Title: Towards a Bootstrap approach to higher orders of epsilon expansion,
Abstract: We employ a hybrid approach in determining the anomalous dimension and OPE
coefficient of higher spin operators in the Wilson-Fisher theory. First we do a
large spin analysis for CFT data where we use results obtained from the usual
and the Mellin Bootstrap and also from Feynman diagram literature. This gives
new predictions at $O(\epsilon^4)$ and $O(\epsilon^5)$ for anomalous dimensions
and OPE coefficients, and also provides a cross-check for the results from
Mellin Bootstrap. These higher orders get contributions from all higher spin
operators in the crossed channel. We also use the Bootstrap in Mellin space
method for $\phi^3$ in $d=6-\epsilon$ CFT where we calculate general higher
spin OPE data. We demonstrate a higher loop order calculation in this approach
by summing over contributions from higher spin operators of the crossed channel
in the same spirit as before.