Constraints on Unparticle Interactions from Invisible Decays of Z, Quarkonia and Neutrinos

Unparticles (\U) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrinos. The constraints on the unparticle interaction scale \Lambda_\U are very sensitive to the dimension d_\U of the unparticles. From invisible $Z$ and $V$ decays, we find that with d_\U close to 1 for vector \U, the unparticle scale \Lambda_\U can be more than $10^4$ TeV, and for d_\U around 2, the scale can be lower than one TeV. From invisible neutrino decays, we find that if d_\U is close to 3/2, the scale can be more than the Planck mass, but with d_\U around 2 the scale can be as low as a few hundred GeV. We also study the possibility of using V (Z)\to \gamma + \U to constrain unparticle interactions, and find that present data give weak constraints.Comment: 12 pages, 4 figures, version to appear in JHEP

Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type), which has a long correlation length $\xi\sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure