Search

We perform a rigorous analysis of the $\pi K$ scattering at an unphysical pion mass $391~$MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the $\pi K$ lattice data in the inelastic region, the lattice data from the crossed $\pi\pi \to K\bar{K}$ channels, the masses of $f_0(500)$ and $K^*$ at the same pion mass from previous study, and the Regge model. Predictions on the elastic $\pi K$ scattering phase shifts and the $K_0^*(700)$ pole content are made. Contrary to the virtual pole scenario obtained using the $K$-matrix method in the literature, we find that lightest strange scalar meson $K_0^*(700)$ remains a broad resonance at $M_\pi=391~$MeV. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position., Comment: 6 pages, 3 figures

Being closely connected to the origin of the nucleon mass, the gravitational form factors of the nucleon have attracted significant attention in recent years. We present the first model-independent precise determinations of the gravitational form factors of the pion and nucleon at the physical pion mass, using a data-driven dispersive approach. The so-called ``last unknown global property'' of the nucleon, the $D$-term, is determined to be $-\left(3.38^{+0.26}_{-0.32}\right)$. The root mean square radius of the mass distribution inside the nucleon is determined to be $0.97^{+0.02}_{-0.03}~\text{fm}$. Notably, this value is larger than the proton charge radius, suggesting a modern structural view of the nucleon where gluons, responsible for most of the nucleon mass, are distributed over a larger spatial region than quarks, which dominate the charge distribution. We also predict the nucleon angular momentum and mechanical radii, providing further insights into the intricate internal structure of the nucleon., Comment: 8 pages, 6 figures

The effective potential of the $O(N)$ model at large $N$ limit is reinvestigated with varying pion mass and temperature. For large pion masses and high temperatures, we find the phenomenologically favored vacuum, located on the upper branch of the double-branched effective potential for physical $m_\pi$, moves to the lower branch and becomes no longer a local minimum but a saddle point. The existence and running of the tachyon pole are also discussed. These phenomena indicate that the applicable energy range of $O(N)$ model is more and more limited as $m_\pi$ becoming larger and temperature going higher. With the effective coupling constant defined from the effective potential, the possible correspondence between the two branches of the effective potential and the two phases of the theory (distinguished by positive or negative coupling) is verified even with nonzero explicit symmetry breaking and at finite temperature. Also, we generalize the $N/D$ modified $O(N)$ model to study the thermal trajectory of the $\sigma$ pole with the cross-channel contributions considered and find the thermal $\sigma$ pole trajectory resembles its counterpart with varying pion mass at zero temperature., Comment: v1: 15 pages, 14 figures; v2: 17 pages, 14 figures, references and some details added; v3: 18 pages, 16 figures, published version

Roy-equation analyses on lattice data of $\pi\pi$ scattering phase shifts at $m_\pi=391$MeV reveals that the lowest $f_0$ meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao et al., Phys. Rev. D 108, 034009 (2023)]. We use the $N/D$ method to partially recover crossing symmetry of the $O(N)$ $\sigma$ model amplitude at leading order of $1/N$ expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The $\sigma$ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying $m_\pi$. As the temperature increases, the complex $\sigma$ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidences that the lowest $f_0$ state extracted from experiments and lattice data plays the role of $\sigma$ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when $m_\pi$ and temperature get large., Comment: 13 pages, 5 figures, 1 table; to match the published version

An extended Roy equation including a bound state pole is used to study $\pi\pi$ scatterings at unphysical large pion masses when $\sigma$ becomes a bound state in one situation and stays as a broad resonance in the other case. The coupled integral equations at large pion masses are solved by taking the lattice driving terms and the Regge amplitudes as inputs. Relying on the solutions of Roy equations that respect unitarity, analyticity and crossing symmetry, we give predictions to the phase shifts with $IJ=00,11,20$ in the elastic energy region. We then perform analytic continuation into the complex $s$ plane to search for various poles, all of which are inside the validity domain of the Roy equation. This is the first time that lattice data at unphysical large pion masses are analyzed within the rigorous Roy equation method., Comment: 20 pages, 13 figures, 4 tables, matches PRD version

The hyperbolic version of Roy-Steiner equation describing low energy $\pi N$ scatterings, with larger analyticity domain in the complex $s$ plane is solved. The numerical results on phase shifts of low partial waves are in agreement with that of Hoferichter et al. [Phys. Rept. 625 (2016) 1]. A subthreshold pole in $S_{11}$ channel is found located at $\sqrt{s}=(918 \pm 3)-i (163 \pm 9)$~MeV., Comment: 12 pages, 4 figures; Minor improvements in numerical results and discussions, conclusions unchanged, final version to appear in JHEP

The $N/D$ method is used to study the $S_{11}$ channel low energy $\pi N$ scattering amplitude. The input of left cuts are obtained from various phenomenological models. With the aid of the production representation, the total phase shifts can be decomposed into different contributions, and it further reveals that the existence of subthreshold resonance $N^*(890)$ doesn't depend on the details of the dynamical input. Additionally, it is found that there exist virtual states in partial waves, which are induced by the $u$ channel nucleon exchanges. These virtual states accumulate at the end point of the $u$ channel segment cut. The end point is hence the essential singularity of the full amplitude on the second sheet of complex $s$ plane.

Manifestly Lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at chiral next-to-leading order $(\mathcal{O}(p^2))$ with a nonzero lepton mass, which are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model calculation, but they are somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry., Comment: 30 pages, 18 figures, 2 tables. Matches published version

It is demonstrated that for the isospin $I=1/2$ $\pi$N scattering amplitude, $T^{I=1/2}(s,t)$, $s={(m_N^2-m_\pi^2)^2}/{m_N^2}$ and $s=m_N^2+2m_\pi^2$ are two accumulation points of poles on the second sheet of complex $s$ plane, and are hence accumulation of singularities of $T^{I=1/2}(s,t)$. For $T^{I=3/2}(s,t)$, $s={(m_N^2-m_\pi^2)^2}/{m_N^2}$ is the accumulation point of poles on the second sheet of complex $s$ plane. The proof is valid up to all orders of chiral expansions., Comment: 6 pages, one reference added, a bug removed, major conclusions remain unchanged

Extensive dynamical $N/D$ calculations are made in the study of $S_{11}$ channel low energy $\pi$N scatterings, based on various phenomenological model inputs of left cuts at tree level. The subtleties of the singular behavior of the partial wave amplitude at the origin of the complex $s$ plane are carefully analysed. Furthermore, { it is found that the dispersion representation for the phase shift, $\delta$, has to be modified in the case of $\pi $N scatterings. An additional contribution from the dispersion integral exists, which is, however, almost exactly cancelled the contribution from two virtual poles located near the end points of the segment cut induced by $u$ channel nucleon exchanges.} Relying very little on the details of the dynamical inputs, the subthreshold resonance $N^*(890)$ survives., Comment: Minor corrections, one reference added. Final version accepted for publication in Chinese Physics C