= Solution
Independent fluctuations add as <variances>. A useful parametrization of the <electromagnetic calorimeter> <energy resolution> is
$$
\boxed{\left(\frac{\sigma_E}{E}\right)^2=\frac{a^2}{E/\mathrm{GeV}}+\frac{b^2}{(E/\mathrm{GeV})^2}+c^2.}
$$
The convention makes $a,b,c$ dimensionless when $E$ is inserted in GeV. The three terms describe different mechanisms.
The stochastic term comes from fluctuations in the <electromagnetic shower>, scintillation production and detected photoelectron counts. If the number of detected photoelectrons is $N=kE$, <Poisson distribution> gives $\sigma_N=\sqrt N$, hence $\sigma_E/E=1/\sqrt{kE}\propto E^{-1/2}$. A sampling <electromagnetic calorimeter> also has fluctuations in the fraction deposited in its active material, contributing to the same approximate scaling. A homogeneous detector suppresses that sampling contribution.
The noise term represents approximately fixed absolute electronics and dark-current noise for a chosen reconstruction window. Additional <collision pileup> fluctuations can behave similarly over a specified operating range. A nearly constant $\sigma_E$ gives $\sigma_E/E\propto E^{-1}$.
The constant term describes residual fractional cell-calibration errors, gain drifts, temperature dependence, nonuniform light collection, dead material, and imperfect correction for longitudinal and transverse leakage. These effects often scale approximately with the incident <energy>, so they approach a constant fractional error. For <electrons>, upstream <bremsstrahlung> and conversion of the radiated <photons> spread the deposit over multiple cells; material mapping and clustering are essential. Leakage and material losses can also produce non-Gaussian tails, so the three-term parametrization describes a resolution core rather than every feature of the response. Noise dominates at low <energy>, stochastic fluctuations at intermediate <energy>, and the constant term eventually limits performance.
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