How To Classify 3-Body Forces -- And Why

For systems with only short-range forces and shallow 2-body bound states, the typical strength of any 3-body force in all partial-waves, including external currents, is systematically estimated by renormalisation-group arguments in the Effective Field Theory of Point-Like Interactions. The underlying principle and some consequences in particular in Nuclear Physics are discussed.Comment: 7 pages LaTeX2e using FBSart-class (provided); 2 figures in 3 .eps files included using graphicx; to appear in Few-Body System

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.Comment: 6 pages, 3 figures, published version, rewritten for clarit

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.Comment: 37 pages, 14 figures, published versio

Spin Polarizabilities of the Nucleon from Polarized Low Energy Compton Scattering

As guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross sections in low energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the Delta(1232) resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Comment: 30 pages, 19 figure

On Parity-Violating Three-Nucleon Interactions and the Predictive Power of Few-Nucleon EFT at Very Low Energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pion-less" Effective Field Theory in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order. The only two linearly independent parity-violating three-nucleon structures with one derivative mix two-S and two-P-half waves with iso-spin transitions Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order. This observation is based on the approximate realisation of Wigner's combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.Comment: 20 pages LaTeX2e, including 9 figures as .eps file embedded with includegraphicx. Minor modifications and stylistic corrections. Version accepted for publication in Eur. Phys. J.

Pion-less Effective Field Theory on Low-Energy Deuteron Electro-Disintegration

In view of its relation to Big-Bang Nucleo-Synthesis and a reported discrepancy between nuclear models and data taken at S-DALINAC, electro-induced deuteron break-up 2H(e,e' p)n is studied at momentum transfer q<100MeV and close to threshold in the low-energy nuclear Effective Field Theory without dynamical pions. The result at N2LO for electric dipole currents and at NLO for magnetic ones converges order-by-order better than quantitatively predicted and contains no free parameter. It is at this order determined by simple, well-known observables. Decomposing the doubly differential cross-section into the longitudinal-plus-transverse (L+T), transverse-transverse (TT) and longitudinal-transverse interference (LT) terms, we find excellent agreement with a potential-model calculation by Arenh"ovel et al using the Bonn potential. Theory and data also agree well on \sigma_{L+T}. There is however no space on the theory-side for the discrepancy of up to 30%, 3-\sigma between theory and experiment in \sigma_{LT}. From universality, we conclude that no theoretical approach with the correct deuteron asymptotic wave-function can explain the data. Un-determined short-distance contributions that could affect \sigma_{LT} enter only at high orders, i.e. at the few-percent level. We notice some issues with the kinematics and normalisation of the data reported.Comment: 30 pages LaTeX2e, including 10 figures as 34 .eps files embedded with includegraphicx. Increased figure sizes; contents identical to version approved for publication in Phys Rev C -- spelling and grammatical difference

Nucleon spin-polarisabilities from polarisation observables in low-energy deuteron Compton scattering

We investigate the dependence of polarisation observables in elastic deuteron Compton scattering below the pion production threshold on the spin-independent and spin-dependent iso-scalar dipole polarisabilities of the nucleon. The calculation uses Chiral Effective Field Theory with dynamical Δ(1232) degrees of freedom in the Small Scale Expansion at next-to-leading order. Resummation of the NN intermediate rescattering states and including the Δ induces sizeable effects. The analysis considers cross-sections and the analysing power of linearly polarised photons on an unpolarised target, and cross-section differences and asymmetries of linearly and circularly polarised beams on a vector-polarised deuteron. An intuitive argument helps one to identify kinematics in which one or several polarisabilities do not contribute. Some double-polarised observables are only sensitive to linear combinations of two of the spin-polarisabilities, simplifying a multipole-analysis of the data. Spin-polarisabilities can be extracted at photon energies ≥ 100 MeV, after measurements at lower energies of . 70 MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from [email protected]

Parity-violating neutron spin rotation in hydrogen and deuterium

We calculate the (parity-violating) spin rotation angle of a polarized neutron beam through hydrogen and deuterium targets, using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading independent low-energy parameters that characterize hadronic parity-violation from few-body observables in one systematic and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Using naive dimensional analysis to estimate the typical size of the couplings, we expect the signal for standard target densities to be 10^-7 to 10^-6 rad/m for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system.Comment: 44 pages, 17 figures; minor corrections; to be published in EPJ

Dispersion Effects in Nucleon Polarisabilities

We present a formalism to extract the dynamical nucleon polarisabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarisabilities, dynamical polarisabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarisabilities from low energy nucleon Compton scattering up to the one pion production threshold and discuss the connection to the definition of static nucleon polarisabilities. As a concrete example, we examine the results of leading order Heavy Baryon Chiral Perturbation Theory for the four leading spin independent iso-scalar polarisabilities of the nucleon. Finally, we consider the possible r{\^o}le of energy dependent effects in low energy extractions of the iso-scalar dipole polarisabilities from Compton scattering on the deuteron.Comment: 17 pages LaTeX2e with 2 figures, using includegraphicx (5 .eps files). Minor corrections, references updated. Contents identical to version to appear in Phys. Rev. C 65, spelling differen