A study of rate dependence in the energy measurement

1. Here the rate is referred as the number of incident kaons (C_K) and pions(C_pi ) per spill. Typically, in the E949 experiment as shown in this scatter plot, the C_k varies from 10 to 16 Million/spill, while C_pi varies from 3 to 7 Million/spill. The ratio of C_k/C_pi depends the experimental condition of the two separators in the beam line.
2. The cause of the rate dependence in the energy measurement may be  explained as the observed rate dependence of the gain factor change in the Range Stack photo tubes and the accidental hits added in the energy measurement.

To study the rate effect, we use Kp21 monitor sample with some basic cuts (tpi-tk>2 ns,  pr_rf > 0.02,  |cos3d| < 0.5, |chi_rm| < 3,   ipiflg =0, trs < 45 ns and |Ptot - 205| < 10 MeV/c).  For a further study, we may apply some stringent cuts (b4abm >1.2 MeV, b4trs < 2ns, cpitrs < 2,  |b4str-tk| < 6ns, |tpi-trs| < 8ns, npe_cka>10, b4nhbm<6, cl_rsdedx > 0.02, itgqualt <2,
nhitz > 4 and layv4 == tlay).
3. A study of Kp2 energy peak as a function of rates shows: a) The C_k/C_pi dependence can have a 0.25 MeV peak position variation, the same conclusion can also be applied to C_k+C_k and C_k; b) When C_pi less than 2 Million/spill (corresponding to C_k+C_pi around 50% less than the normal rate), the peak shifts by 1 MeV. Further study by comparing with the prediction from the UTC indicates this one MeV shift is from the Range Stack Measurement. With the stringent cuts, the results do not change ( See this plot). All of which can be corrected offline. Some improvement is seen.
4. As expected, the energy resolution varies with the rates: a) Tiny dependence on the C_k/C_pi and C_pi ; b) Clear evidence on the  C_k+C_pi and C_k dependence and the magnitude is about 0.3 MeV. With the stringent cuts, the resolution is improved but the dependence still persists (see this plot). We might not be able to get rid of this effect.