arXiv subjects
Publications and source records attributed to Keh-Fei Liu.
We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.
We report the results on the proton mass decomposition and also on the 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 volumes, and several pion masses including the physical pion mass. With 1-loop perturbative calculation and proper normalization of the glue operator, we find that the $u, d,$ and $s$ quark masses contribute 9(2)\% to the proton mass. The quark energy and glue field energy contribute 31(5)\% and 37(5)\% respectively in the $\overline{MS}$ scheme at $μ= 2$ GeV. The trace anomaly gives the remaining 23(1)\% contribution. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are consistent with the global analysis at $μ= 2$ GeV.
It has been revealed from the path-integral formulation of the hadronic tensor that there are connected sea and disconnected sea partons. The former is responsible for the Gottfried sum rule violation primarily and evolves the same way as the valence. Therefore, the DGLAP evolution equations can be extended to accommodate them separately. We discuss its consequences and implications vis-a-vis lattice calculations.
A feasibility study of fusion reactors based on accelerators is carried out. We consider a novel scheme where a beam from the accelerator hits the target plasma on the resonance of the fusion reaction and establish characteristic criteria for a workable reactor. We consider the reactions $ d + t \rightarrow n + α, d + {}^3H_e \rightarrow p + α$, and $p + {}^{11}B \rightarrow 3 α$ in this study. The critical temperature of the plasma is determined from overcoming the stopping power of the beam with the fusion energy gain. The needed plasma lifetime is determined from the width of the resonance, the beam velocity and the plasma density. We estimate the critical beam flux by balancing the energy of fusion production against the plasma thermo-energy and the loss due to stopping power for the case of an inert plasma. The product of critical flux and plasma lifetime is independent of plasma density and has a weak dependence on temperature. Even though the critical temperatures for these reactions are lower than those for the thermonuclear reactors, the critical flux is in the range of $10^{22} - 10^{24}/\rm{cm^2/s}$ for the plasma density $ρ_t = 10^{15}/{\rm cm^3}$ in the case of an inert plasma. Several approaches to control the growth of the two-stream instability are discussed. We have also considered several scenarios for practical implementation which will require further studies. Finally, we consider the case where the injected beam at the resonance energy maintains the plasma temperature and prolongs its lifetime to reach a steady state. The equations for power balance and particle number conservation are given for this case.
We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_π = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange $g_A(q^2)$ at $q^2 =0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with $g_A(q^2)$ and the induced pseudoscalar form factor $h_A(q^2)$ at finite $q^2$. The chiral extrapolation to the physical pion mass gives $Δs + Δ{\bar{s}} = -0.0403(44)(78)$.
We report a lattice calculation of nucleon forward matrix elements on a $48^3 \times 96$ lattice at the physical pion mass and a spatial size of 5.5 fm. The $2+1$ flavor dynamical fermion configurations are generated with domain-wall fermions (DWF) and the overlap fermions are adopted for the valence quarks. The isovector $g_A^3$ and $g_S^3$, and the connected insertion part of $g_S^0$ are reported for three source-sink separations. With local current, we obtain $g_A^3 = 1.18(4)$ from a two-state fit. For the quark momentum fraction $\langle x \rangle_{u-d}$, we have included smaller lattices (i.e. $24^3 \times 64$ and $32^3 \times 64$ lattice with pion mass at 330 and 290 MeV respectively) for a fit which includes partially quenched cases as well as finite volume and continuum corrections. A global fit with perturbative renormalization gives $\langle x \rangle_{u-d} (\overline{MS},\, μ= 2\, {\rm GeV}) = 0.170(14)$. We made a cost comparison of calculating the nucleon matrix elements with those from the twisted mass fermion on similar sized lattice at the physical pion point and the domain-wall fermion calculation on the same DWF lattice. We also compare cost with the clover fermion calculation on similar sized lattice at about the same quark mass. The comparison shows that with several improvements, such as many-to-all correlator with grid source and low-mode substitution in the connected insertion and low-mode average in the quark loop can make the overlap as efficient as the twisted-mass and clover fermions in calculating the three-point functions. It is more efficient than the DWF. When the multi-mass feature is invoked, the overlap can be more efficient in reaching the same precision than the single mass comparison made so far.
We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of $0.051 \,\text{GeV}^2 \lesssim Q^2 \lesssim 1.31 \,\text{GeV}^2 $. The finite lattice spacing and finite volume corrections are included in a global fit with $24$ valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment $G^s_M(0) = - 0.064(14)(09)\, μ_N$. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius $\langle r_s^2\rangle_E = -0.0043 (16)(14)\,$ $\text{fm}^2$.
We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin $S_{G}$ in the Coulomb gauge in the $\overline{\text{MS}}$ scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of $S_G$ in the range $0\leq |\vec{p}| < 1.5$ GeV is very mild, and we determine it in the large momentum limit to be $S_{G}=0.251(47)(16)$ at the physical pion mass in the $\overline{\text{MS}}$ scheme at $μ^2=10$ GeV$^2$. If the matching procedure in large momentum effective theory is neglected, $S_G$ is equal to the glue helicity measured in high-energy scattering experiments.
We present the 1-loop renormalization of the energy momentum tensor using the overlap fermion and a HYP-smeared Iwasaki gauge action. We also calculate the 1-loop matching coefficient that convert the lattice simulation results renormalized in the RI/MOM scheme to the $\overline{\textrm{MS}}$ scheme. The dependence of the renormalization on the gauge action and the number of HYP smearing steps are also investigated.
We report the renormalization and mixing constants to one-loop order for the quark and gluon energy-momentum (EM) tensor operators on the lattice. A unique aspect of this mixing calculation is the definition of the glue EM tensor operator. The glue operator is comprised of gauge-field tensors constructed from the overlap Dirac operator. The resulting perturbative calculations are performed using methods similar to the Kawai approach using the Wilson action for all QCD vertices and the overlap Dirac operator to define the glue EM tensor. Our results are used to connect the lattice QCD results of quark and glue momenta and angular momenta to the $\overline{\text{MS}}$ scheme at input scale $μ$
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $πN σ$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
Lattice QCD calculations with chiral fermions of the $π$N sigma term $σ_{πN}$ and strangeness sigma term $σ_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $σ_{πN}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $σ_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $σ_{πN}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1).
The path-integral formulation of the hadronic tensor W_{μν} of deep inelastic scattering is reviewed. It is shown that there are 3 gauge invariant and topologically distinct contributions. The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion. We shall discuss numerical issues associated with lattice calculation of the hadronic tensor involving a four-point function, such as large hadron momenta and improved maximum entropy method to obtain the spectral density from the hadronic tensor in Euclidean time. We also draw a comparison between the large momentum approach to the parton distribution function (PDF) and the hadronic tensor approach.
We report the progress on the lattice QCD calculation of the glue spin contribution to proton spin. This calculation is carried out with valence overlap fermion on 2+1 flavor DWF gauge configurations at two lattice spacings with the momentum of the frame in the kinematic range $0\leq p^2 \leq 2$ GeV$^2$. A mild frame dependence is observed. The matching and mixing with large-momentum effective field theory are in progress. The unrenormalized result at $p^2=4$ GeV$^2$ with $O(a^2)$ correction gives $S_G$ = 0.13(3).
We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_π = 330$ MeV with lattice spacing $a = 0.114$ fm.
It is commonly believed that the lowest-lying scalar glueball lies somewhere in the isosinglet scalar mesons $f_0(1370), f_0(1500)$ and $f_0(1710)$ denoted generically by $f_{0}$. In this work we consider lattice calculations and experimental data to infer the glue and $q\bar q$ components of $f_0$. These include the calculations of the scalar glueball masses in quenched and unquenched lattice QCD, measurements of the radiative decays $J/ψ\toγf_{0}$, the ratio of $f_{0}$ decays to $ππ$ and $K\bar K$, the ratio of $J/ψ$ decays to $f_0(1710)ω$ and $f_0(1710)ϕ$, the $f_0$ contributions to $B_s\to J/ψπ^+π^-$, and the near mass degeneracy of $a_0(1450)$ and $K_0^*(1430)$. All analyses suggest the prominent glueball nature of $f_0(1710)$ and the flavor octet structure of $f_0(1500)$.
Theoretical progress on the formulation and classification of the quark and gluon orbital angular momenta (OAM) is reviewed. Their relation to parton distributions and open questions and puzzles are discussed. We give a status report on the lattice calculation of the parton kinetic and canonical OAM and point out several strategies to calculate the quark and gluon canonical OAM on the lattice.
We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/ψ$ as inputs, Sommer's scale parameter $r_0$ and the masses of charm quark and strange quark in the $\overline{\rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{\overline{\rm MS}}(2\,{\rm GeV})=1.118(6)(24)$ GeV (or $m_c^{\overline{\rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{\overline{\rm MS}}(2\,{\rm GeV})=0.101(3)(6)\,{\rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/ψ}-M_{η_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $χ_{c0}, χ_{c1}$ and $h_c$ are also in good agreement with experiments.