Effective String Theory Inspired Potential and Meson Masses in Higher Dimension

TL;DR

This paper explores how meson masses vary with extra spatial dimensions using a string-inspired potential, revealing they grow towards the Planck scale at an extremely large dimension, thus defining the limits of quantum mechanical applicability.

Contribution

It introduces a higher-dimensional analysis of meson masses based on a string-inspired potential, highlighting the asymptotic approach to the Planck scale at very large dimensions.

Findings

Meson masses increase with the number of extra dimensions.

Masses approach the Planck scale at around 10^{11} dimensions.

Schrodinger equation's applicability limits are set by this dimensional threshold.

Abstract

Nambu-Goto action in classical bosonic string model for hadrons predicts quark-antiquark potential to be\cite{Nambu-Goto} $V(r)=-\frac{\gamma}{r}+\sigma r +\mu_0$. In this report we present studies of masses of heavy flavour mesons in higher dimension with our recently developed wave functions obtained following string inspired potential. We report the dimensional dependence of the masses of mesons. Our results suggest that as the meson mass increases with the number of extra spatial dimension, it will attain the Planck scale ($ \sim 10^{19}GeV$) asymptotically at an astronomically large spatial dimension (we call it Planck dimension) $D_{Planck} \sim 10^{11}$, which sets the limit of applicability of Schrodinger equation in large dimension.