Using numerical simulations of lattice QCD we calculate the effect of an external magnetic field on the equation of state of the quark-gluon plasma. The results are obtained using a Taylor expansion of the pressure with respect to the magnetic field
for the first time. The coefficients of the expansion are computed to second order in the magnetic field. Our setup for the external magnetic field avoids complications arising from toroidal boundary conditions, making a Taylor series expansion straightforward. This study is exploratory and is meant to serve as a proof of principle.
We calculate pseudoscalar masses on gauge configurations containing the effects of 2+1 flavors of dynamical asqtad quarks and quenched electromagnetism. The lattice spacings vary from 0.12 to 0.06 fm. The masses are fit with staggered chiral perturba
tion theory including NLO electromagnetic terms. We attempt to extract the fit parameters for the electromagnetic contributions, while taking into account the finite volume effects, and extrapolate them to the physical limit.
The properties of hot hadronic matter are of great importance to the studies of heavy-ion collisions, cosmology and compact star formation. I briefly outline the current methods in use in the lattice simulations of QCD thermodynamics at zero and nonz
ero density. I discuss the most recent results for the QCD phase transition, critical behavior and the equation of state.
In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams are considered small and are typically ignored. We aim to estimate nonperturbatively the size of the resulting correction, which may eventually b
e needed in high precision calculations of the charmonium spectrum. We study this problem in the quenched and unquenched QCD cases. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the interpretation of the signal is simplified. We present results from lattices with $aapprox 0.09$ fm and $aapprox 0.06$ fm.
We extend our work on QCD thermodynamics with 2+1 quark flavors at nonzero chemical potential to finer lattices with $N_t=6$. We study the equation of state and other thermodynamic quantities, such as quark number densities and susceptibilities, and
compare them with our previous results at $N_t=4$. We also calculate the effects of the addition of the charm and bottom quarks on the equation of state at zero and nonzero chemical potential. These effects are important for cosmological studies of the early Universe.
We report on calculations of the charmonium and bottomonium spectrum in lattice QCD. We use ensembles of gauge fields with three flavors of sea quarks, simulated with the asqtad improved action for staggered fermions. For the heavy quarks we employ t
he Fermilab interpretation of the clover action for Wilson fermions. These calculations provide a test of lattice QCD, including the theory of discretization errors for heavy quarks. We provide, therefore, a careful discussion of the results in light of the heavy-quark effective Lagrangian. By and large, we find that the computed results are in agreement with experiment, once parametric and discretization errors are taken into account.
We study the effects of the addition of the charm quark on the QCD equation of state at zero and nonzero chemical potential on lattices with $N_t=6$. Our ensembles are quenched with respect to charm and the charm quark is a valence staggered quark. A
long the trajectory of constant physics the ratio $m_s/m_c$ is kept constant after tuning the charm quark mass at a lattice spacing of about 0.09 fm. We find that the charm quark has a significant contribution to the equation of state at zero chemical potential already at temperatures between about $1.2T_c$ and $2T_c$. The additional contribution at nonzero chemical potential vanishes within the current statistical uncertainty.
In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams is considered small and is typically ignored. We aim to estimate nonperturbatively the size of the resulting error, which could potentially affec
t the high precision calculations of the charmonium spectrum. Following our work on the effects of the disconnected diagrams in unquenched QCD presented at Lattice 2007, we study the same problem in the quenched case. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the interpretation of the signal is simplified. We present results from lattices with $aapprox 0.09$ fm and $aapprox 0.063$ fm.
We present results for the QCD equation of state, quark densities and susceptibilities at nonzero chemical potential, using 2+1 flavor asqtad ensembles with $N_t=4$. The ensembles lie on a trajectory of constant physics for which $m_{ud}approx0.1m_s$
. The calculation is performed using the Taylor expansion method with terms up to sixth order in $mu/T$.
Experimentally the charmonium hyperfine splitting is $M_{J/psi}-M_{eta_c}=117$ MeV and current lattice results are generally below this value. The difference could be due to the effects of the disconnected flavor singlet diagrams which have not been
included in these calculations. Previous attempts to determine the disconnected flavor singlet corrections have led just to rough estimates in the range of $pm 20$ MeV. We present preliminary results for these corrections calculated on fine ($aapprox 0.09$ fm) Asqtad 2+1 flavor lattices provided by the MILC Collaboration.
