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U. van Kolck

Publications and source records attributed to U. van Kolck.

At least 19 recordsLinked to original sources
arXiv2026

Universality in strongly interacting bosonic clusters

We develop an effective field theory (EFT) for strongly interacting bosonic clusters, using $^4$He as a paradigmatic example of universality in systems with large scattering length. At leading order (LO), two- and three-body zero-range interactions are entirely determined by the dimer and trimer ground-state energies. We show that ground-state energies for up to $N=15$ particles converge to cutoff-independent limits with extrapolation coefficients of natural size. At next-to-leading order (NLO), corrections stemming from the two-body interaction range and a four-body force, calibrated to the tetramer ground-state energy, reduce cutoff sensitivity. Close agreement with results from a realistic potential is found at LO and improved at NLO, demonstrating systematic convergence with few parameters at each order. The resulting EFT is directly applicable to larger clusters and bulk helium.

cond-mat.quant-gas↗
arXiv2026

Two-Pion Exchange Contributions to the Nucleon-Nucleon Interaction from the Roper Resonance

We derive the long-range components of the nucleon-nucleon (NN) two-pion-exchange potential with an intermediate Roper resonance. Leading-order interactions in heavy-baryon chiral perturbation theory are considered. NN phase shifts with orbital angular momentum $L\geq 2$ are calculated in first-order perturbation theory and compared to those obtained without the Roper resonance. We show that the Roper contribution is sizeable for $D$ waves and improves the description of phase shifts for all the partial waves slightly. We also discuss the role of the Roper resonance in the NN interaction in the framework of resonance saturation.

nucl-th↗
arXiv2025

Improved Actions for Nuclear Effective Field Theories

Effective field theories have been successful in describing nuclei up to the alpha particle but face significant challenges for larger nuclei due to leading-order instabilities. These issues can be addressed with the introduction of a fake interaction range at leading order, whose effects are compensated for in perturbation theory at higher orders. The calculation of two-body phase shifts and ground-state energies for up to five $^4$He atoms in a theory with only contact interactions shows that, as long as it remains smaller or comparable to the experimental effective range, the fake range does not alter the convergence of the EFT expansion but is often beneficial at the lowest orders. I discuss the implications of this improved-action approach to the ground-state energies of nuclei such as $^6$Li, $^{12}$C, and $^{16}$O.

nucl-th↗
arXiv2025

A renormalizable theory for not-so-light nuclei

We present an improved action for Pionless Effective Field Theory (EFT). Previous formulations of renormalizable nuclear EFTs have encountered instabilities in systems with more than four nucleons. We resolve this issue by introducing a finite interaction range at leading order, which is compensated for in perturbation theory at next-to-leading order. Calculated ground-state energies of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O converge and agree with experiment within theoretical uncertainties. This first successful implementation of systematic renormalizability beyond the lightest nuclei enables not only applications to larger nuclei but also extensions to other EFTs in the strong-coupling regime.

nucl-th↗
arXiv2024

The Four-Boson First-Excited State Near Two-Body Unitarity

Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for "halo" states.

physics.atom-ph↗
arXiv2024

Limits on an improved action for contact effective field theory in two-body systems

We consider a possible resummation of subleading effects in two-body systems with a large scattering length as described by a short-range effective field theory (EFT). In particular, we investigate the consequences of a resummation of part of the range corrections. Explicit calculations of the two-body phase shifts and charge form factor indicate that, except for extreme choices, resummations do not alter the convergence of the EFT expansion and are often beneficial at lowest orders. We have considered the expansion when the regulator cutoff is removed as well as when it is finite, and find that the cutoff is not an important factor for resummations. Our results connect with other works where the partial resummation is induced by potentials with finite cutoffs or interaction ranges.

nucl-th↗
arXiv2024

Improved action for contact effective field theory

We present an improved action for renormalizable effective field theories (EFTs) of systems near the two-body unitarity limit. The ordering of EFT interactions is constrained, but not entirely fixed, by the renormalization group. The remaining freedom can be used to improve the theory's convergence, to simplify its applications, and to connect it to phenomenological models. We exemplify the method on a contact theory applied to systems of up to five $^4$He atoms. We solve the EFT at leading order including a subleading interaction that accounts for part of the two-body effective range. We show that the effects of such fake range can be compensated in perturbation theory at next-to-leading order, as long as the fake range is smaller or comparable to the experimental effective range. These results open the possibility of using similar improved actions for other many-body systems.

physics.atm-clus↗
arXiv2024

Two-body double pole and three-body bound states: physical and unphysical quark masses

We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations. Neglecting shape parameters, the two-body bound state is a double pole. For bosons we obtain a correlation between three- and two-body energies. For nucleons, this correlation depends additionally on the ratio of effective ranges in the two two-body $S$-wave channels. When this ratio takes the value suggested by lattice QCD, our three-body energy agrees well with a direct lattice determination. When this ratio takes the experimental value, we find a three-body bound state with energy close to that of the physical triton. We suggest that results could be improved systematically with distorted-wave perturbation theory around a separable potential whose form factor is an inverse square root of momentum squared.

nucl-th↗
arXiv2023

The importance of few-nucleon forces in chiral effective field theory

We study the importance of few-nucleon forces in chiral effective field theory for describing many-nucleon systems. A combinatorial argument suggests that three-nucleon forces -- which are conventionally regarded as next-to-next-to-leading order -- should accompany the two-nucleon force already at leading order (LO) starting with mass number $A\approx 10-20$. We find that this promotion enables the first realistic description of the $^{16}$O ground state based on a renormalization-group-invariant LO interaction. We also performed coupled-cluster calculations of the equation of state for symmetric nuclear matter and our results indicate that LO four-nucleon forces could play a crucial role for describing heavy-mass nuclei. The enhancement mechanism we found is very general and could be important also in other many-body problems.

nucl-th↗
arXiv2022

Weinberg and few-nucleon forces

Weinberg's contributions to the power counting and derivation of few-nucleon forces in Chiral EFT are briefly recalled. Subsequent improvements are reviewed, concluding with the recent suggestion of a combinatorial enhancement.

nucl-th↗
arXiv2022

Weinberg's Compositeness

Nearly 60 years ago Weinberg suggested a criterion for particle "compositeness", which has acquired new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg's creations, the model-independent framework of effective field theories.

hep-ph↗
arXiv2022

Renormalization of One-Pion Exchange in Chiral Effective Field Theory for Antinucleon-Nucleon Scattering

The renormalization of iterated one-pion exchange (OPE) is studied in Chiral Effective Field Theory ($χ$EFT) for the antinucleon-nucleon ($\overline{N}\!N$) system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}\!N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional analysis. Results after renormalization are compared with the state-of-the-art energy-dependent partial-wave analysis of $\overline{N}\!N$ data. We compare our conclusions with applications of $χ$EFT to the nucleon-nucleon system.

nucl-th↗
arXiv2021

Nucleon decay in the deuteron

We calculate the lifetime of the deuteron from dimension-six quark operators that violate baryon number by one unit. We construct an effective field theory for $|ΔB|=1$ interactions that give rise to nucleon and $ΔB=1$ deuteron decay in a systematic expansion. We show that up to and including next-to-leading order the deuteron decay rate is given by the sum of the decay rates of the free proton and neutron. The first nuclear correction is expected to contribute at the few-percent level and comes with an undetermined low-energy constant. We discuss its relation to earlier potential-model calculations.

nucl-th↗
arXiv2021

Nuclear Effective Field Theories: Reverberations of the early days

Effective field theories are recognized nowadays as the framework to describe low-energy nuclear structure and reactions consistently with the underlying theory of the strong interactions, QCD. It was not always so. As we celebrate the 30 years of the first publications, I collect here some memories from those early days. I also discuss some of the key issues that were raised back then and, despite all progress, are still with us. Dedicated to the memory of Steven Weinberg, whose ideas will not die, wherever they may lead.

nucl-th↗
arXiv2021

Nonrelativistic Effective Field Theory with a Resonance Field

We discuss shallow resonances in the nonrelativistic scattering of two particles using an effective field theory (EFT) that includes an auxiliary field with the quantum numbers of the resonance. We construct the manifestly renormalized scattering amplitude up to next-to-leading order in a systematic expansion. For a narrow resonance, the amplitude is perturbative except in the immediate vicinity of the resonance poles. It naturally has a zero in the low-energy region, analogous to the Ramsauer-Townsend effect. For a broad resonance, the leading-order amplitude is nonperturbative almost everywhere in the regime of validity of the EFT. We regain the results of an EFT without the auxiliary field, which is equivalent to the effective-range expansion with large scattering length and effective range. We also consider an additional fine tuning leading to a low-energy amplitude zero even for a broad resonance. We show that in all cases the requirement of renormalizability when the auxiliary field is not a ghost ensures the resonance poles are in the lower half of the complex momentum plane, as expected by other arguments. The systematic character of the EFT expansion is exemplified with a toy model serving as underlying theory.

hep-ph↗
arXiv2020

Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances

Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy $S$-wave resonance. Our starting point is the most general Lagrangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an $S$ matrix with two low-energy poles. The pole positions are restricted by renormalization at leading order, where the common feature is a non-positive effective range. We carry out the expansion explicitly to next-to-leading order and illustrate how it systematically accounts for the results of a toy model -- a spherical well with a delta shell at its border.

nucl-th↗
arXiv2020

Clustering of Four-Component Unitary Fermions

Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.

cond-mat.quant-gas↗