The refractive index of the medium within the volume of deep inelastic $ep$ scattering: I. Group velocity of interaction carriers

Abstract

We propose a new method for measuring several characteristics of a fermion-boson medium formed during deep inelastic particle scattering. This method involves measuring the group and phase velocities of the accompanying wave process. The phase and group velocities of a wave process are related by the Rayleigh differential condition. The refractive index of a medium is determined by the phase velocity, while the group velocity characterises the medium's dispersion properties. In the case of deep inelastic $ep$ scattering under consideration, the wave process in an individual event is understood to be the exchange between an electron and a proton of an effective, non-perturbative mediator of interaction ($\mathcal{B}$) with the quantum numbers of a neutral current. In the first report, we present new data on the group velocity of interaction carriers $\mathcal{B}$. We extracted the group velocity modulus values, $U_{{}_{\mathcal{B}}}^{\ast }$, from the HERA collider data using a formula derived from modified Heisenberg uncertainty relations and applying the indirect measurement method. The HERA data demonstrate that in the selected kinematic domain the speed of the mediator $\mathcal{B}$ exceeds the speed of light $c$ in free space, $U_{{}_{\mathcal{B}}}^{\ast }>c$. To compare with the obtained data on group velocity, we analyse a simplest model of dispersion relation occurring due to the relativistic relationship between the energy, mass and momentum of a particle, supplemented by de Broglie relations.

10 pages, 5 figures, 1 table. Updated the Abstract, Conclusions, the style of references. RevTex4-2