Nuclear Effective Field Theory Research Articles

Deuteron Compton scattering in effective field theory: Spin-dependent cross sections and asymmetries

Polarized Compton scattering on the deuteron is studied in nuclear effective field theory. A set of tensor structures is introduced to define 12 independent Compton amplitudes. The scalar and vector amplitudes are calculated up to ${\cal O}((Q/\Lambda)^2)$ in low-energy power counting. Significant contribution to the vector amplitudes is found to come from the spin-orbit type of relativistic corrections. A double-helicity dependent cross section $\Delta_1 \sigma = (\sigma_{+1-1}-\sigma_{+1+1})/2$ is calculated to the same order, and the effect of the nucleon isoscalar spin-dependent polarizabilities is found to be smaller than the effect of isoscalar spin-independent ones. Contributions of spin-independent polarizabilities are investigated in various asymmetries, one of which has as large as 12 (26) percent effect at the center-of-mass photon energy 30 (50) MeV.

Orthonormalization procedure for chiral effective nuclear field theory

We show that the Qˆ-box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the construction of a hermitean and energy-independent potential for arbitrary scattering processes on nucleons and nuclei to a given order in the chiral expansion. Various examples are discussed in some detail.

Drell–Hearn–Gerasimov sum-rule for the deuteron in nuclear effective field theory

The Drell–Hearn–Gerasimov sum rule for the deuteron is studied in nuclear effective field theory. The low-energy theorem for the spin-dependent Compton amplitude f1(ω) is derived to the next-to-leading order in low-energy expansion. The spin-dependent photo-disintegration cross-section σP−σA is calculated to the same order, and its contribution to the dispersive integral is evaluated.

Electroweak matrix elements in the two-nucleon sector from lattice QCD

We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross section of n p → d γ . Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.

Solar neutrinos, SNO and neutrino–deuteron reactions

The standard nuclear physics approach and effective field theory approach for calculations of neutrino–deuteron cross sections for the solar neutrino energies are considered. Their main features, the level of accuracy and problems to be addressed for further developments are discussed.

Nucleon polarisabilities from Compton scattering on the deuteron

An analytic calculation of the differential cross section for elastic Compton scattering on the deuteron at photon energies \omega in the range of 25-50 MeV is presented to next-to-next-to-leading order, i.e. to an accuracy of \sim 3%. The calculation is model-independent and performed in the low energy nuclear Effective Field Theory without dynamical pions. The iso-scalar, scalar electric and magnetic nucleon polarisabilities \alpha_0 and \beta_0 enter as free parameters with a theoretical uncertainty of about 20%. Using data at $\omega_{Lab}=49 MeV$ we find $\alpha_0=8.4\pm 3.0(exp)\pm 1.7(theor)$, $\beta_0=8.9\pm 3.9(exp)\pm 1.8(theor)$, each in units of $10^{-4} fm^3$. With the experimental constraint for the iso-scalar Baldin sum rule, $\alpha_0=7.2\pm 2.1(exp)\pm 1.6(theor)$, $\beta_0=6.9\mp 2.1(exp)\mp 1.6(theor)$. A more accurate result can be achieved by: (i) better experimental data, and (ii) a higher order theoretical calculation including contributions from a couple of so far undetermined four-nucleon-two-photon operators.

Recent developments in nuclear effective field theory

Recent developments in nuclear effective field theory

Long and short of nuclear effective field theory expansions

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.