Analyses of pion-nucleon elastic scattering amplitudes up to O(p4)O(p^4) in extended-on-mass-shell subtraction scheme

We extend the analysis of elastic pion-nucleon scattering up to $O(p^4)$ level using extended-on-mass-shell subtraction scheme within the framework of covariant baryon chiral perturbation theory. Numerical fits to partial wave phase shift data up to $\sqrt{s}=1.13$ GeV are performed to pin down the free low energy constants. A good description to the existing phase shift data is achieved. We find a good convergence for the chiral series at $O(p^4)$, considerably improved with respect to the $O(p^3)$-level analyses found in previous literature. Also, the leading order contribution from explicit $\Delta(1232)$ resonance and partially-included $\Delta(1232)$ loop contribution are included to describe phase shift data up to $\sqrt{s}=1.20$ GeV. As phenomenological applications, we investigate chiral correction to the Goldberger-Treiman relation %$\Delta_{GT}$ and find that it converges rapidly, and the $O(p^3)$ correction is found to be very small: $\simeq 0.2$. We also get a reasonable prediction of pion-nucleon sigma term $\sigma_{\pi N}$ up to $O(p^4)$ by performing fits including both the pion-nucleon partial wave phase shift data and the lattice QCD data. We report that $\sigma_{\pi N}=52\pm7$ MeV from the fit without $\Delta(1232)$, and $\sigma_{\pi N}=45\pm6$ MeV from the fit with explicit $\Delta(1232)$.Comment: The final version published in Phys.Rev. D 87, 054019 (2013

Chromopolarizability of charmonium and ππ\pi\pi final state interaction revisited

The chromopolarizability of a quarknonium describes the quarknonium's interaction with soft gluonic fields and can be measured in the heavy quarkonium decays. Within the framework of dispersion theory which consider the $\pi\pi$ final state interaction (FSI) model-independently, we analyze the transition $\psi^\prime\to J/\psi\pi^+\pi^-$ and obtain the chromopolarizability $\alpha_{\psi^\prime \psi}$ and the parameter $\kappa$. It is found that the $\pi\pi$ FSI plays an important role in extracting the chromopolarizability from the experimental data. The obtained chromopolarizability with the FSI is reduced to about 1/2 of that without the FSI. With the FSI, we determine the chromopolarizability $|\alpha_{\psi^\prime\psi}|=(1.44\pm 0.02)$ GeV$^{-3}$ and the parameter $\kappa=0.139\pm 0.005.$ Our results could be useful in studying the interactions of charmonium with light hadrons.Comment: 8 pages, 1 figur

On improvement of a Hilbert-type inequality

AbstractIn this paper, by using the Euler–Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive an improvement of a Hilbert-type inequality proved by B.C. Yang