Nuclear Physics from QCD
Effective field theories provide a bridge between QCD and nuclear physics. I discuss light nuclei from this perspective, emphasizing the role of fine-tuning.
hep-ph↗
arXiv subjects
U. van Kolck
Publications and source records attributed to U. van Kolck.
alpha-alpha Scattering in Halo Effective Field Theory
We study the two-alpha-particle (alpha-alpha) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy alpha-alpha phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the Be-8 ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles.
nucl-th↗
Renormalization of Singular Potentials and Power Counting
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.
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Pion Interactions in the X(3872)
We consider pion interactions in an effective field theory of the narrow resonance X(3872), assuming it is a weakly bound molecule of the charm mesons D^{0} \bar D^{*0} and D^{*0} \bar D^{0}. Since the hyperfine splitting of the D^{0} and D^{*0} is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are non-relativistic. We show that pion exchange can be treated in perturbation theory and calculate the next-to-leading-order correction to the partial decay width Γ[X \to D^0 \bar D^{0} π^0].
hep-ph↗
Effective Theory for Trapped Few-Fermion Systems
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semi-analytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.
cond-mat.other↗
No-core shell model in an effective-field-theory framework
We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact terms from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first (0^+;0) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first (0^+;0) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT.
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Realistic Few-Body Physics in the $dd\to απ^0$ Reaction
We use realistic two- and three-nucleon interactions in a hybrid chiral-perturbation-theory calculation of the charge-symmetry-breaking reaction $dd\toαπ^0$ to show that a cross section of the experimentally measured size can be obtained using LO and NNLO pion-production operators. This result supports the validity of our power counting scheme and demonstrates the necessity of using an accurate treatment of ISI and FSI.
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Effective Field Theory of Nucleon-Nucleon Scattering on Large Discrete Lattices
Nuclear effective field theory is applied to the effective range expansion of S-wave nucleon-nucleon scattering on a discrete lattice. Lattice regularization is demonstrated to yield the effective range expansion in the same way as in the usual continuous open space. The relation between the effective range parameters and the potential parameters is presented in the limit of a large lattice.
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The electric dipole form factor of the nucleon
The electric dipole form factor of the nucleon stemming from the QCD $\barθ$ term is calculated in chiral perturbation theory in leading order. To this order, the form factor originates from the pion cloud. Its momentum-dependence is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for momentum variation--appearing, in particular, in the radius of the form factor--is the pion mass.
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Renormalization of One-Pion Exchange and Power Counting
The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be absorbed by counterterms expected at that order. In the other partial waves additional contact interactions are necessary. The implications of this finding for the effective-field-theory program in nuclear physics are discussed.
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Delta Effects in Pion-Nucleon Scattering and the Strength of the Two-Pion-Exchange Three-Nucleon Interaction
We consider the relationship between P-wave pi-N scattering and the strength of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain why effective theories that do not contain the delta resonance as an explicit degree of freedom tend to overestimate the strength of the TPE3NI. The overestimation can be remedied by higher-order terms in these ``delta-less'' theories, but such terms are not yet included in state-of-the-art chiral EFT calculations of the nuclear force. This suggests that these calculations can only predict the strength of the TPE3NI to an accuracy of +/-25%.
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Nucleon Polarizabilities from Low-Energy Compton Scattering
An effective field theory is used to give a model-independent description of Compton scattering at energies comparable to the pion mass. The amplitudes for scattering on the proton and the deuteron, calculated to fourth order in small momenta in chiral perturbation theory, contain four undetermined parameters that are in one-to-one correspondence with the nucleon polarizabilities. These polarizabilities are extracted from fits to data on elastic photon scattering on hydrogen and deuterium. For the proton we find: alpha_p = 12.1 +/- 1.1 +/- 0.5, beta_p = 3.4 +/- 1.1 +/- 0.1, both in units of 10^{-4} fm^3. For the isoscalar polarizabilities we obtain: alpha_N = 13.0 +/- 1.9 +3.9/-1.5 (in the same units) while beta_N is consistent with zero, within sizeable error bars.
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Effective Field Theories of Light Nuclei
Effective field theories have been developed for the description of light, shallow nuclei. I review results for two- and three-nucleon systems, and discuss their extension to halo nuclei.
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Charge-Symmetry-Breaking Three-Nucleon Forces
Leading-order three-nucleon forces that violate isospin symmetry are calculated in Chiral Perturbation Theory. The effect of the charge-symmetry-breaking three-nucleon force is investigated in the trinucleon systems using Faddeev calculations. We find that the contribution of this force to the 3He - 3H binding-energy difference is approximately 5 keV.
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Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)
We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q^4) $γ$p amplitude of McGovern to experimental data in the region $ω,\sqrt{|t|} \leq 180$ MeV, obtaining a chi^2/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: alpha_p=12.1 +/- 1.1 (stat.) +/- 0.5 (theory) and beta_p=3.4 +/- 1.1 (stat.) +/- 0.1 (theory), both in units of 10^{-4} fm^3. We also compute Compton scattering on deuterium to O(Q^4). The $γ$d amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent $γ$d scattering experiments with a chi^2/d.o.f.=26.6/20, and find alpha_N=13.0 +/- 1.9 (stat.) +3.9/-1.5 (theory) and a beta_N that is consistent with zero within sizeable error bars.
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The Nucleon-Mass Difference in Chiral Perturbation Theory and Nuclear Forces
A new method is developed for treating the effect of the neutron-proton mass difference in isospin-violating nuclear forces. Previous treatments utilized an awkward subtraction scheme to generate these forces. A field redefinition is used to remove that mass difference from the Lagrangian (and hence from asymptotic nucleon states) and replace its effect by effective interactions. Previous calculations of static Class II charge-independence-breaking and Class III charge-symmetry-breaking potentials are verified using the new scheme, which is also used to calculate Class IV nuclear forces. Two-body forces of the latter type are found to be identical to previously obtained results. A novel three-body force is also found. Problems involving Galilean invariance with Class IV one-pion-exchange forces are identified and resolved.
nucl-th↗
An effective field theory for coupled-channel scattering
The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally small and the cross section at low energy is unnaturally large is considered. It is shown that the lowest-order point coupling associated with the mixing of the channels scales as $Λ^{-2}$ rather than $Λ^{-1}$ (the scaling of the same-channel coupling and the scaling in a single-channel case) where $Λ$ is the ultraviolet cutoff. The renormalization of the theory at lowest order is given explicitly. The treatment of higher orders is straightforward. The potential implications for systems with deep open channels are discussed.
nucl-th↗
Survey of charge symmetry breaking operators for dd -> alpha pi0
The charge-symmetry-breaking amplitudes for the recently observed d d -> alpha pi0 reaction are investigated. Chiral perturbation theory is used to classify and identify the leading-order terms. Specific forms of the related one- and two-body tree level diagrams are derived. As a first step toward a full calculation, a few tree-level two-body diagrams are evaluated at each considered order, using a simplified set of d and alpha wave functions and a plane-wave approximation for the initial dd state. The leading-order pion-exchange term is shown to be suppressed in this model because of poor overlap of the initial and final states. The higher-order one-body and short-range (heavy-meson-exchange) amplitudes provide better matching between the initial and final states and therefore contribute significantly and coherently to the cross section. The consequences this might have for a full calculation, with realistic wave functions and a more complete set of amplitudes, are discussed.
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