On the scalar $\pi K$ form factor beyond the elastic region

Abstract

Pion-kaon ($\pi K$) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $\pi K$ scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of $\pi K$ scattering in a given partial wave are related to the phases of the respective $\pi K$ form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar $\pi K$ form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $\pi K$ scattering and maintaining the correct analytic structure. As a first application, we consider the decay $\tau \to K_S\pi {\nu }_{\tau }$, in particular, we study to which extent the $S$-wave $K_0^{\ast }(1430)$ and the $P$-wave $K^{\ast }(1410)$ resonances can be differentiated and provide an improved estimate of the $CP$ asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ resonances via Padé approximants, $\sqrt{s_{K_0^{\ast }(1430)}}=[1408(48)-i180(48)]$ MeV and $\sqrt{s_{K_0^{\ast }(1950)}}=[1863(12)-i136(20)]$ MeV, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for $\tau \to K_0^{\ast }(1430){\nu }_{\tau }$ in terms of the corresponding residue, leading to the upper limit $\text{BR}(\tau \to K_0^{\ast }(1430){\nu }_{\tau })<1.6\times 10^{-4}$.

arXiv comment18 pages, 12 figures; journal version

References in corpus (61)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• FLAG Review 2019
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Flavor Physics in the Quark Sector
• Roy-Steiner-equation analysis of pion-nucleon scattering
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• S-wave Kpi scattering in chiral perturbation theory with resonances
• Strangeness-changing scalar form factors
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Roy-Steiner equations for gamma gamma -> pi pi
• 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
• Detailed Report of the MuLan Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant
• Extracting the chiral anomaly from gamma pi --> pi pi
• K-matrix analysis of the K-pi S-wave in the mass region 900-2100 Mev and nonet classification of scalar qqbar-states
• The $\kappa$ resonance in s wave $\pi K$ scatterings
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Roy-Steiner equations for pion-nucleon scattering
• Anomalous decay and scattering processes of the eta meson
• CP Violation in τ->νπK_S and D->πK_S: The Importance of K_S-K_L Interference
• Final State Interactions in Hadronic D decays
• Dispersive analysis of the scalar form factor of the nucleon
• Dispersive representation and shape of the Kl3 form factors: robustness
• K^L_{mu3} decay: A Stringent Test of Right-Handed Quark Currents
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays
• $\pi K$ Scattering in Three Flavour ChPT
• A new parametrization for the scalar pion form factors
• What can be learned from the Belle spectrum for the decay tau- -> nu_tau K_S pi-
• Matrix elements of the electromagnetic operator between kaon and pion states
• Analyticity constraints on the strangeness changing vector current and applications to $\tau \to K\pi {\nu }_{\tau }$, $\tau \to K\pi \pi {\nu }_{\tau }$
• K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays
• An improved study of the kappa resonance and the non-exotic $s$ wave $\pi K$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The $a_0(980)$, $a_0(1450)$ and $K_0^{\ast }(1430)$ Scalar Decay Constants and the Isovector Scalar Spectrum
• $\pi \pi \to K\bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations
• Dispersion-theoretical analysis of the D^+ --> K^- pi^+ pi^+ Dalitz plot
• The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
• A no-go theorem for non-standard explanations of the $\tau \to K_S\pi {\nu }_{\tau }$ CP asymmetry
• The kappa in E791 data for D->K-pi-pi
• Strange resonance poles from $K\pi$ scattering below 1.8 GeV
• Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes in terms of analytic and unitary meson-meson form factors
• Precise determination of resonance pole parameters through Padé approximants
• The Kl3 scalar form factors in the standard model
• Padé Approximants and Resonance Poles
• Predicting the tau strange branching ratios and implications for V_{us}
• A Dispersive Treatment of $K_{\ell 4}$ Decays
• Consistent Dalitz plot analysis of Cabibbo-favored $D^{+}\to \bar{K}\pi {\pi }^{+}$ decays
• Novel patterns for vector mesons from the large-Nc limit
• Analysis Tools for Next-Generation Hadron Spectroscopy Experiments
• Effective-field theory analysis of the ${\tau }^{-}\to (K\pi {)}^{-}{\nu }_{\tau }$ decays
• Determination of the lightest strange resonance $K_0^{\ast }(700)$ or $\kappa$, from a dispersive data analysis
• $\tau \to \pi K\nu$ Decay and $\pi K$ Scattering
• An update on the Kappa
• Kpi form factors and final state interactions in D+ --> K- pi+ pi+ decays
• CP asymmetry in $\tau \to K_S\pi {\nu }_{\tau }$ decays within the Standard Model and beyond
• Can the observed CP asymmetry in tau --> K pi nu_tau be due to Non-Standard Tensor interactions?
• Dispersive representation of the scalar and vector Kpi form factors for tau --> K pi nu_tau and K_{l3} decays
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$

Cited by in corpus (14)

• Novel approaches in Hadron Spectroscopy
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Nucleon resonance parameters from Roy-Steiner equations
• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• $CP$ asymmetry in the angular distributions of $\tau \to K_S\pi {\nu }_{\tau }$ decays -- II: general effective field theory analysis
• Light-Cone Sum Rules for $S$-wave $B\to K\pi$ Form Factors
• From pole parameters to line shapes and branching ratios
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• Decays of a bino-like particle in the low-mass regime
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• $\tau$ lepton decays with production of strange scalar mesons $K_0^{\ast }(700)$ and $K_0^{\ast }(1430)$ in the extended NJL model
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• On the scalar $\pi K$ form factor beyond the elastic region
• Amplitude analysis of $\psi (3686)\to \gamma K_S^0{K}_S^0$