The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of m pi 806 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, Phys. Rev. D 107, 094508 (2023).] 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.

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, μ_I, bounds the partition function for a baryon chemical potential μ_B=3μ_I/2, these calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time.

Forward photoproduction of π+π− pairs with invariant mass of the order of mρ∼770 MeV is traditionally attributed to Pomeron exchange. Based on a detailed analysis of the CEBAF Large Acceptance Spectrometer photoproduction data collected at photon energies below 4 GeV, it is shown from a study of the angular moments that the dynamics of two-pion photoproduction for |t|≳0.5 GeV2 cannot be explained by Pomeron exchange alone. This motivates the development of a new theoretical model of two-pion photoproduction which incorporates both two-pion and pion-nucleon resonant contributions. After fitting free parameters, the model provides an excellent description of the low moments of the angular distribution measured at CLAS and enables an assessment of the relative contributions of particular production mechanisms and an interpretation of the various features of the data in terms of these mechanisms. Published by the American Physical Society 2025

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, 6C, to be about 3 times larger than the Wilson loop string tension, 6F. It is far above the Zwanziger variational bound, 6C >= 6F. We argue that the value often reported in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension's enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as 6C/6F = 2.0 + 0.4 and discuss its phenomenological implications.

The Reggeized pion is expected to provide the main contribution to the forward cross section in light meson photoproduction reactions with charge exchange at high energies. We discuss the Reggeization of pion exchange in charged pion photoproduction with an emphasis on consistency with current conservation. We show that the gauge-invariant amplitude for the exchange of a particle with a generic even spin J >= 2 in the t channel is analytic at J 1/4 0 and that it can be interpreted in terms of the nucleon electric current. This enables us to reconcile the dynamics in the s and u channel, which involves also nucleon exchanges, with the amplitude expressed in terms of t-channel partial waves, as required by Regge theory.

In the domain of hadron spectroscopy, the investigation of meson resonances plays a pivotal role. This study focuses on the significance of twopion photoproduction as a prominent avenue for studying meson resonances in the ππ system. By employing the Regge formalism, our model incorporates the background contribution from the well-known “Deck Mechanism” and emphasizes the significant ρ(770) resonance, representing the P-wave contribution arising from pomeron and f2 exchanges. The model is extended by accounting for scalar mesons, namely σ, f0(980) and f0(1370), contributing to the S-wave behavior, as well as the tensor meson f2(1270) corresponding to the D-wave contributions, while also considering non-resonant P- and S-wave components. The model contains a number of free parameters, which are constrained from a global fit of the available experimental data for angular moments up to L = 2 for M = 0, …, 2. The fitted angular moments are compared with experimental data obtained from CLAS. The key physical insights gained from the model are summarized. Furthermore, we extract the t-dependence of the Regge amplitude residue function for the subdominant exchanges, shedding light on their contribution to the overall dynamics.

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of $n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N \times N$ matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 $\pi^+$s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass $m_\pi = 170$ MeV and spacetime volumes of $(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential $\mu_I\sim 1.5 m_\pi$, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq 1/3$) over a wide range of chemical potential before falling towards the asymptotic expectation at $\mu_I\sim 15 m_\pi$. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA The NSF AI Institute for Artificial Intelligence and Fundamental Interactions RIKEN Center for Computational Science, Kobe 650-0047, Japan Institute of Physics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan Centre for Theoretical and Computational Physics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan

We highlight the need for the development of comprehensive amplitude analysis methods to further our understanding of hadron spectroscopy. Reaction amplitudes constrained by first principles of $S$-matrix theory and by QCD phenomenology are needed to extract robust interpretations of the data from experiments and from lattice calculations.

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. This article describes the progress in the lattice QCD calculation of the fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion (HOPE).

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. In this article, we discuss the calculation of the second and fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion. The resulting value for the second Mellin moment is $ \langle{ \xi^2 }\rangle(\mu = 2~\text{GeV})= 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}$. This result is compatible with those from previous determinations of this quantity.

Parton distribution functions (PDFs) and light cone distribution amplitudes (LCDAs) are central nonperturbative objects of interest in high-energy inelastic and elastic scattering, respectively. As a result, an ab initio determination of these objects is highly desirable. In this paper we present theoretical details for the calculation of the PDFs and LCDAs using a heavy-quark operator product expansion method. This strategy was proposed in a previous paper [Phys. Rev. D 73, 014501 (2006)] for computing higher moments of the PDFs using lattice QCD. Its central feature is the introduction of a fictitious, valence heavy quark. In the current article, we show that the operator product expansion of the hadronic matrix element we study can also be expressed as the convolution of a perturbative matching kernel and the corresponding light cone distribution, which in principle can be inverted to determine the parton momentum fraction dependence. Regarding the extraction of higher moments, this work also provides the one-loop Wilson coefficients in the operator product expansion formulas for the unpolarized PDF, helicity PDF and pseudoscalar meson LCDAs. Although theseWilson coefficients for the PDFs can be inferred from existing results in the literature, those for the LCDAs are new.

Current measurements of the high energy behavior of the pion form factor are obtained from pion electroproduction data. These values are model dependent, utilizing the Vanderhaeghen, Guidal and Laget Regge (VGL) Model for their extraction. Recent work which examined the implementation of gauge invariance in that model suggested that it might lead to extracted pion form factors larger than the true values. Here we introduce a new model which preserves the successes of the VGL Model but implements gauge invariance in a new way. To demonstrate the validity of this new approach, we first use it to extract the pion form factor in a simple toy model. When compared with the previous extraction method, the improved model leads to a more reliable extraction. The success in this simple model leads us to reanalyze the electroproduction cross section data, where we obtain comparable values for the pion form factor to those obtained using the VGL procedure.

We explore the feasibility of determining Mellin moments of the pion's light cone distribution amplitude using the heavy quark operator product expansion (HOPE) method. As the first step of a proof of principle study we pursue a determination of the second Mellin moment. We discuss our choice of kinematics which allows us to successfully extract the moment at low pion momentum. We describe the numerical simulation, and describe the data analysis, which leads us to a preliminary determination of the second Mellin moment in the continuum limit in the quenched approximation as ⟨ξ^2⟩=0.19(7) in the M̅S̅ scheme at 2 GeV.

In 2008 the Jefferson Laboratory F-pi Collaboration released results for the pion electromagnetic form factor, which they extracted from pion electroproduction data. The measured values for the pion form factor are model dependent, and require the use of the Vanderhaeghen, Guidal, and Laget Regge model for their extraction. While agreement between this model and data is impressive, the theoretical implementation of gauge invariance is less satisfying. We would like to establish how well the extracted form factor corresponds to the true form factor. To do this, we use a simple toy model, which imposes gauge invariance in a more theoretically satisfying way. The model form factor is extracted from our model cross section using the method employed by the F-pi Collaboration to extract the experimental pion form factor. We conclude that the reconstructed model form factor is a reasonable representation of the true model form factor for the kinematics chosen, although we note that the extracted form factor is smaller than the true form factor. This suggests that current extracted values of the pion form factor may be overestimated.

Corrections motivated by chiral symmetry arguments have long been known to give important contributions to hadronic observables, particularly at low momentum transfer. It is possible to separate these approaches into two broad groups; either the corrections are implemented at the parton level, or at the hadron level. We explore the results of incorporating pion loop corrections at the hadron level to a calculation of electromagnetic form factors in the NJL model. These calculations are compared with the result of an earlier implementation of pion loops at the parton level using the same NJL model formalism. A particular parameter set yields a good description of low energy nucleon properties within both approaches. However, for the there is a remarkable improvement when the chiral corrections are implemented at the hadronic level.

It has long been known that corrections motivated by chiral symmetry arguments give important contributions to hadronic observables. Results of incorporating pion loop corrections to the NJL Model - a constituent quark model - are presented here. A particular parameter set yields a good fit to the nucleon charge radius $$ and a slightly low prediction of the nucleon magnetic moment $\mu$.

Dear Editor, I would just like to comment on what I feel is an incorrect statement in the Quiz Corner of the Nov 2011 CVJ (Can Vet J 2011;52:1175–1176;1246). In the answer to question 2 regarding perianal fistulae, there is a comment made that it is a surgical disease. I would disagree with that. I think you will find that it is now considered an immune-mediated disease that is treated with cyclosporin or tacrolimus.