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1. Hydrogen energy levels from the anomalous energy-momentum QED trace

   https://doi.org/10.1103/PhysRevD.110.076020  

   Eides, Michael I (October 2024, Physical Review D)

   Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb shift one-loop diagrams. Our calculations provide an argument against inclusion of the anomalous trace contribution as a separate term in the decomposition of the QED quantum field Hamiltonian and serve as an illustration how the trace anomaly is realized in the bound state QED. 

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2. 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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3. 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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4. Mass sum rules of the electron in quantum electrodynamics

   https://doi.org/10.1007/JHEP09(2020)067  

   Rodini, S.; Metz, A.; Pasquini, B. (September 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon. 

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5. Coulomb-free 1S0 p − p scattering length from the quasi-free p + d → p + p + n reaction and its relation to universality

   https://doi.org/10.1038/s42005-023-01221-0  

   Tumino, Aurora; Rapisarda, Giuseppe G.; La Cognata, Marco; Oliva, Alessandro; Kievsky, Alejandro; Bertulani, Carlos A.; D’Agata, Giuseppe; Gattobigio, Mario; Guardo, Giovanni L.; Lamia, Livio; et al (May 2023, Communications Physics)

   Abstract The Coulomb-free¹S₀proton-proton (p-p) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shellp-pscattering cross section measured at center-of-mass energies below 1 MeV using the quasi-freep + d → p + p + nreaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned ap-pscattering length$${a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}\pm 0.0{1}_{syst}$$ $a_{pp}=-18.17_{-0.58}^{+0.52}{\mid }_{stat}\pm 0.01_{syst}$fm and effective ranger₀ = 2.80 ± 0.05_stat ± 0.001_systfm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shiftδdoes in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking. 

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