Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD.

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings a={0.098,0.085,0.064,0.049} fm and various pion masses ranging between 220 and 350 MeV, with proton momenta up to 2.8 GeV. The result is nonperturbatively renormalized in the hybrid scheme with self-renormalization, which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass, and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.

Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass.

We present a state-of-the-art calculation of the isovector quark-helicity Bjorken-x distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasidistributions at proton momenta P_{z}∈{2.2,2.6,3.0} GeV on the lattice and match them systematically to the physical parton distribution using the large-momentum effective theory. We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data, in particular, Δu[over ¯](x)>Δd[over ¯](x).

Short-Range Correlations and the EMC Effect in Effective Field Theory.

We show that the empirical linear relation between the magnitude of the EMC effect in deep inelastic scattering on nuclei and the short-range correlation scaling factor a_{2} extracted from high-energy quasielastic scattering at x≥1 is a natural consequence of scale separation and derive the relationship using effective field theory. While the scaling factor a_{2} is a ratio of nuclear matrix elements that individually depend on the calculational scheme, we show that the ratio is independent of this choice. We perform Green's function Monte Carlo calculations with both chiral and Argonne-Urbana potentials to verify this and determine the scaling factors for light nuclei. The resulting values for ^{3}He and ^{4}He are in good agreement with experimental values. We also present results for ^{9}Be and ^{12}C extracted from variational Monte Carlo calculations.

Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation.

We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases.

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

Gene-mating dynamic evolution theory: fundamental assumptions, exactly solvable models and analytic solutions.

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. A model is studied to describe a large class of systems within population genetics. We focus on a single locus, any number of alleles in a two-gender dioecious population. Our governing equations are time-dependent continuous differential equations labeled by a set of parameters, where each parameter stands for a population percentage carrying certain common genotypes. The full parameter space consists of all allowed parameters of these genotype frequencies. Our equations are uniquely derived from four fundamental assumptions within any population: (1) a closed system; (2) average-and-random mating process (mean-field behavior); (3) Mendelian inheritance; and (4) exponential growth and exponential death. Even though our equations are nonlinear with time-evolutionary dynamics, we have obtained an exact analytic time-dependent solution and an exactly solvable model. Our findings are summarized from phenomenological and mathematical viewpoints. From the phenomenological viewpoint, any initial parameter of genotype frequencies of a closed system will eventually approach a stable fixed point. Under time evolution, we show (1) the monotonic behavior of genotype frequencies, (2) any genotype or allele that appears in the population will never become extinct, (3) the Hardy-Weinberg law and (4) the global stability without chaos in the parameter space. To demonstrate the experimental evidence for our theory, as an example, we show a mapping from the data of blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions. From the mathematical viewpoint, our highly symmetric governing equations result in continuous global stable equilibrium solutions: these solutions altogether consist of a continuous curved manifold as a subspace of the whole parameter space of genotype frequencies. This fixed-point manifold is a global stable attractor known as the Hardy-Weinberg manifold, attracting any initial point in any Euclidean fiber bounded within the genotype frequency space to the fixed point where this fiber is attached. The stable base manifold and its attached fibers form a fiber bundle, which fills in the whole genotype frequency space completely. We can define the genetic distance of two populations as their geodesic distance on the equilibrium manifold. In addition, the modification of our theory under the process of natural selection and mutation is addressed.

Model-independent results for SU(3) violation in light-cone distribution functions.

Using chiral symmetry we investigate the leading SU(3) violation in light-cone distribution functions phi(M)(x) of the pion, kaon, and eta. It is shown that terms nonanalytic in the quark masses do not affect the shape, and only appear in the decay constants. Predictive power is retained including the leading analytic m(q) operators. With the symmetry violating corrections we derive useful model-independent relations between phi(pi),phi(eta),phiK+(,K0), and phiK(0)(,K-). Using the soft-collinear effective theory we discuss how factorization generates the subleading chiral coefficients.

Lattice theory for low energy fermions at nonzero chemical potential.

We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the two-body potential and does not suffer from a sign problem. In particular, the theory could be useful in studying the thermodynamic limit of fermion systems for which the scattering length is much larger than the interparticle spacing, with applications to realistic atomic systems and dilute neutron gases.

Leading chiral contributions to the spin structure of the proton.

The leading chiral contributions to the quark and gluon components of the proton spin are calculated using heavy-baryon chiral perturbation theory. Similar calculations are done for the moments of the generalized parton distributions relevant to the quark and gluon angular momentum densities. These results provide useful insight into the role of pions in the spin structure of the nucleon and can serve as a guide for extrapolating lattice QCD calculations at large quark masses to the chiral limit.

Inequalities for light nuclei in the Wigner symmetry limit.

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three- and four-nucleon force terms.