We extend the analysis of elastic pion-nucleon scattering up to $O({p}^{4})$ level using the 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 $\sqrt{s}=1.13\text{ }\text{ }\mathrm{GeV}$ are performed to pin down the free low energy constants. A good description of 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 the phase shift data up to $\sqrt{s}=1.20\text{ }\text{ }\mathrm{GeV}$. As phenomenological applications, we investigate chiral corrections to the Goldberger-Treiman relation and find that it converges rapidly, and the $O({p}^{3})$ correction is found to be very small: $$\simeq${}0.2%$. We also get a reasonable prediction of the pion-nucleon sigma term ${$\sigma${}}_{$\pi${}N}$ up to $O({p}^{4})$ by performing fits including both the pion-nucleon partial wave phase shift data and the lattice QCD data. We report that ${$\sigma${}}_{$\pi${}N}=52\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{MeV}$ from the fit without $$\Delta${}(1232)$, and ${$\sigma${}}_{$\pi${}N}=45\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{MeV}$ from the fit with explicit $$\Delta${}(1232)$.

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

Since 2003 many new hadrons, including the lowest-lying positive-parity charm-strange mesons $D_{s0}^{*}(2317)$ and $D_{s1}(2460)$, have been observed that do not conform with quark-model expectations. It was recently demonstrated that various puzzles in the charm-meson spectrum find a natural resolution if the SU(3) multiplets for the lightest scalar and axial-vector states, among them the $D_{s0}^{*}(2317)$ and the $D_{s1}(2460)$, owe their existence to the nonperturbative dynamics of Goldstone-boson scattering off $D_{(s)}$ and $D_{(s)}^{*}$ mesons. Most importantly the ordering of the lightest strange and nonstrange scalars becomes natural. We demonstrate for the first time that this mechanism is strongly supported by the recent high quality data on the $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ provided by the LHCb experiment. This implies that the lowest quark-model positive-parity charm mesons, together with their bottom counterparts, if realized in nature, do not form the ground-state multiplet. This is similar to the pattern that has been established for the scalar mesons made from light up, down, and strange quarks, where the lowest multiplet is considered to be made of states not described by the quark model. In a broader view, the hadron spectrum must be viewed as more than a collection of quark-model states.

Through the scattering of light-pseudoscalar mesons $(\pi ,K,\eta ,{\eta }^{\prime })$ off charmed mesons $(D,D_s)$, we study the $D_{s0}^{*}(2317)$ state and other relevant charm scalar mesons in a unitarized chiral effective field theory approach. We investigate the charm scalar meson poles with different strangeness ($S$) and isospin ($I$) quantum numbers as well as their corresponding residues, which provide the coupling strengths of the charm scalar mesons. Both the light-quark mass and $N_C$ dependences of the pole positions of the $D_{s0}^{*}(2317)$ and the poles with $(S,I)=(0,1/2)$ are analyzed in detail in this work. Interestingly we observe quite similar pion mass trajectories for the resonance pole at around 2.1 GeV with $(S,I)=(0,1/2)$ to those of the $f_0(500)$ given in the literature. When increasing the values of $N_C$ we find that a bound state and a virtual state in the $(S,I)=(1,0)$ channel asymmetrically approach the $DK$ threshold for $N_C<6$, and they meet at this threshold at $N_C=6$. When $N_C>6$, the bound and virtual states move into the complex plane on the second Riemann sheet and become a symmetric pair of resonance poles. For large enough values of $N_C$, neither the $D_{s0}^{*}(2317)$ pole nor the poles with $(S,I)=(0,1/2)$ tend to fall down to the real axis, indicating that they do not behave like a standard quark-antiquark meson at large $N_C$.

We derive the scattering amplitude for Goldstone bosons of chiral symmetry off the pseudoscalar charmed mesons up to leading one-loop order in a covariant chiral effective field theory, using the so-called extended-on-mass-shell renormalization scheme. Then we use unitarized chiral perturbation theory to fit to the available lattice data of the S-wave scattering lengths. The lattice data are well described. However, most of the low-energy constants determined from the fit bear large uncertainties. Lattice simulations in more channels are necessary to pin down these values which can then be used to make predictions in other processes related by chiral and heavy quark symmetries.

Partial wave analysis is performed, with effective potentials as dynamical inputs, to scrutinize the recent LHCb data on the di-$J/\psi$ invariant mass spectrum. Coupled-channel effects are incorporated in the production amplitude via final state interactions. The LHCb data can be well described. A dynamically generated pole structure, which can be identified as the $X(6900)$ state, is found. Our analysis also provides hints for the existence of three other possible states: a bound state $X(6200)$, a broad resonant state $X(6680)$ and a narrow resonant state $X(7200)$. The $J^{PC}$ quantum numbers of the $X(6680)$ and $X(6900)$ states should be $2^{++}$, while the $X(6200)$ and $X(7200)$ states prefer $0^{++}$. To determine the above states more precisely, more experimental data for the channels, such as $J/\psi \psi (2S)$, $J/\psi \psi (3770)$, di-$\psi (2S)$, are required.