Mei-Zhu Yan, Dan Zhou, Zhi-Hui Guo
In this note we first introduce the theoretical formalism of the unitarization of the two-body scattering both in the infinite and finite volumes. Then we apply this formalism to the study of the $Z_c(3900)$ resonance in the $J/ψ\,π$ and $D\bar{D}^{*}$ coupled-channel scattering. The recent lattice finite-volume spectra are confronted with our predictions.
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We use a unitary coupled-channel model to study the $\bar{D} Λ_c - \bar{D} Σ_c$ interactions. In our calculation, SU(3) flavor symmetry is applied to determine the coupling constants. Several resonant and bound states with different spin and parity are dynamically generated in the mass range of the recently observed pentaquarks. The approach is also extended to the hidden beauty sector to study the $B Λ_b - B Σ_b$ interactions. As the $b$-quark mass is heavier than the $c$-quark mass, there are more resonances observed for $B Λ_b - B Σ_b$ interactions and they are more tightly bound.
The well-known discrepancy in the muon $g-2$ between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon $g-2$ using full QCD.
We improve the excluded volume hadron resonances gas model (EHRG) to cure the acausal behavior of the sound velocity which is typical of excluded volume models. We achieve this by including temperature (T) and density (μ) dependent hadron masses in the partition function of EHRG. The temperature and density dependent masses of the constituent quarks (u,d,s) and the light mesons are obtained within Nambu-Jona-Lasinio model while for the heavy hadrons we use linear scaling rule in terms of constituent quarks. With this improvement, we observe that the velocity of sound flattens at high temperatu…
In present work, we explore and experiment an alternative approach of studying resonance properties in finite volume. By analytic continuing finite lattice size $L$ into complex plane, the oscillating behavior of finite volume Green's function is mapped into infinite volume Green's function corrected by exponentially decaying finite volume effect. The analytic continuation technique thus can be applied to study resonance properties directly in finite volume dynamical equations.
In this work we discuss a modified version of Excluded Volume Hadron Resonance Gas model and also study the effect of Lorentz contraction of the excluded volume on scaled pressure and susceptibilities of conserved charges. We find that the Lorentz contraction, coupled with the variety of excluded volume parameters reproduce the lattice QCD data quite satisfactorily.
Under the assumption of separable interactions, we illustrate how the few-body quantization condition may be formulated in terms of phase shifts in general, which may be useful for describing and modeling of few-body resonances in finite volume.
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the Delta-resonance a clear resonance structure emerges in such an analysis. Consequently, measuring the volume-dependence of the energy levels in lattice QCD will allow to determine the mass and the width of the Delta with reasonable accuracy.
We develop a theoretical framework to quantify the structure of unstable hadron resonances. With the help of the corresponding system in a finite volume, we define the compositeness of resonance states which can be interpreted as a probability. This framework is used to study the structure of the scalar mesons f_0(980) and a_0(980). In both mesons, the Kbar K component dominates about a half of the wave function. The method is also applied to the Lambda(1405) resonance. We argue that a single energy level in finite volume represents the two eigenstates in infinite volume. The KbarK N component…
We calculate the self-energy of the Delta (1232) resonance in a finite volume, using chiral effective field theory with explicit spin-3/2 fields. The calculations are performed up-to-and-including fourth order in the small scale expansion and yield an explicit parameterization of the energy spectrum of the interacting pion-nucleon pair in a finite box in terms of both the quark mass and the box size L. It is shown that finite-volume corrections can be sizeable at small quark masses.
We calculate the energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian for pions, nucleons, deltas and the Roper resonance at leading one-loop order. We show that the Roper mass can be extracted from these levels for not too large lattice volumes.
The thermodynamics of hot and dense matter created in heavy-ion collision experiments are usually studied as a system of infinite volume. Here we report on possible effects for considering a finite system size for such matter in the framework of the Hadron Resonance Gas model. The bulk thermodynamic variables as well as the fluctuations of conserved charges are considered. We find that the finite size effects are insignificant once the observables are scaled with the respective volumes. The only substantial effect is found in the fluctuations of electric charge which may therefore be used to e…
The effects of volume corrections and resonance decays (the resulting correlations between positive charges and negative charges) on cumulants of net-proton distributions and net-charge distributions are investigated by using a Monte Carlo hadron resonance gas ({\tt MCHRG}) model. The required volume distributions are generated by a Monte Carlo Glauber ({\tt MC-Glb}) model. Except the variances of net-charge distributions, the {\tt MCHRG} model with more realistic simulations of volume corrections, resonance decays and acceptance cuts can reasonably explain the data of cumulants of net-proton …
The finite-volume energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian at leading one-loop order are investigated. It is shown that the Roper mass can be extracted from these levels for not too large lattice volumes. Further, to include three-body $N ππ$ dynamics, a non-relativistic effective field theory for the Roper resonance within a covariant particle-dimer picture is introduced. This particle-dimer approach is a suitable framework to investigate three-particle scattering relevant for the Roper channel. The appearing dimer fields are analyze…
Spectral weight functions are easily obtained from two-point correlation functions and they might be used to distinguish single-particle from multi-particle states in a finite-volume lattice calculation, a problem crucial for many lattice QCD simulations. In previous studies, it is shown that the spectral weight function for a broad resonance shares the typical volume dependence of a two-particle scattering state i.e. proportional to $1/L^3$ in a large cubic box of size $L$ while the narrow resonance case requires further investigation. In this paper, a generalized formula is found for the spe…
Here we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm$^3$. The derived expressions of the induced surface tension equation of state are analyzed in details. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtain…
We present temperature ($T$) and baryonic chemical potential ($μ_B$) dependence of higher order fluctuations and correlation between conserved charges in Excluded Volume Hadron Resonance Gas (EVHRG) model. Products of moments, such as ratio of variance to mean ($σ^2/M)$, product of skewness and standard deviation ($Sσ$), product of kurtosis and variance ($κσ^2$), for net-proton, net-kaon and net-charge have been evaluated on the phenomenologically determined freeze-out curve. Further, products of moments for net-proton and net-charge have been compared with the experimental data measured by ST…
The Monte Carlo (MC) procedure for sampling the hadron yields within hadron resonance gas (HRG) model is presented. The effects of excluded-volume due to the finite hadron eigenvolumes and of exact charge conservation within the canonical ensemble (CE) formulation are simultaneously taken into account with the help of the importance sampling technique combined with the rejection sampling. The MC procedure allows one to calculate arbitrary moments of the event-by-event hadron yields. Note that the CE formulation for the excluded-volume HRG has not been considered before. The MC simulations coin…
An SU(4) extrapolation of the chiral unitary theory in coupled channels done to study the scalar mesons in the charm sector is extended to produce results in finite volume. The theory in the infinite volume produces dynamically the $D_{s^*0}(2317)$ resonance by means of the coupled channels $KD$, $ηD_s$. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is addressed. We observe that it is possible to obtain accurate $KD$ phas…
We study the extraction of Delta-resonance parameters from lattice data for small quark masses, corresponding to the case of an unstable Delta. To this end, we calculate the spectrum of the correlator of two Delta-fields in a finite Euclidian box up-to-and-including O(epsilon^3) in the small scale expansion using infrared regularization. On the basis of our numerical study, we argue that the extraction of the parameters of the Delta-resonance (in particular, of the mass and the pion-nucleon-delta coupling constant) from the measured volume dependence of the lowest energy levels should be feasi…
Particle-dimer approach for the Roper resonance in a finite volume
提出基于有效场论和粒子-二聚体图像的有限体积方法，用于Roper共振，预测能量本征值并与格点QCD结果比较，指导谱精度需求。
We compute finite-volume corrections to nucleon matrix elements of the axial-vector current. We show that knowledge of this finite-volume dependence --as well as that of the nucleon mass-- obtained using lattice QCD will allow a clean determination of the chiral-limit values of the nucleon and Delta-resonance axial-vector couplings.
General Hamiltonian Approach to the $\mathbf{N}$-Body Finite-Volume Formalism: Extracting the $\mathbfω$ Resonance Parameters from Lattice QCD
本文提出一种非微扰哈密顿框架，用于从格点QCD中提取ω介子共振参数，通过分析三体系统实现对共振动力学的提取。
An approach for relating the nucleon resonances extracted from $πN$ reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of $πN$ reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance pole positions can be related to the probability $P_{N^*}(E)$ of finding the bare state, $N^*$, in the $πN$ scattering states in infinite volume. We further demonstrate that the probability $P_{N^*}^V(E)$ of finding the same bare states in the eigenfunctions of the underlying Ham…
In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy spectrum of the finite-volume lattice with the asymptotic behaviour of the S-matrix. A new technique for comparing energy eigenvalues with scattering phase shifts is introduced, which involves the construction of an exactly solvable matrix Hamiltonian model. The model framework is applied to the case of $Δ\rightarrow Nπ$ decay, but is easily generalized to includ…
We perform an exploratory lattice QCD simulation of $D \bar D$ scattering, aimed at determining the masses as well as the decay widths of charmonium resonances above open charm threshold. Neglecting coupling to other channels, the resulting phase shift for $D \bar D$ scattering in p-wave yields the well-known vector resonance $ψ(3770)$. For $m_π= 156$ MeV, the extracted resonance mass and the decay width agree with experiment within large statistical uncertainty. The scalar charmonium resonances present a puzzle, since only the ground state $χ_{c0}(1P)$ is well understood, while there is no co…
Simulating the kappa(800) on the lattice is a challenging task that starts to become feasible due to the rapid progress in recent-years lattice QCD calculations. As the resonance is broad, special attention to finite-volume effects has to be paid, because no sharp resonance signal as from avoided level crossing can be expected. In the present article, we investigate the finite volume effects in the framework of unitarized chiral perturbation theory using next-to-leading order terms. After a fit to meson-meson partial wave data, lattice levels for piK scattering are predicted. In addition, leve…
A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of the Lüscher method in the presence of such a field. It is shown that the resonance form factor is given by the derivative of the resonance pole position in the complex plane with respect to the coupling constant to the external field. Unlike the standard approach, this proposal does not suffer from problems caused by the presence of the triangle diagram.
Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $π$, $K$ and $η$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain coupled-channel scattering amplitudes from lattice QCD. Using large diverse bases of operators it is possible to obtain reliable finite volume spectra at energies where multiple channels are open. Utilising the finite volume formalism proposed by Lüscher and extended by several others, scattering amplitudes can be extracted from the finite volume spectra. Recent applicati…
We estimate dissipative properties viz: shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within ambit of excluded volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($η/s$) decreases with temperature while at finite baryon chemical potential this ratio shows same behavior as a function of temperature but reaches close to Kovtun-Son-Starinets (KSS) bound. Further along chemical freezout curve, ratio $η/s$ is almost constant apart from small initial monot…
The structures of the hyperon resonance $Λ(1405)$ and the scalar mesons $σ$, $f_{0}(980)$, and $a_{0}(980)$ are investigated based on the coupled-channels chiral dynamics with finite volume effect. The finite volume effect is utilized to extract the coupling constant, compositeness, and mean squared distance between two constituents of a Feshbach resonance state as well as a stable bound state. In this framework, the real-valued size of the resonance can be defined from the downward shift of the resonance pole according to the decreasing finite box size $L$ on a given closed channel. As a resu…
In this work the interaction of the coupled channels $DN$ and $πΣ_c$ in an SU(4) extrapolation of the chiral unitary theory, where the $Λ_c(2595)$ resonance appears as dynamically generated from that interaction, is extended to produce results in finite volume. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the phase shifts in the infinite volume from the lattice results is solved. We observe that it is possible to obtain accurate $πΣ_c$ phase shifts and the position of the $Λ_c(2595)$ resonance, but…
Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered $X$, $Y$ and $Z$ resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. Here we review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship…
Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with nonzero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the pi pi and pi K phase shifts in the sectors with total isospin I=0 and I=1/2, respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect th…
We present the first lattice QCD calculation of coupled $πω$ and $πϕ$ scattering, incorporating coupled $S$ and $D$-wave $πω$ in $J^P=1^+$. Finite-volume spectra in three volumes are determined via a variational analysis of matrices of two-point correlation functions, computed using large bases of operators resembling single-meson, two-meson and three-meson structures, with the light-quark mass corresponding to a pion mass of $m_π\approx 391$ MeV. Utilizing the relationship between the discrete spectrum of finite-volume energies and infinite-volume scattering amplitudes, we find a narrow axial…
For resonances decaying in a finite volume, the simple identification of state and eigenvalue is lost. The extraction of the scattering amplitude is a major challenge as we demonstrate by extrapolating the physical S_{11} amplitude of pion-nucleon scattering to the finite volume and unphysical quark masses, using a unitarized chiral framework including all next-to-leading order contact terms. We show that the pole movement of the resonances N(1535)1/2^- and N(1650)1/2^- with varying quark masses is non-trivial. In addition, there are several strongly coupled S-wave thresholds that induce a sim…
We develop a scheme for the extraction of the properties of the scalar mesons $f_0(600)$, $f_0(980)$, and $a_0(980)$ from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by Lüscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured from finite periodic lattices. In this work, we generalize the formalism to the case where the total momentum of the particles is non-zero; i.e. the lattice frame is not the center-of-mass frame of the scattering particles. There are several advantages to this procedure including making a wider variety of center of mass energies accessible with a fixed lattice vo…
The Monte Carlo results in lattice QCD for the pressure and energy density at small temperature $T < 155$ MeV and zero baryonic chemical potential are analyzed within the hadron resonance gas model. Two extensions of the ideal hadron resonance gas are considered: the excluded volume model which describes a repulsion of hadrons at short distances and Hagedorn model with the exponential mass spectrum. Considering both of these models one by one we do not find the conclusive evidences in favor of any of them. The controversial results appear because of rather different sensitivities of the pressu…
Roberge-Weiss periodicity and singularity in hadron resonance gas model with excluded volume effects
针对含体积排斥效应的强子共振气体模型，研究其在纯虚重子数化学势下的Roberge-Weiss周期性，发现T≈211MeV时θ=(2k+1)π处存在奇异性，可由对偶体积排斥效应解释，且该效应在TRW下方可见并可通过格点QCD探测。
Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying $J^P=1/2^-$ nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also …
We examine the phase shifts and inelasticities associated with the $N^*(1440)$ Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. All three hypotheses are able to describe the scattering data well. In the third hypothesis the Roper resonance couples the low-lying bare basis-state component associated with the ground state nucleon with the virtual meson-baryon contributions. Here the non-trivial superpositions of the meson-baryon…
In an exploratory study, using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, the $ππ$ scattering length in the I=2 channel is calculated within quenched approximation. A new method is proposed which enables us to make chiral extrapolation of our lattice results without calculating the decay constant on the lattice. Finite volume and finite lattice spacing errors are analyzed and the results are extrapolated towards the infinite volume and continuum limit. Comparisons of our lattice results with the new experiment and the results from Chiral Perturba…
Two different descriptions of the existing pion-nucleon scattering data in the region of the Roper resonance are constructed. Both descriptions fit the experimental data very well. In one scenario the resonance is the result of strong rescattering between coupled meson-baryon channels, while in the other scenario, the resonance has a large bare-baryon (or quark-model like) component. The predictions of these two scenarios are compared with the latest lattice QCD simulation results in this channel. Consideration of the finite volume spectra, the manner in which the states are excited from the v…
We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
We present for the first time a determination of the energy dependence of the isoscalar $ππ$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_π= 236…
Low-lying baryon resonances from lattice QCD
本研究利用格点量子色动力学的非微扰蒙特卡罗方法，结合散射K矩阵参数化拟合有限体积能谱，得到Δ共振态结果，发现Λ(1405)附近的双极点结构，并探讨了该方法应用于Roper共振态的前景。
In this project, we will compute the form factors relevant for $B \to K^*(\to K π)\ell^+\ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B \to K π$ matrix elements, the $K π$ scattering amplitude needs to be determined using Lüscher's method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K π$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.
In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quan…
Isospin-1/2 $Dπ$ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately $(3.6\; \mathrm{fm})^3$ and with a light quark mass corresponding to $m_π\approx239$ MeV. The spectrum of the elastic $Dπ$ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic $Dπ$ scattering. By analytically continuing a range of scattering amplitudes, a $D_0^\ast$ resona…
The ab-initio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the infinite volume. We present the first application of such a formalism to a physical system in form of three interacting positively charged pions. The results for the ground state energies agree with the available lattice QCD results by the NPLQCD collaboration at unphysical pion masses. Extrapolations to physical pion masses are performed using input from effectiv…
Resonances at finite temperature from the lattice
研究有限温度下强子共振性质，利用热粒子概念定义有限温度两粒子散射并建立幺正关系，通过有限体积关联函数推导量子化条件，求解该条件约束热散射振幅及共振性质，还可研究真空分析中的有限时间尺寸效应。
We investigate an application of twisted boundary conditions for study of low-energy hadron-hadron interactions with Lüshcer's finite size method. It allows us to calculate the phase shifts for elastic scattering of two hadrons at any small value of the scattering momentum even in a finite volume. We then can extract model independent information of low-energy scattering parameters such as the scattering length, the effective range and the effective volume from the $S$-wave and $P$-wave scattering phase shifts through the effective range expansion. This approach also enables us to examine the …
Understanding the nature of the $Δ(1600)$ resonance
基于HEFT框架对 $ J^P = 3/2^+ Δ$-重子谱进行耦合道分析，结合格点QCD结果发现 $ Δ(1600) $ 共振态主要源于 $ πN $ 和 $ πΔ$ 道的强再散射，而非类夸克模型核心。
We investigate the $a_0(980)$ resonance within chiral effective field theory through a three-coupled-channel analysis, namely $πη$, $K\bar{K}$ and $πη'$. A global fit to recent lattice finite-volume energy levels from $πη$ scattering and relevant experimental data on a $πη$ event distribution and the $γγ\toπη$ cross section is performed. Both the leading and next-to-leading-order analyses lead to similar and successful descriptions of the finite-volume energy levels and the experimental data. However, these two different analyses yield different $πη$ scattering phase shifts for the physical ma…
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