MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints

Abstract

We reconsider Muskhelishvili-Omnès (MO) dispersive representations of photon-photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the low-energy $\pi \pi$ scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the left-hand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to $\simeq 1.3$ GeV are included. The tensor contributions to the left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum rule result on the $p^6$ chiral coupling $c_{34}$. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further $p^6$ couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the $f_0(980)$ region is discussed.

arXiv comment44 pages, 12 figures

References in corpus (37)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Roy equation analysis of pi pi scattering
• The Mesonic Chiral Lagrangian of Order $p^6$
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Renormalization of chiral perturbation theory to order p^6
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• Low-Energy Photon-Photon Collisions to Two-Loop Order
• Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• Charged Pion-Pair Production and Pion Polarizabilities to two Loops
• Revisiting γγ->π^+π^- at low energies
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Photon-Photon Scattering, Pion Polarizability and Chiral Symmetry
• High statistics study of f_0(980) resonance in gamma gamma --> pi^+ pi^- production
• Observation of a cusp-like structure in the pizero-pizero invariant mass distribution from K+- ==> pi+- pizero pizero decay and determination of the pi-pi scattering lengths
• Measurement of the pi^+ meson polarizabilities via the gamma p->gamma pi^+ n reaction
• High statistics measurement of the cross sections of gamma gamma -> pi^+ pi^- production
• Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays
• Low-energy photon-photon collisions to two loops revisited
• Investigation of a0-f0 mixing
• Amplitude Analysis of High Statistics Results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and the Two Photon Width of Isoscalar States
• Glueball nature of the sigma/f_0(600) from pi-pi and gamma-gamma scatterings
• Analytic Structure of Amplitudes in Gauge Theories with Confinement
• Improved dispersion relations for γγ\to π^0π^0
• High-statistics study of neutral-pion pair production in two-photon collisions
• Lightest scalar and tensor resonances in $\gamma \gamma \to \pi \pi$ after the Belle experiment
• Determination of ${\pi }^{+}-$ meson polarizabilities from the $\gamma \gamma ->{\pi }^{+}{\pi }^{-}$ process
• Search for the photo-excitation of exotic mesons in the pi+pi+pi- system
• A Dispersive Analysis on the $f_0(600)$ and $f_0(980)$ Resonances in $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ Processes
• The Reaction $\gamma \gamma \to {\pi }^0{\pi }^0$ in Generalized Chiral Perturbation Theory
• Integrating out strange quarks in ChPT: terms at order p^6
• Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory
• Determination of π^0 meson quadrupole polarizabilities from the process γγ-> π^0π^0
• Manifestation of the $a_0^0(980)-f_0(980)$ mixing in the reaction ${\pi }^{-}p\to \eta {\pi }^{0}n$ on a polarized target
• Isospin-Breaking Vector Meson Decay Constants From Continuous Families of Finite Energy Sum Rules
• Quadrupole polarizabilities of the pion in the Nambu--Jona-Lasinio model

Cited by in corpus (74)

• The anomalous magnetic moment of the muon in the Standard Model
• Two-pion contribution to hadronic vacuum polarization
• Three-pion contribution to hadronic vacuum polarization
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Towards a data-driven analysis of hadronic light-by-light scattering
• Dispersive approach to hadronic light-by-light scattering
• B_l4 decays and the extraction of |V_ub|
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Roy-Steiner equations for gamma gamma -> pi pi
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• $\Delta I=1/2$ rule for kaon decays derived from QCD infrared fixed point
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Anomalous decay and scattering processes of the eta meson
• Kaon electromagnetic form factors in dispersion theory
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process
• A dispersive estimate of scalar contributions to hadronic light-by-light scattering
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Asymptotic behavior of meson transition form factors
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• Coupled-channel approach in hadron-hadron scattering
• Virtual photon-photon scattering
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• Extended chiral Khuri-Treiman formalism for $\eta \to 3\pi$ and the role of the $a_0(980)$, $f_0(980)$ resonances
• Hadron Polarizabilities
• 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 $K_0^{\ast }(700)$
• Effects of $Z_b$ states and bottom meson loops on ${\rm Y}(4S)\to {\rm Y}(1S,2S){\pi }^{+}{\pi }^{-}$ transitions
• The nucleon as a test case to calculate vector-isovector form factors at low energies
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• Radiative corrections to the forward-backward asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$
• Final-state interactions in the CP asymmetries of charm-meson two-body decays
• Nature of the $Y(4260)$: A light-quark perspective
• An optimized basis for hadronic light-by-light scattering
• Pion magnetic polarisability using the background field method
• Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
• Theoretical analysis of the $\gamma \gamma \to {\pi }^0\eta$ process
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• How to employ ${\bar{B}}_d^0\to J/\psi (\pi \eta ,\bar{K}K)$ decays to extract information on $\pi \eta$ scattering
• Dispersive analysis of the $\gamma \gamma \to D\bar{D}$ data and the confirmation of the $D\bar{D}$ bound state
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Amplitude analysis of the anomalous decay ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$
• Pion Polarizabilities from $\gamma \gamma \to \pi \pi$ Analysis
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$
• Compton Scattering off Pions and Electromagnetic Polarizabilities
• Isospin-conserving hadronic decay of the $D_{s1}(2460)$ into $D_s{\pi }^{+}{\pi }^{-}$
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Dispersive treatment of $K_S\to \gamma \gamma$ and $K_S\to \gamma {\ell }^{+}{\ell }^{-}$
• Theoretical analysis of the $\gamma {\gamma }^{(\ast )}\to {\pi }^0\eta$ process
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region
• Cross sections for inelastic meson-meson scattering via quark-antiquark annihilation
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Dipole polarizabilities of charged pions
• Polarizabilities from kaon Compton scattering
• Low-energy photon and pion scattering in holographic QCD
• Dispersive analysis of low energy ${\gamma }^{\ast }N\to \pi N$ process
• Deciphering the mechanism of $J/\psi$-nucleon scattering
• Phenomenological model for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction
• Study of the $Y(4660)$ from a light-quark perspective
• Amplitude determination for $MM\to MM$, $M=\pi ,K$ and cross-sections for $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0,{\pi }^0\eta$ in a chiral model
• Coupled-channel analysis of the process $\gamma \gamma \to {\pi }^0{\pi }^0$
• Dispersive Treatments of $K_{\ell 4}$ Decays and Hadronic Light-by-Light Scattering
• $\varphi (2170)$ decaying to $\varphi \pi \pi$ and $\varphi K\bar{K}$
• Dipole Polarizabilities of ${\pi }^{\pm }$-Mesons
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$