Π0 Transition Research Articles

Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

Semileptonic decay of [formula omitted] via neutral meson mixing

Based on the mechanism of neutral meson mixing, we predict the branching fraction of the semileptonic decay of Ds+→π0ℓ+νℓ (ℓ=e, μ) using recently measured branching fraction of Ds+→ηe+νe by BESIII experiment. We also give a formula that can describe the neutral meson mixing of π0, η, η′ and a pseudoscalar gluonium G in a unified way. The predicted branching fraction of Ds+→π0e+νe decay is B(Ds+→π0e+νe)=(2.65±0.38)×10−5. It is important to search for the decay Ds+→π0ℓ+νℓ in experiment, in order to understand the mechanism of π0 production in Ds+→π0 transition in semileptonic decay. We also estimate the branching fraction of Ds+→π0τ+ντ, which is the only kinematically allowed semi-tauonic decay mode of the charmed meson, since the mass value of Ds+ meson is just slightly above the threshold of π0τ+ generation in the semi-tauonic decay.

Pion transition form factor through Dyson-Schwinger equations

In the framework of Dyson-Schwinger equations (DSE), we compute the γ*γ→π0 transition form factor, G(Q2). For the first time, in a continuum approach to quantun chromodynamics (QCD), it was possible to compute G(Q2) on the whole domain of space-like momenta. Our result agrees with CELLO, CLEO and Belle collaborations and, with the well- known asymptotic QCD limit, 2ƒπ. Our analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor.

Results and prospects on hadronic cross section and γγ physics at KLOE/KLOE-2

The KLOE experiment was the first to exploit Initial State Radiation (ISR) processes to obtain the e+e−→π+π−(γ) cross section below 1 GeV. Three measurements have been published with small angle photon in the initial state: normalized using luminosity from Bhabha in 2005 and 2008 and using ππγ/μμγ ratio in 2014. An independent measurement with the large angle photon normalized to Bhabha has been published in 2011. These measurements are in good agreement, showing a good consistency among different analyses. A preliminary Gounaris-Sakurai fit of the pion form factor of the combined KLOE measurements is presented. We also discuss the γγ physics program of KLOE-2 experiment, made possible after the recent KLOE upgrade with new small angle tagging detectors along the DAFNE beam line. These detectors allow to detect the final leptons coming from process e+e−→e+e−γ⁎γ⁎ giving the possibility to measure the π0→γγ decay and γ⁎γ→π0 transition form factor. These measurements provide constraints to the models used to calculate the hadronic light-by-light contribution to the muon anomaly.

DISPERSION THEORY METHODS FOR TRANSITION FORM FACTORS

Dispersion-theoretical analyses of transition form factors are stepping stones to a model-independent determination of the light-by-light scattering contribution to (g - 2)μ. We extend a calculation of the conversion decays of the lightest isoscalar vector mesons, ω/ϕ → π0ℓ+ℓ-, that builds on a previous dispersive analysis of the ω/ϕ → 3π partial-wave amplitudes and the pion vector form factor as its sole ingredients. We construct a good parametrization of e+e- → 3π that, together with information on the anomalous process γπ → ππ, allows us to obtain a description of the π0 transition form factor measured in e+e- → π0γ.

GAMMA GAMMA PHYSICS AT BELLE

We report a high-statistics measurement of the differential cross section of the process [Formula: see text] with the Belle detector. We study spectroscopy of light-quark resonances and charmonia and test QCD models using the data. We summarize our systematic measurements of different processes of γγ → meson-pair production based on the parameterization of the cross sections and comparison with QCD models. We also report on the measurement of the two-photon π0 transition form factor at Belle.

THE ANOMALOUS PROCESS γπ → ππ AND ITS IMPACT ON THE π0 TRANSITION FORM FACTOR

The process γπ → ππ, in the limit of vanishing photon and pion energies, is determined by the chiral anomaly. This reaction can be investigated experimentally using Primakoff reactions, as currently done at COMPASS. We derive a dispersive representation that allows one to extract the chiral anomaly from cross-section measurements up to 1 GeV, where effects of the ρ resonance are included model-independently via the ππ P-wave phase shift. We discuss how this amplitude serves as an important input to a dispersion-theoretical analysis of the π0 transition form factor, which in turn is a vital ingredient to the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.

Measurement of [formula omitted] transition form factor at Belle

We report a measurement of the exclusive π0 production in the process of e+e− scattering in kinematic region where the π0 and the final-state electron or positron are detected (i.e., tagged). We use 759 fb−1 data sample recorded with the Belle detector at the KEKB asymmetric-energy e+e− collider to measure the γγ⁎→π0 transition form factor F(Q2) in the momentum transfer region 4 GeV2⩽Q2⩽40 GeV2. The reported values of Q2|F(Q2)| agree well with previous measurements at Q2⩽9 GeV2, are reasonably consistent with recent results reported by the BaBar experiment but do not support their hypothesis of the rapid increase of Q2|F(Q2)| at higher Q2 values.

BaBar and Belle Measurements of the [formula omitted] Transition Form Factor and Chiral Anomaly

The BaBar measurements of the γγ⁎→π0 transition form factor F(Q2 show that Q2F(Q2) rises steadily with Q2 and at 34 GeV2 is more than 50% above the perturbative QCD(pQCD) prediction. In this talk, I would like to discuss a recent work on the chiral anomaly effects in the γγ⁎→π0 transition form factor F(Q2) at large momentum transfer squared Q2. Using PCAC and the Adler-Bell-Jackiw chiral anomaly triangle graph, we find that, F(Q2) at large Q2 behaves as (m2Q2)×(ln(Q2/m2))2 and is in striking agreement with the BaBar data with m=135MeV which also reproduces very well the CLEO data at lower Q2. The new Belle measurements could also be fitted with m=120MeV.

CHIRAL ANOMALY EFFECTS AND THE BABAR MEASUREMENTS OF THE γγ* → π0 TRANSITION FORM-FACTOR

The recent BaBar measurements of the γγ*→π0 transition form-factor show spectacular deviation from perturbative QCD prediction for large spacelike Q2 up to 34 GeV2. When plotted against Q2, Q2F(Q2) shows steady increase with Q2 in contrast with the flat Q2 behavior predicted by perturbative QCD, and at 34 GeV2 is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes Z0→π0γ, e+e- → π0γ and apply our results to the γ*γ→π0 transition form-factor measured in the e+e- → e+e-π0 process with one highly virtual photon. We find that, the transition form-factor F(Q2) behaves as [Formula: see text] and produces a striking agreement with the BaBar data for Q2F(Q2) with m = 132 MeV which also reproduces very well the CLEO data at lower Q2.

Measurements of the γγ* → π0 and γγ →ηc transition form factors at BABAR

We present measurements of the γγ* → π0 transition form factor for the momentum transfer range Q2 = 4–40 GeV2 and the γγ* → ηc transition form factor for the range Q2 = 2–50 GeV2. The current status of measurements of the meson-photon transition form factors for the η and η′ mesons is discussed. The results of the measurement of the ηc mass, total and two-photon widths are also presented.

γ*ρ0→π0 transition form factor in extended AdS/QCD models

The γ * ρ 0→π 0 transition form factor is extracted from recent result for the γ * γ * π 0 form factor obtained in the extended hard-wall AdS/QCD model with a Chern–Simons term. In the large momentum region, the form factor exhibits a 1/Q 4 behavior, in accordance with the perturbative QCD analysis, and also with the Light-Cone Sum Rule (LCSR) result if the pion wave function exhibits the same endpoint behavior as the asymptotic one. The appearance of this power behavior from the AdS side and the LCSR approach seem to be rather similar: both of them come from the “soft” contributions. Comparing the expressions for the form factor in both sides, one can obtain the duality relation $z\propto \sqrt{u(1-u)}$ , which is compatible with one of the most important relations of the Light-Front holography advocated by Brodsky and de Teramond. In the moderate Q 2 region, the comparison of the numerical results from both approaches also supports a asymptotic-like pion wave function, in accordance with previous studies for the γ * γ * π 0 form factor. The form factor at zero momentum transfer gives the γ * ρ 0 π 0 coupling constant, from which one can determine the partial width for the ρ 0(ω)→π 0 γ decay. We also calculate the form factor in the time-like region, and study the corresponding Dalitz decays ρ 0(ω)→ π 0 e + e −, π 0 μ + μ −. Although all these results are obtained in the chiral limit, numerical calculations with finite quark masses show that the corrections are extremely small. Some of these calculations are repeated in the Hirn–Sanz model and similar results are obtained.

Strong decays Bs0→Bsπ and Bs1→B* sπ with light-cone QCD sum rules

In this article, we calculate the strong coupling constants gBs0Bsη and gBs1B*sη with the light-cone QCD sum rules. Then we take into account the small η–π0 transition matrix according to Dashen’s theorem, and we obtain the small decay widths for the isospin violation processes Bs0→Bsη→Bsπ0 and Bs1→Bs *η→Bs *π0. We can search the strange-bottomed (0+,1+) mesons Bs0 and Bs1 in the invariant Bsπ0 and B* sπ0 mass distributions, respectively.

Finite-Width Correction to FormFactors of γγ*→π0 Transition

Instead of the usual zero-width approximation for one resonance, we usethe finite-width approximation for the two low resonances, i.e. theρ−ω mesons, to investigate the light-conelocal QCD sum rules for the form factor of the transition γγ*→π0. According to the method of theanalytic continuation by duality, the weight function, thepolynomial of a low order N, is added to the dispersion integralto annihilate the integrand in the region where both resonancesaturation and the QCD asymptotic expression are least reliable.The resultant form factor in the cases for the zero- andfinite-widths are almost the same, both agree well with theexperimental measurements. A comparison with the result from theLaplacian transformed light-cone sum rules and a brief discussionare given.

Study of theππmass spectra in the processe+e−→π+π−π0ats≃1020MeV

The invariant mass spectra of the π+π− and π±π0 pairs in the process e+e−→π+π−π0 were studied in the Spherical Neutral Detector experiment at the VEPP-2M collider in the energy region s≃1020 MeV. These studies were based on about 0.5×106 events. The spectra were analyzed in the framework of the vector meson dominance model. It was found that the experimental data can be described assuming the e+e−→ρπ→π+π−π0 transition only. An upper limit on the branching ratio of the φ(1020)→π+π−π0 decay through intermediate states different from ρπ was obtained at the 90% confidence level: B(φ→π+π−π0)<6×10−4. The ρ-meson mass and width which follow from the spectra analysis are mρ=775.0±1.3 MeV, Γρ=150.4±3.0 MeV. The mass difference of the neutral and charged ρ mesons was found to equal mρ±−mρ0=−1.3±2.3 MeV. In the π+π− mass spectrum the ρ−ω interference was seen at a two standard deviation level.Received 13 June 2001DOI:https://doi.org/10.1103/PhysRevD.65.032002©2002 American Physical Society

γ★γ→ π0 transition and asymptotics of γ★γ and γ★γ★ transitions of unflavored pseudoscalar mesons

For the spacelike momenta k of the virtual photon γ ★, the π 0( p) γ ★( k) γ( k ′) transition form factor is considered in the coupled Schwinger–Dyson and Bethe-Salpeter approach in conjunction with the generalized impulse approximation using the dressed quark–photon–quark vertices of the Ball–Chiu and Curtis-Pennington type. These form factors are compared with the ones predicted by the vector meson dominance, operator product expansion, QCD sum rules, and the perturbative QCD for the large spacelike transferred momenta k. The most important qualitative feature of the asymptotic behavior, namely the 1/ k 2 dependence, is in our approach obtained in the model-independent way. Again model-independently, our approach reproduces also the Adler–Bell–Jackiw anomaly result for the limit of both photons being real. For the case of one highly virtual photon, we find in the closed form the asymptotic expression which is then easily generalized both to the case of other unflavored pseudoscalar mesons P 0= π 0, η 8, η 0, η c , η b , and to the case of arbitrary virtuality of the other photon.

QCD sum rule calculation of γγ* → π0 transition form factor

We discuss QCD sum rule analysis of the form factor Fγ * γ * π o ( q 2 , Q 2 ) in the region where virtuality of one of the spacelike photons is small q 2 ≪ 1 GeV 2 while another is large: Q 2 ≳ 1 GeV 2 . Our approach, in contrast to pQCD, does not require explicit assumptions about the shape of the pion distribution amplitude φ π ( X ). The absolute value of the 1/ Q 2 term obtained in this paper favours φ π ( X ) close to the asymptotic form φ π as ( X ) = 6 ƒ π x (1 − x).