Harald W. Griesshammer

Compton scattering from the proton: An analysis using the delta expansion up to N3LO

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 Mπ < ∆≡M∆−MN < Λχ , through a counting Mπ/∆ ∼ ∆/Λχ ∼ δ . 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. This is designed to extend the region of χPT applicability to momenta p∼ ∆. We have computed the nucleon Compton amplitude in the delta expansion up to N3LO— O(e2δ 4)—for photon energies ω ∼ Mπ . 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 ∼ Λχ . 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 αp and βp.

New results for Compton scattering on deuterium : A better determination of the neutron electromagnetic polarizabilities

The electric and magnetic polarizabilities of the proton are now well known, owing to Compton scattering measurements on hydrogen targets; however, the neutron polarizabilities are still relatively uncertain, compared to the proton values. To address this problem, a multiinstitutional collaboration has conducted a program of elastic Compton scattering experiments on deuterium at the MAX IV Laboratory in Lund, Sweden using tagged photons in the energy range Eγ= 65-115 MeV. We assembled at one laboratory, for the first time, three of the worlds largest NaI detectors, each having better than ΔE/E ∼ 2% photon energy resolution. We have measured elastic Compton scattering cross sections at lab angles of θγ= 60°, 120° and 150° over this energy range in 8 MeV steps. This effectively doubles the worlds set of elastic Compton scattering data from deuterium and provides valuable input for chiral effective field theory (χEFT) calculations. These new deuterium data overlap previous measurements and extend them by 20 MeV to higher energies. Based on χEFT fits to the expanded world data set, new values for the neutron electric and magnetic polarizabilities have been obtained with greater accuracy than previously achieved, decreasing the statistical error by more than 30%. (Less)

Nucleon Polarisabilities from Deuteron Compton Scattering, and Its Lessons for Chiral Power Counting

A brief review of Compton scattering off the deuteron in Chiral Effective Field Theory, including gauge invariance and the correct Thomson limit. We model-independently determine the iso-scalar, spin-independent dipole polarisabilities of the nucleon at zero energy from all Compton data below 100 MeV as \alpha_{E1}^s=11.3+-0.7_{stat}\+-0.6_{Baldin}+-1_{theory}, \beta_{M1}^s=3.2-+0.7_{stat}+-0.6_{Baldin}+-1_{theory}, each in 10^{-4} fm^3. Proton and neutron polarisabilities are therefore identical within (predominantly statistical) errors.

Polarisabilities of the proton and neutron from Compton scattering

We have recently completed a high-precision extraction of the proton spin-independent polarisabilities from the world database of low-energy Compton scattering experiments, within the framework of chiral effective field theory (ChEFT) with pions, nucleons, and the Delta(1232) as explicit degrees of freedom. Our Baldin-sum-rule-constrained results are, in units of

Nucleon Spin Polarisabilities from Polarised Deuteron Compton Scattering

10^{-4}

The S Wave Pion Deuteron Scattering Length in Effective Field Theory

~fm

Theory Viewpoint on Extracting Nucleon Polarisabilities in Low-Energy Compton Scattering

^3

Compton scattering and nucleon polarisabilities in chiral EFT: The next steps

, alphae_p=10.65 \pm 0.35(stat)\pm 0.2(Baldin)\pm 0.3(theory) betam_p=3.15 \mp 0.35(stat)\pm 0.2(Baldin)\mp 0.3(theory).These were obtained in the heavy-baryon formulation, but almost identical results have been obtained ina covariant calculation.With the publication this year by Myers et al of the results of the deuteron Comptonscattering experiment using the Tagged-Photon Facility at the MAX IV Laboratory in Lund,Sweden, the world database has doubled in size, allowing the extraction of the isoscalar polarisabilities with unprecedented accuracy, and combined with the proton results we obtain alphae_n =11.65 \pm 1.25(stat) \pm 0.2(Baldin)\pm 0.8(theory), betam_n = 3.55 \mp 1.25(stat) \pm 0.2(Baldin) \mp 0.8(theory).A new generation of experiments with polarised beams have been performed at the Mainz Microtron, with the first results published this year by Martel et al, These experiments are sensitive to the spin polarisabilities, and we will discuss the predictions of ChEFT for the relevant cross sections and asymmetries.

Universality in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

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) 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 \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.