Rigorous Limits on the Interaction Strength in Quantum Field Theory

Abstract

We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.

Figures (3)

• Figure 1: Theoretical upper bound for the OPE coefficient $c_{\phi\phi O}$ as a function of the dimension $\bar{\Delta}$ of the scalar field $O$. The curves correspond to the $\phi$'s dimension fixed at $d=1.005,\,1.02,\,1.05,\,1.1$ (from below up). The bound was computed for each of the shown points, and the curves in between were obtained by interpolation.
• Figure 2: Same as Fig. 1 for the $\phi$'s dimension fixed at $d=1.2\,,1.3\,,1.4\,,1.5\,,1.6\,,1.7$ (from below up).
• Figure 3: Theoretical upper bound for the OPE coefficient $c_{\phi \phi\phi}$ as a function of $\phi$'s dimension $d$.