During the workshop Compton Scattering off Protons and Light Nuclei: pinning down the nucleon polarisabilities (ECT*, Trento, Italy, 29 July -- 2 August 2013, http://www.ectstar.eu/node/98), recent developments had been reviewed in experimental and t
heoretical studies of real and virtual Compton scattering, static and generalized dipole scalar and spin polarisabilities of nucleons, as well as related phenomena in physics of muonic atoms. A vivid topic at the workshop was pathways towards the most precise extraction of the static polarisabilities from low-energy Compton cattering---including pertinent theoretical uncertainties. Being asked by our experimental colleagues, we prepared during the workshop a short letter with conclusions of the discussion, emphasising future prospects.
A complete set of linearly independent observables in Compton scattering with arbitrarily polarised real photons off an arbitrarily polarised spin-1 target is introduced, for the case that the final-state polarisations are not measured. Adopted from
the one widely used e.g. in deuteron photo-dissociation, it consists of 18 terms: the unpolarised cross section, the beam asymmetry, 4 target asymmetries and 12 asymmetries in which both beam and target are polarised. They are expressed by the helicity amplitudes and -- where available -- related to observables discussed by other authors. As application to deuteron Compton scattering, their dependence on the (isoscalar) scalar and spin dipole polarisabilities of the nucleon is explored in Chiral Effective Field Theory with dynamical Delta(1232) degrees of freedom at order $e^2delta^3$. Some asymmetries are sensitive to only one or two dipole polarisabilities, making them particularly attractive for experimental studies. At a photon energy of 100 MeV, a set of 5 observables is identified from which one may be able to extract the spin polarisabilities of the nucleon. These are experimentally realistic but challenging and mostly involve tensor-polarised deuterons. Relative to Compton scattering from a nucleon, sensitivity to the mixed spin polarisabilities $gamma_{E1M2}$ and $gamma_{M1E2}$ is increased because of interference with the D wave component of the deuteron and with its pion-exchange current. An interactive Mathematica 9.0 notebook with results for all observables at photon energies up to 120 MeV is available from [email protected]. Note May 2017/April 2018: This arXiv version presents the article including the corrections in the Errata Eur. Phys. J. A53 (2017) 113 and A54 (2018) 57 to ibid. A49 (2013) 100. This affects Eqs. (2.12) to (2.14), Figs. 4, 7 to 10, 12, 14 to 16, 18 to 20, 22 and 23, and the corresponding, related text.
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 Ch
iral Effective Field Theory with dynamical Delta(1232) degrees of freedom in the Small Scale Expansion 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 gtrsim 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 [email protected].
We report on a chiral effective field theory calculation of Compton scattering from the proton. Our calculation includes pions, nucleons, and the Delta(1232) as explicit degrees of freedom. It uses the delta expansion, and so implements the hierarchy
of scales m_pi < M_Delta-M_N < Lambda_chi. In this expansion the power counting in the vicinity of the Delta peak changes, and resummation of the loop graphs associated with the Delta width is indicated. We have computed the nucleon Compton amplitude in the delta expansion up to N3LO for photon energies of the order of m_pi. This is the first order at which the proton Compton scattering amplitudes receive contributions from contact operators which encode contributions to the spin-independent polarisabilities from states with energies of the order of Lambda_chi. We fit the coefficients of these two operators to the experimental proton Compton data that has been taken in the relevant photon-energy domain, and are in a position to extract new results for the proton polarisabilities alpha and beta.
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 Delta(1232) d
egree 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 Delta, 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.
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 b
ound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(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 a_0(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 (1.6pm 0.2) fm, for the 4He binding energy of (28pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66pm 0.03) MeV. The discrepancy to data of (0.10mp 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.
