arXiv subjects

Qu-Zhi Li

Publications and source records attributed to Qu-Zhi Li.

17 recordsLinked to original sources

arXiv2026

Lattice QCD study of the $K^*(892)$ resonance at the physical point

We present a lattice QCD study of the $K^*(892)$ resonance using eight $N_f=2+1$ Wilson-Clover ensembles with three lattice spacings and six pion masses ranging from 135 to 320 MeV. For each ensemble, a large number of finite volume energy levels in the $P$-wave $Kπ$ channel are determined. The energy dependence of the scattering phase shift is then obtained from Lüscher's finite-volume method. To systematically assess parametrization dependence, the amplitude is described using three different models, which yield consistent results. The resulting phase shifts show a clear resonant behavior for all ensembles, and the corresponding $K^*(892)$ resonance pole is identified on the second Riemann sheet in the complex energy plane. The pole positions are extrapolated to the physical pion mass and the continuum limit, yielding a $K^*(892)$ resonance located at $\sqrt{s_0} = [883(22)-i20(13)]\mathrm{MeV}$, which is in excellent agreement with the experimental value. This study provides a first-principles QCD determination of the $K^*(892)$ mass and width with controlled systematic uncertainties.

hep-lat↗

arXiv2026

$I=\frac{3}{2}$ $πK$ $s$-wave scattering length from lattice QCD

The $I=\frac{3}{2}$ $πK$ $s$-wave scattering phase shift is computed by lattice quantum chromodynamics with $N_f=3$ flavors of Asqtad-improved staggered fermions. The energy-eigenvalues of $πK$ systems at one center of mass frame and six moving frames using moving wall source technique are used to get phase shifts by Lüscher's formula and its extensions. The calculations are good enough to acquire effective range expansion parameters: scattering length $a$, effective range $r$, and shape parameter $P$, which are in good agreement with our explicit analytical predictions in three-flavor chiral perturbation theory at next-to-leading order. All results are fairly consistent with experimental measurements, phenomenological studies, and lattice estimations. Numerical computations are implemented at a fine ($a\approx0.082$ fm, $L^3 T = 40^3 96$) lattice ensemble with physical quark masses.

hep-lat↗

arXiv2025

Studies on quark-mass dependence of the $N^*(920)$ pole from $πN$ $χ$PT amplitudes

The quark-mass dependence of the $N^*(920)$ pole is analyzed using $K$-matrix method, with the $πN$ scattering amplitude calculated up to $O(p^3)$ order in chiral perturbation theory. As the quark mass increases, the $N^*(920)$ pole gradually approaches the real axis in the complex $w$-plane (where $w=\sqrt{s}$). Eventually, in the $O(p^2)$ case, it crosses the $u$-cut on the real axis and enters the adjacent Riemann sheet when the pion mass reaches $526~{\rm MeV}$. At order $O(p^3)$, the rate at which it approaches the real axis slows down; however, we argue that it will ultimately cross the $u$-cut and enter the adjacent Riemann sheet as well. Additionally, the trajectory of the $N^*(920)$ pole is in qualitative agreement with the results from the linear $σ$ model calculation.

hep-ph↗

arXiv2025

Gravitational form factors of pions, kaons and nucleons from dispersion relations

The gravitational form factors of pions, kaons and the nucleons are investigated by employing modern dispersive techniques and chiral perturbation theory. We determine the gravitational form factors of pions and kaons, extending our analysis to explore the pion mass dependence of these form factors at several unphysical pion masses up to 391 MeV, for which lattice results exist for the meson-meson scattering phase shifts. We also review our analysis on the nucleon gravitational form factors at the physical pion mass, and then systematically calculate various three-dimensional spatial and two-dimensional transverse density distributions for the nucleons. These results provide new insights into the mass distribution inside nucleons. As a by-product, we match our dispersion relation results and those obtained from chiral perturbation theory with external gravitational source at the next-to-next-to-leading order, yielding values for the low-energy constants $c_8=-4.28_{-0.38}^{+0.37} ~\mathrm{GeV}^{-1}$ and $c_9=-0.68_{-0.05}^{+0.06} ~\mathrm{GeV}^{-1}$. These results offer a robust benchmark for future experimental and theoretical studies.

hep-ph↗

arXiv2025

Review on recent progress in the study of the $N^*(920)$ subthreshold singularity and the $σ/f_0(500)$ meson

We summarize recent results on studies of $ππ$ and $πN$ scatterings. They include the finding of a negative-parity nucleon pole with a mass lower than the nucleon mass, and the pole trajectory of $f_0(500)$ as the pion mass varies. The results are obtained from model-independent dispersion analyses. We also study the thermal properties of $f_0(500)$ based on the $O(N)$ $σ$ model and $N/D$ method.

hep-ph↗

arXiv2025

Rigorous Roy-Steiner equation analysis of $πK$ scattering at unphysical quark masses

We perform a rigorous analysis of the $πK$ 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 $πK$ lattice data in the inelastic region, the lattice data from the crossed $ππ\to K\bar{K}$ 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 $πK$ 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 $m_π=391$ MeV. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

hep-ph↗

arXiv2025

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

A comprehensive analysis of $πK\rightarrow πK$ and $ππ\rightarrow K\bar K$ amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice QCD data at $m_π=391$ MeV. In the present analysis, the amplitudes for the $S$- and $P$-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the $K$-matrix formalism. At $m_π=391$ MeV, the rigorous Roy-Steiner-type equation approach allows us to determine the $S$-wave scattering lengths, $m_πa_0^{1/2}=\left(0.92_{-0.28}^{+0.06}\right)$, $m_πa_0^{3/2}=-\left(0.32_{-0.02}^{+0.05}\right)$, and the $κ$ (also known as $K_0^*(700)$) pole position, $\sqrt{s_κ}=\left(966_{-24}^{+41}-i 198_{-17}^{+38}\right)$ MeV. We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

hep-ph↗

arXiv2025

Dispersive Determination of Nucleon Gravitational Form Factors

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 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 global unknown property" of the nucleon, the $D$-term, is determined to be $-3.38^{+0.34}_{-0.35}$. The root mean square radius of the scalar trace density inside the nucleon is determined to be $(0.97 \pm0.03)~\text{fm}$. 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, indicating that the radius of the trace density may be regarded as a confinement radius. We also predict the nucleon angular momentum and mechanical radii, providing further insights into the intricate internal structure of the nucleon.

hep-ph↗

arXiv2025

On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses

We study the pole trajectory of the recently established subthreshold negative parity nucleon pole, namely the $N^*(920)$, with varying pion masses, in the scheme of linear $σ$ model with nucleons using the $N/D$ unitarization method. We find that as the pion mass increases, the pole moves toward the real axis. For larger pion masses, at tree level, the pole falls to a specific point on $u$-channel cut and crosses to the adjacent Riemann sheet defined by the logarithmic $u$ channel cut. At one-loop level, the pole does not meet the $u$-cut up to $m_π=0.36$GeV. We also re-examined the $σ$ pole trajectory and find it in good agreement with Roy equation analysis result.

hep-ph↗

arXiv2024

Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal $σ$ pole trajectory with cross-channel improvements

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 $m_π$, 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 $m_π$ 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 $σ$ pole with the cross-channel contributions considered and find the thermal $σ$ pole trajectory resembles its counterpart with varying pion mass at zero temperature.

hep-ph↗

arXiv2024

Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures

Roy-equation analyses on lattice data of $ππ$ scattering phase shifts at $m_π=391$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 $O(N)$ $σ$ 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 $σ$ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying $m_π$. As the temperature increases, the complex $σ$ 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 $σ$ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when $m_π$ and temperature get large.

hep-ph↗

arXiv2023

Roy equation analyses of $ππ$ scatterings at unphysical pion masses

An extended Roy equation including a bound state pole is used to study $ππ$ scatterings at unphysical large pion masses when $σ$ 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.

hep-ph↗

arXiv2022

A possible subthreshold pole in $S_{11}$ channel from $πN$ Roy-Steiner equation analyses

The hyperbolic version of Roy-Steiner equation describing low energy $πN$ 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.

hep-ph↗

arXiv2022

Singularities and Accumulation of Singularities of $π$N Scattering amplitudes

It is demonstrated that for the isospin $I=1/2$ $π$N scattering amplitude, $T^{I=1/2}(s,t)$, $s={(m_N^2-m_π^2)^2}/{m_N^2}$ and $s=m_N^2+2m_π^2$ 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 $T^{I=3/2}(s,t)$, $s={(m_N^2-m_π^2)^2}/{m_N^2}$ 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.

nucl-th↗

arXiv2022

Radiative Correction to Lepton Proton Scatterings in Manifestly Lorentz-Invariant Chiral Perturbation Theory

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.

hep-ph↗

arXiv2022

The $N/D$ study on the singularity structure of $πN$ scattering amplitudes

The $N/D$ method is used to study the $S_{11}$ channel low energy $πN$ 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.

hep-ph↗

arXiv2021

An $N/D$ study of the $S_{11}$ channel $πN$ scattering amplitude

Extensive dynamical $N/D$ calculations are made in the study of $S_{11}$ channel low energy $π$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, $δ$, has to be modified in the case of $π$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.

nucl-th↗