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Various thermodynamic quantities and the phase diagram of stronglyinteracting hot and dense magnetized quark matter are obtained with the $ 2$-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite valuesof the anomalous magnetic moment (AMM) of the quarks. Susceptibilitiesassociated with constituent quark mass and traced Polyakov loop are used toevaluate chiral and deconfinement transition temperatures. It is found that,inclusion of the AMM of the quarks in presence of the background magnetic fieldresults in a substantial decrease in the chiral as well as deconfinementtransition temperatures in contrast to an enhancement in the chiral transitiontemperature in its absence. Using standard techniques of finite temperaturefield theory, the two point thermo-magnetic mesonic correlation functions inthe scalar ($\sigma$) and neutral pseudoscalar ($\pi^0$) channels are evaluatedto calculate the masses of $\sigma $ and $ \pi^0 $ considering the AMM of thequarks.

european physical journal. a, hadrons and nuclei

Effects of quark anomalous magnetic moment on the thermodynamical  properties and mesonic excitations of magnetized hot and dense matter in PNJL  model