# Muon pT resolution

The muon $p_{\mathrm{T}}$ is measured from the curvature of its trajectory in the magnetic field. The curvature is proportional to $1/p_{\mathrm{T}}$. So, the error in the curvature measurement is related to the $p_{\mathrm{T}}$ resolution:

\[\begin{align} \Delta\left(\frac{1}{p}\right) &= -\frac{\Delta p}{p^2} \\ \frac{\Delta p}{p} &= -\left[\Delta\left(\frac{1}{p}\right)\right] \cdot p \\ &= k(p) \cdot p \end{align}\]If the error in the curvature measurement is independent of $p_{\mathrm{T}}$, i.e. $k(p) = k$, then we find that the fractional $p_{\mathrm{T}}$ resolution is proportional to $p_{\mathrm{T}}$:

\[\frac{\Delta p}{p} \propto p\]