Observed Deviations from Scale Invariance in High-Energy Muon Scattering

Abstract

Scale noninvariance is observed in 150- and 56-GeV muon scattering from an iron target. In the range $1<{q}^{2}<40$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, $\ensuremath{\nu}{W}_{2}$ rises with ${q}^{2}$ at fixed ${\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{\gtrsim}6$ and falls at ${\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{\lesssim}6$. The scale breaking is statistically and systematically significant, and persists with alternative choices of scaling variable. It is parametrized roughly by a constant $b=\frac{{\ensuremath{\partial}}^{2}\mathrm{ln}(\ensuremath{\nu}\ifmmode\times\else\texttimes\fi{}{W}_{2})}{\ensuremath{\partial}\mathrm{ln}({\ensuremath{\omega}}^{\ensuremath{'}})\ensuremath{\partial}\mathrm{ln}({q}^{2}}$ with a value near 0.09.