Limits on Sizes of Fundamental Particles and on Gravitational Mass of a Scalar

Abstract

We review the experimental limits on mass of excited fundamental particles and contact interaction energy scale parameters $\Lambda$ for QCD, QED and electroweak reactions. In particular we have focused on the QED reaction $ \EEGG $ at the energies from 91GeV{} to 202GeV{} using the differential cross-sections measured by the L3 Collaboration from 1991 to 1999. A global fit leads to lower limits at $ 95 % $ CL on $\Lambda > 1687$ GeV, which restricts the characteristic QED size of the interaction region to $ R_{e} < 1.17 \times 10^{-17} $ cm. All the interaction regions are found to be smaller than the Compton wavelength of the fundamental particles. This constraint is used to estimate a lower limit on the size of a fundamental particle related to gravitational interaction, applying the model of self-gravitating particle-like structure with the de Sitter vacuum core. It gives $r_{\tau} \geq 2.3 \times {10^{-17}}$ cm and $r_{e} \geq 1.5 \times 10^{-18} $ cm, if leptons get masses at the electroweak scale, and $r_{\tau} \geq 3.3 \times {10^{-27}}$ cm, $r_{e} \geq 4.9 \times 10^{-26} $ cm, as the most stringent limits required by causality arguments. This sets also an upper limit on the gravitational mass of a scalar $m_{scalar} \leq{154} $ GeV{} at the electroweak scale and (m_{scalar} \leq \sqrt{3/8} m_{Pl}) as the most stringent limit.