A new parametrization for the scalar pion form factors

Abstract

We derive a new parametrization for the scalar pion form factors that allows us to analyze data over a large energy range via the inclusion of resonances, and at the same time to ensure consistency with the high-accuracy dispersive representations available at low energies. As an application the formalism is used to extract resonance properties of excited scalar mesons from data for ${\bar{B}}_s^0\to J/\psi \pi \pi$. In particular we find for the pole positions of $f_0(1500)$ and $f_0(2020)$ $1465\pm 18-i(50\pm 9)\text{MeV}$ and $1910\pm 50-i(199\pm 40)\text{MeV}$, respectively. In addition, from their residues we calculate the respective branching ratios into $\pi \pi$ to be $(58\pm 31)\%$ and $(1.3\pm 1.8)\%$.

arXiv comment18 pages, 11 figures; v2: discussion+figure on pi pi --> K Kbar added, version published in EPJC

References in corpus (42)

• ππscattering
• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Glueball Spectrum and Matrix Elements on Anisotropic Lattices
• Mass and width of the lowest resonance in QCD
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Roy equation analysis of pi pi scattering
• Efficient glueball simulations on anisotropic lattices
• The Status of Glueballs
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Vector meson-vector meson interaction in a hidden gauge unitary approach
• Scalar Quarkonium Masses and Mixing with the Lightest Scalar Glueball
• Decay and Detection of a Light Scalar Boson Mixing with the Higgs
• The ρρinteraction in the hidden gauge formalism and the f_0(1370) and f_2(1270) resonances
• Regge analysis of the pi pi scattering amplitude
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• K-matrix analysis of the (IJ^{PC}=00^{++})-wave in the mass region below 1900 MeV
• A new Parameterization for the Pion Vector Form Factor
• Measurement of resonant and $CP$ components in ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Lepton flavor violation in the Higgs sector and the role of hadronic tau-lepton decays
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Analysis of the resonant components in Bs->J/ψπ+π-
• Flatte-like distributions and the a_0(980)/f_0(980) mesons
• Analysis of the resonant components in B0->J/ψpi+pi-
• Dispersive analysis of the scalar form factor of the nucleon
• Rescattering and chiral dynamics in B\to ρπdecay
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• The $a_0(980)$, $a_0(1450)$ and $K_0^{\ast }(1430)$ Scalar Decay Constants and the Isovector Scalar Spectrum
• Three channel model of meson-meson scattering and scalar meson spectroscopy
• $\pi \pi \to K\bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations
• A chiral covariant approach to $\rho \rho$ scattering
• Precise determination of resonance pole parameters through Padé approximants
• Padé Approximants and Resonance Poles
• Observation of B^0_(s) -> J/ψf_1(1285) decays and measurement of the f_1(1285) mixing angle
• Resonances and $CP$ violation in $B_s^0$ and ${\overline{B}}_s^0\to J/\psi K^{+}{K}^{-}$ decays in the mass region above the $\varphi (1020)$
• Chiral Extrapolations of the $\mathbf{\rho }(770)$ Meson in ${\mathbf{N}}_{\mathbf{f}}=2+1$ Lattice QCD Simulations
• Improving the Hadron Physics of Non-Standard-Model Decays: Example Bounds on R-parity Violation
• Zweig rule violation in the scalar sector and values of low-energy constants
• On the uncertainty estimates of the $\sigma$-pole determination by Padé approximants
• Time-dependent Dalitz-plot formalism for B_q -> J/ψ h+ h-
• How to employ ${\bar{B}}_d^0\to J/\psi (\pi \eta ,\bar{K}K)$ decays to extract information on $\pi \eta$ scattering

Cited by in corpus (54)

• Two-pion contribution to hadronic vacuum polarization
• Three-pion contribution to hadronic vacuum polarization
• 50 Years of Quantum Chromodynamics
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Scalar isoscalar mesons and the scalar glueball from radiative $J/\psi$ decays
• Is the existence of a $J/\psi J/\psi$ bound state plausible?
• Novel approaches in Hadron Spectroscopy
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Enhancement of charm CP violation due to nearby resonances
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Scalar mesons and the fragmented glueball
• Three-body scattering: Ladders and Resonances
• ${\bar{B}}_s\to f_0(980)$ form factors and the width effect from light-cone sum rules
• Nature of the $Y(4260)$: A light-quark perspective
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• What can we learn about light-meson interactions at electron-positron colliders?
• Newly observed $a_0(1817)$ as the scaling point of constructing the scalar meson spectroscopy
• Measurement of the $CP$-violating phase ${\varphi }_s$ from $B_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays in 13 TeV $pp$ collisions
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• On the scalar $\pi K$ form factor beyond the elastic region
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Study for a model-independent pole determination of overlapping resonances
• Phenomenological studies on the $B_{d,s}^0\to J/\psi f_0(500)[f_0(980)]$ decays
• Two-Meson Form Factors in Unitarized Chiral Perturbation Theory
• From pole parameters to line shapes and branching ratios
• Analysis of rescattering effects in $3\pi$ final states
• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• $Z\to {\pi }^{+}{\pi }^{-},K^{+}{K}^{-}$: A touchstone of the PQCD approach
• Decays of a bino-like particle in the low-mass regime
• $\rho \rho$ scattering revisited with coupled-channels of pseudoscalar mesons
• Dispersion relations for $B^{-}\to {\ell }^{-}{\bar{\nu }}_{\ell }{\ell }^{\prime -}{\ell }^{\prime +}$ form factors
• $S$-wave contribution to rare $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decays in the Standard Model and sensitivity to New Physics
• Chromopolarizability of charmonium and $\pi \pi$ final state interaction revisited
• Polarizabilities from kaon Compton scattering
• Uncertainties of hadronic scalar decay calculations
• Amplitude analysis of $B^{+}\to \psi (2S)K^{+}{\pi }^{+}{\pi }^{-}$ decays
• A study on the correlation between poles and cuts in $\pi \pi$ scattering
• A model-independent parameterization of $B\to \pi \pi \ell \nu$ decays
• Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes
• Understanding the Valence Quark Structure of the Pion through GTMDs
• Deciphering the mechanism of $J/\psi$-nucleon scattering
• Study of the $Y(4660)$ from a light-quark perspective
• Likelihood analysis of the newly observed $f_0(2020)$, $f_0(2330)$, and $f_0(2470)$ in $J/\psi \to \gamma {\eta }^{\prime }{\eta }^{\prime }$ as high-lying unflavored scalar mesons
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Observation of the $B_s^0\to {\chi }_{c1}(3872){\pi }^{+}{\pi }^{-}$ decay
• Non-diagonal DVCS and transition GPDs: A unified framework for spinless hadron case ${\gamma }^{\ast }\pi \to \gamma \pi \pi$
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• $\varphi (2170)$ decaying to $\varphi \pi \pi$ and $\varphi K\bar{K}$
• Unified study of $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ and $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ processes
• The Fragmented Glueball: A Personal View
• Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods
• On the scalar $\pi K$ form factor beyond the elastic region
• A note on scalar meson dominance