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 $\text{EEGG}$ 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 $r_{\tau }\ge 2.3\times 10^{-17}$ cm and $r_e\ge 1.5\times 10^{-18}$ cm, if leptons get masses at the electroweak scale, and $r_{\tau }\ge 3.3\times 10^{-27}$ cm, $r_e\ge 4.9\times 10^{-26}$ cm, as the most stringent limits required by causality arguments. This sets also an upper limit on the gravitational mass of a scalar $m_{scalar}\le 154$ GeV{} at the electroweak scale and (m_{scalar} \leq \sqrt{3/8} m_{Pl}) as the most stringent limit.

Comments: 8 pages, 2 pictures; Minor changes have been made