Polarized Gluon Distribution Delta g(x) in the Proton

We study the polarized gluon distribution $\Delta g(x)$ in a longitudinally polarized proton. We argue that the distribution can be calculated approximately from the quark color currents found in simple quark models. The first result from the MIT bag model as well as the non-relativistic quark model shows that $\Delta g(x)$ is positive at all $x$. If this feature holds in QCD, it imposes a strong constraint on phenomenological fits to experimental data. The total gluon helicity $\Delta G$ from the bag model is about $0.3\hbar$ at the scale of 1 GeV, considerably smaller than previous theoretical expectations.Comment: 6 pages, 3 figure

Topological Z2\mathbb{Z}_2 Resonating-Valence-Bond Spin Liquid on the Square Lattice

A one-parameter family of long-range resonating valence bond (RVB) state on the square lattice was previously proposed to describe a critical spin liquid (SL) phase of the spin-$1/2$ frustrated Heisenberg model. We provide evidence that this RVB state in fact also realises a topological (long-range entangled) $\mathbb{Z}_2$ SL, limited by two transitions to critical SL phases. The topological phase is naturally connected to the $\mathbb{Z}_2$ gauge symmetry of the local tensor. This work shows that, on one hand, spin-$1/2$ topological SL with $C_{4v}$ point group symmetry and $SU(2)$ spin rotation symmetry exists on the square lattice and, on the other hand, criticality and nonbipartiteness are compatible. We also point out that, strong similarities between our phase diagram and the ones of classical interacting dimer models suggest both can be described by similar Kosterlitz-Thouless transitions. This scenario is further supported by the analysis of the one-dimensional boundary state.Comment: v2: improve presentation, present new evidence and add reference

Measuring the P-odd Pion-Nucleon Coupling h_{\pi NN}^{(1)} in \pi^+ Photoproton Production Near the Threshold

We show that polarized gamma p -> \pi^+ n in the threshold region is an excellent candidate for measuring the leading parity-violating pion-nucleon coupling h_{\pi NN}^{(1)} to an uncertainty of 20% if it has a natural size from dimensional analysis. The conclusion is based on a large unpolarized cross section, a new low-energy theorem for the photon polarization asymmetry at the threshold A_\gamma|_{th} = \sqrt{2} f_\pi (\mu_p-\mu_n) h_{\pi NN}^{(1)}/g_A m_N \sim h_{\pi NN}^{(1)}/2, and its strong dominance at forward and backward angles in the threshold region.Comment: 4 pages, 3 figures. More data points in fig. 1 and note added in proof adde