Vector meson spectral function and dilepton production rate in a hot and dense medium within an effective QCD approach

The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalarvector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vector meson retains its bound property up to a moderate value of temperature above the phase transition. Using the vector meson spectral function we, for the first time, obtained the dilepton production rate from a hot and dense medium within the framework of PNJL model that takes into account the nonperturbative effect through the Polyakov Loop fields. The dilepton production rate in PNJL model is enhanced compared to NJL and Born rate in the deconfined phase due to the suppression of color degrees of freedom at moderate temperature. The presence of isoscalar-vector interaction further enhances the dileption rate over the Born rate in the low mass region. Further, we also have computed the Euclidean correlation function in vector channel and the conserved density fluctuation associated with temporal correlation function appropriate for a hot and dense medium. The dilepton rate and the Euclidean correlator are also compared with available lattice data and those quantities in PNJL model are found to agree well in certain domain.Comment: 30 pages, 16 figures, typos corrected, references added, to appear in JHE

The role of U(1)AU(1)_A symmetry breaking in the QCD corrections to the pion mass difference

The charged and neutral pion mass difference can be attributed to both the QED and QCD contributions. The current quark mass difference ($\Delta m$) is the source of the QCD contribution. Here, in a two-flavour non-local NJL model, we try to estimate the QCD contribution. Interestingly, we find that the strength of the $U(1)_A$ symmetry-breaking parameter $c$ plays a crucial role in obtaining the pion mass difference while intertwined with the current quark mass difference. To obtain the QCD contribution for the pion mass difference, we scan the parameter space in $\{\Delta m,\; c\}$, and by comparing this with the existing results, we constrained the parameter space. Further, using a fitted value of $c$, we determine the allowed range for the $\Delta m$ in the model. The model estimated $\Delta m$ ranges enable us to extract the chiral perturbation theory low-energy constant, $l_7$ and verify the dependence of the pion mass difference on $\Delta m$. We also find out its dependence on $c$ \textemdash\, it increases with the decreasing value of $c$, i.e., toward an axial anomaly restored phase.Comment: 12 pages, 6 captioned figures, discussion on l7 has been added, accepted in JP

Unveiling the Potential of Big Data Analytics for Transforming Higher Education in Bangladesh; Needs, Prospects, and Challenges

Big Data Analytics has gained tremendous momentum in many sectors worldwide. Big Data has substantial influence in the field of Learning Analytics that may allow academic institutions to better understand the learners needs and proactively address them. Hence, it is essential to understand Big Data and its application. With the capability of Big Data to find a broad understanding of the scientific decision making process, Big Data Analytics (BDA) can be a piece of the answer to accomplishing Bangladesh Higher Education (BHE) objectives. This paper reviews the capacity of BDA, considers possible applications in BHE, gives an insight into how to improve the quality of education or uncover additional values from the data generated by educational institutions, and lastly, identifies needs and difficulties, opportunities, and some frameworks to probable implications about the BDA in BHE sector. Keywords; Big Data Analytics, Learning Analytics, Quality of Education, Challenges, Higher Education, Banglades