Pi Gamma Research Articles

Scalar and tensor resonances in J/psi radiative decays

We perform a systematic analysis of the J/psi rightarrow gamma pi ^0pi ^0 and rightarrow gamma K_S^0 K_S^0 partial waves measured by BESIII. We use a large set of amplitude parametrizations to reduce the model bias. We determine the physical properties of seven scalar and tensor resonances in the 1–2.5 , {mathrm {GeV}} mass range. These include the well known f_0(1500) and f_0(1710), that are considered to be the primary glueball candidates. The hierarchy of resonance couplings determined from this analysis favors the latter as the one with the largest glueball component.

Revisiting gamma ^*rightarrow gamma pi ^0eta near the phi (1020) using analyticity and the left-cut structure

Amplitudes of the form gamma ^*(q^2)rightarrow gamma P_1P_2 appear as sub-processes in the computation of the muon g-2. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at q^2=m^2_phi . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of P_1P_2=pi eta , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from gamma gamma scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the I=1 scalar form factors and to the a_0(980) resonance complex pole are presented.

Radiative three-body D-meson decays in and beyond the standard model

We study radiative charm decays D rightarrow P_1 P_2 gamma , P_{1,2}=pi ,K in QCD factorization at leading order and within heavy hadron chiral perturbation theory. Branching ratios including resonance contributions are around sim 10^{-3} for the Cabibbo-favored modes into K pi gamma and sim 10^{-5} for the singly Cabibbo-suppressed modes into pi ^+ pi ^- gamma , K^+ K^- gamma , and thus in reach of the flavor factories BES III and Belle II. Dalitz plots and forward–backward asymmetries reveal significant differences between the two QCD frameworks; such observables are therefore ideally suited for a data-driven identification of relevant decay mechanisms in the standard-model dominated D rightarrow K pi gamma decays. This increases the potential to probe new physics with the D rightarrow pi ^+ pi ^- gamma and D rightarrow K^+ K^- gamma decays, which are sensitive to enhanced dipole operators. CP asymmetries are useful to test the SM and look for new physics in neutral |Delta C|=1 transitions. Cuts in the Dalitz plot enhance the sensitivity to new physics due to the presence of both s- and t, u-channel intermediate resonances.

QCD sum rule studies on the s s {bar{s}} {bar{s}} tetraquark states of J^{PC} = 0^{-+}

We apply the method of QCD sum rules to study the s s {bar{s}} {bar{s}} tetraquark states of J^{PC} = 0^{-+}. We construct all the relevant s s {bar{s}} {bar{s}} tetraquark currents, and find that there are only two independent ones. We use them to further construct two weakly-correlated mixed currents. One of them leads to reliable QCD sum rule results and the mass is extracted to be 2.51^{+0.15}_{-0.12} GeV, suggesting that the X(2370) or the X(2500) can be explained as the ss{bar{s}}{bar{s}} tetraquark state of J^{PC} = 0^{-+}. To verify this interpretation, we propose to further study the pi pi /K {bar{K}} invariant mass spectra of the J/psi rightarrow gamma pi pi eta ^prime /gamma K {bar{K}} eta ^prime decays in BESIII to examine whether there exists the f_0(980) resonance.

The pi eta interaction and a_0 resonances in photon\u2013photon scattering

We revisit the information on the two lightest a_0 resonances and S-wave pi eta scattering that can be extracted from photon–photon scattering experiments. For this purpose we construct a model for the S-wave photon–photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic T-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV. We perform a combined fit of the gamma gamma rightarrow pi eta and gamma gamma rightarrow K_SK_S high statistics experimental data from the Belle collaboration. Minimisation of the chi ^2 is found to have two distinct solutions with approximately equal chi ^2. One of these exhibits a light and narrow excited a_0 resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the J=0 and J=2 resonance effects which is likely to be unphysical. In both solutions the a_0(980) resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be m-ivarGamma /2=1000.7^{+12.9}_{-0.7} -i,36.6^{+12.7}_{-2.6} MeV. The solutions are also compared to experimental data in the kinematical region of the decay eta rightarrow pi ^0gamma gamma . In this region an isospin violating contribution associated with {pi ^+}{pi ^-} rescattering must be added for which we provide a dispersive evaluation.

The photon polarization in radiative D decays, phenomenologically

We work out the phenomenology of untagged time-dependent analysis with radiative D^0-decays into CP eigenstates, which allows to probe the photon polarization by means of the charm mesons’ finite width difference. We show that D^0 rightarrow phi gamma or D^0 rightarrow bar{K}^{0 *} gamma decays, which are SM-dominated, or SM-like, respectively, together with U-spin allow to obtain chirality-predictions for radiative decay amplitudes. The order of magnitude of wrong-chirality contributions in the SM can be cross-checked with an up–down asymmetry in D^0 rightarrow bar{K}_1^0 (rightarrow bar{K} pi pi ) gamma . We explore the sensitivity to new physics in |Delta c|=|Delta u|=1 dipole couplings in the decays D^0 rightarrow rho ^0 gamma . We point out the possibility to test the SM with D_s rightarrow K_1^+( rightarrow K pi pi ) gamma decays.

Angular analysis of B→J/ψK1: Towards a model independent determination of the photon polarization with B→K1γ

We propose a model independent extraction of the hadronic information needed to determine the photon polarization of the b-> s gamma process by the method utilizing the B -> K1 gamma -> K pi pi gamma angular distribution. We show that exactly the same hadronic information can be obtained by using the B -> J/psi K1 -> J/psi K pi pi channel, which leads to a much higher precision.

Form factors of the isovector scalar current and the [Formula: see text] scattering phase shifts.

A model for S-wave eta pi scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the K{bar{K}} channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order p^4 exactly for the eta pi rightarrow eta pi , eta pi rightarrow K{bar{K}} amplitudes and approximately for K{bar{K}}rightarrow K{bar{K}}. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili–Omnès problem, thus allowing one to compute the eta pi and K{bar{K}} form factor matrix elements of the I=1 scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the a_0(980), a_0(1450) resonances, as well as the chiral results of the eta pi and K{bar{K}} scalar radii, which are predicted to be remarkably small at O(p^4). This T-matrix model could be used for a unified treatment of the eta pi final-state interaction problem in processes such as eta 'rightarrow eta pi pi , phi rightarrow eta pi gamma , or the eta pi initial-state interaction in eta rightarrow 3pi .

Dispersive analysis of the pion transition form factor.

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the e^+e^-rightarrow 3pi cross section, generalizing previous studies on omega ,phi rightarrow 3pi decays and gamma pi rightarrow pi pi scattering, and verify our result by comparing to e^+e^-rightarrow pi ^0gamma data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1,text {GeV}, and extract the slope of the form factor at vanishing momentum transfer a_pi =(30.7pm 0.6)times 10^{-3}. We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

VV′Pform factors in resonance chiral theory and theπ−η−η′light-by-light contribution to the muong−2

The description of the VV'P form factors (V,V' stands for vector particles and P for a pseudoscalar meson) for different particles virtualities remains a challenge for the theory of strong interactions. While their chiral limit is well understood, recent measurements of the gamma^* omega pi^0 and gamma^* gamma pi^0 form factors at high photon virtualities seem to depart from the simplest scaling behavior suggested by QCD. Here we attempt to describe them in their whole measured energy regimes within the Resonance Chiral Theory, a framework which naturally incorporates the chiral limit constraints and extends to higher energies by including the resonances as active fields. Specifically, we obtained an accurate description of the data up to 2 GeV on the former form factor by including three multiplets of vector resonances. Good agreement with measurements of the latter was possible even in the single resonance approximation, although we propose to measure the e^+e^- to mu^+mu^-pi^0 cross-section and di-muon invariant mass distribution to better characterize this form factor. We have then evaluated the pion exchange contribution to the muon g-2 obtaining (6.66\pm0.21)x10^{-10} with an accurate determination of the errors. We have also recalled that approximating the whole pion exchange by the pion pole contribution underestimates the corresponding result for the anomaly (by (15,20)%). Based on these results, we have predicted the eta^(\prime) transition form factors obtaining good agreement with data and obtained their respective contributions to the muon anomaly. In this way, the contribution of the three lightest pseudoscalars to it yields (10.47\pm0.54)x10^{-10}, in agreement with previous evaluations but with smaller error.

Study ofe+e−→ωπ0→π0π0γin the energy range 1.05–2.00 GeV with the SND detector

The cross section for the process e+e- --> omega pi0 --> pi0 pi0 gamma has been measured in the energy range 1.05--2.00 GeV. The experiment has been performed at the e+e- collider VEPP-2000 with the SND detector. The measured e+e- --> omega pi0 cross section above 1.4 GeV is the most accurate to date. Below 1.4 GeV our data are in good agreement with the previous SND and CMD-2 measurements. Data on the e+e- --> omega pi0 cross section are well described by the VMD model with two excited rho-like states. From the measured cross section we have extracted the gamma^* --> omega pi0 transition form factor. It has been found that the VDM model cannot describe simultaneously our data and data obtained from the omega --> pi0 mu+ mu- decay. We have also tested CVC hypothesis comparing our results on the e+e- --> omega pi0 cross section with data on the tau- --> omega pi- nu_{tau} decay.

An update of the HLS estimate of the muon g−2

A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to the muon g-2. The latter is dominated by the annihilation channel e+e- -> pi+pi-, for which data are available by scan (CMD-2 and SND) and ISR (KLOE-2008, KLOE-2010 and BaBar) experiments. It is well known that the different data sets are not in satisfactory agreement. In fact it is possible to fix the model parameters without using the pi+pi- data, by using instead the dipion spectra measured in the tau decays together with experimental spectra for the pi0 gamma, eta gamma, pi+pi-pi0, K+K-, K0bar K0 final states supplemented by specific meson decay properties. Among these, the accepted decay width for rho0 -> e+e- and the partial widths and phase information for the omega/phi -> pi+pi- transitions, are considered. It is then shown that, relying on this global data set, the HLS model, appropriately broken, allows to predict accurately the pion form factor up to 1.05 GeV. It is shown that the data samples provided by CMD-2, SND and KLOE-2010 behave consistently with each other and with the other considered data. Consistency problems with the KLOE-2008 and BaBar data samples are substantiated. "All data" global fits are investigated by applying reweighting the conflicting data sets. Constraining to our best fit, the broken HLS model yields a_mu(th) = (11659169.55 [+1.26 -0.59]_phi +[+0.00 -2.00]_tau +/- 5.21_(th))~10**-10 associated with a very good global fit probability. Correspondingly, we find that Delta a_mu=a_mu (exp)- a_mu (th) exhibits a significance ranging between 4.7 and 4.9 sigma.

Extracting the chiral anomaly fromγπ→ππ

We derive dispersive representations for the anomalous process gamma pi --> pi pi with the pi pi P-wave phase shift as input. We investigate how in this framework the chiral anomaly can be extracted from a cross-section measurement using all data up to 1 GeV, and discuss the importance of a precise representation of the gamma pi --> pi pi amplitude for the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.

On the possibility to measure the π 0→γγ decay width and the γ ∗ γ→π 0 transition form factor with the KLOE-2 experiment

A possibility of KLOE-2 experiment to measure the width Gamma(pi0 to gamma gamma) and the (pi0 gamma gamma*) form factor F(Q^2) at low invariant masses of the virtual photon in the space-like region is considered. This measurement is an important test of the strong interaction dynamics at low energies. The feasibility is estimated on the basis of a Monte-Carlo simulation. The expected accuracy for Gamma(pi0 to gamma gamma) is at a per cent level, which is better than the current experimental world average and theory. The form factor will be measured for the first time at Q^2 less or equal 0.1 GeV^2 in the space-like region. The impact of these measurements on the accuracy of the pion-exchange contribution to the hadronic light-by-light scattering part of the anomalous magnetic moment of the muon is also discussed.

Shell-model calculations for p-shell hypernuclei

The interpretation of hypernuclear gamma-ray data for p-shell hypernuclei in terms of shell-model calculations that include the coupling of Lambda- and Sigma-hypernuclear states is briefly reviewed. Next, Lambda 8Li, Lambda 8Be, and Lambda 9Li are considered, both to exhibit features of Lambda-Sigma coupling and as possible source of observed, but unassigned, hypernuclear gamma rays. Then, the feasibility of measuring the ground-state doublet spacing of Lambda 10Be, which, like Lambda 9Li, could be studied via the (K-,pi0 gamma) reaction, is investigated. Structural information relevant to the population of states in these hypernuclei in recent (e,e'K+) studies is also given. Finally, the extension of the shell-model calculations to sd-shell hypernuclei is briefly considered.

Confirmation of theX(1835)and Observation of the ResonancesX(2120)andX(2370)inJ/ψ→γπ+π−η′

With a sample of (225.2\pm2.8)*10^{6} J/psi events registered in the BESIII detector, J/psi->gamma pi^+ pi^- eta' is studied using two eta' decay modes: eta'->pi^+ pi^- eta and eta' -> gamma rho^0. The X(1835), which was previously observed by BESII, is confirmed with a statistical significance that is larger than 20\sigma. In addition, in the pi^+pi^-eta' invariant mass spectrum, the X(2120) and the X(2370), are observed with statistical significances larger than 7.2\sigma and 6.4\sigma, respectively. For the X(1835), the angular distribution of the radiative photon is consistent with expectations for a pseudoscalar.

The ρ → γπ and ω → γπ decays in quark-model approach and estimation of coupling for pion emission by quark

In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($\Gamma^{(exp)}_{\rho^{\pm} \to\gamma\pi^{\pm}}=68\pm 30$ keV, $\Gamma^{(exp)}_{\rho^{0}\to\gamma\pi^0}=77\pm 28$ keV, $\Gamma^{(exp)}_{\omega\to\gamma\pi^0}=776\pm 45$ keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks $g_\pi\equiv g_\pi (u\to d \pi)$. We have found two values for the pion bremsstrahlung coupling: $|g_\pi|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and $|g_\pi|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{\pi NN}^2/(4\pi) \le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{\pi NN}^2/(4\pi)\simeq 14$. For excited states, we have estimated the partial widths in Solution I as follows: $\Gamma (\rho_{2S}^\pm\to \gamma\pi)\simeq 10 - 130$ keV, $\Gamma (\rho_{2S}^0\to \gamma\pi)\simeq 10 -130$ keV, $\Gamma (\omega_{2S}\to \gamma\pi)\simeq 60 - 1080$ keV. The large uncertainties emphasise the necessity to carry out measurements of the meson radiative processes in the region of large masses.

Radiative π0 photoproduction on protons in the Δ+ (1232) region

The reaction gamma p -> p pi0 gamma' has been measured with the Crystal Ball / TAPS detectors using the energy-tagged photon beam at the electron accelerator facility MAMI-B. Energy and angular differential cross sections for the emitted photon gamma' and angular differential cross sections for the pi0 have been determined with high statistics in the energy range of the Delta+(1232) resonance. Cross sections and the ratio of the cross section to the non-radiative process gamma p -> p pi0 are compared to theoretical reaction models, having the anomalous magnetic moment kappa_Delta+ as free parameter. As the shape of the experimental distributions is not reproduced in detail by the model calculations, currently no extraction of kappa_Delta+ is feasible.

Measurement of the η mass at KLOE⋆

An integrated luminosity of 410 pb^(-1), corresponding to ~ 17 million of eta events, has been analyzed to measure the eta mass using the decay eta to gamma gamma. The measurement is insensitive to the calorimeter energy calibration and the systematic error on the measurement is dominated by the uniformity of the detector response. As a cross check of the method the pi0 mass from the decay phi to pi0 gamma, pi0 to gamma gamma has been measured and it is in agreement with the most accurate previous determinations. The result obtained is m(eta) = 547.873 +/- 0.007 (stat.) +/- 0.031 (syst.) MeV, that is today best measurement of the eta mass.

Radiative decays with scalar mesons and in Resonance Chiral Theory

The phi(1020) radiative decays form a good playground for study of the low-lying a0(980) and f0(980) scalar mesons. The complicated interplay of kaon loop mechanism, isoscalar meson mixing and momentum dependence of the effective couplings manifests itself in the invariant mass distributions in the phi(1020) -> pi0 pi0 gamma and pi eta gamma spectra. These distributions are fitted in framework of Resonance Chiral Theory.