Soft pion momentum (and )

Currently there is a small problem with momentum determination in the spectrometer. This causes the masses of states to be measured on $\mathcal{O}(0.1\%)$ too high; the exact value depends on the kinematics of the decay. This will be corrected in the future, but for now we include this as a systematic effect. In order to assess the magnitude of this effect, we measure this shift for several prominent decay modes. (We expect that the will be most similar to the kinematically similar .) These measurements are presented in sc_mass:mass_errors. The and results are from 25% of the data sample while the signal is from the whole data sample.

 

Table 6.5: Mass errors for high statistics decays. FOCUS values and PDG [4] values are compared for several high statistics modes. Masses are in .

sc_mass:mass_errors

Mode	PDG Value	FOCUS Value	$\Delta M$	$\Delta M / M$
1	$145.40\pm 0.03$	$145.50\pm0.01$	$0.10\pm0.03$	$6.9\times10^{-4}$
	$1864.6\pm 0.50$	$1867.55\pm0.08$	$3.0\pm0.50$	$1.6\times10^{-3}$
	$1869.3\pm 0.50$	$1871.69\pm0.06$	$2.4\pm0.50$	$1.3\times10^{-3}$
	$1864.6\pm 0.50$	$1866.87\pm0.03$	$2.3\pm0.50$	$1.2\times10^{-3}$
	$2284.9\pm 0.60$	$2288.85\pm0.11$	$4.0\pm0.60$	$1.8\times10^{-3}$

¹ The value quoted is the $\dsp - \dzero$ mass difference.

As a reasonable estimate, we choose a relative error ( $\Delta M / M$) for the measurements of 0.15% which gives an error on the mass difference of 0.25 MeV. This error is likely correlated with the error reported in sc_mass:recon_syst so that the true systematic is probably being inflated by considering the same problem twice. Also, this effect is negligible in the measurement of $m_{\Sigma_c^{++}} - m_{\Sigma_c^{0}}$ since both masses are shifted by essentially the same amount.