The 3-state Potts model as a heavy quark finite density laboratory

The 3-D Z(3) Potts model is a model for finite temperature QCD with heavy quarks. The chemical potential in QCD becomes an external magnetic field in the Potts model. Following Alford et al.cite{Alford_et_al}, we revisit this mapping, and determine the phase diagram for an arbitrary chemical potential, real or imaginary. Analytic continuation of the phase transition line between real and imaginary chemical potential can be tested with precision. Our results show that the chemical potential weakens the heavy-quark deconfinement transition in QCD.

The N to Delta electromagnetic transition form factors from Lattice QCD

The magnetic dipole, the electric quadrupole and the Coulomb quadrupole amplitudes for the transition gamma Nto Delta are calculated in quenched lattice QCD at beta=6.0 with Wilson fermions. Using a new method combining an optimal combination of interpolating fields for the $Delta$ and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios of the electric and Coulomb quadrupole amplitudes to the magnetic dipole amplitude, R_{EM} and R_{SM}, up to momentum transfer squared 1.5 GeV^2. We show for the first time using lattice QCD that both R_{EM} and R_{SM} are non-zero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the N- Delta system.

Momentum dependence of the N to Delta transition form factors

We present a new method to determine the momentum dependence of the N to Delta transition form factors and demonstrate its effectiveness in the quenched theory at $beta=6.0$ on a $32^3 times 64$ lattice. We address a number of technical issues such as the optimal combination of matrix elements and the simultaneous overconstrained analysis of all lattice vector momenta contributing to a given momentum transfer squared, $Q^2$.

$gamma N to Delta$ transition form factors in Quenched and $N_F=2$ QCD

Calculations of the magnetic dipole, electric quadrupole and Coulomb quadrupole amplitudes for the transition $gamma Nto Delta$ are presented both in quenched QCD and with two flavours of degenerate dynamical quarks.

N to Delta electromagnetic transition form factors from Lattice QCD

The magnetic dipole, the electric quadrupole and the Coulomb quadrupole amplitudes for the transition $gamma Nto Delta$ are evaluated both in quenched lattice QCD at $beta=6.0$ and using two dynamical Wilson fermions simulated at $beta=5.6$. The dipole transition form factor is accurately determined at several values of momentum transfer. On the lattices studied in this work, the electric quadrupole amplitude is found to be non-zero yielding a negative value for the ratio, $ R_{EM}$, of electric quadrupole to magnetic dipole amplitudes at three values of momentum transfer.

QCD simulations at small chemical potential

Within the reweighting approach, one has the freedom to choose the Monte Carlo action so that it provides a good overlap with the finite-mu measure but remains simple to simulate. We explore several choices of action in the regime of small mu. Simulating with a finite isospin chemical potential mu_I=mu gives a better overlap than the standard choice mu=0, with no computational overhead.

The Static Baryon Potential

Using state of the art lattice techniques we investigate the static baryon potential. We employ the multi-hit procedure for the time links and a variational approach to determine the ground state with sufficient accuracy that, for distances up to $sim 1.2$ fm, we can distinguish the $Y$- and $Delta$- Ansatze for the baryonic Wilson area law. Our analysis shows that the $Delta$-Ansatz is favoured. This result is also supported by the gauge-invariant nucleon wave function which we measure for the first time.

Screening mass responses to the chemical potential at finite temperature

Responses to chemical potential of the pseudoscalar meson screening mass and the chiral condensate in lattice QCD are investigated. On a $16 times 8^2 times 4$ lattice with two flavors of staggered quarks the first and second responses below and above $T_c$ are evaluated. Different behavior in the low and the high temperature phases are observed, which may be explained as a consequence of the chiral symmetry breaking and restoration.

Responses of hadrons to chemical potential at finite temperature

We present a framework to compute the responses of hadron masses to the chemical potential in lattice QCD simulations. As a first trial, the screening mass of the pseudoscalar meson and its first and second responses are evaluated. We present results on a $16times 8^2times 4$ lattice with two flavors of staggered quarks below and above $T_c$. The responses to both the isoscalar and isovector chemical potentials are obtained. They show different behavior in the low and the high temperature phases, which may be explained as a consequence of chiral symmetry breaking and restoration, respectively.