Long ago an unexpected and unexplainable phenomena was observed. The distribution of muons from positive pion decay at rest was anisotropic with an excess in the backward direction relative to the direction of the proton beam from which the pions were created. Although this effect was observed by several different groups with pions produced by different means, the result was not accepted by the physics community, because it is in direct conflict with a large set of other experiments indicating that the pion is a pseudoscalar particle. It is possible to satisfy both sets of experiments if helicity-zero vector particles exist and the pion is such a particle. Helicity-zero vector particles have direction but no net spin. For the neutral pion to be a vector particle requires an additional modification to conventional theory as discussed herein. An experiment is proposed which can prove that the asymmetry in the distribution of muons from pion decay is a genuine physical effect because the asymmetry can be modified in a controllable manner. A positive result will also prove that the pion is NOT a pseudoscalar particle.
I present a short review of the present status of the Standard Model prediction of the anomalous magnetic moment of the muon, with special emphasis on the hadronic contributions.
Chiral Ward identities lead to consistent accounting for the sigma's width in the linear sigma model's Feynman rules. Reanalysis of pion scattering data at threshold imply a mass for the sigma of 600+ 200 - 100 MeV.
An implicit four dimensional regularization is applied to calculate the axial-vector-vector anomalous amplitude. The present technique always complies with results of Dimensional Regularization and can be easily applied to processes involving odd numbers of $γ_5$ matrices. This is illustrated explicitely in the example of this letter.
The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is reanalyzed in the unitary gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the 't Hooft-Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_μ^2/m_Z^2$. The…
The non-photonic neutrino exchange mechanism of the lepton flavor violating muon-electron conversion in nuclei is revisited. First we determine the nucleon coupling constants for the neutrino exchange mechanism in a relativistic quark model taking into account quark confinement and chiral symmetry requirements. This includes a new, previously overlooked tree-level contribution from neutrino exchange between two quarks in the same nucleon. Then for the case of an additional sterile neutrino we reconsider the coherent mode of this process. The presence of a mixed sterile-active neutrino state he…
We discuss hadronic light-by-light scattering contribution to the muon anomalous magnetic moment a_μ^{\rm lbl}, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that the short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50 per cent increase in the central value of a_μ^{\rm lbl}, compared to existing estimates. The hadronic light-by-light scattering contribution becomes a_μ…
The electromagnetic form factor of the pion is calculated in the "point-form" of relativistic quantum mechanics using simple, phenomenological wave functions. It is found that the squared charge radius of the pion is predicted one order of magnitude larger than the experimental value and the asymptotic behavior expected from QCD cannot be reproduced. The origin of these discrepancies is analyzed. The present results confirm previous ones obtained from a theoretical model and call for major improvements in the implementation of the "point-form" approach.
We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering $μ^- γ\to μ^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. We find that the anomalous magnetic moment $α/2π$ provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon-nucleus bremsstrahlung process (or …
We investigate restrictions on the hadronic contribution to the muon $(g-2)$ factor and to the pion electromagnetic formfactor from the analytical properties of the pion formfactor and the experimental data of the pion formfactor in the space-like [1] region. The values of the pion formfactor of [1] have been improved (see Table 1) and the values of the pion formfactor have been calculated at 20 additional points (see Table 2).
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.
Single pion leptoproduction in the region of the (3,3) resonance is currently of high interest for at least two reasons: (i) These reactions constitute an important part of the total cross section in low energy reactions and are utilized to detect neutrino oscillations in current and future long baseline experiments. (ii) Intranuclear rescattering of the pions in heavy nuclei results in interesting and sizable modifications of the free nucleon cross sections which are testable in electroproduction experiments. In this article we give a basic introduction to the pion multiple scattering model o…
We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was mistaken.
Using constituent quark model constraints we calculate the gluon and sea-quark content of pions solely in terms of their valence density (fixed by πN Drell-Yan data) and the known sea and gluon distributions of the nucleon, using the most recent updated valence-like input parton densities of the nucleon. The resulting small-x dynamical QCD predictions for g^π(x,Q^2) and \bar{q}^π(x,Q^2) are unique and parameter free. Simple analytic parametrizations of the resulting parton distributions of the pion are presented in LO and NLO. These results and parametrizations will be important, among other t…
We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, $a_μ= (g_μ-2)/2$. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain $a_μ^{{\rm LBL},π^0} = +56 \times 10^{-11}$.
We re-evaluate our model predictions in Phys. Rev. D 79, 013002 (2009) for different observables in neutrino induced coherent pion production. This comes as a result of the new improved fit to old bubble chamber data of the dominant axial C_5^A nucleon-to-Delta form factor. We find an increase of 20%-30% in the values for the total cross sections. Uncertainties induced by the errors in the determination of C_5^A are computed. Our new results turn out to be compatible within about $1σ$ with the former ones. We also stress the existing tension between the recent experimental determination of the…
In models where the breaking of lepton number is spontaneous a massless Goldstone boson, the Majoron ($J$), appears. We calculate the theoretically allowed range for the branching ratios of Majoron emitting charged lepton decays, such as Br($μ\to e J$) and Br($μ\to e J γ$), in a supersymmetric model with spontaneous breaking of R-parity. Br($μ\to eJ$) is maximal in the same region of parameter space for which the lightest neutralino decays mainly invisibly. A measurement of Br($μ\to eJ$) thus potentially provides information on R-parity violation complementary to accelerator searches. We also …
We make use of recent accurate results obtained for the pion and kaon vector form factors within a chiral unitary approach in order to calculate the decay widths of the $τ$ lepton to these mesons and also to evaluate the contribution of this two mesons to the anomalous magnetic moment of the muon, the running of the fine structure constant and the muonium hyperfine splitting.
Two-pion transitions in charmonium and bottomonium are considered with the leading relativistic effects taken into account. The contribution of the chromo- magnetic interaction of the charmed quarks to the amplitude of the decay $ψ(2S) \to ππJ/ψ$ is estimated from the available data. This contribution is enhanced by a factor of three in the decay $η_c(2S) \to ππη_c$ and should produce a noticeable modification of the rate and the spectrum in the latter decay. It is argued that the peculiar observed spectrum in the decay $Υ(3S) \to ππΥ$ arises due to a dynamical suppression of the leading nonre…
We analyze new QCD sum rules for the pion wave function $ϕ_π(x)$, obtained recently by A.V. Radyushkin in the framework of the non-local vacuum condensates method for non-diagonal correlators, and suggest a new approach for extracting wave functions of the $π$-meson and of its first resonances. As a result we obtain approximately the same form of the pion wave function by using two different methods and for two different ansatzes of non-local quark condensates. We predict the mass of the $π'$-resonance and obtain the form of its wave function. The first method uses integrated (in a sense) prop…
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.
We revisit the procedure for comparing the pi pi spectral function measured in tau decays to that obtained in e+e- annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the tau- --> pi- pi0 nu_tau branching fraction measurement and its prediction using the isospin-breaking-corrected e+e- --> pi+pi- spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g-2 using e+e- and tau data with the new corrections, and find a reduced difference bet…
The mass structure of hadron multiplets is understood to imply the inexactness of SU(3) symmetry. Here we show that these symmetry broken mass splittings amongst baryon and meson multiplet members are close integral multiples of the mass difference between a neutral pion and a muon, the first excitation within the elementary particle mass spectrum. This is found to be equally true for the mass intervals amongst the particles belonging to the multiplets having different spin and parity characteristics. The results reinforce our earlier contention that the mass difference between a neutral pion …
We present predictions for the flux averaged muon energy spectra of quasi-elastic (QE) and 1-pion production events for the K2K long-baseline experiment. Using the general kinematical considerations we show that the muon energy spectra closely follow the neutrino energy spectrum with downward shift of the energy scale by 0.15 GeV (QE) and 0.4 GeV (1-pion production). These predictions seem to agree with the observed muon energy spectra in the K2K nearby detector. We also show the spectral distortion of these muon energy spectra due to the neutrino oscillation for the SK detector. Comparison of…
A direct connection can be made between mixing angles in negative parity baryons and the spin coupling of constituent quarks. The mixing angles do not depend on spectral data. These angles are recalculated for gluon exchange and pion exchange between quarks. For pion exchange the results of Glozman and Riska are corrected. The experimental data on mixing are very similar to those derived from gluon exchange but substantially different from the values obtained for pion exchange.
We calculate the pion pole term of the light-by-light contribution to the $g-2$ of the muon in the framework of an effective chiral quark model with instanton-like nonlocal quark--quark interaction. The full kinematic dependence of the pion-photon transition form factors is taken into account. The dependence of form factors on the pion virtuality decreases the result by about 15% in comparison to the calculation where this dependence is neglected. Further, it is demonstrated that the QCD constraints suggested by Melnikov and Vainshtein are satisfied within the model. The corresponding contribu…
The production of positive pions and neutrons by cosmic muons at underground sites of various depths is investigated. We first test the equivalent photon method in the particular case of $Δ$ excitation by the muon. We find that this method, when it neglects the momentum dependence of the transverse response, reproduces remarkably well the theoretical muon cross-section. This success has lead us to apply the method to higher energies, where it has not been tested. We evaluate in this way the production of positive pions in liquid scintillator from known photo-absorption cross-sections. At a sha…
This thesis investigates the Hadronic Light by Light (HLL) scattering contribution to the muon $g-2$, which is one of the most important low energy hadronic effects and consists mainly of the quark loop, the pion pole and the charged pion and kaon loops. In this work the charged pion loop has been investigated more closely. After reviewing the subject a preliminary introduction to Chiral Perturbation Theory (ChPT), Hidden Local Symmetry (HLS) model and the full Vector Meson Dominance (VMD) model is given, and they are used to calculate the pion loop HLL scattering contribution to the muon anom…
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.
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…
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.
After a decade of no measurements of pion and muon rare decays, PIBETA, a new experimental program is producing its first results. We report on a new experimental study of the pion beta decay, Pi(+) -> Pi(0) e(+) Nu, the Pi(e2 gamma) radiative decay, Pi(+) -> e(+) Nu Gamma, and muon radiative decay, Mu -> e Nu Gamma. The new results represent four- to six-fold improvements in precision over the previous measurements. Excellent agreement with Standard Model predictions is observed in all channels except for one kinematic region of the Pi(e2 gamma) radiative decay involving energetic photons and…
The largest error in the theoretical determination of the muon anomalous magnetic moment is due to the low-energy hadronic vacuum polarization, which cannot be calculated by perturbative QCD and requires nonperturbative techniques. Recently, an accurate determination of the low-energy two-pion contribution to muon $g-2$ has been obtained by a parametrization-free analytic continuation of the pion vector form factor from other kinematical regions. In this work we compare the results of the analytic continuation with direct determinations at low momenta from experiment and lattice QCD. We also e…
The muon energy spectra of the quasi-elastic and 1-pion production events in a LBL experiment, like K2K, are predicted to follow closely the neutrino energy spectrum, with downward shifts of the energy scale by $<Q^2>/2 M$ and $(<Q^2> + M_Δ^2 - M^2)/2 M$ respectively. These predictions seem to agree with the observed muon spectra in the K2K nearby detector. The corresponding muon spectra in the far-away (SK) detector are predicted to show characteristic spectral distortions induced by $ν_μ$ oscillation. Comparison of the predicted spectral distortions with the observed muon spectra of the 1-Ri…
At temperatures less than a few MeV, the efficiency of the neutrino-pair bremsstrahlung from nucleons interracting with the condensed pion field is much less than previously estimated by other authors. The physical reason for this is a periodic structure of the developed pion condensate. The repeated interactions of a nucleon with the periodic pion field modify the nucleon spectrum, which is split into two bands. The energy gap between the bands is about a few MeV or larger, even if the amplitude of the pion field is small compared with the pion mass.
The pion form factor calculation in the ``point-form'' of relativistic quantum mechanics is re-considered. Particular attention is given to the relation between the momentum of the system and the momentum transfer as well as to the quark current.
This paper contains some new results on the hadronic light-by-light contribution (HLbL) to the muon $g-2$. The first part argues that we can expect large effects from disconnected diagrams in present and future calculations by lattice QCD of HLbL. The argument is based on the dominance of pseudo-scalar meson exchange. In the second part, we revisit the pion loop HLbL contribution to the muon anomalous magnetic moment. We study it in the framework of some models studied earlier, pure pion loop, full VMD and hidden local symmetry for inclusion of vector mesons. In addition we study possible ways…
Predictions are presented for the oscillation phase in neutrino oscillations following pion decay at rest and in flight, muon decay and nuclear $β-$decay at rest as well as for muon oscillations following pion decay at rest and in flight. The neutrino oscillation phases found disagree with the conventionally used value: $ϕ_{12} = Δm^2 L/(2P)$. The same oscillation phase is found for neutrino and muon oscillations following pion decay at rest. Shortcomings of previous treatments of the quantum mechanics of neutrino oscillations are commented on.
We reanalyze the anomalous angular distribution of lepton pairs produced in a pion-induced Drell-Yan process by taking into account the Glauber gluon effect in the $k_T$ factorization theorem. Compared to the previous study, we adopt the realistic parton distribution functions (PDFs) for a proton from the CTEQ and for a pion from the xFitter, include the QCD evolutions of the strong coupling and the PDFs, and integrate the differential cross section over the kinematic regions for the NA10, E615 and COMPASS experiments. These improvements then allow rigorous confrontations of theoretical result…
The signals of the neutral top-pion $π^{0}_{t}$ at the first muon collider (FMC) are discussed by calculating its contributions to the processes $μ^{+}μ^{-}\longrightarrow b\bar{b}$ and $μ^{+}μ^{-}\longrightarrow \bar{t}c$. We find that the contributions to the process $μ^{+}μ^{-}\longrightarrow b\bar{b}$ are very small and the ratio of signal over square root of the background ($S/\sqrt{B})$ is smaller than 0.2. However, in most of the parameter space, the $π^{0}_{t}$ can generate 36 and up to 649 observable $\bar{t}c$ events at the FMC. The signals of the neutral top-pion $π^{0}_{t}$ may be …
For any inelastic process $v_{\ell} + I \to \ell^- + F$ with $m_{\ell} = 0$, the cross section at $θ_{\ell} = 0$ is given by Adler's PCAC theorem. Inclusion of the lepton mass has a dynamical effect (``PCAC-screening'') caused by interference of spin-zero ($π^+$) and spin-one exchanges. This effect may be relevant to the forward suppression reported in recent experiments.
We develop a theory of the EPR-like effects due to neutrino oscillations in the $π\to μν$ decays. Its experimental implications are space-time correlations of neutrino and muon when they are both detected, while the pion decay point is not fixed. However, the more radical possibility of muon oscillations in experiments where only muons are detected (as it has been suggested in hep-ph/9509261), is ruled out. We start by discussing decays of monochromatic pions, and point out a few ``paradoxes''. Then we consider pion wave packets, solve the ``paradoxes'', and show that the formulas for $μnu$ co…
We calculate isospin breaking in pion-nucleon scattering in the threshold region in the framework of covariant baryon chiral perturbation theory. All effects due to quark mass differences as well as real and virtual photons are consistently included. As an application, we discuss the energy dependence of the triangle relation that connects elastic scattering on the proton pi+- p --> pi+- p with the charge exchange reaction pi- p --> pi0 n.
We re-examine one-pion exchange as a possible binding mechanism in the X(3872) charmonium-like state and argue it to be not sufficiently binding for this purpose. We conclude therefore that other short-range dynamics are responsible for the X formation.
The most fundamental to the elementary particles is the mass they posses and it would be of importance to explore a possible relationship amongst their masses. Here, an attempt is made to investigate this important aspect irrespective of their nature or scheme of classification. We show that there exists a striking tendency for successive mass differences between elementary particles to be close integral/half integral multiple of the mass difference between a neutral pion and a muon. Thus indicating discreteness in the nature of the mass occurring at elementary particle level. Further, this ma…
We revisit the evaluations for the spacelike and timelike $ρπ$ transition form factors $F_{ρπ}(Q^2)$ and $G_{ρπ}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form fact…
Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which …
We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude $E_{0+}$ to three orders in $μ$, the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low--energy theorems in the P--waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multip…
We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_μwhich relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_μ(LbyL;π^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for t…
The Higgs boson of 125 GeV requires large stop masses, leading to the large $μ$-parameter in most cases of gauge mediation. On the other hand, the explanation for the muon $g-2$ anomaly needs small slepton and neutralino/chargino masses. Such disparity in masses may be obtained from a mass splitting of colored and non-colored messenger fields. However, even if the required small slepton and neutralino/chargino masses are realized, all parameter regions consistent with the muon g-2 are excluded by the recent updated ATLAS result on the wino search in the case that the messenger fields are in ${…
We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form …
We revisit the process of inverse neutrino-less double beta decay (e e -> W W) at future linear colliders. The cases of Majorana neutrino and Higgs triplet exchange are considered. We also discuss the processes e mu -> W W and mu mu -> W W, which are motivated by the possibility of muon colliders. For heavy neutrino exchange and center-of-mass energies larger than 1 TeV, we show that masses up to 10^6 (10^5) GeV could be probed for e-e and e-mu machines, respectively. The stringent limits for mixing of heavy neutrinos with muons render mu mu -> W W less promising, even though this process is n…
We consider the production of muon pairs from the scattering of pions on longitudinally polarized protons. We calculate the cross section and the single spin asymmetry for this process, taking into account pion bound state effects. We work in the kinematic region where the photon has a large longitudinal momentum fraction, which allows us to treat the bound state problem perturbatively. Our predictions are directly proportional to the pion distribution amplitude. A measurement of the polarized Drell-Yan cross section thus allows the determination of the shape of the pion distribution amplitude…
We discuss the decay tau^- -> nu_tau pi^- pi^0 gamma in terms of a model with the correct low-energy structure and with the relevant resonance degress of freedom. The nontrivial radiative dynamics becomes visible for large photon momenta only. We use the model to calculate electromagnetic corrections for the two-pion contribution to hadronic vacuum polarization extracted from photon-inclusive two-pion decays. The corrections are insensitive to the details of the model and depend on the pion form factor only. Putting all relevant isospin violating corrections together, we obtain a shift Delta a…
Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Beihang University（北京航空航天大学）；Universität Bonn（波恩大学）；Forschungszentrum Jülich（于利希研究中心）；Tbilisi State University（第比利斯国立大学）
In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before. We make use of the chiral Lagrangian at order p^6 now available, and of improved techniques to evaluate the two-loop diagrams. Here, we present the result for the neutral pions. The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent. We present analytic results for the dipole and quadrupol…
We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the $X(3872)$. We confirm that, if the $X(3872)$ were a $D\bar{D}^*$ molecular state with the quantum numbers $J^{PC}=1^{++}$, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the $X(3872)$, with the quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$ in line with previous results reported in the literature. We demonstrate that this result is robust with respect to the inclusion of the one-pion exchange interaction between the $D$ mesons. However, thi…
In the present work, we investigate several theoretical models of the pion vector form factor and aim at getting the best fit for the two-pion cross sections to reduce the uncertainties of the calculation of two-pion contribution to the muon anomalous magnetic moment. Combined with a polynomial description to the pion vector form factor, we obtain the best fit from the Gounaris-Sakurai (or Kühn-Santamaria) model for the experimental data up to 1 GeV. By product, the branching ratio of $ω\to ππ$ can be extracted as $\text{Br}(ω\toππ)=(1.52\pm 0.06) \%$, which is consistent with the one of Parti…
