arXiv subjects

Ziwen Fu

Publications and source records attributed to Ziwen Fu.

At least 19 recordsLinked to original sources

arXiv2026

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

The $I=\frac{3}{2}$ $\pi K$ $s$-wave scattering phase shift is computed by lattice quantum chromodynamics with $N_f=3$ flavors of Asqtad-improved staggered fermions. The energy-eigenvalues of $\pi K$ systems at one center of mass frame and six moving frames using moving wall source technique are used to get phase shifts by L\"uscher'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.

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arXiv2024

$I=2$ $\pi\pi$ $s$-wave scattering length from lattice QCD

The $I=2$ $\pi\pi$ elastic $s$-wave scattering phase shift is measured by lattice QCD with $N_f=3$ flavors of the Asqtad-improved staggered fermions. The lattice-calculated energy-eigenvalues of $\pi\pi$ systems at one center of mass frame and some moving frames using the moving wall source technique are utilized to secure phase shifts by L\"uscher's formula. Our computations are fine enough to obtain threshold parameters: scattering length $a$, effective range $r$, and shape parameter $P$, which can be extrapolated at the physical point by NLO in chiral perturbation theory, and our relevant NNLO predictions from expanding NPLQCD's works are novelly considered as the systematic uncertainties. Our outcomes are consistent with Roy equation determinations, newer experimental data, and lattice estimations. Numerical computations are performed with a coarse ($a\approx0.12$~fm, $L^3 T = 32^3 64$), two fine ($a\approx0.09$~fm, $L^3 T = 40^3 96$) and a superfine ($a\approx0.06$~fm, $L^3 T = 48^3 144$) lattice ensembles at four pion masses of $m_\pi\sim247~{\rm MeV}$, $249~{\rm MeV}$, $275~{\rm MeV}$, and $384~{\rm MeV}$, respectively.

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arXiv2018

$I=0$ $ππ$ $s$-wave scattering length from lattice QCD

We deliver lattice results for the $I=0$ $ππ$ elastic $s$-wave scattering length calculated with the MILC $N_f=3$ flavors of the Asqtad-improved staggered fermions. The scattering phase shifts are determined by Lüscher's formula from the energy-eigenvalues of $ππ$ systems at one center of mass frame and four moving frames using the moving wall source technique. Our measurements are good enough to resolve the scattering length $a$ and effective range $r$, moreover, it allows us to roughly estimate the shape parameter $P$. Using our lattice results, the scattering length $a$ and effective range $r$ at the physical point are extrapolated by chiral perturbation theory. Our results are reasonably consistent with the Roy equation determinations and the newer experimental data. Numerical computations are carried out with two MILC fine ($a\approx0.09$~fm, $L^3 \times T = 40^3\times 96$) and one MILC superfine ($a\approx0.06$~fm, $L^3 \times T = 48^3\times 144$) lattice ensembles at three pion masses of $m_π\sim247~{\rm MeV}$, $249~{\rm MeV}$, and $314~{\rm MeV}$, respectively.

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arXiv2017

Hadronic coupling constants of $g_{σππ}$ in lattice QCD

We investigate the coupling constant $g_{σππ}$ for the hadronic decay $σ\toππ$ only using the relevant three-point function, which is evaluated by the moving-wall source technique with a pretty good noise-to-signal ratio. This simulation is carried out on a $40^3\times96$ MILC gauge configuration with $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at the lattice spacing $a \approx 0.09$ fm. Our estimated value for this given MILC fine lattice gauge ensemble $g_{σππ}=2.71(42)$ GeV.

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arXiv2016

Studying the $ρ$ resonance parameters with staggered fermions

We deliver a lattice study of $ρ$ resonance parameters with p-wave $ππ$ scattering phases, which are extracted by finite-size methods at one center-of-mass frame and four moving frames for six MILC lattice ensembles with pion masses ranging from $346$ to $ 176$ MeV. The effective range formula is applied to describe the scattering phases as a function of the energy covering the resonance region, this allows us to extract $ρ$ resonance parameters and to investigate the quark-mass dependence. Lattice studies with three flavors of the Asqtad-improved staggered fermions enable us to use the moving-wall source technique on large lattice spatial dimensions ($L=64$) and small light $u/d$ quarks. Numerical computations are carried out at two lattice spacings, $a \approx 0.12$ and $0.09$ fm.

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arXiv2014

I=1/2 low-lying mesons in lattice QCD

Using conventional constituent-quark model, $I=1/2$ scalar $κ$, vector $K^\ast(892)$, and axial vector $K_1$ mesons are studied in the asqtad-improved staggered fermion with the wall-source and point-sink interpolators. The mass ratio of $m_κ/m_{K^\ast(892)}$ is numerically confirmed to vary apparently with quark mass, and the experimental ordering $m_{K^\ast(892)} > m_κ$ is elegantly hold when the light $u/d$ quark masses are sufficiently small, while the valence strange quarks are fixed to its physical values. We also get reasonable signals for $K_1$ meson suggested by SCALAR Collaboration from lattice QCD. The computations are conducted with the MILC $N_f=3$ flavor gauge configurations at three lattice spacings: $a\approx 0.15$, $0.12$, and $0.09$ fm.

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arXiv2013

Preliminary lattice study of $I=0$ $K \overline{K}$ scattering

We deliver the realistic ab initio lattice investigations of $K \overline{K}$ scattering. In the Asqtad-improved staggered dynamical fermion formulation, we carefully measure $K\overline{K}$ four-point function in the $I=0$ channel by moving wall sources without gauge fixing, and clearly find an attractive interaction in this channel, which is in agreement with the theoretical predictions. An essential ingredient in our lattice calculation is to properly treat the disconnected diagram. Moreover, we explain the difficulties of these lattice calculations, and discuss the way to improve the statistics. Our lattice investigations are carried out with the MILC $2+1$ gauge configuration at lattice spacing $a \approx 0.15$~fm.

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arXiv2013

Bubble contributions to scalar correlators with mixed actions

WWithin mixed-action chiral perturbation theory (MA$χ$PT), Sasa's derivation of the bubble contribution to scalar $a_0$ meson is extended to those of scalar $κ$ and $σ$ mesons. We revealed that $κ$ bubble has two double poles and $σ$ bubble contains a quadratic-in-$t^2$ growth factor stemming from the multiplication of two double poles for a general mass tuning of valence quarks and sea quarks. The corresponding preliminary analytical expressions in MA$χ$PT with 2+1 chiral valence quarks and 2+1 staggered sea quarks will be helpful for lattice studies of scalar mesons.

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arXiv2013

Studying $κ$ meson with a MILC fine lattice

Using the lattice simulations in the Asqtad-improved staggered fermion formulation we compute the point-to-point $κ$ correlators, which are analyzed by the rooted staggered chiral perturbation theory (rS$χ$PT). After chiral extrapolation, we secure the physical $κ$ mass with $835\pm93$ MeV, which is in agreement with the BES experimental results. The computations are performed using a MILC 2+1 flavor fine gauge configuration at a lattice spacing of $a \approx 0.09$ fm.

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arXiv2013

Lattice QCD study of the s-wave $ππ$ scattering lengths in the I=0 and 2 channels

The s-wave pion-pion ($ππ$) scattering lengths are computed below the inelastic threshold by the Lüscher technique with pion masses ranging from 240 MeV to 463 MeV. In the Asqtad-improved staggered fermion formulation, we calculate the $ππ$ four-point functions for the I=0 and 2 channels with "moving" wall sources without gauge fixing, and analyze them at the next-to-leading order in the continuum three-flavor chiral perturbation theory. At the physical pion mass, we secure the s-wave $ππ$ scattering lengths as $m_πa_{ππ}^{I=0} = 0.214(4)(7)$ and $m_πa_{ππ}^{I=2} = -0.04430(25)(40)$ for the I=0 and 2 channels, respectively, where the first uncertainties are statistical and second ones are our estimates of several systematic effects. Our lattice results for the s-wave $ππ$ scattering lengths are in well accordance with available experimental reports and theoretical forecasts at low momentum. A basic ingredient in our study for the I=0 case is properly incorporating disconnected diagram. These lattice computations are carried out with the MILC 2+1 flavor gauge configurations at two lattice spacings $a \approx 0.15$ and 0.12 fm.

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arXiv2012

Hybrid meson decay from lattice QCD

Besides the conventional hadrons containing valence quarks and valence antiquarks, quantum chromodynamics (QCD) suggests the existence of the hybrid hadrons containing valence gluons in addition to the quarks and antiquarks, and some experiments may have found some. A decisive experimental confirmation of its existence, however, is still needed. At present, lattice simulations have offered the practicable ways of theoretically guiding us to search for the hybrid states. In this dissertation, we study the spectroscopy and the decay rate of the heavy hybrid mesons made of a heavy $b$ quark, a heavy $\bar b$ antiquark, and a gluon ($b\bar{b}g$) to selected channels, and use lattice methods to extract the transition matrix elements in full QCD. We are particular interested in the spin-exotic hybrid mesons. For sufficiently heavy quarks (e.g., $b$ quark), we use the leading Born-Oppenheimer (LBO) approximation to calculate the static potential energy at all $b\bar{b}$ separations. Then, by solving the Schrödinger equation with this potential, we reconstruct the motion of the heavy quarks. In a similar way we can determine decay rates. In this dissertation, we use the numerical lattice method to calculate the mass of the $f_0$ meson at a single lattice spacing and light quark mass, namely, $m_{f_0} = (768 \pm 136)$ MeV. Most of all we consider the decay channels involving the production of a scalar meson. We obtain the partial decay rate ($Γ$) for the channel $ H \rightarrow χ_b + π+ π$, namely, $ Γ= 3.62(98)$ MeV. All of our results are consistent with those of other researchers. Knowledge of the masses and the decay rates should help us considerably in experimental searches for the hybrid mesons.

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arXiv2012

Lattice QCD study on $K^\ast(892)$ meson decay width

We deliver an exploratory lattice QCD examination of the $K^\ast(892)$ meson decay width with the help of the p-wave scattering phase $δ_1$ of pion-kaon ($πK$) system in the isospin $I=1/2$ channel, which are extracted by the modified Rummukainen-Gottlieb formula for two-particle system with arbitrary mass, and it clearly reveals the entity of a resonance at a mass around $K^\ast(892)$ meson mass. The effective range formula is applied to describe the energy dependence of the scattering phase and we obtain the effective $K^\ast \to πK$ coupling constant as $g_{K^\ast πK} = 6.38(78)$, and subsequently achieve the decay width to be $64.9 \pm 8.0$ MeV, which is in reasonable accordance with the current experiment. Our lattice investigations are conducted on a $20^3\times48$ MILC full QCD gauge configuration at $(m_π+ m_K) / m_{K^\ast} \approx 0.739$ and the lattice spacing $a \approx 0.15$ fm.

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arXiv2012

The preliminary lattice QCD calculation of $κ$ meson decay width

We present a direct lattice QCD calculation of the $κ$ meson decay width with the s-wave scattering phase shift for the isospin $I=1/2$ pion-kaon ($πK$) system. We employ a special finite size formula, which is the extension of the Rummukainen-Gottlieb formula for the $πK$ system in the moving frame, to calculate the scattering phase, which indicates a resonance around $κ$ meson mass. Through the effective range formula, we extract the effective $κ\to πK$ coupling constant $g_{κπK} = 4.54(76)$ GeV and decay width $Γ= 293 \pm 101$ MeV. Our simulations are done with the MILC gauge configurations with $N_f=2+1$ flavors of the "Asqtad" improved staggered dynamical sea quarks on a $16^3\times48$ lattice at $(m_π+ m_K) / m_κ\approx 0.8$ and lattice spacing $a \approx 0.15$ fm.

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arXiv2012

Preliminary lattice study of the I=1 $K \bar{K}$ scattering length

The s-wave kaon-antikaon ($K \bar{K}$) elastic scattering length is investigated by lattice simulation using pion masses $m_π= 330 - 466$ MeV. Through moving wall sources without gauge fixing, we calculate $K \bar{K}$ four-point correlation functions for isospin I=1 channel in the "Asqtad" improved staggered fermion formulation, and observe a clear signal of attraction, which is consistent with other pioneering lattice studies on $K \bar{K}$ potential. Extrapolating $K \bar{K}$ scattering length to the physical point, we obtain $m_{K} a^{I=1}_{K\bar{K}} = 0.211(33)$. These simulations are performed with MILC gauge configurations at lattice spacing $a \approx 0.15$ fm.

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arXiv2012

Lattice QCD calculation of $ππ$ scattering length

We study s-wave pion-pion ($ππ$) scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the "Asqtad" improved staggered fermion formulation, we calculate the $ππ$ four-point functions for isospin I=0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass gives the scattering lengths as $m_πa_0^{I=2} = -0.0416(2)$ and $m_πa_0^{I=0} = 0.186(2)$ for isospin I=2 and 0 channels, respectively. Our lattice simulation for $ππ$ scattering length in the I=0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are performed with MILC 2+1 flavor gauge configurations at lattice spacing $a \approx 0.15$ fm.

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arXiv2012

Preliminary lattice study of $σ$ meson decay width

We report an exploratory lattice investigation of $σ$ meson decay width using s-wave scattering phase for isospin I=0 pion-pion ($ππ$) system. Rummukainen-Gottlieb formula is used to estimate the scattering phase, which demonstrate the presence of a resonance around $σ$ meson. Using the effective range formula we extract the effective $σ\to ππ$ coupling constant as $g_{σππ} = 2.69(44)$ GeV, which is consistent with theoretical predictions. The estimated decay width is about $236 \pm 49$ MeV. These simulations are carried out on a $16^3\times48$ MILC gauge configuration with the $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at $ m_π/ m_σ\approx 0.414$ and the lattice spacing $a \approx 0.15$ fm.

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arXiv2012

Rummukainen-Gottlieb's formula on two-particle system with different mass

Lüscher established a non-perturbative formula to extract the elastic scattering phases from two-particle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system of two identical particles. In this work, we generalize Rummukainen-Gottlieb's formula to the generic two-particle system where two particles are explicitly distinguishable, namely, the masses of the two particles are different. The finite size formula are achieved for both $C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpful for the study of some resonances, such as kappa, vector kaon, and so on.

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arXiv2012

Lattice study on $πK $ scattering with moving wall source

The s-wave pion-kaon ($πK$) scattering lengths at zero momentum are calculated in lattice QCD with sufficiently light $u/d$ quarks and strange quark at its physical value by the finite size formula. The light quark masses correspond to $m_π= 0.330 - 0.466$ GeV. In the "Asqtad" improved staggered fermion formulation, we measure the $πK$ four-point correlators for both isospin $I=1/2$ and 3/2 channels, and analyze the lattice simulation data at the next-to-leading order in the continuum three-flavor chiral perturbation theory, which enables us a simultaneous extrapolation of $πK$ scattering lengths at physical point. We adopt a technique with the moving wall sources without gauge fixing to obtain the substantiable accuracy, moreover, for $I = 1/2$ channel, we employ the variational method to isolate the contamination from the excited states. Extrapolating to the physical point yields the scattering lengths as $m_πa_{3/2} = -0.0505(19)$ and $m_πa_{1/2} = 0.1827(37)$ for $I=3/2$ and 1/2 channels, respectively. Our simulation results for $πK$ scattering lengths are in agreement with the experimental reports and theoretical predictions, and can be comparable with other lattice simulations. These simulations are carried out with MILC $N_f = 2+1$ flavor gauge configurations at lattice spacing $a \approx 0.15$ fm.

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