The effects of deformation parameter on thermal width of moving quarkonia in plasma

In general we can say that the thermal width of quarkonia corresponds to imaginary part of its potential. Gravity dual of theories give explicit form of potential as $V_{Q\bar{Q}}$ . Since there is an explicit formula for $Im V_{Q\bar{Q}}$ one can consider different gravity duals and study the results of contribution of various parameters. Variable gravity duals of moving pair in plasma have different results for potential. Our paper shows that deformation parameter c in warp factor leads to new results that we present them for arbitrary angles of the pair with respect to its velocity. We compare our results with the case that no deformation parameter is in metric background. We will see that the thermal width of the pair increases with increasing deformation parameter. Also, for nonzero values of deformation parameter the pair feels moving plasma in all distances. In addition our results indicate that contribution of deformation parameter leads to larger dissociation length for the moving pair reverse to the effect of the pairs velocity in the plasma.