We investigate the Landau-level structures encoded in the famous Heisenberg-Euler (HE) effective action in constant electromagnetic fields. We first discuss the HE effective actions for scalar and spinor QED, and then extend it to the QCD analogue in
the covariantly constant chromo-electromagnetic fields. We identify all the Landau levels and the Zeeman energies starting out from the proper-time representations at the one-loop order, and derive the vacuum persistence probability for the Schwinger mechanism in the summation form over independent contributions of the all-order Landau levels. We find an enhancement of the Schwinger mechanism catalyzed by a magnetic field for spinor QED and, in contrast, a stronger exponential suppression for scalar QED due to the zero-point energy of the Landau quantization. For QCD, we identify the discretized energy levels of the transverse and longitudinal gluon modes on the basis of their distinct Zeeman energies, and explicitly confirm the cancellation between the longitudinal-gluon and ghost contributions in the Schwinger mechanism. We also discuss the unstable ground state of the perturbative gluon excitations known as the Nielsen-Olesen instability.
We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is margi
nal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu--Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.
The QCD Kondo effect stems from the color exchange interaction in QCD with non-Abelian property, and can be realized in a high-density quark matter containing heavy-quark impurities. We propose a novel type of the QCD Kondo effect induced by a strong
magnetic field. In addition to the fact that the magnetic field does not affect the color degrees of freedom, two properties caused by the Landau quantization in a strong magnetic field are essential for the magnetically induced QCD Kondo effect; (1) dimensional reduction to 1+1-dimensions, and (2) finiteness of the density of states for lowest energy quarks. We demonstrate that, in a strong magnetic field $B$, the scattering amplitude of a massless quark off a heavy quark impurity indeed shows a characteristic behavior of the Kondo effect. The resulting Kondo scale is estimated as $Lambda_{rm K} simeq sqrt{e_qB} alpha_{s}^{1/3} {rm{exp}}{-{4}pi/N_{c} alpha_{s} {rm{log}}( 4 pi/alpha_{s}) }$ where $alpha_{s}$ and $N_c$ are the fine structure constant of strong interaction and the number of colors in QCD, and $e_q$ is the electric charge of light quarks.
We develop a Monte-Carlo event generator based on combination of a parton production formula including the effects of parton saturation (called the DHJ formula) and hadronization process due to the Lund string fragmentation model. This event generato
r is designed for the description of hadron productions at forward rapidities and in a wide transverse momentum range in high-energy proton-proton collisions. We analyze transverse momentum spectra of charged hadrons as well as identified particles; pion, kaon, (anti-)proton at RHIC energy, and ultra-forward neutral pion spectra from LHCf experiment. We compare our results to those obtained in other models based on parton-hadron duality and fragmentation functions.
The two-flavor color superconductivity is studied over a wide range of baryon density with a single model. We pay a special attention to the spatial-momentum dependence of the gap and to the spatial-structure of Cooper pairs. At extremely high baryon
density (O(10^{10} rho_0) with rho_0 being the normal nuclear matter density), our model becomes equivalent to the usual perturbative QCD treatment and the gap is shown to have a sharp peak near the Fermi surface due to the weak-coupling nature of QCD. On the other hand, the gap is a smooth function of the momentum at lower densities (O(10 rho_0)) due to strong color magnetic and electric interactions. To study the structural change of Cooper pairs from high density to lower density, quark correlation in the color superconductor is studied both in the momentum space and in the coordinate space. The size of the Cooper pair is shown to become comparable to the averaged inter-quark distance at low densities. Also, effects of the momentum-dependent running coupling and the antiquark pairing, which are both small at high density, are shown to be non-negligible at low densities. These features are highly contrasted to the standard BCS superconductivity in metals.
