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

Pion–kaon ($$\pi K$$ π K ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $$\pi K$$ π 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 $$\pi K$$ π K scattering in a given partial wave are related to the phases of the respective $$\pi K$$ π K form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar $$\pi K$$ π K form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $$\pi K$$ π K scattering and maintaining the correct analytic structure. As a first application, we consider the decay $${\tau \rightarrow K_S\pi \nu _\tau }$$ τ → K S π ν τ , in particular, we study to which extent the S-wave $$K_0^*(1430)$$ K 0 ∗ ( 1430 ) and the P-wave $$K^*(1410)$$ K ∗ ( 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 $$K_0^*(1430)$$ K 0 ∗ ( 1430 ) and $$K_0^*(1950)$$ K 0 ∗ ( 1950 ) resonances via Padé approximants, $$\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]\,\text {MeV}$$ s K 0 ∗ ( 1430 ) = [ 1408 ( 48 ) - i 180 ( 48 ) ] MeV and $$\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]\,\text {MeV}$$ s K 0 ∗ ( 1950 ) = [ 1863 ( 12 ) - i 136 ( 20 ) ] MeV , as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for $${\tau \rightarrow K_0^*(1430)\nu _\tau }$$ τ → K 0 ∗ ( 1430 ) ν τ in terms of the corresponding residue, leading to the upper limit $${\text {BR}(\tau \rightarrow K_0^*(1430)\nu _\tau )<1.6 \times 10^{-4}}$$ BR ( τ → K 0 ∗ ( 1430 ) ν τ ) < 1.6 × 10 - 4 .

EXTRACTION OF RESONANCE PARAMETERS AND ROLE OF THE FINAL STATE INTERACTIONS

We present an overview of the SAID group effort to analyze new γn → π-p cross sections vs. the world database to get new multipoles and determine neutron electromagnetic couplings. The differential cross section for the processes γn → π-p was extracted from new measurements at CLAS and MAMI-B accounting for Fermi motion effects in the impulse approximation (IA) as well as NN- and πN-FSI effects beyond the IA. We evaluated results of several pion photoproduction analyses and compared πN PWA results as a constraint for analyses of pion photoproduction data (Watson's theorem).

A TRANSFORMATION FORMULA FOR THE KAMPÉ DE FÉRIET FUNCTION

In 1997, Exton have obtained an interesting case of the transformation of Kampé de Fériet function by employing classical Watson’s theorem on the sum of a 3F2 . The aim of this research note is to obtain one result contiguous to that of Exton.

Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem

Some generalizations of Bailey's theorem involving the product of two Kummer functions1F1are obtained by using Watson's theorem and Srivastava's identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric functionsFp(4), Srivastava's triple and quadruple hypergeometric functionsF(3),F(4), Lauricella's quadruple hypergeometric functionFA(4), Exton's multiple hypergeometric functionsXE:G;HA:B;D,K10,K13,X8,(k)H2(n),(k)H4(n), Erdélyi's multiple hypergeometric functionHn,k, Khan and Pathan's triple hypergeometric functionH4(P), Kampé de Fériet's double hypergeometric functionFE:G;HA:B;D, Appell's double hypergeometric function of the second kindF2, and the Srivastava-Daoust functionFD:E(1);E(2);…;E(n)A:B(1);B(2);…;B(n). Some known results of Buschman, Srivastava, and Bailey are obtained.