= Solution
At high <momentum>, the fixed spatial <measurement uncertainty> dominates because <4/a/ii> grows as $p$. At lower, still relativistic <momentum>, <Multiple Coulomb scattering> dominates the relative uncertainty, which approaches the approximately constant term in <4/b/iv>. Below the relativistic regime the additional velocity dependence of scattering must also be included.
Three complementary improvements are: increase $B$ and the tracking lever arm $L$ to enlarge the magnetic bend; improve hit-position resolution and alignment to reduce $\sigma(s)$; and reduce passive material and detector-layer thickness to reduce $x$ and hence <Multiple Coulomb scattering>. For independent contributions one commonly writes
$$
\frac{\sigma(p)}p\simeq\sqrt{(Ap)^2+C^2},
\qquad A=\frac{8\sigma(s)}{|q|BL^2},
$$
where $C$ is the scattering term for the specified material distribution and track estimator.
Back to article page
