We derive an analytic expression for one-loop effective action of QCD+QED at zero and finite temperatures by using the Schwingers proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic f
ields but also the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED+QCD, and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this Euler-Heisenberg-Weiss action in QCD+QED, we investigate quark pair productions induced by QCD+QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.
We investigate an application of twisted boundary conditions for study of low-energy hadron-hadron interactions with Lushcers finite size method. It allows us to calculate the phase shifts for elastic scattering of two hadrons at any small value of t
he scattering momentum even in a finite volume. We then can extract model independent information of low-energy scattering parameters such as the scattering length, the effective range and the effective volume from the $S$-wave and $P$-wave scattering phase shifts through the effective range expansion. This approach also enables us to examine the existence of near-threshold and narrow resonance states, of which characteristic is observed in many of newly discovered charmonium-like $XYZ$ mesons. As a simple example, we demonstrate our method for low-energy $J/psi$-$phi$ scatterings to search for Y(4140) resonance using 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $m_{pi}=156$ MeV.
