arXiv subjects

Thomas R. Richardson

Publications and source records attributed to Thomas R. Richardson.

18 recordsLinked to original sources

arXiv2026

Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory

We study quantum resources in the spin degrees of freedom, such as entanglement, stabilizer magic, and non-local magic, in low-energy nucleon-nucleon scattering through next-to-leading order in pionless effective field theory. Treating each nucleon spin as a qubit, we calculate the corresponding resource-generating powers of the scattering operator at generic center-of-mass momentum and scattering angle $Θ$. The analysis retains $S$- and $P$-wave channels generated by two-derivative contact interactions. When the microscopic physics exhibits Wigner's $SU(4)$ spin-flavor symmetry, the neutron-proton amplitude becomes proportional to the spin-space identity operator and therefore generates no new resources after scattering, extending an observation previously made for leading-order $S$-wave scattering. The same-nucleon channel remains resource-generating because constraints from identical particles project out part of the Hilbert space. These results show how enhanced symmetries, partial-wave structure, and resource generation are intertwined in low-energy two-body scattering.

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arXiv2026

Determining universal spectra from probability distributions

The probability distribution of a two-particle correlation function computed over background auxiliary field configurations, used to generate the interactions, has been shown to inform about the spectra of universal $n$-body clusters [1]. Here, we utilize two approaches, a numerical lattice computation and an analytic expansion in the limit of large numbers of identical species, in an attempt to refine the initial predictions. Exploratory calculations in these directions are presented, and future investigations laid out.

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arXiv2026

$F_K/F_π$ as a precision test of a new four flavor Domain Wall Fermion action

We present a new set of lattice QCD ensembles with four flavors of smeared Möbius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{π^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

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arXiv2025

Strong CP Violation and large-$N_c$ spin-flavor symmetry

We revisit the contribution of the QCD $\bar θ$ term to the CP violating pion-nucleon couplings and the nucleon electric dipole moment in a combined large-$N_c$ and chiral perturbation theory framework. In particular, we approach this issue through the emergent spin-flavor symmetry of the baryon sector at large but finite $N_c$. We obtain good agreement with previous analyses for the pion-nucleon couplings and show that the large-$N_c$ framework indicates that tree-level contributions to the electric dipole moment possibly play a dominant role. The spin-flavor symmetry also enables us to provide novel constraints on CP violating pion-$Δ$ couplings as well as the $Δ$ electric dipole moment and $ΔN$ transition moment.

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arXiv2025

Improved nuclear-structure corrections to the hyperfine splitting of electronic and muonic deuterium

We calculate the nuclear-structure correction to the hyperfine splitting in both electronic and muonic deuterium using interactions from chiral effective field theory. We explore the sensitivity to different parameterizations of the nucleon-nucleon force, study the convergence pattern in the order-by-order chiral expansion, and estimate remaining uncertainties. Our results are consistent with earlier calculations from pionless effective field theory, offering new insights for a robust uncertainty quantification. Thanks to the order-of-magnitude reduction in uncertainty achieved with chiral effective field theory, the two-photon exchange contribution in electronic deuterium agrees with experimental extractions within $0.7σ$, in contrast to the $2.7σ$ discrepancy observed in muonic deuterium. This study lays the groundwork for extending TPE calculations to HFS in heavier atomic systems.

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arXiv2025

The role of intermediate $ΔΔ$ states in nucleon-nucleon scattering in the large-$N_c$ and unitary limits, and $ΔΔ$ and $ΩΩ$ scattering

We explore potential explanations for why using large-$N_c$ ($N_c$ is the number of colors) scaling to determine the relative size of few-nucleon low-energy operators agrees with experiment even when dynamical $Δ$'s are not explicitly included. Given that the large-$N_c$ analysis is predicated on the nucleons and $Δ$'s being degenerate, this is a curious result. We show that for purely $S$-wave interactions the relationships dictated by large-$N_c$ scaling are unaffected whether the $Δ$ is included or not. In the case of higher partial waves that do not mix with $S$-waves, the impact of the $Δ$ is perturbative, which makes the agreement with naive ($Δ$-less) large-$N_c$ ordering unsurprising. For higher partial waves that mix with $S$-waves, the nucleon and $Δ$ would need to decouple to get agreement with naive large-$N_c$ ordering. We find all $NN$, $ΔN$, and $ΔΔ$ low energy coefficients for leading-order baryon-baryon scattering in $Δ$-full pionless effective field theory in terms of the two independent parameters dictated by the SU($2F$) spin-flavor symmetry that arises in the $N_c \rightarrow \infty$ limit. Because of recent lattice QCD results and experimental interest, we extend our analysis to the three-flavor case to study $ΩΩ$ scattering. We show that in the unitary limit (where scattering lengths become infinite) one of the two SU($2F$) parameters is driven to zero, resulting in enhanced symmetries, which agree with those found in spin-1/2 entanglement studies.

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arXiv2025

Renormalization group analysis of electromagnetic properties of the deuteron

The role of radiative corrections in low energy nuclear physics is beginning to receive more scrutiny. We examine the impact of these corrections for the deuteron charge form factor and the radiative capture process $np \to d γ$ through the velocity renormalization group. In both cases, we find percent level shifts in the relevant observables after evolving the subtraction velocity to the typical velocity of nucleons in the bound state. This suggests that electromagnetic corrections constitute a non-negligible source of uncertainty in existing few-body calculations.

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arXiv2025

Towards the determination of CP-odd pion-nucleon couplings

The nucleon matrix elements (NMEs) associated with quark chromo-magnetic dipole moments (cMDMs) play a crucial role in determining the CP-odd pion-nucleon couplings induced by quark chromo-electric dipole moments. In recent years, it has been argued that the NMEs of cMDMs can be related to the third moment of the nucleon's higher-twist (specifically, twist-three) parton distribution function (PDF) $e(x)$, which can, in principle, be measured through dihadron production in semi-inclusive deep inelastic scattering processes. By applying the spin-flavor expansion to the cMDM operators in the large-$N_c$ limit, where $N_c$ is the number of quark colors, we show that the NMEs receive contributions not only from the twist-three PDF $e(x)$ but also from an additional, previously neglected nucleon form factor. Incorporating constraints from the spin-flavor expansion, recent experimental data on $e(x)$, as well as model calculations of $e(x)$, we estimate the NMEs of the cMDM operators. Our analysis indicates that the NMEs are dominated by the nucleon form factors, and the cMDM contributions to pion-nucleon couplings can be comparable to those from the quark sigma terms.

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arXiv2025

Signs of Non-Monotonic Finite-Volume Corrections to $g_A$

We study finite-volume (FV) corrections to determinations of $g_A$ via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that $SU(2)$ Heavy Baryon Chiral Perturbation Theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-$N_c$ constraints on the axial couplings. We further show that non-monotonic FV corrections are naturally allowed when one considers either including explicit $Δ$-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of $g_A$ using models of FV corrections that are monotonic and non-monotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of non-monotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1%-1%-level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of $g_A$ in the isospin limit with sub-percent precision, $g_A^{\rm QCD} = 1.2674(96)$.

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arXiv2024

Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory

We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon-nucleon potential and the binding energy of the deuteron. In order to do so, we present a modified version of pionless effective field theory inspired by earlier work in nonrelativistic quantum electrodynamics. The renormalization group improvement of the deuteron binding energy leads to a shift on the order of a few percent and is consistent with the experimental value. This work serves as a starting point for a dedicated study of radiative corrections in few-body systems relevant for precision tests of the Standard Model in an effective field theory framework.

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arXiv2024

Worldline Monte Carlo method for few body nuclear physics

In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $\exp(-βH)$ where $H$ is the lattice Hamiltonian and $β$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $β$ which are not very large. Computing these bound state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective field theory and show how it would work in the one and two body sectors.

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arXiv2024

Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections

Measurements of the difference between the squared charge radii of the helion ($^3$He nucleus) and the $α$-particle ($^4$He nucleus) have been characterized by longstanding tensions, recently spotlighted in the 3.6 $σ$ discrepancy of the extractions from ordinary atoms versus those from muonic atoms. Here, we present a novel analysis of uncertainties in nuclear structure corrections that must be supplied by theory to enable the extraction of the difference in radii from spectroscopic experiments. We use modern Bayesian inference techniques to quantify uncertainties stemming from the truncation of the chiral effective field theory expansion of the nuclear force for both muonic and ordinary atoms. With the new nuclear structure input, the helium isotope-shift puzzle cannot be explained, rather it is reinforced to a 4 $σ$ discrepancy.

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arXiv2023

Topological terms with qubit regularization and relativistic quantum circuits

Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.

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arXiv2022

Implications of Large-$N_c$ QCD for the NN Interaction

We present a method for ordering two-nucleon interactions based upon their scaling with the number of QCD colors, $N_c$, in the limit that $N_c$ becomes large. Available data in the two-nucleon sector shows general agreement with this ordering, indicating that the method may be useful in other contexts where data is less readily available. However, several caveats and potential pitfalls can make the large-$N_c$ ordering fragile and/or vulnerable to misinterpretation. We discuss the application of the large-$N_c$ analysis to two- and three-nucleon interactions, including those originating from weak and beyond-the-standard-model interactions, as well as two-nucleon external currents. Finally, we discuss some open questions in the field.

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arXiv2022

Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory

Recent proposals for the use of light nuclei as dark matter direct detection targets necessitate a strong theoretical understanding of the nuclear physics involved. We perform relevant calculations for dark matter-light nucleus scattering in a combined pionless effective field theory and large-$N_c$ expansion, where $N_c$ is the number of quark colors. We include a general set of one-nucleon currents that have been used in other effective theories, as well as novel two-nucleon contact currents. First, we obtain constraints for the relative sizes of the dark matter couplings to the one- and two-nucleon currents through the large-$N_c$ expansion. Then, we use these constraints to make predictions for the relative sizes of spin-dependent and spin-independent cross sections for dark matter scattering off of a nucleon, a deuteron, a triton, and helium-3.

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arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

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arXiv2021

Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms

The interpretation of experiments that search for neutrinoless double beta decay relies on input from nuclear theory. Cirigliano et al. recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\to pp e^- e^-$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors $N_c$ being large. We also obtain a large-$N_c$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.

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arXiv2020

Large-$N_c$ analysis of magnetic and axial two-nucleon currents in pionless effective field theory

We analyze magnetic and axial two-nucleon contact terms in a combined large-$N_c$ and pionless effective field theory expansion. These terms play important roles in correctly describing, e.g., the low-energy cross section of radiative neutron capture and the deuteron magnetic moment. We show that the large-$N_c$ expansion hints towards a hierarchy between the two leading-order magnetic terms that matches that found in phenomenological fits. We also comment on the issue of naturalness in different Lagrangian bases.

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