Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNeutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory
369
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.
rate research
Read More
We study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory (BChPT) up to the next-to-next-to-leading order. The inherent power counting breaking terms are removed within extended-on-mass-shell scheme. We perform the first combined study of the pion-nucleon and kaon-nucleon scattering data in covariant BChPT and show that it can provide a reasonable description of the experimental data. In addition, we find that it is possible to fit the experimental baryon masses and the pion-nucleon and kaon-nucleon scattering data simultaneously at this order, thus providing a consistent check on covariant BChPT. We compare the scattering lengths of all the pertinent channels with available experimental data and those of other approaches. In addition, we have studied the leading order contributions of the virtual decuplet and found that they can improve the description of the $pi N$ phase shifts near the $Delta(1232)$ peak, while they have negligible effects on the description of the $K N$ phase shifts.
We employ an effective field theory (EFT) that exploits the separation of scales in the p-wave halo nucleus $^8mathrm{B}$ to describe the process $^7mathrm{Be}(p,gamma)^8mathrm{B}$ up to a center-of-mass energy of 500 keV. The calculation, for which we develop the lagrangian and power counting, is carried out up to next-to-leading order (NLO) in the EFT expansion. The power counting we adopt implies that Coulomb interactions must be included to all orders in $alpha_{rm em}$. We do this via EFT Feynman diagrams computed in time-ordered perturbation theory, and so recover existing quantum-mechanical technology such as the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the ${}^7$Be core, $Lambda approx 70$ MeV. Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature. Each of these models corresponds to a particular point in the space of EFTs. The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of $^7mathrm{Be}(p,gamma)^8mathrm{B}$. We also demonstrate that the only N$^2$LO corrections in $^7mathrm{Be}(p,gamma)^8mathrm{B}$ come from an inelasticity that is practically of N$^3$LO size in the energy range of interest, and so the truncation error in our calculation is effectively N$^3$LO. We also discuss the relation of our extrapolated $S(0)$ to the previous standard evaluation.
We study the three-body systems of ${}^{3}mathrm{He}$ and $pd$ scattering and demonstrate, both analytically and numerically, that a new $pd$ three-body force is needed at next-to-leading order in pionless effective field theory. We also show that at leading order these observables require no new three-body force beyond what is necessary to describe $nd$ scattering. We include electromagnetic effects by iterating only diagrams that involve a single photon exchange in the three-body sector.
We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory ($mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use this formula to compute the EEC in $mathcal{N}=4$ sYM at next-to-next-to-leading order in perturbation theory. Our result is given by a two-fold integral representation that is straightforwardly evaluated numerically. We find that some of the integration kernels are equivalent to those appearing in sunrise Feynman integrals, which evaluate to elliptic functions. Finally, we use the new formula to provide the expansion of the EEC in the back-to-back and collinear limits.
We calculate the octet baryon magnetic moments in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-leading order. At this order, there are nine low-energy constants, which cannot be uniquely determined by the seven experimental data alone. We propose two strategies to circumvent this problem. First, we assume that chiral perturbation theory has a certain convergence rate and use this as one additional constraint to fix the low-energy constants by fitting to the experimental data. Second, we fit to lattice QCD simulations to determine the low-energy constants. We then compare the resulting predictions of the light and strange quark mass dependence of the octet baryon magnetic moments by the three mostly studied formulations of baryon chiral perturbation theory, namely, the extended-on-mass-shell, the infrared, and the heavy baryon approach. It is shown that once more precise lattice data become available, one will learn more about the convergence pattern of baryon chiral perturbation theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
