arXiv subjects

Keh-Fei Liu

Publications and source records attributed to Keh-Fei Liu.

At least 19 recordsLinked to original sources

arXiv2026

Pressure-Energy Equations of State of the Nucleon

The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parametrize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. The pressure and energy densities naturally separate into two distinct components. The static pressure distribution, arising from the Lorentz trace part of the EMT, as manifested in the spatial stress $\frac{1}{3} T^{ii}$, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as a consequence of the full or partial depletion of the gluon and quark condensates through the pressure-volume relation. The resulting trace anomaly- and sigma term-induced pressure is shown, through its volume scaling, to play a pivotal role in QCD confinement. In contrast, the dynamic pressure distribution, associated with the traceless part of the stress tensor equals $1/d$ of the corresponding traceless part of the energy density, where $d$ is the spatial dimension. These static and dynamic components together satisfy the pressure-balance condition in the nucleon. We further show that the same pressure-energy equations of state hold for vortices in type-II superconductors, where the static pressure-energy relation originates from the depletion of the Cooper-pair condensate. Moreover, these equations of state are identical to those of the $Λ{\rm CDM}$ cosmological model, where the static pressure-energy relation is generated by the cosmological constant.

hep-ph↗

arXiv2026

Direct lattice QCD calculation of the $θ$-induced CP-violating pion-nucleon coupling

We present the first direct lattice QCD determination of the $θ$-induced CP-violating pion-nucleon-nucleon coupling $\tilde g_{πNN}$. Using overlap valence fermions on three $2+1$-flavor domain-wall ensembles at a single lattice spacing, we calculate the forward proton matrix element of the isovector pseudoscalar density in the $θ$-vacuum to first order in $\barθ$. The parity-mixing effect in the external nucleon states is included in the extraction. The cluster-decomposition error-reduction method is used to improve the statistical precision. A simultaneous extrapolation in the valence- and sea-pion masses, with model averaging over 7 forms based on the Akaike information criterion, gives $\tilde g_{πNN}=0.0306(56)(124)\,\barθ$ at the physical point. The first uncertainty includes the statistical and matrix-element-fit systematic uncertainties, whereas the second reflects the spread among the extrapolation forms. Within these uncertainties, the result is consistent with the indirect determination based on the strong neutron-proton mass splitting. The present precision is limited primarily by the extrapolation from the relatively heavy sea-pion masses.

hep-lat↗

arXiv2026

Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics

We compute the Euclidean hadronic tensor from charge density operators and extract elastic and resonance structures by employing exponential fits to the four-point correlator, as well as a Bayesian reconstruction inverse algorithm to obtain the corresponding spectral density for qualitative comparison. We present the determination of the nucleon's Sachs electric form factor using the hadronic tensor formalism and verify that it is consistent with that from the conventional three-point function calculation. Beyond the elastic peak, we observe a structure located approximately $0.5-0.7$ GeV above the nucleon mass in the Bayesian reconstruction. The structure is interpreted as a mixture of the Roper resonance $(N(1440))$, and states with both positive and negative parities in this mass region, as well as multi-hadron states. Assuming the observed structure is dominated by $J^P=1/2^{\pm}$ states, we extract the transition electric form factor $G_E^{*}(Q^2)$ and the corresponding longitudinal helicity amplitude $S_{1/2}(Q^2)$, and compare them with those determined from the CLAS experimental data of nucleon-to-Roper transition. Although fitting to the four-point correlation function or using the inverse algorithm does not resolve individual resonances, it nevertheless enables the determination of total inclusive lepton-nucleon scattering cross sections in appropriate energy bins. This lattice QCD calculation presents the first major step toward studying the inclusive $N \to X$ contributions with the hadronic tensor formalism.

hep-lat↗

arXiv2026

The hadronic tensor from four-point functions on the lattice

The hadronic tensor is the central non-perturbative object in the calculation of the cross section of lepton-hadron interactions like neutrino-nucleon scattering. It is usually parameterized in terms of structure functions, which encode all necessary information for all kinematic regions. Moreover, the structure functions can be factorized in terms of parton distribution functions (PDFs) and contains information on hadron resonances. On the lattice, we can calculate the corresponding matrix element of two quark-bilinear currents with a relative Euclidean time separation. The reconstruction of the hadronic tensor in Minkowski space requires appropriate dealing with the corresponding inverse problem. In our current work, we extend previous calculations on the nucleon by considering a much larger range of momentum transfers, which is inevitable in the context of structure functions. This can be achieved by using stochastic sources, which allows us to calculate the required four-point functions in a broad kinematic region. We employ a clover fermion ensemble at pion mass $m_π= 223~\mathrm{MeV}$ and lattice spacing $a=0.085~\mathrm{fm}$. In these proceedings, we will give an overview of our simulation and present some first preliminary results.

hep-lat↗

arXiv2025

Unveiling the Strong Interaction origin of Baryon Masses with Lattice QCD

Both the Higgs mechanism and strong interactions contribute to the masses of visible matter, yet how the six Higgs-generated quark masses and uniform strong interaction strength determine the hundreds of hadron masses remains unclear. Additionally, the role of massless, flavor-neutral gluons on hadron mass formation is central to the unresolved Millennium Prize problem on the mass gap in Yang-Mills theory. Addressing these questions requires advanced simulations on state-of-the-art supercomputers using Lattice Quantum Chromodynamics (QCD), which offers a rigorous, non-perturbative definition of QCD solvable numerically. Here we present first-principles lattice QCD calculations using comprehensive gauge ensembles that accurately predict ground state spin-1/2 and spin-3/2 baryon masses with light, strange, and charm quarks within 1\% of experimental values. At the $\overline{\mathrm{MS}}$ 2 GeV scale, our results unveil two fundamental mass generation mechanisms for those baryon masses in QCD: 1) the flavor-dependent enhancement of Higgs contributions, 4-8 for light, 2-3 for strange, and 1.2-1.3 for charm quarks; and 2) the flavor-insensitive contribution 0.8-1.2 GeV from gluon quantum anomaly. This breakthrough significantly advances our comprehension of strong interaction dynamics and the genesis of visible matter's mass.

hep-lat↗

arXiv2025

Form factors in semileptonic decay of D mesons

We study the vector, scalar and tensor form factors for the semileptonic process $D\rightarrow K$ by using lattice Quantum Chromodynamcs (QCD). Chiral lattice fermions are used in our study: overlap fermion for the valence quark and domain-wall fermion for the sea. The 2+1-flavor configurations are from the RBC-UKQCD Collaborations with an inverse lattice spacing $1/a=2.383(9)$ GeV. A modified $z$-expansion taking into account valence quark mass dependence is used to fit our numerical results of the form factors at a fixed pion mass $\sim360$ MeV in the sea. At the physical valence quark mass point we give the preliminary results $f_+(0)=f_0(0)=0.760(39)$ and $f_T(0)=0.733(50)$ with only statistical uncertainties. For $f_T$ the number is given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV.

hep-lat↗

arXiv2025

Temperature Dependence of Beam on Plasma Stopping Power in the Resonance Regions of Fusion Reactions

A recent proposal of accelerator based fusion reactor considers a scheme where an ion beam from the accelerator hits the target plasma on the resonance of the fusion reaction so that the reactivity ($σv$) can be an order of magnitude larger than that of a thermonuclear reactor. One of the important inputs is the stopping power which is needed to assess the energy loss of the beam in the plasma. In this work, we shall use the analytic formulation of Brown, Preston and Singleton~\cite{Brown:2005ji} to calculate the temperature dependence of the stopping power due to the target $t, {}^3H_e$, and ${}^{11}B$ plasmas in the resonance regions of their respective fusion reactions, i.e., $ d + t \rightarrow n + α, d + {}^3H_e \rightarrow p + α$, and $p + {}^{11}B \rightarrow 3 α$. It is found that the calculated stopping power, especially when the quantum corrections are included, does not go down with temperature as fast at $T^{-3/2}$. Instead it decreases slower, more like $T^{-x}$ with $x \le 1$ in the range of T from $\sim$ 5 to 50 keV for $d$ on $t$ and ${}^3H_e$ plasmas around their resonance energies.

physics.plasm-ph↗

arXiv2024

Separation of Infrared and Bulk in Thermal QCD

A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N$_f$=0) and ``real-world" (N$_f$=2+1 at physical quark masses) QCD. In this {\it IR phase}, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra ($λ_{\rm IR} \!=\! 0$, $\pm λ_\text{A} \!\neq\! 0$), as manifested in the dimension function $d_{\rm IR} (λ)$. Here, we present the first evidence, based on lattice QCD calculation at $a$=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at $T\!=\!234\,$MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity ($d_{\rm IR} \!=\!3$ to $d_{\rm IR} \!\simeq\! 2$), similar to the IR phase of pure-glue QCD, at $T\!=\!187\,$MeV we observe a continuous $λ$-dependence. This suggests that thermal states just {\it above} the chiral crossover are non-analytically (in $T$) connected to thermal state at $T\!=\!234\,$MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.

hep-lat↗

arXiv2024

Lattice QCD and the Neutron Electric Dipole Moment

The recent lattice QCD calculations of the neutron and proton electric dipole moments (EDMs) and the CP-violating $π{\rm NN}$ coupling constant due to the $θ$ term are reviewed. Progress towards nucleon EDM calculations, including the Weinberg three-gluon operator, and the quark chromoelectric dipole moment operator and their renormalization, is also discussed.

hep-lat↗

arXiv2024

Detecting the flavor content of the vacuum using the Dirac operator spectrum

We compute the overlap Dirac spectrum on three gauge ensembles generated using $2+1$-flavor domain wall fermions. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. The spectral density is determined up to $λ\sim$100 MeV with subpercentage statistical uncertainty. We find that the density is close to a constant below $λ\sim$ 20 MeV as predicted by chiral perturbative theory ($χ$PT), and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order $χ$PT form and using the non-perturbative RI/MOM renormalization, the $\rm SU(2)$ (keeping the strange quark mass at the physical point) and $\rm SU(3)$ chiral condensates at $\overline{\textrm{MS}}$ 2 GeV are determined to be $Σ=(265.4(0.5)(4.2)\ \textrm{MeV})^3$ and $Σ_0=(234.3(0.5)(25.8)\ \textrm{MeV})^3$, respectively. The pion decay constants are also determined to be $F=84.1(1.9)(8.0)$ and $F_0=58.6(0.5)(10.0)$ MeV. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant $L_6$. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with {$\sim10\%-20\%$} statistical uncertainties using the Dirac spectral density.

hep-lat↗

arXiv2024

Charm physics with overlap fermions on 2+1-flavor domain wall fermion configurations

Decay constants of pseudoscalar mesons $D$, $D_s$, $η_c$ and vector mesons $D^*$, $D_s^*$, $J/ψ$ are determined from $N_f=2+1$ lattice QCD at a lattice spacing $a\sim0.08$ fm. For vector mesons, the decay constants defined by tensor currents are given in the $\overline{\rm MS}$ scheme at $2$ GeV. The calculation is performed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations and the overlap fermion action is used for the valence quarks. Comparing the current results with our previous ones at a coarser lattice spacing $a\sim0.11$ fm gives us a better understanding of the discretization error. We obtain $f_{D_s^*}^T(\overline{\rm MS},\text{2 GeV})/f_{D_s^*}=0.907(20)$ with a better precision than our previous result. Combining our $f_{D_s^*}=277(11)$ MeV with the total width of $D_s^*$ determined in a recent work gives a branching fraction $4.26(52)\times10^{-5}$ for $D_s^*$ leptonic decay.

hep-lat↗

arXiv2024

Trace anomaly form factors from lattice QCD

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to $Q^2\sim 4.3~\mathrm{GeV}^2$ and the nucleon up to $Q^2\sim 1~\mathrm{GeV}^2$. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from $\sim 250$ to $\sim 540$ MeV, including the unitary point $\sim 340$ MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the $z$ expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion's form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit.

hep-lat↗

arXiv2024

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays

We present the first lattice QCD calculation of the universal axial $γW$-box contribution $\square_{γW}^{VA}$ to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of $|V_{ud}|$ from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon 4-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at $\square_{γW}^{VA}=3.65(8)_{\mathrm{lat}}(1)_{\mathrm{PT}}\times10^{-3}$. Consequently, this yields a slightly higher value of $|V_{ud}|=0.97386(11)_{\mathrm{exp.}}(9)_{\mathrm{RC}}(27)_{\mathrm{NS}}$, reducing the previous $2.1σ$ tension with the CKM unitarity to $1.8σ$. Additionally, we calculate the vector $γW$-box contribution to the axial charge $g_A$, denoted as $\square_{γW}^{VV}$, and explore its potential implications.

hep-lat↗

arXiv2024

Fast Fermion Smearing Scheme with Gaussian-like Profile

We propose a novel smearing scheme which gives a Gaussian-like profile and is more efficient than the traditional Gaussian smearing in terms of computer time consumption. We also carry out a detailed analysis of the profiles, smearing sizes, and the behaviors of hadron effective masses of different smearing schemes, and point out that having a sufficient number of gauge paths in a smearing scheme is essential to produce strong smearing effects. For a moderate smearing size $\bar{r}\sim 10a$, the time cost for the novel smearing is less than $1/8$ of that for the traditional Gaussian smearing. In practical lattice calculations with larger smearing sizes or finer lattice spacings the improvement will be more substantial.

hep-lat↗

arXiv2023

Hadrons, Superconductor Vortices, and Cosmological Constant

We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element, emerging from the glue condensate in the vacuum, gives a negative constant pressure that leads to confinement, much like the confinement mechanism for the vortices in type II superconductors where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein's equation are associated with the metric term which contributes to both energy and pressure. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

hep-ph↗

arXiv2023

RI/(S)MOM renormalizations of overlap quark bilinears with different levels of hypercubic smearing

On configurations with 2+1-flavor dynamical domain-wall fermions, we calculate the RI/(S)MOM renormalization constants (RC) of overlap quark bilinears. Hypercubic (HYP) smearing is used to construct the overlap Dirac operator. We investigate the possible effects of the smearing on discretization errors in the RCs by varying the level of smearing from 0 to 1 and 2. The lattice is of size $32^3\times64$ and with lattice spacing $1/a=2.383(9)$ GeV. The RCs in the $\overline{\rm MS}$ scheme at 2 GeV are given at the end, with the uncertainty of $Z_T$ reaching $\le1$% for the tensor current. Results of the renormalized quark masses and hadron matrix elements show that the renormalization procedure suppresses the $\sim$ 30% difference of the bare quantities with or without HYP smearing into the 3%-5% level.

hep-lat↗

arXiv2023

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

hep-ph↗

arXiv2023

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

hep-ph↗