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1. Constraints on the finite volume two-nucleon spectrum at $m_{\pi }\approx 806\mathrm{MeV}$

   https://doi.org/10.1103/PhysRevD.111.114501  

   Detmold, William; Illa, Marc; Jay, William I; Parreño, Assumpta; Perry, Robert J; Shanahan, Phiala E; Wagman, Michael L (June 2025, Physical Review D)

   The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of $m_{\pi }\approx 806\mathrm{MeV}$ is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, .] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated. Published by the American Physical Society2025 

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2. Gluon moment and parton distribution function of the pion from $N_f=2+1+1$ lattice QCD

   https://doi.org/10.1103/PhysRevD.109.114509  

   Good, William; Hasan, Kinza; Chevis, Allison; Lin, Huey-Wen (June 2024, Physical Review D)

   We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with $2+1+1$ flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain $⟨x{⟩}_g=0.394\left(58{)}_{\mathrm{stat}+\mathrm{NPR}}\right(39{)}_{\text{mixing}}$ in the $\overline{\mathrm{MS}}$ scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates. Published by the American Physical Society2024 

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3. Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the fourth moment of the pion distribution amplitude

   https://doi.org/10.1103/xs4z-nblq  

   Detmold, William; Grebe, Anthony V; Kanamori, Issaku; Lin, C-J David; Perry, Robert J; Zhao, Yong (January 2026, Physical Review D)

   The pion light-cone distribution amplitude (LCDA) is an essential nonperturbative input for a range of high-energy exclusive processes in quantum chromodynamics. Building on our previous work, the continuum limit of the fourth Mellin moment of the pion LCDA is determined in quenched QCD using quark masses which correspond to a pion mass of $m_{\pi }=550\mathrm{MeV}$ . This calculation finds $⟨{\xi }^2⟩=0.202\left(8\right)\left(9\right)$ and $⟨{\xi }^4⟩=0.039\left(28\right)\left(11\right)$ where the first error indicates the combined statistical and systematic uncertainty from the analysis and the second indicates the uncertainty from working with Wilson coefficients computed to next-to-leading order. These results are presented in the $\overline{\mathrm{MS}}$ scheme at a renormalization scale of $\mu =2\mathrm{GeV}$ . 

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4. Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Tensor case

   https://doi.org/10.1103/tlkb-ykgp  

   Bhattacharya, Shohini; Cichy, Krzysztof; Constantinou, Martha; Metz, Andreas; Miller, Joshua; Petreczky, Peter; Steffens, Fernanda (December 2025, Physical Review D)

   The calculation of generalized parton distributions (GPDs) in lattice QCD was traditionally done by calculating matrix elements in the symmetric frame. Recent advancements have significantly reduced computational costs by calculating these matrix elements in the asymmetric frame, allowing us to choose the momentum transfer to be in either the initial or final states only. The theoretical methodology requires a new parametrization of the matrix element to obtain Lorentz-invariant amplitudes, which are then related to the GPDs. The formulation and implementation of this approach have already been established for the unpolarized and helicity GPDs. Building upon this idea, we extend this formulation to the four leading-twist quark transversity GPDs ( $H_T$ , $E_T$ , ${\tilde{H}}_T$ , ${\tilde{E}}_T$ ). We also present numerical results for zero skewness using an $N_f=2+1+1$ ensemble of twisted mass fermions with a clover improvement. The light quark masses employed in these calculations correspond to a pion mass of about 260 MeV. Furthermore, we include a comparison between the symmetric and asymmetric frame calculations to demonstrate frame independence of the Lorentz-invariant amplitudes. Analysis of the matrix elements in the asymmetric frame is performed at several values of the momentum transfer squared, $-t$ , ranging from $0.17$ to $2.29{\mathrm{GeV}}^2$ . 

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5. Trace anomaly form factors from lattice QCD

   https://doi.org/10.1103/PhysRevD.109.094504  

   Wang, Bigeng; He, Fangcheng; Wang, Gen; Draper, Terrence; Liang, Jian; Liu, Keh-Fei; Yang, Yi-Bo (May 2024, Physical Review D)

   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 $\sim 540\mathrm{MeV}$ , including the unitary point $\sim 340\mathrm{MeV}$ . 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. Published by the American Physical Society2024 

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