Correlated diphoton mass resolution (${\sigma }_M^2/M^2=(s_1^2+s_2^2+2\rho s_1{s}_2)/4$ at fixed opening angle)

Logarithmic differentiation of the diphoton mass gives $dM/M=(d{E}_1/E_1+d{E}_2/E_2)/2$ at fixed angle. If $s_i$ are fractional energy standard deviations and $\rho$ their correlation coefficient, covariance propagation gives the displayed formula. A common multiplicative calibration error transfers directly to the reconstructed mass; independent errors combine differently. Angular errors, if present, add the corresponding derivative and covariance terms.