We show that in the quadratic curvature theory of gravity, or simply $R_{\mu \nu} ^2$ tree-level unitariy bound (tree unitarity) is violated UV region but an analog for $S$-matrix unitarity ($SS^{\dagger} = 1$) satisfied. This renormalizable, and hence failure tree a counter example Llewellyn Smith's conjecture on relation between them. have recently proposed new gives same conditions as renorm...

Michael Gronau, 2 Dan Pirjol, Amarjit Soni, and Jure Zupan 6 Physics Department, Technion–Israel Institute of Technology 32000 Haifa, Israel Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Center for Theoretical Physics, Massachusetts Institute for Technology, Cambridge, MA 02139 Physics Department, Brookhaven National Laboratory, Upton, New York 11973 5 Department o...