TL;DR: In this paper, a lower bound for inelastic electron-nucleon scattering at high momentum transfer is derived on the basis of U(6)⊗U(6), at least for spin-averaged diagonal single-particle states.
Abstract: Consequences of the local commutation relations of vector and axial currents proposed by Gell-Mann are explored: (1) A recipe for detecting and isolating Schwinger terms in the commutators, proportional to derivatives of the δ function, is discussed. (2) Under assumptions of smooth asymptotic behavior of form factors for forward scattering of the isovector current from a proton, we show that the U(3)⊗U(3) algebra for the time components of the currents implies the U(6)⊗U(6) algebra for space components, at least for spin-averaged diagonal single-particle states. (3) The derivation of the Adler-Weisberger formula for GAGV is sharpened by giving arguments that, at fixed energy, the forward π−p Green's function satisfies an unsubtracted dispersion relation in the pion mass. (4) A lower bound for inelastic electron-nucleon scattering at high momentum transfer is derived on the basis of U(6)⊗U(6). (5) The contribution of very virtual photons to the hyperfine anomaly in hydrogen is shown to be related to an equal-time commutator of currents; this contribution is crudely estimated to be <4 parts per million (ppm). (6) The logarithmically divergent part of electromagnetic mass differences of hadrons is shown to be proportional to matrix elements of the equal-time commutator of the electromagnetic current with its time derivative. It is suggested that this "divergent" part be identified with the Coleman-Glashow "tadpoles"; this suggestion is discussed in the framework of a simple quark model. (7) The logarithmically divergent part of the electromagnetic correction to the process π−→π0+e−+ν¯ is, on the basis of the U(6)⊗U(6) current algebra, shown to be nonvanishing, and is computed. (8) A speculative argument is presented that the rate e++e−→hadrons is comparable to the rate e++e−→μ++μ− in the limit of large energies.
TL;DR: A review of recent applications of self-consistent relativistic mean field models to exotic nuclear structure can be found in this article, where the authors provide a rich theoretical framework for studies of nuclei along the valley of β-stability, exotic nuclei with extreme groundstate isospin values and close to the particle drip lines.
TL;DR: An accurate measurement of the neutron radius in 208Pb-via parity violating electron scattering-may have important implications for the structure of the crust of neutron stars.
Abstract: We study relationships between the neutron-rich skin of a heavy nucleus and the properties of neutron-star crusts. Relativistic effective field theories with a thicker neutron skin in ${}^{208}\mathrm{Pb}$ have a larger electron fraction and a lower liquid-to-solid transition density for neutron-rich matter. These properties are determined by the density dependence of the symmetry energy which we vary by adding nonlinear couplings between isoscalar and isovector mesons. An accurate measurement of the neutron radius in ${}^{208}\mathrm{Pb}$---via parity violating electron scattering---may have important implications for the structure of the crust of neutron stars.
TL;DR: In this article, a review of lattice results related to pion, kaon, D-meson, neutral kaon mixing, B-meon, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities is presented.
Abstract: We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \rightarrow \pi $ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi $ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha _s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.
TL;DR: In this article, the meson-meson potentials provided by the lowest order chiral Lagrangian were used to obtain singularities in the S-wave amplitudes corresponding to the σ, f0 and a0 resonances.