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Entanglement between chiral and deconfinement transitions under strong uniform magnetic background field

Effects of a uniform (electro-) magnetic background field are investigated in the two-flavor nonlocal Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Temperature-dependences of the chiral order-parameter and the Polyakov-loop are investigated under the magnetic field. In the nonlocal PNJL model with four-dimensional momentum dependent distribution function, pseudo-critical temperatures of the chiral and deconfinement transitions are coincident each other even if the magnetic field is strong. It means that we can check the reliability of the distribution function under the strong magnetic field by comparing with lattice QCD data, particularly from the viewpoint of the entanglement between the chiral and deconfinement transitions.