Neutron-Antineutron Operator Renormalization

Baryon number symmetry violating theories beyond the standard model with suppressed proton decay rates can be experimentally constrained by data on neutron-antineutron transition rates. In order to apply this constraints, theoretical predictions for the neutron-antineutron transition rates in various models must be available for comparison. Reliable predictions of transition rates between hadronic states must include non-perturbative quantum chromodynamic effects. These can be calculated in a model independent way by calculating six-quark operator matrix elements with lattice quantum chromodynamics. Preliminary lattice calculations have been performed, but operator renormalization effects must be included in order to match beyond the standard model calculations performed in $\overline{MS}$ renormalized perturbation theory with lattice regularized matrix element results. In particular, a perturbative calculation of the two-loop anomalous dimensions and one-loop renormalization scheme matching coefficients of these six-quark operators is necessary in order to determine leading order corrections at lattice matching scales. This describes our ongoing calculation of these perturbative operator renormalization effects.Comment: 7 pages, presented at the 32nd International Symposium on Lattice Field Theory - Lattice 2014, June 23-28, 2014, Columbia University, New York, N

Color Superconductivity at Large N: A New Hope

At zero density, the `t Hooft large N_c limit often provides some very useful qualitative insights into the non-perturbative physics of QCD. However, it is known that at high densities the `t Hooft large N_c world looks very different from the N_c=3 world, which is believed to be in a color superconducting phase at high densities. At large N_c, on the other hand, the DGR instability causes a chiral-density wave phase to dominate over the color superconducting phase. There is an alternative large N_c limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at N_c=3 reduces to QCD but looks quite different at large N_c. We show that in this alternative large N_c limit, the DGR instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when N_c is large. This revives the hope that a large N_c approximation might be useful for getting some insights into the high-density phenomenology of QCD.Comment: 8 pages, 1 figur

S-wave scattering of strangeness -3 baryons

We explore the interactions of two strangeness -3 baryons in multiple spin channels with lattice QCD. This system provides an ideal laboratory for exploring the interactions of multi-baryon systems with minimal dependence on light quark masses. Model calculations of the two-$\Omega^-$ system in two previous works have obtained conflicting results, which can be resolved by lattice QCD. The lattice calculations are performed using two different volumes with $L\sim2.5$ and 3.9 fm on anisotropic clover lattices at $m_\pi \sim 390$ MeV with a lattice spacing of $a_s \sim 0.123$ fm in the spatial direction and $a_t\sim{a}_s/3.5$ in the temporal direction. Using multiple interpolating operators from a non-displaced source, we present scattering information for two ground state $\Omega^-$ baryons in both the S=0 and S=2 channels. For S=0, $k\cot\delta$ is extracted at two volumes, which lead to an extrapolated scattering length of $a^{\Omega\Omega}_{S=0}=0.16 \pm 0.22 \ \text{fm}$, indicating a weakly repulsive interaction. Additionally, for S=2, two separate highly repulsive states are observed. We also present results on the interactions of the excited strangeness -3, spin-1/2 states with the ground spin-3/2 states for the spin-1 and spin-2 channels. Results for these interactions are consistent with attractive behavior.Comment: 21 pages, 10 fig

Finite isospin density probe for conformality

A new method of employing an isospin chemical potential for QCD-like theories with different number of colors, number of fermion flavors, and in different fermion representations is proposed. The isospin chemical potential, which can be simulated on the lattice due to its positive definite determinant gives a means to probe both confining theories and IR conformal theories without adjusting the lattice spacing and size. As the quark mass is reduced, the isospin chemical potential provides an avenue to extract the chiral condensate in confining theories through the resulting pseudoscalar condensate. For IR conformal theories, the mass anomalous dimension can be extracted in the conformal window through "finite density" scaling since the isospin chemical potential is coupled to a conserved current. In both of these approaches, the isospin chemical potential can be continuously varied for each ensemble at comparable costs while maintaining the hierarchy between the lattice size and lattice spacing. In addition to exploring these methods, finite volume and lattice spacing effects are investigated.Comment: 18 pages, 3 figures, v3: typos corrected and discussions improved. Phys. Rev. D 85, 074503 (2012

Classification of Minimally Doubled Fermions

We propose a method to control the number of species of lattice fermions which yields new classes of minimally doubled lattice fermions. We show it is possible to control the number of species by handling $O(a)$ Wilson-term-like corrections in fermion actions, which we will term ``Twisted-ordering Method". Using this method we obtain new minimally doubled actions with one exact chiral symmetry and exact locality. We classify the known minimally doubled fermions into two types based on the locations of the propagator poles in the Brillouin zone.Comment: 23 pages, 6 figures; version accepted in Phys.Rev.