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U. van Kolck

Publications and source records attributed to U. van Kolck.

At least 37 records · Page 2Linked to original sources
arXiv2020

Nuclear effective field theory: status and perspectives

The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs -- Chiral, Pionless, Halo/Cluster -- highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input.

nucl-th↗
arXiv2020

Naturalness in Nuclear Effective Field Theories

Nuclear effective field theories (EFTs) have been developed over the last quarter-century with considerable impact on the description of light and even medium-mass nuclei. At the core of any EFT is a systematic expansion of observables, which is usually obtained from a rule based on an assumption of naturalness. I discuss naturalness in the context of the relatively weak binding of nuclei, where discrete scale invariance plays a role in the emergence of complexity.

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arXiv2020

The Problem of Renormalization of Chiral Nuclear Forces

Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on "chiral potentials" with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange --- Pionless EFT --- has been formulated where renormalization is achieved order by order in a systematic expansion of low-energy nuclear observables. I describe how lessons from Pionless EFT are being applied to the construction of a properly renormalized Chiral EFT.

nucl-th↗
arXiv2020

Finite-Size Effects in Heavy Halo Nuclei from Effective Field Theory

Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as $1/A_c$, where $A_c$ is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account for the small factors of $1/A_c$. As a specific example, we discuss the implications of this organizational scheme for the inclusion of finite-size effects in expressions for the charge radii of halo nuclei. We show in particular that a short-range operator could be the dominant effect in the charge radius of one-neutron halos bound by a P-wave interaction. The point-particle contribution remains the leading piece of the charge radius for one-proton halos, and so Halo EFT has more predictive power in that case.

nucl-th↗
arXiv2019

Triton and Neutron-Deuteron Scattering up to Next-to-Leading Order in Chiral EFT

Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Erratum to the original article is included)

nucl-th↗
arXiv2019

A renormalized approach to neutrinoless double-beta decay

The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

nucl-th↗
arXiv2019

Baryon-number violation by two units and the deuteron lifetime

We calculate the lifetime of the deuteron with dimension-nine quark operators that violate baryon number by two units. We construct an effective field theory for $|ΔB|=2$ interactions that give rise to neutron-antineutron ($n$-$\bar{n}$) oscillations and dinucleon decay within a consistent power counting. We calculate the ratio of the deuteron lifetime to the square of the $n$-$\bar{n}$ oscillation time up to next-to-leading order. Our result, which is analytical and has a quantified uncertainty, is smaller by a factor $\simeq 2.5$ than earlier estimates based on nuclear models, which impacts the indirect bound on he $n$-$\bar{n}$ oscillation time and future experiments. We discuss how combined measurements of $n$-$\bar{n}$ oscillations and deuteron decay can help to identify the sources of baryon-number violation.

hep-ph↗
arXiv2019

Les Houches Lectures on Effective Field Theories for Nuclear and (some) Atomic Physics

These lectures are a pedagogical -- not comprehensive -- introduction to the applications of effective field theory in the context of nuclear and atomic physics. A common feature of these applications is the interplay between nonperturbative physics (needed at leading order to produce nonrelativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, Pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. Some of the challenges and rewards of including long-range forces -- pion exchange in Chiral EFT for nuclear systems or Van der Waals forces between atoms -- are briefly described.

nucl-th↗
arXiv2018

A new leading contribution to neutrinoless double-beta decay

Within the framework of chiral effective field theory we discuss the leading contributions to the neutrinoless double-beta decay transition operator induced by light Majorana neutrinos. Based on renormalization arguments in both dimensional regularization with minimal subtraction and a coordinate-space cutoff scheme, we show the need to introduce a leading-order short-range operator, missing in all current calculations. We discuss strategies to determine the finite part of the short-range coupling by matching to lattice QCD or by relating it via chiral symmetry to isospin-breaking observables in the two-nucleon sector. Finally, we speculate on the impact of this new contribution on nuclear matrix elements of relevance to experiment.

hep-ph↗
arXiv2017

Ground-state properties of unitary bosons: from clusters to matter

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this paper we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- and three-body contacts and the condensate fraction. We find that uniform matter is more bound than three-body clusters by nearly two orders of magnitude, the two-body contact is very large in absolute terms, and yet the condensate fraction is also very large, greater than 90%. Equilibrium properties of these systems may be experimentally accessible through rapid quenching of weakly-interacting boson superfluids.

cond-mat.quant-gas↗
arXiv2017

Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.

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arXiv2017

Nuclear Physics Around the Unitarity Limit

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system.

nucl-th↗
arXiv2017

The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory

We present a new rearrangement of short-range interactions in the $^1S_0$ nucleon-nucleon channel within Chiral Effective Field Theory. This is intended to reproduce the amplitude zero (scattering momentum $\simeq$ 340 MeV) at leading order, and it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to the pion-production threshold. An approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.

nucl-th↗
arXiv2017

Ground-State Properties of $^{4}$He and $^{16}$O Extrapolated from Lattice QCD with Pionless EFT

We extend the prediction range of Pionless Effective Field Theory with an analysis of the ground state of $^{16}$O in leading order. To renormalize the theory, we use as input both experimental data and lattice QCD predictions of nuclear observables, which probe the sensitivity of nuclei to increased quark masses. The nuclear many-body Schrödinger equation is solved with the Auxiliary Field Diffusion Monte Carlo method. For the first time in a nuclear quantum Monte Carlo calculation, a linear optimization procedure, which allows us to devise an accurate trial wave function with a large number of variational parameters, is adopted. The method yields a binding energy of $^{4}$He which is in good agreement with experiment at physical pion mass and with lattice calculations at larger pion masses. At leading order we do not find any evidence of a $^{16}$O state which is stable against breakup into four $^4$He, although higher-order terms could bind $^{16}$O.

nucl-th↗
arXiv2016

Power Counting in Peripheral Partial Waves: The Singlet Channels

We analyze the power counting of the peripheral singlet partial waves in nucleon-nucleon scattering. In agreement with conventional wisdom, we find that pion exchanges are perturbative in the peripheral singlets. We quantify from the effective field theory perspective the well-known suppression induced by the centrifugal barrier in the pion-exchange interactions. By exploring perturbation theory up to fourth order, we find that the one-pion-exchange potential in these channels is demoted from leading to subleading order by a given power of the expansion parameter that grows with the orbital angular momentum. We discuss the implications of these demotions for few-body calculations: though higher partial waves have been known for a long time to be irrelevant in these calculations (and are hence ignored), here we explain how to systematize the procedure in a way that is compatible with the effective field theory expansion.

nucl-th↗
arXiv2016

Effective Theory of 3H and 3He

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV.

nucl-th↗
arXiv2015

Effective Field Theory and Time-Reversal Violation in Light Nuclei

Thanks to the unnaturally small value of the QCD vacuum angle $\barθ< 10^{-10}$, time-reversal ($T$) violation offers a window into physics beyond the Standard Model (SM) of particle physics. We review the effective-field-theory framework that establishes a clean connection between $T$-violating mechanisms, which can be represented by higher-dimensional operators involving SM fields and symmetries, and hadronic interactions, which allow for controlled calculations of low-energy observables involving strong interactions. The chiral properties of $T$-violating mechanisms leads to a pattern that should be identifiable in measurements of the electric dipole moments of the nucleon and light nuclei.

hep-ph↗