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Register a new userProton-proton fusion in pionless effective theory
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S. Ando
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The proton-proton fusion reaction, $ppto de^+ u$, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon-di-baryon contact vertex is fixed through the ratio of two- and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%.
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The astrophysical S-factor for proton-proton fusion, S_11(E), is obtained with the nuclear matrix element analytically calculated in pionless effective field theory. To the third order, the zero-energy result S_11(0) and the first energy derivative S_11(0) are found to be (3.99 pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. The second energy derivative is also calculated for the first time, and the result S_11(0) = S_11(0)*(170 pm 2) MeV^-2 contributes at the level of 0.5% to the fusion rate at the solar center, which is smaller than 1% as previously estimated.
We compute the $S$-factor of the proton-proton ($pp$) fusion reaction using chiral effective field theory ($chi$EFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the $pp$ cross section in momentum space, (ii) the statistical uncertainties in the low-energy coupling constants of $chi$EFT, (iii) the systematic uncertainty due to the $chi$EFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon-nucleon interaction. We also examine the robustness of the polynomial extrapolation procedure, which is commonly used to extract the threshold $S$-factor and its energy-derivatives. By performing a statistical analysis of the polynomial fit of the energy-dependent $S$-factor at several different energy intervals, we eliminate a systematic uncertainty that can arise from the choice of the fit interval in our calculations. In addition, we explore the statistical correlations between the $S$-factor and few-nucleon observables such as the binding energies and point-proton radii of $^{2,3}$H and $^3$He as well as the $D$-state probability and quadrupole moment of $^2$H, and the $beta$-decay of $^{3}$H. We find that, with the state-of-the-art optimization of the nuclear Hamiltonian, the statistical uncertainty in the threshold $S$-factor cannot be reduced beyond 0.7%.
Pionless effective field theory in a finite volume (FVEFT$_{pi!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{pi!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $Ain{2,3}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{pi!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.
A systematic description of low-energy observables in light nuclei is presented. The effective field theory formalism without pions is extended to: i) predictions with next-to-leading-order (non-perturbatively) accuracy for the 4-helium binding energy B({alpha}), the triton charge radius, and the 3-helium-neutron scattering length; ii) phase shifts for neutron-deuteron scattering and {alpha}-neutron low-energy scattering at leading order; iii) the ground states of the 5-helium (with and without Coulomb interaction) and 6-helium isotopes up to next-to-leading order; The convergence from leading- to next-to-leading order of the theory is demonstrated for correlations between: i) the triton binding energy B(t) and the triton charge radius; ii) B(t) and the 4-helium binding energy B({alpha}); Furthermore, a correlation between B(t) and the scattering length in the singlet S-wave channel of neutron-helium-3 scattering is discovered, and a model-independent estimate for the trinucleon binding energy splitting is provided. The results provide evidence for the usefulness of the applied power-counting scheme, treating next-to-leading-order interactions nonperturbatively and four-nucleon interactions as, at least, one order higher. The 5- and 6-helium ground states are analyzed with a power-counting scheme which includes the momentum-dependent next-to-leading order vertices perturbatively. All calculations include a full treatment of the Coulomb interaction. The assessment of numerical uncertainties associated with the solution of the few-body equation of motion through the Resonating Group Method parallels the report of the results for light nuclei in order to establish this method as practical for the analysis of systems with up to six particles interacting via short-range interactions.
We present a systematic calculation of the cross section for the lepton-proton bremsstrahlung process l + p --> l + p + gamma in chiral perturbation theory at next-to-leading order. This process corresponds to an undetected background signal for the proposed MUSE experiment at PSI. MUSE is designed to measure elastic scattering of low-energy electrons and muons off a proton target in order to extract a precise value of the protons r.m.s. radius. We show that the commonly used peaking approximation, which is used to evaluate the radiative tail for the elastic cross section, is not applicable for muon-proton scattering at the low-energy MUSE kinematics. Furthermore, we point out a certain pathology with the standard chiral power counting scheme associated with electron scattering, whereby the next-to-next-to-leading order contribution from the pion loop diagrams is kinematically enhanced and numerically of the same magnitude as the next-to-leading order corrections. We correct a misprint in a commonly cited review article.
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