arXiv subjects

Zhaofeng Liu

Publications and source records attributed to Zhaofeng Liu.

At least 37 records · Page 2Linked to original sources

arXiv2023

$η$-glueball mixing from $N_f=2$ lattice QCD

We perform the first lattice study on the mixing of the isoscalar pseudoscalar meson $η$ and the pseudoscalar glueball $G$ in the $N_f=2$ QCD at the pion mass $m_π\approx 350$ MeV. The $η$ mass is determined to be $m_η=714(6)(16)$ MeV. Through the Witten-Veneziano relation, this value can be matched to a mass value of $\sim 981$ MeV for the $\mathrm{SU(3)}$ counterpart of $η$. Based on a large gauge ensemble, the $η-G$ mixing energy and the mixing angle are determined to be $|x|=107(15)(2)$ MeV and $|θ|=3.46(46)^\circ$ from the $η-G$ correlators that are calculated using the distillation method. We conclude that the $η-G$ mixing is tiny and the topology induced interaction contributes most of $η$ mass owing to the QCD $\mathrm{U_A(1)}$ anomaly.

hep-lat↗

arXiv2023

$1^{-+}$ Hybrid in $J/ψ$ Radiative Decays from Lattice QCD

We present the first theoretical prediction of the production rate of $1^{-+}$ light hybrid meson $η_1$ in $J/ψ$ radiative decays. In the $N_f=2$ lattice QCD formalism with the pion mass $m_π\approx 350$ MeV, the related electromagnetic multipole form factors are extracted from the three-point functions that involve necessarily quark annihilation diagrams, which are calculated through the distillation method. The partial width of $J/ψ\to γη_1$ is determined to be $2.29(77)~\mathrm{eV}$ at the $η_1$ mass $m_{η_1}=2.23(4)$ GeV. If $η_1$ corresponds to the recently observed $η_1(1855)$ in the process $J/ψ\to γη_1(1855)\to γηη'$ by BESIII, then the branching fraction $\mathrm{Br}(J/ψ\to γη_1(1855))$ is estimated to be $6.2(2.2)\times 10^{-5}$, which implies $\mathrm{Br}(η_1(1855)\to ηη')\sim 4.3\%$.

hep-lat↗

arXiv2023

Radiative Decay Width of $J/ψ\to γη_{(2)}$ from $N_f=2$ Lattice QCD

The large radiative production rate for pseudoscalar mesons in the $J/ψ$ radiative decay remains elusive. We present the first lattice QCD calculation of partial decay width of $J/ψ$ radiatively decaying into $η_{(2)}$, the $\mathrm{SU(2)}$ flavor singlet pseudoscalar meson, which confirms QCD $\mathrm{U_A(1)}$ anomaly enhancement to the coupling of gluons with flavor singlet pseudoscalar mesons. The lattice simulation is carried out using $N_f=2$ lattice QCD gauge configurations at the pion mass $m_π \approx 350$ MeV. In particular, the distillation method has been utilized to calculate light quark loops. The results are reported here with the mass $m_{η_{(2)}}= 718(8)$ MeV and the decay width $Γ(J/ψ\toγη_{(2)})=0.385(45)$ keV. By assuming the dominance of $\mathrm{U_A(1)}$ anomaly and flavor singlet-octet mixing angle $θ=-24.5^\circ$, the production rates for the physical $η$ and $η'$ in $J/ψ$ radiative decay are predicted to be $1.15(14)\times 10^{-3}$ and $4.49(53)\times 10^{-3}$, respectively, which agree well with the experimental measurement data. Our study manifests the potential of lattice QCD studies on the light hadron production in $J/ψ$ radiative decays.

hep-lat↗

arXiv2022

RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions

We present the vector, scalar and tensor renormalization constants (RCs) using overlap fermions with either regularization independent momentum subtraction (RI/MOM) or symmetric momentum subtraction (RI/SMOM) as the intermediate scheme on the lattice with lattice spacings $a$ from 0.04 fm to 0.12 fm. Our gauge field configurations from the MILC and RBC/UKQCD collaborations include sea quarks using either the domain wall or the HISQ action, respectively. The results show that RI/MOM and RI/SMOM can provide consistent renormalization constants to the $\overline{\textrm{MS}}$ scheme, after proper $a^2p^2$ extrapolations. But at $p\sim 2$\,GeV, both RI/MOM and RI/SMOM suffer from nonperturbative effects which cannot be removed by the perturbative matching. The comparison between the results with different sea actions also suggests that the renormalization constant is discernibly sensitive to the lattice spacing but not to the bare gauge coupling in the gauge action.

hep-lat↗

arXiv2022

$T_{cc}^{+}(3875)$ relevant $DD^*$ scattering from $N_f=2$ lattice QCD

The $S$-wave $DD^*$ scattering in the isospin $I=0,1$ channels is studied in $N_f=2$ lattice QCD at $m_π\approx 350$ MeV. It is observed that the $DD^*$ interaction is repulsive in the $I=1$ channel when the $DD^*$ energy is near the $DD^*$ threshold. In contrast, the $DD^*$ interaction in the $I=0$ channel is definitely attractive in a wide range of the $DD^*$ energy. This is consistent with the isospin assignment $I=0$ for $T_{cc}^+(3875)$. By analyzing the components of the $DD^*$ correlation functions, it turns out that the quark diagram responsible for the different properties of $I=0,1$ $DD^*$ interactions can be understood as the charged $ρ$ meson exchange effect. This observation provides direct information on the internal dynamics of $T_{cc}^+(3875)$.

hep-lat↗

arXiv2022

Annihilation diagram contribution to charmonium masses

In this work, we generate gauge configurations with $N_f=2$ dynamical charm quarks on anisotropic lattices. The mass shift of $1S$ and $1P$ charmonia owing to the charm quark annihilation effect can be investigated directly in a manner of unitary theory. The distillation method is adopted to treat the charm quark annihilation diagrams at a very precise level. For $1S$ charmonia, the charm quark annihilation effect almost does not change the $J/ψ$ mass, but lifts the $η_c$ mass by approximately 3-4 MeV. For $1P$ charmonia, this effect results in positive mass shifts of approximately 1 MeV for $χ_{c1}$ and $h_c$, but decreases the $χ_{c2}$ mass by approximately 3 MeV. We have not obtain a reliable result for the mass shift of $χ_{c0}$. In addition, it is observed that the spin averaged mass of the spin-triplet $1P$ charmonia is in a good agreement with the $h_c$, as expected by the non-relativistic quark model and measured by experiments.

hep-lat↗

arXiv2022

The Glueball content of $η_c$

We carry out the first lattice QCD derivation of the mixing energy and the mixing angle of the pseudoscalar charmonium and glueball on two gauge ensembles with $N_f=2$ degenerate dynamical charm quarks. The mixing energy is determined to be $49(6)$ MeV on the near physical charm ensemble, which seems insensitive to charm quark mass. By the assumption that $X(2370)$ is predominantly a pseudoscalar glueball, the mixing angle is determined to be approximately $4.6(6)^\circ$, which results in a $+3.9(9)$ MeV mass shift of the ground state pseudoscalar charmonium. In the mean time, the mixing can raise the total width of the pseudoscalar charmonium by 7.2(8) MeV, which explains to some extent the relative large total width of the $η_c$ meson. As a result, the branching fraction of $η_c\to γγ$ can be understood in this $c\bar{c}$-glueball mixing framework. On the other hand, the possible discrepancy of the theoretical predictions and the experimental results of the partial width of $J/ψ\toγη_c$ cannot be alleviated by the $c\bar{c}$-glueball mixing picture yet, which demands future precise experimental measurements of this partial width.

hep-lat↗

arXiv2021

Color halo scenario of charmonium-like hybrids

The internal structures of $J^{PC}=1^{--}, (0,1,2)^{-+}$ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function $Φ_n(r)$ in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator $\bar{c}{c}g$ between the vacuum and $n$-th state for each $J^{PC}$ with $r$ being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their $r$-behaviors (no node for the ground states and one node for the first excited states) imply that $r$ can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a "color halo" charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of $Y(4260)$ and suggests LHCb and BelleII to search for $(0,1,2)^{-+}$ charmonium-like hybrids in $χ_{c0,1,2}η$ and $J/ψω(ϕ)$ final states.

hep-lat↗

arXiv2021

An Event-based Parameter Switching Method for Controlling Cybersecurity Dynamics

This paper proposes a new event-based parameter switching method for the control tasks of cybersecurity in the context of preventive and reactive cyber defense dynamics. Our parameter switching method helps avoid excessive control costs as well as guarantees the dynamics to converge as our desired speed. Meanwhile, it can be proved that this approach is Zeno-free. A new estimation method with adaptive time windows is used to bridge the gap between the probability state and the sampling state. With the new estimation method, several practical experiments are given afterwards.

cs.CR↗

arXiv2020

Charmed and $ϕ$ meson decay constants from 2+1-flavor lattice QCD

On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of $D_{s}^{(*)}$, $D^{(*)}$ and $ϕ$. The lattice size is $48^3\times96$, which corresponds to a spatial extension of $\sim5.5$ fm with the lattice spacing $a\approx 0.114$ fm. For the valence light, strange and charm quarks, we use overlap fermions at several mass points close to their physical values. Our results at the physical point are $f_D=213(5)$ MeV, $f_{D_s}=249(7)$ MeV, $f_{D^*}=234(6)$ MeV, $f_{D_s^*}=274(7)$ MeV, and $f_ϕ=241(9)$ MeV. The couplings of $D^*$ and $D_s^*$ to the tensor current ($f_V^T$) can be derived, respectively, from the ratios $f_{D^*}^T/f_{D^*}=0.91(4)$ and $f_{D_s^*}^T/f_{D_s^*}=0.92(4)$, which are the first lattice QCD results. We also obtain the ratios $f_{D^*}/f_D=1.10(3)$ and $f_{D_s^*}/f_{D_s}=1.10(4)$, which reflect the size of heavy quark symmetry breaking in charmed mesons. The ratios $f_{D_s}/f_{D}=1.16(3)$ and $f_{D_s^*}/f_{D^*}=1.17(3)$ can be taken as a measure of SU(3) flavor symmetry breaking.

hep-lat↗

arXiv2020

Strangeonium-like hybrids on the lattice

The strangeonium-like $s\bar{s}g$ hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for $1^{--}$ and $(0,1,2)^{-+}$ states with the color octet $s\bar{s}$ component being separated from the chromomagnetic field strength by spatial distances $r$, whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the $(1,2)^{-+}$ channels, the masses and the BS wave functions are reliably derived. The $1^{-+}$ ground state mass is around 2.1-2.2 GeV, and that of $2^{-+}$ is around 2.3-2.4 GeV, while the masses of the first excited states are roughly 1.4 GeV higher. This mass splitting is much larger than the expectation of the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to $r$ show clear radial nodal structures of non-relativistic two-body system, which imply that $r$ is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids that the color octet $s\bar{s}$ is surrounded by gluonic degrees of freedom. In the $1^{--}$ channel, the properties of the lowest two states comply with those of $ϕ(1020)$ and $ϕ(1680)$. We have not obtained convincing information relevant to $ϕ(2170)$ yet, however, we argue that whether $ϕ(2170)$ is a conventional $s\bar{s}$ meson or a $s\bar{s}g$ hybrid within the color halo scenario, the ratio of partial decay widths $Γ(ϕη)$ and $Γ(ϕη')$ observed by BESIII can be understood by the mechanism of hadronic transition of a strangeonium-like meson along with the $η-η'$ mixing.

hep-lat↗

arXiv2020

A Lattice Study of the Two-photon Decay Widths for Scalar and Pseudo-scalar Charmonium

In this exploratory study, two photon decay widths of pseudo-scalar ($η_c$) and scalar ($χ_{c0}$) charmonium are computed using two ensembles of $N_f=2$ twisted mass lattice QCD gauge configurations. The simulation is performed two lattice ensembles with lattice spacings $a=0.067$ fm with size $32^3\times{64}$ and $a=0.085$ fm with size $24^3\times{48}$, respectively. The results for the decay widths for the two charmonia are obtained which are in the right ballpark however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.

hep-lat↗

arXiv2020

Trace anomaly and dynamical quark mass

We investigated the origin of the RI'/MOM quark mass under the Landau gauge at the non-perturbative scale, using the chiral fermion with different quark masses and lattice spacings. Our result confirms that such a mass is non-vanishing based on the linear extrapolation to the chiral and continuum limit, and shows that such a mass comes from the spontaneous chiral symmetry breaking induced by the near zero modes with the eigenvalue $λ<{\cal O}(5m_q)$, and is proportional to the quark matrix element of the trace anomaly at least down to $\sim $1.3 GeV.

hep-lat↗

arXiv2020

The nucleon isovector tensor charge from lattice QCD using chiral fermions

In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 fm to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadratic and a logarithmic term to fit the pion mass dependence, which describes well the lattice data. The lattice matrix element is renormalized non-perturbatively, and the final result is $g_T=1.096(30)$ in the $\overline{\rm MS}$ scheme at a renormalization scale of 2 GeV.

hep-lat↗

arXiv2019

A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$

In this exploratory study, near-threshold scattering of $D$ and $\bar{D}^*$ meson is investigated using lattice QCD with $N_f=2+1+1$ twisted mass fermion configurations. The calculation is performed within the coupled-channel Lüscher's finite-size formalism. The study focuses on the channel with $I^G(J^{PC})=1^+(1^{+-})$ where the resonance-like structure $Z_c(3900)$ was discovered. We first identify the most relevant two channels of the problem and the lattice study is performed within the two-channel scattering model. Combined with a two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results on the scattering length parameters suggest that, at the particular lattice parameters that we studied, the best fitted parameters do not correspond to a peak behavior in the elastic scattering cross section near the threshold. Furthermore, within the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond $3σ$ level.

hep-lat↗

arXiv2018

Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_π\sim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_π\sim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $ε_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $q\bar{q}$ meson. This indicates that the operator $ε_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $q\bar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.

hep-lat↗

arXiv2018

Proton Mass Decomposition from the QCD Energy Momentum Tensor

We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)\% and 37(5)(4)\% respectively in the $\overline{MS}$ scheme at $μ= 2$ GeV. A quarter of the trace anomaly gives a 23(1)(1)\% contribution to the proton mass based on the sum rule, given 9(2)(1)\% contribution from the $u, d,$ and $s$ quark scalar condensates. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are in good agreement with global analyses at $μ= 2$ GeV.

hep-lat↗

arXiv2018

Anatomy of the $ρ$ resonance from lattice QCD at the physical point

We propose a strategy to access the $q\bar{q}$ component of the $ρ$ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $q\bar{q}$ component is derived at different valence quark masses, and shows a linear dependence on $m_π^2$. The slope is determined to be $c_1=0.505(3)\,{\rm GeV}^{-1}$, from which the valence $πρ$ sigma term is extracted to be $σ_{πρ}^{(\rm val)}=9.82(6)$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $q\bar{q}$ component is interpolated to be $m_ρ=775.9\pm 6.0\pm 1.8$ MeV, which is close to the $ρ$ resonance mass. We also obtain the leptonic decay constant of the $q\bar{q}$ component to be $f_{ρ^-}=208.5\pm 5.5\pm 0.9$ MeV, which can be compared with the experimental value $f_ρ^{\rm exp}\approx 221$ MeV through the relation $f_ρ^{\rm exp}=\sqrt{Z_ρ}f_{ρ^\pm} $ with $Z_ρ\approx 1.13$ being the on-shell wavefunction renormalization of $ρ$ owing to the $ρ-π$ interaction. We emphasize that $m_ρ$ and $f_ρ$ of the $q\bar{q}$ component, which are obtained for the first time from QCD, can be taken as the input parameters of $ρ$ in effective field theory studies where $ρ$ acts as a fundamental degree of freedom.

hep-ph↗