This is a hard problem, it is about the conditions which ensure that scale invariance implies conformal invariance. In two dimensions any unitary local scale invariant theory is conformally invariant. In four dimensions it is not yet known a set of necessary and sufficient conditions. Here are some references.
 J. Polchinski, Scale and Conformal Invariance in Quantum Field Theory, Nucl. Phys. B
303 (1988) 226.
 M. A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the Asymptotics of 4D
Quantum Field Theory, JHEP 01 (2013) 152 1204.5221.
 Y. Nakayama, Scale invariance vs conformal invariance, Phys. Rept. 569 (2015) 1
 A. Dymarsky, Z. Komargodski, A. Schwimmer and S. Theisen, On Scale and
Conformal Invariance in Four Dimensions, JHEP 10 (2015) 171 1309.2921.