation channels: nu-antinu, b-bbar, tau-taubar, c-cbar, light quarks, ZZ, W^+W^-. We present the appropriate formalism for computing the combined effect of oscillations, absorptions, nu_tau-regeneration. Total rates are modified by an O(0.1--10) factor, comparable to astrophysical uncertainties, that instead negligibly affect the spectra. We then calculate different signal topologies in neutrino telescopes: through-going muo…
Tau decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate these processes. Within an effective field theory-like framework, namely Resonance Chiral Theory, we analyse the decays ot the tau into K K pion modes and compare the results with CLEO and BaBar data. In this way, we provide bounds on the couplings entering our Lagrangian and predict the corresponding spectral functions. As a main result -an…
Recent measurement of the $γγ^\ast$ form factor of the neutral pion in the high $Q^2$ region disagrees with {\em a priori} predictions of QCD-based calculations. We comment on existing explanations, and analyze a possibility that this discrepancy is not due to poorly understood QCD effects, but is a result of some new physics beyond the standard model (SM). We show that such physics would necessarily involve a new neutral light state with mass close to the mass of $π^0$, and with stronger than $π^0$ couplings to heavier SM flavors such as $c$, $τ$, and $b$. It is found that only the coupling t…
Bose-Einstein correlations of pairs of identical charged pions produced in hadronic Z decays and in 7 TeV pp minimum bias interactions are investigated within the framework of the tau-model.
We consider the bremsstrahlung and model-dependent contributions to the radiative decay $τ^- \to π^-π^0ν_τγ$ in the context of a meson dominance model. We focus on several observables related to this decay, including the branching ratio and the photon and di-pion spectra. Particular attention is paid to the sensitivity of different observables upon the effects of model-dependent contributions and of the magnetic dipole moment of the $ρ^-(770)$ vector meson. Important numerical differences are found with respect to results obtained in the framework of chiral perturbation theory.
An $ω$-meson in motion with respect to a nuclear medium can couple to a $σ$-meson through a particle-hole excitation. This coupling is large. We investigate its consequences for the width of $ω$-mesons in matter and for the s-wave annihilation of pions into lepton pairs which can take place in relativistic heavy ion collisions. We find that the two pion decay of $ω$-mesons, resulting from the $ω-σ$ transition and the subsequent $2π$ decay of the $σ$-meson, leads to a substantial broadening of $ω$-mesons in matter and possibly to an observable effect in experiments measuring the $e^+e^-$ decay …
We study possible so far unaccounted isospin breaking effects in the relation between the pion form factor as determined in e^+e^- experiments and the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the tau--decay spectra. In fact the observed 10% discrepancy in the respective pion form factors may be explained by the isospin breaking which is due to the difference between masses and widths of the charged and neutral rho mesons. Since the hadronic contribution to the muon anomalous magnetic moment can be calculated directly in ter…
The excitation curve of e+e- annihilation into four charged pions in the rho(770) region is calculated using three existing models with rho mesons and pions in intermediate states supplemented by Feynman diagrams with the a_1(1260)pi intermediate states. A two-term phenomenological Lagrangian of the a_1-rho-pi interaction is used. The mixing angle is determined by fitting the e+e- --> pi+pi-pi+pi- cross section data of the Novosibirsk CMD-2 collaboration and also its combination with the low-energy part of the BaBar collaboration data. It is shown that the inclusion of the a_1-pi intermediate …
