118407568
Chiral potentials, perturbation theory and the 1S0 channel of NN scattering
We use nucleon–nucleon phase shifts obtained from experimental data, together with the chiral expansion for the long-distance part of the NN interaction, to obtain information about the short-distance piece of the NN potential that is at work in the 1S0 channel. We find that if the scale R that defines the separation between 'long-' and 'short-' distance is chosen to be 1.8 fm then the energy dependence produced by short-distance dynamics is well approximated by a two-term polynomial for Tlab ≤ 200 MeV. We also find that a quantitative description of NN dynamics is possible, at least in this channel, if one treats the long-distance parts of the chiral NN potential in perturbation theory. However, in order to achieve this we have to choose a separation scale R that is larger than 1.0 fm.
16338161
Nucleon Spin Polarisabilities from Polarised Deuteron Compton Scattering
We present recent results on elastic deuteron Compton scattering calculations for polarised beans and targets up to next-to-leading order within Chiral Effective Field Theory in the Small Scale Expansion variant to implement a dynamical Δ(1232) degree of freedom. A simple power-counting argument discloses that np-intermediate rescattering states must be explicitly included at leading order already. This automatically results in the correct Thomson limit and guarantees current conservation. In view of ongoing effort at MAXlab, proposals at HIGS and plans at MAMI, we address in detail single- and double-polarised observables with linearly or circularly polarised photons on both unpolarised and vector-polarised deuterons. Our results indicate that several of the polarisation observables can be instrumental to extract not only spin-independent nucleon polarisabilities, but also the so-far practically un-determined spin-dependent polarisabilities which parameterise the stiffness of the nucleon spin in external electro-magnetic fields. Amongst the questions addressed are: convergence of the expansion for including the Δ, the role of the np-rescattering contributions, and sensitivity to the deuteron wave function. An interactive Mathematica 7.0 notebook of these findings is available from the authors.
53550289
Analyzing the effects of neutron polarizabilities in elastic Compton scattering off 3He
Abstract Motivated by the fact that a polarized 3He nucleus is expected to behave approximately as a polarized neutron, we examine manifestations of neutron electromagnetic polarizabilities in elastic Compton scattering from the Helium-3 nucleus. We calculate both unpolarized and double-polarization observables using chiral perturbation theory to next-to-leading order ( O ( e 2 Q ) ) at energies, ω ≲ m π , where m π is the pion mass. Our results show that the unpolarized differential cross-section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.
55918790
Compton Scattering on Light Nuclei
Compton scattering on light nuclei (A = 2, 3) has emerged as an effective avenue to search for signatures of neutron polarizabilities, both spin-independent and spin-dependent ones. In this discussion I will focus on the theoretical aspect of Compton scattering on light nuclei; giving first a brief overview and therafter concentrating on our Compton scattering calculations based on Chiral effective theory at energies of the order of pion mass. These elasticγd andγHe-3 calculations include nucleons, pions as the basic degrees of freedom. I will also discuss γd results where the� -isobar has been included explicitly. Our results on unpolarized and polarization observables suggest that a combination of experiments and further theoretical efforts will provide an extraction of the neutron polarizabilities.
119110936
Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons
Abstract.The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of 3H and 4He , and for the singlet S -wave 3He -neutron scattering length a0(3He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of 3H of (1.6±0.2) fm, for the 4He binding energy of (28±2.5) MeV, and for Re{a0(3He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.
119263975
Nucleon spin-polarisabilities from polarisation observables in low-energy deuteron Compton scattering
Abstract.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 ($ \chi$ EFT) with dynamical $ \Delta$(1232) degrees of freedom in the Small Scale Expansion (SSE) at next-to-leading order. Resummation of the NN intermediate rescattering states and including the $ \Delta$ 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 $ \lesssim$ 70 MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from hgrie@gwu.edu.
119097482
A NOVEL OBSERVATION IN THE BRST APPROACH TO A FREE SPINNING RELATIVISTIC PARTICLE
For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0+1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge, Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and ghost-scale symmetry transformations. We deduce the underlying algebra amongst the continuous symmetry operators and corresponding conserved charges. We point out a novel observation that emerges, for this specific SUSY system, when we discuss it within the framework of BRST formalism. In particular, the requirement of the physicality criteria with the (anti-)BRST charges leads to a completely new observation because, as it turns out, one of the primary constraints does not annihilate the physical state of the theory. We have never come across this kind of result in the realm of BRST approach to usual gauge theories. We provide the physical and theoretical reasons behind the above observation.