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Register a new userNear Threshold Proton-Proton Fusion in Effective Field Theory
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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.
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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%.
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%.
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.
We present results for the $p p to p p omega$ reaction studied by considering two different scenarios: with and without the inclusion of nucleon resonance excitations. The recently measured angular distribution by the COSY-TOF Collaboration at an excess energy of $Q = 173$ MeV and the energy dependence of the total cross section data for $pi^- p to omega n$ are used to calibrate the model parameters. The inclusion of nucleon resonances improves the theoretical prediction for the energy dependence of the total cross section in $pp to ppomega$ at excess energies $Q < 31$ MeV. However, it still underestimates the data by about a factor of two, and remains a problem in understanding the reaction mechanism.
The near threshold total cross section and angular distributions of K+K- pair production via the reaction pp --> ppK+K- have been studied at an excess energy of Q = 17 MeV using the COSY-11 facility at the cooler synchrotron COSY. The obtained cross section as well as an upper limit at an excess energy of Q = 3 MeV represent the first measurements on the K+K- production in the region of small excess energies where production via the channel pp --> pp Phi --> ppK+K- is energetically forbidden. The possible influence of a resonant production via intermediate scalar states f0(980) and a0(980) is discussed.
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