Abstract
We have calculated the electromagnetic spectral function (SF) vis-\`{a}-vis the dilepton rate (DR) by evaluating the one-loop photon polarisation tensor for a strongly magnetised hot and dense medium. The calculation is performed in the ambit of mean field models namely Nambu\textendash Jona-Lasinio (NJL) and its Polyakov loop extended version (PNJL) in the lowest Landau level approximation. These models allow for a dynamical generation of quark mass which, evidently, gets affected in the presence of a magnetised medium. We have shown that the strength of the SF gets boosted because of the presence of dynamical quarks in lieu of the current quarks. It increases as we increase the magnetic field for a given value of temperature in both NJL and PNJL models. This increment is further reflected in the DR which is enhanced as compared to the Born rate for certain values of invariant masses. We also discuss the impact of chemical potential on DR within the present scenario.
Highlights
Understanding quantum chromodynamics (QCD) in the presence of a magnetic background has gained lots of contemporary research interests [1]
Electroweak phase transition which may reach up to eB ≈ 200m2π [10], they are strong enough to cast significant influence on the deconfined medium of strongly interacting quarks and gluons known as quark gluon plasma (QGP) which is created in such heavy-ion collision (HIC) [11,12]
In the left panel 2(a) we have shown how the constituent mass increases with the increase of the magnetic field (i.e., magnetic catalysis (MC) effect)
Summary
Understanding quantum chromodynamics (QCD) in the presence of a magnetic background has gained lots of contemporary research interests [1]. Ongoing investigations provide us a strong hint that the QGP created in the HICs is a strongly interacting one [65,66,67,68,69,70,71,72] Such nonperturbative nature of the medium can be mimicked roughly, through the PNJL model where a background gauge field is added to the usual NJL model. Spectral properties are influenced to quite an extent, especially the DR gets enhanced due to the nonperturbative effect through the Polyakov loop fields [49] This makes the present study more interesting where the effect of the strong magnetic field will be further influenced by the presence of a background gauge field, through PNJL model augmented with magnetic field [73,74,75,76].
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